Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.47.0-wmf.1 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk Event Event talk 5 6121 2807905 2631976 2026-05-08T09:09:27Z ~2026-27795-53 3071052 /* love,live, and let go */ Reply 2807905 wikitext text/x-wiki {{Talk header}} == There should be people watching the sandbox == Dave and I have been watching the Sandbox constantly, is anyone else interested in volunteering? --[[User:Goldenburg111|Goldenburg111]] ([[User talk:Goldenburg111|talk]]) 15:22, 14 December 2013 (UTC) :Yes I will, but what do I have to do? --[[Special:Contributions/71.235.232.65|71.235.232.65]] ([[User talk:71.235.232.65|discuss]]) 21:44, 28 March 2014‎ (UTC) ::Cleanup the sandbox by reverting cleanup edits! --~~{{font|face=Utah MT-SJ-NI|[[User:Goldenburg111|{{font|color=red|Golden}}]]_{[[User talk:Goldenburg111|{{font|color=orange|burg}}]][[Special:Contributions/Goldenburg111|111]]}}} 21:46, 28 March 2014 (UTC) :::Yes, it just needs to be reset occasionally, but not over-zealously. In particular, don't reset it if a user has been editing within the last hour or so. They may still be testing something. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 23:46, 28 March 2014 (UTC) :Keep up the good work. --[[User:Rockchalk 03|Rockchalk 03]] ([[User talk:Rockchalk 03|discuss]] • [[Special:Contributions/Rockchalk 03|contribs]]) 12:20, 31 July 2014 (UTC) :Maybe, but it is really necessary? I can see in the page history that a robot is running sometimes ("Robot: Automatically cleaned"). If it was written in the information box when it was running (for example at a specified day and time every week), then nobody should be surprised if what they have written, will disappear. /[[User:PatrikN|Patrik Näsfors]] ([[User talk:PatrikN|discuss]] • [[Special:Contributions/PatrikN|contribs]]) 19:05, 12 October 2016 (UTC) ::I clean it when what is already there might discourage another editor from testing their own edits. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 19:13, 12 October 2016 (UTC) :::Sorry Dave if I don't understand your answer (so clarify if you like), but if it is reset often enough, I can't see why it should be necessary to watch and do it manually. At [http://www.opensourcecms.com/scripts/details.php?scriptid=153&name=MediaWiki OpenSourceCMS] (where you also can try a demo of MediaWiki, which the link points to), demos are deleted and re-installed every hour. I don't know how much a bot can be programmed to do, but as you stated above, it could be fine if the bot could see if there is more than an hour since the last edit before purging the page. Could that be done? It's just a suggestion so people don't have to check and clean manually like now. /[[User:PatrikN|Patrik Näsfors]] ([[User talk:PatrikN|discuss]] • [[Special:Contributions/PatrikN|contribs]]) 20:34, 12 October 2016 (UTC) ::::It isn't reset often enough. The bot that is active here only resets the sandbox on Saturday mornings. It's certainly possible to write a bot to do this. I don't run mine unattended, but I'd be happy to help someone else learn how to write the code to do this if they're interested. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 20:58, 12 October 2016 (UTC) :::::Thanks for the clarification. I'd be happy to help with that. I also have a server running continuously if that's a requirement. I haven't learned to program in Python yet, but it's on my to-learn list and I'd like to learn what else is necessary. (I'm also a quick learner). But actually it seems the [[User:Mu301Bot|Mu301Bot]] does not run anything at the moment (and the task to clean the Sandbox have been inactive since July 2016). :::::I can also see why it's necessary to do it manually once in a while, because the page is totally changed sometimes. That raises another question. Is it possible to protect a section at the top (the header) and prevent that it is modified, or can only whole pages be protected? Or might a solution be to create subpages for sandboxing? /[[User:PatrikN|Patrik Näsfors]] ([[User talk:PatrikN|discuss]] • [[Special:Contributions/PatrikN|contribs]]) 22:40, 12 October 2016 (UTC) ::::::I'm a bit biased, but there's a good Python course at [[Python Programming]]. There's sample bot code at [[MediaWiki API/Pywikibot]]. The [[Pywikibot]] course is very outdated, but the instructions at [[mw:Manual:Pywikibot]] were good the last time I tried them (maybe six months ago). -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 00:28, 13 October 2016 (UTC) == Education == I would like to find out more information about free learning resources on the internet that once completed and I pass the course I would earn a free certificate showing my accomplishments. [[User:ChrisREdG33|ChrisREdG33]] ([[User talk:ChrisREdG33|discuss]] • [[Special:Contributions/ChrisREdG33|contribs]]) 20:48, 20 July 2018 (UTC) :{{At|ChrisREdG33}} In most cases, free certificates are worth what you pay for them. Free learning is great. Free proof of learning doesn't go very far. I encourage you to look at your goals and determine what proof of education is necessary for those goals. If it is a portfolio, create your own proof of experience. If certification is required, you'll likely need to pay for that testing or proof. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:07, 21 July 2018 (UTC) == Science == I think we should a develop scientific project [[User:Umeh elochukwu|Umeh elochukwu]] ([[User talk:Umeh elochukwu|discuss]] • [[Special:Contributions/Umeh elochukwu|contribs]]) 13:59, 8 November 2020 (UTC) We should try making a drone [[User:Umeh elochukwu|Umeh elochukwu]] ([[User talk:Umeh elochukwu|discuss]] • [[Special:Contributions/Umeh elochukwu|contribs]]) 14:01, 8 November 2020 (UTC) == love,live, and let go == I just wanted to see if anyone is actually interested in conversation on this choice of a topic that I chose. If you are interested then please say so and I will begin. [[User:Ronniewaddle79|Ronniewaddle79]] ([[User talk:Ronniewaddle79|discuss]] • [[Special:Contributions/Ronniewaddle79|contribs]]) 21:14, 15 November 2023 (UTC) :I am interested , please proceed @[[User:Ronniewaddle79|Ronniewaddle79]] [[User:Luminary77|Sierra Seven]] ([[User talk:Luminary77|discuss]] • [[Special:Contributions/Luminary77|contribs]]) 13:17, 9 June 2024 (UTC) ::Me too!@[[User:Ronniewaddle79|Ronniewaddle79]] [[Special:Contributions/&#126;2026-27795-53|&#126;2026-27795-53]] ([[User talk:&#126;2026-27795-53|talk]]) 09:09, 8 May 2026 (UTC) cuebt21judl9so6bv38t8qdc3k8c6v5 11 49339 2807888 1497757 2026-05-07T22:12:17Z ~2026-27765-67 3070973 /* Group size */ 2807888 wikitext text/x-wiki <div style="width:100%;text-align:center;font-size:12pt;font-weight:bold">Template documentation</div> == Activity == The type of activity, for example "lecture" or "group work". == Group size == The recommended size of the group. (e.g. unlimited, more than 20, less than 15) Daniel Drtil 2026 == Preparation == The necessary preparation for the instructors. == Instructors == The recommended number of instructors. == Duration == The recommended duration. "?" means that the duration of the unit is likely to be subject to change or hasn't yet been determined. 13lwfgx6k3o2qwg8m1h62m5cs5k6790 2807891 2807888 2026-05-08T00:10:05Z Atcovi 276019 Reverted edits by [[Special:Contributions/~2026-27765-67|~2026-27765-67]] ([[User_talk:~2026-27765-67|talk]]) to last version by [[User:MaintenanceBot|MaintenanceBot]] using [[Wikiversity:Rollback|rollback]] 1497757 wikitext text/x-wiki <div style="width:100%;text-align:center;font-size:12pt;font-weight:bold">Template documentation</div> == Activity == The type of activity, for example "lecture" or "group work". == Group size == The recommended size of the group. (e.g. unlimited, more than 20, less than 15) == Preparation == The necessary preparation for the instructors. == Instructors == The recommended number of instructors. == Duration == The recommended duration. "?" means that the duration of the unit is likely to be subject to change or hasn't yet been determined. 5a7ya2d3yq53q59bi66ghx0lz3cpt4o 0 124151 2807882 2807850 2026-05-07T17:26:09Z Tola73 3020076 /* Synopsis */ Added three words so the direct quote is more accurate. 2807882 wikitext text/x-wiki '''Katherine "Katie" Harwood''' is a fictional character in the 2002 film ''Ghost Ship'' where an innocent young girl goes on a sea voyage of a lifetime, only to be caught up in a living nightmare aboard the ill-fated ocean liner. In the film, Katie is the supporting deuteragonist to the main character (Maureen Epps) and stands in stark contrast to the completely evil and demonic antagonist (Jack Ferriman). In many regards, Katie is just as much of a heroine as Maureen Epps for enduring unfathomable suffering and risking the wrath of Jack Ferriman through her unyielding efforts to save the souls and lives of others on the ship.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Katie is portrayed by a young [[w:Emily Browning|Emily Jane Browning]]. == Significance == Katie is an iconic representation of childhood from an earlier era, at a time when life was simpler, and childhood more innocent.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> She stands out in a coarse mixed reviewed horror film as a compelling, distinctive and enduring character who subverts common horror child tropes.<ref>https://michellepatterson.net/2018/03/23/ghostship-film-review/Michelle Patterson Publications</ref><ref>https://moviefilmreview.com/186187/movie-review-of-ghost-ship-2002?utm_source=chatgpt.com/ Cal Knox Movie Review</ref><ref>https://lmariewood.com/2025/05/23/horror-tropes-when-to-use-them-and-when-to-subvert-them/ L. Marie Wood; Horror Tropes: When to Use Them and When to Subvert Them</ref> With the Shout! Factory 20-year anniversary Blue-ray rerelease of ''Ghost Ship,'' Katie is made the new face of the film in the promotional artwork, elevating a morally intact child to iconic status; something very few horror children achieve, and even more so as a tragic and sympathetic figure without villainy.<ref>https://www.blu-ray.com/news/?id=27285/ Shout! Factory Ghost Ship 20-year anniversary collector’s edition Blu-ray disc</ref> == Synopsis == In May of 1962, an endearing Katie waves goodbye to her grandparents in [[Europe]] and journeys solo aboard the exquisite ''Antonia Graza'' on an exclusive cruise to rejoin her family in New York City. Since Katie is the only child onboard, she receives special care and attention. In describing her voyage Katie states, ”The whole ship was my playground, also beautiful. I was the only child onboard, so the ship’s purser and captain took special care of me. I felt so safe and happy with them.”<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> However, after the Antonia Graza rescues a lone survivor and cargo from a sinking ship, Katie’s exciting journey suddenly takes a horrendous turn for the worse. Unbeknownst to Katie and her shipmates, the single survivor (Jack Ferriman) is literally a demonic henchman for Satan set on destroying lives and collecting souls. Ferriman informs select members of the crew about the millions in gold recovered from his sinking ship, and influences them to launch an elaborate plot to seize control of the Graza and the gold, by killing everyone onboard. Although several crewmembers and passengers try to save her life from the murderous conspirators, Katie is eventually caught and tragically hanged to death, with her body concealed behind the partitioning door of her cabin.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Instead of ascending to her rightful place in heaven, Katie’s spirit is trapped on the ship by demonic forces along with the entire compliment of murdered passengers and crew. However, since Katie is still a young child, her soul is completely innocent and therefore beyond the influence and control of the demonic Ferriman. Over the next 40 years, the evil Ferriman along with the help of the wicked “marked” souls, try to use the ship as a trap to destroy unsuspecting lives, and collect a quota of souls for hell. Despite being the only flicker of good on the ship, Katie bravely opposes Ferriman and the evil spirits, and attempts to warn and save the lives of anyone who has the misfortune of being lured aboard the condemned vessel. Concerning these things, Katie says, ““Without the mark, Jack can’t control me and because of this, he hates me most of all; scaring me at every turn and chasing me away when I try to warn those who come here.”<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> When Maureen Epps and her ship salving crew are lured aboard the Graza by Ferriman, Katie attempts to warn them about the dangerous ship. Katie has very perceptive eyes, and finds Epps to be more open to the truth than her cohorts. Katie tries to leave Epps messages and clues, and even appears to her on several occasions. When Katie senses that Ferriman has sabotaged the salvage crew’s tugboat, she boldly tries to warn the crew, but is forcibly carried away by Ferriman. Epps witnesses Katie’s warning and sets off in search for the mysterious little girl. Epps locates Katie’s cabin and comes face to face with her remains and her spirit. Katie allows Epps to have her cherished heart-shaped locket, and then proceeds to speak directly about the ship being a demonic trap. However, before Katie can finish explaining, she is overheard by an invisible Ferriman and lets out a frightened scream as he removes her from the cabin. Undeterred, Katie returns and tries to help Epps and her remaining crewmembers escape. Endowed with supernatural power from above, Katie transports Epps back to May 21, 1962 through her memories and reveals to her the horrifying events that led to everyone’s death, including her own. Furthermore, Katie reveals the true identity of Jack Ferriman and his goal to use the ship as a conduit to collect souls for Satan.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> After experiencing Katie’s heartbreaking vision, Epps decides to risk almost certain death by destroying the cursed ship with explosives. However, Katie helps Epps escape the rapidly sinking vessel, while emancipated souls rise from the ship. Katie stays faithfully by Epps and gives her a grateful smile as her spirit ascends toward heaven.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> == Religious & Symbolic Implications == At its core, the story is deeply religious and the plot hinges on the concept of a young girl trying to save the lives (and ultimately souls) of others from demonic forces.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Metaphorical Murals===== The religious implications and [[Christian symbolism]] surrounding Katie’s story are rich. <ref>http://www.worsleyschool.net/socialarts/symbolism/page.html</ref> Although only lightly touched on in the final version of the film, the most obvious religious connections come through the [[Gustave Dore]] inspired murals displayed throughout the ship. The murals are depictions based on Dante Alighieri’s Divine Comedy and The Inferno. The metaphorical murals hint at the struggle between Katie and Ferriman over the lives and souls on the ship.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Lead actress Julianna Margulies says, “Katie is like Virgil in Dante’s Inferno. Margulies explains that Katie is like a “little guide” trying to lead others through hell and then safely onto the other side.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> As in the mural of Charon, Ferriman is literally a “ferry man” using a boat in the attempt to ferry souls to hell and eternal damnation. Conversely, Katie opposes Ferriman by trying to protect and warn all unsuspecting visitors and sharing the truth about the demonic ship. =====Marked Souls===== An additional concept presented in the plot are the “marked” souls. Like the murals in the story, the souls of the sinful and the “lost”<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN |page=563 | year=1983}}</ref> are marked with a hooked-shaped indention on their hand. Katie says the mark is “a sign of their sins” and that they are bound to the will of Satan and his demons, in addition to eventually sharing in their same flaming judgment.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> However, not all the murals are somber. The depiction of angels defeating the demons and casting them down foreshadows the eventual defeat of Ferriman and ultimately all evil.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====The Dove and Locket===== Another subtle, but implicit [[Christian symbolism]] is Katie’s heart-shaped locket with the image of a raised dove in flight.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=383}}</ref> In Christian tradition, this type of dove can symbolize innocence, purity, faith, hope, God’s peace, God’s presence through the [[Holy Spirit (Christianity)|Holy Spirit]] and God’s guidance and deliverance.<ref>http://www.newadvent.org/cathen/05144b.htm</ref> The dove also indicated God’s bestowal of fortitude necessary to bear suffering and death<ref>{{cite book| last=Gauding |first=Madonna | title=The Signs and Symbols Bible |publisher=Sterling Publishing Co |location=New York, NY | year=2009 |page=82}}</ref>. In this sense, the remains of the dead dove on the bridge of the ship, foreshadows Katie’s death, but at the same time indicates that there could still be hope. When Epps puts on Katie’s locket, it implies that Epps now has a renewed heart, or possibly even salvation as stated in Bible scripture. In this manner, the locket could also represent that Epps’ soul is not "marked".<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Parallel of an Innocent and Sacrificial Life===== A striking parallel could also be drawn between Katie and Jesus Christ. In the bible, Christ lives a completely innocent life, but is hung on a cross to sacrificially die for the sins of all humanity.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |pages=2228-2229}}</ref> Christ tastes the sting of death and hell in order to offer salvation to all who will put their faith in Him.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=966}}</ref> Similarly, innocent Katie is hung by a rope behind a dividing door, but through her death she is able to lead others to "salvation" and safety. Because of her young age and innocent death, Katie is the only voice of hope for all the suppressed souls held captive on the demonic ship. Katie also endures small tastes of hell from Ferriman in her efforts to save others. However, Katie’s love and compassion for the lives of others is greater than her fear and pain, and in similarity to Christ, Katie rises victoriously to heaven in the end.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Forty Years and the Promised Land===== 40 years is a significant reoccurring number in the Christian faith.<ref>Collins English Dictonary http://dictionary.reference.com/browse/promised land</ref> The [[Israelites]] endured 40 years of great trial and testing in the wilderness before they were able to enter their promised land of rest. In Christian tradition, the earthly life is often compared to a time of trial in the wilderness and the Promised Land a metaphor for heaven.<ref>Collins English Dictonary http://dictionary.reference.com/browse/promised land</ref> Correspondingly, Katie has endured the “wilderness” and trials of the ship for 40 years, but as the result of Epps’ help she is inevitably freed to enter the “promised land” of heaven. =====Concept of Free Will===== Free will is both discussed and demonstrated in the story.<ref>{{cite book| last=Keck |first=Leander | title=The New Interpreter's Bible vol. 9 |publisher=Abingdon Press |location=Nashville, TN | year=2002 |pages=61-62}}</ref> Ultimately, the crew members who die are led to destruction by their own sins and their selfish desire for greed, lust and power. Epps is spared the fate of her shipmates through listening to Katie’s warnings and humbly responding to the truth.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Elevated Status of Children===== In the Christian bible God often uses the most humble and unlikely people to work through <ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=2283}}</ref> – Out of hundreds on the ship, Katie is the meekest, humblest and most unlikely to do anything significant, yet every soul on the ship ends up depending on her.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page production notes]</ref> Katie is also reminiscent of Christ elevating the status of children when he gave them special attention and profoundly declared that unless one humbles them self and has the faith of a little child, they will not enter the kingdom of heaven. This is further illustrated when Christ took a lowly child and placed him in the midst of his followers and stated that only those with childlike faith will be the greatest in the kingdom of heaven.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=963}}</ref> This concept is demonstrated by Epps' willingness to humble herself to Katie's level.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> The role of children in Christian scripture – Comparisons could be made between Katie and several unpretentious bible characters such as the lowly shepherd boy David who defeated the warrior Goliath and became king. Outwardly both young Katie and David appear to be nothing more that mere children, however, inwardly they possess vast unforeseen potential and a tremendous strength of character.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=563}}</ref> <ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Eternal Destinations===== In the film, as with [[Christian soteriology]] there are two clear eternal destinations which souls go to after death; ether heaven or hell. A heart of child-like faith will put one on the path to heaven, but a sinful life eventually leads to destruction.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=1902}}</ref> =====The Destructiveness of Sinful Choices===== One of the morals of the story is the corrupting dangers of pursuing riches. This theme also fits aptly within the religious concepts of the film.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> Sinful greed, lust, debauchery and selfish desire can influence ordinarily good people to do horribly evil things (1Timothy 6:9-10).<ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=2195 | year=1991}}</ref> The choices made by the characters in the story illustrate this principle. “Be sure your sins will find you out” – As the story goes, sinful activities have consequences and will eventually have to be accounted for, and the ultimate payment for sin in the end is both physical and spiritual death (Romans 6:20-23). <ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=2039 | year=1991}}</ref> <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Loving Others before Ourselves===== “Greater love has no one than this – To lay one’s life down for their friends.” Katie and Epps are both willing put themselves at risk to save lives. Through the process of trying to help others both Epps and Katie experience help for themselves.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> “Those who seek to save their life will lose it, but those who are willing to lose their life will save it.”<ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=1842 | year=1991}}</ref> In this sense Epps' life is saved, because she places the needs of others first. Katie also inherits eternal life in heaven by risking herself to help others. =====Purgatory===== The concept of purgatory (Whalen p. 1034-1039)<ref>{{cite book| last=Whalen |first=John | title=New Catholic Encyclopedia Vol. 11|publisher=Catholic University of America |location=Washington, D.C. | year=1983}}</ref> is also mentioned when Katie states that the ship had become like a “prison” where souls are trapped among the living between heaven and hell.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> ====Additional Symbolism==== =====Life as a Voyage on a Ship===== Life itself is comparable to a voyage on ship...illustrating that our lives are like a ship that is bound for one of two possible destinations.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> In the context of Ghost Ship, the voyage ends in destruction (death and hell) unless we get off. In this sense, Katie pleads with us to get off, but that involves humbly changing our ways and giving up the allure and pursuit of vain things such as wealth and power.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Symbols of Changing Times===== The once elegant and decaying ship is a symbol of changing times.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> In a similar manner, Katie can be viewed as a symbolic representation of childhood from a more innocent era. Just as the ship decays to ruin from its glorious 1950’s splendor, Katie’s deteriorating childhood possessions and even Katie herself, are evocative symbols of changing times and eroding childhood innocence.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> == Dichotomy and Contrasts == Katie is in some ways a complicated paradox: She has been deeply hurt and traumatized by all she has experienced, but by the same token, she is still very much an innocent child – Even after 40 years of resilient growth as a character. Katie exhibits a wide array of emotions from timid youthful innocence and joy, to extreme terror, sadness, loneliness, and solemn distress.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> ====Characters==== Even under tremendously trying circumstances Katie demonstrates an incredible inner strength of character without compromising the sweet kind-hearted "girly" girl she really is. The fact that Katie remains true to herself in spite of all the evil and suffering she experienced transcends their eroding influence and distinguishes her from the other characters.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Ferriman===== Ferriman is representative of Satan and the crafty deceptiveness of evil in destroying people’s lives. Katie and Ferriman are at completely opposite ends of the Christian spectrum – The demonic Ferriman is totally depraved and evil while Katie is sweet and innocent. Katie is motivated by love and compassion, Ferriman is motivated by hate and rage.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> <ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Epps===== Although Katie and Epps are two completely dissimilar characters from different eras, they still grow quite close. Epps is "a woman working in a man's world"<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> and appears somewhat tough and masculine on the exterior like a tomboy. Although not specifically stated, the story indicates that Epps is likely from a broken home. On the other hand, Katie comes from a close, traditional nuclear family. In contrast to Epps, Katie is more of a typical "girly" girl and is slightly timid, but possess a stout inner fortitude despite her diminutive and delicate appearance.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Francesca===== The sultry Francesca lives the more representative life of a performing artist. Unlike Epps who feels the need to downplay her femininity, Francesca leans toward the other extreme and attempts to flaunt her femininity to her own advantage, even to the point of her own exploitation. Conversely, Katie is still a virtuous and modest little girl, who has yet to be tainted by any corrupting influences of the world.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Captain Murphy===== Captain Murphy appears to be a strong imposing ship captain on the outside, however, when confronted with trials and tribulations, his perceived strength is shown to be superficial. This is evident by his emotional breakdown where he shuts off emotionally and withdraws to himself while attempting to drown his problems in alcohol. In contrast, Katie appears to be very delicate in both physical appearance and personality. However, despite her dainty appearance, Katie proves her true strength and fortitude from within through dealing with her pain and problems directly, instead of allow it to define her<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> ====General Themes==== Light vs. darkness, good vs. evil, childhood innocence vs. wickedness, tragedy vs. triumph, simpler more wholesome times, vs. the complexity and loss of innocence of today.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> == Conclusion == On the surface, Katie’s story is an emotional tale of heartache and tragedy – Something that no young person should ever have to endure. However, Katie’s story is also essential to the plot. <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> Through helping each other and being willing to put themselves at risk, Katie and Epps together achieve a triumph out of the tragedy and deliver a major blow to Ferriman and the forces of evil. Although the struggle over the souls of people will continue, this victory of the human spirit gives hope even in the face of terrible suffering, evil and even death.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> “Katie is really a very sweet girl. She's completely innocent…“ says Emily Jane Browning, who obviously became completely immersed in her character. “…She's been hoping someone would come onto the ship to be her friend, so when Epps arrives she's very excited – they develop a real friendship."<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> ”Emily did an amazing job,” Director Steve Beck enthuses. “She gave Katie a real complexity…she's not just a little girl caught up in a ghost story…” Both Browning and Beck also added that underneath all her heartfelt emotions, Katie longs for vindication and justice.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> The deeply symbolic and metaphorical aspects surrounding Katie’s story along with the close relationships she develops with others lends support to the notion that the film was originally intended to be more than just another Hollywood “slasher” horror. This is further substantiated by Katie’s tearful and heartfelt story – Emotionally poignant and touching drama not usually associated with a horror picture.<ref>http://www.dailyscript.com/scripts/ghost_ship_info.txt</ref> == References == ===Footnotes=== {{Reflist|colwidth=30em}} ===Cited Texts=== {{refbegin}} *{{cite book| last=Barclay | first=William | title=The Gospel of Mark |publisher=Westminster Press | location=Philadelphia, PA | isbn=0664213022 | year=1975}} *{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | isbn=0-19-875500-7 | year=2001}} *{{cite book| last=Boettner |first=Loraine | title=Roman Catholicism |publisher=Presbyterian & Reformed Publishing Co. |location=Phillipsburg, NJ |isbn=0875521304 | year=1985}} *{{cite book| last=Buttrick |first=George | title=The Interpreter's Bible vol. 12 |publisher=Abingdon Press |location=Nashville, TN |asin=B000HTP248 | year=1957}} *{{cite book |title=Collins English Dictionary - Complete & Unabridged 10th Edition |date=2009 | publisher=Harper Collins |location=New York, NY}} *{{cite book| last=Dummelow |first=J.R. | title=Commentary on the Whole Bible |publisher=Macmillian Publishing Co. |location=New York, NY | year=1936}} *{{cite book| last=Gaebelein |first=Frank | title=The Expositors Bible Commentary vol. 1 |publisher=Zondervan |location=Grand Rapids, MI |isbn=0310364302 | year=1979}} *{{cite book| last=Gauding |first=Madonna | title=The Signs and Symbols Bible |publisher=Sterling Publishing Co. |location=New York, NY |isbn=1402770049| year=2009}} *{{cite book| last=Jamieson |first=Fausset | title=Commentary on the Whole Bible |publisher=Zondervan |location=Grand Rapids, MI| asin=B004BCQP8O | year=1971}} *{{cite book| last=Keck |first=Leander | title=New Interpreter's Bible vol. 9 |publisher=Abingdon Press |location=Nashville, TN |isbn=0687278228 | year=2002}} *{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | lccn=90-71553| year=1991}} *{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN |isbn=0840752954 | year=1983}} *{{cite book| last=Wall |first=Robert | title=The New Interpreter's Bible vol. 10 |publisher=Abingdon Press |location=Nashville, TN |isbn=0687278236 | year=2002}} *{{cite book| last=Whalen |first=John | title=New Catholic Encyclopedia Vol. 11 |publisher=Catholic University of America |location=Washington D.C. | lccn=66-22292 | year=1967}} {{refend}} == External links == * [http://www.dailyscript.com/scripts/ghost_ship_info.txt/ Daily Script_Ghost Ship] * [http://www.imdb.com/title/tt0288477/ Internet Movie Database_Ghost Ship 2002] * [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes] * [http://www.rottentomatoes.com/m/ghost_ship/ Rotten Tomatoes movie review_Ghost Ship] [[Category:Analysis]] [[Category:Film]] o3tu9wmavrvywkygjqgxyefz9ca192g 2807893 2807882 2026-05-08T01:19:21Z Tola73 3020076 /* Synopsis */ Changed a few words and added a short sentence for better readability. 2807893 wikitext text/x-wiki '''Katherine "Katie" Harwood''' is a fictional character in the 2002 film ''Ghost Ship'' where an innocent young girl goes on a sea voyage of a lifetime, only to be caught up in a living nightmare aboard the ill-fated ocean liner. In the film, Katie is the supporting deuteragonist to the main character (Maureen Epps) and stands in stark contrast to the completely evil and demonic antagonist (Jack Ferriman). In many regards, Katie is just as much of a heroine as Maureen Epps for enduring unfathomable suffering and risking the wrath of Jack Ferriman through her unyielding efforts to save the souls and lives of others on the ship.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Katie is portrayed by a young [[w:Emily Browning|Emily Jane Browning]]. == Significance == Katie is an iconic representation of childhood from an earlier era, at a time when life was simpler, and childhood more innocent.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> She stands out in a coarse mixed reviewed horror film as a compelling, distinctive and enduring character who subverts common horror child tropes.<ref>https://michellepatterson.net/2018/03/23/ghostship-film-review/Michelle Patterson Publications</ref><ref>https://moviefilmreview.com/186187/movie-review-of-ghost-ship-2002?utm_source=chatgpt.com/ Cal Knox Movie Review</ref><ref>https://lmariewood.com/2025/05/23/horror-tropes-when-to-use-them-and-when-to-subvert-them/ L. Marie Wood; Horror Tropes: When to Use Them and When to Subvert Them</ref> With the Shout! Factory 20-year anniversary Blue-ray rerelease of ''Ghost Ship,'' Katie is made the new face of the film in the promotional artwork, elevating a morally intact child to iconic status; something very few horror children achieve, and even more so as a tragic and sympathetic figure without villainy.<ref>https://www.blu-ray.com/news/?id=27285/ Shout! Factory Ghost Ship 20-year anniversary collector’s edition Blu-ray disc</ref> == Synopsis == In May of 1962, an endearing Katie waves goodbye to her grandparents in [[Europe]] and journeys solo aboard the exquisite ''Antonia Graza'' on an exclusive cruise to rejoin her family in New York City. Since Katie is the only child onboard, she receives special care and attention. In describing her voyage Katie states, ”The whole ship was my playground, also beautiful. I was the only child onboard, so the ship’s purser and captain took special care of me. I felt so safe and happy with them.”<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> However, after the Antonia Graza rescues a lone survivor and cargo from a sinking ship, Katie’s exciting journey suddenly takes a horrendous turn for the worse. Unbeknownst to Katie and her shipmates, the single survivor (Jack Ferriman) is literally a demonic henchman for Satan set on destroying lives and collecting souls. Ferriman informs select members of the crew about the millions in gold recovered from his sinking ship, and influences them to launch an elaborate plot to seize control of the Graza and the gold, by killing everyone onboard. Remarkably, Katie survives the opening massacre scene on the foredeck, nevertheless, as the lone survivor and witness this also makes her a liability for the conspirators. Although several crewmembers and passengers try to save her life from the homicidal conspirators, Katie is eventually caught and tragically hanged to death, with her murder concealed behind the partitioning door of her cabin.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Instead of ascending to her rightful place in heaven, Katie’s spirit is trapped on the ship by demonic forces along with the entire compliment of murdered passengers and crew. However, since Katie is still a young child, her soul is completely innocent and therefore beyond the influence and control of the demonic Ferriman. Over the next 40 years, the evil Ferriman along with the help of the wicked “marked” souls, try to use the ship as a trap to destroy unsuspecting lives, and collect a quota of souls for hell. Despite being the only flicker of good on the ship, Katie bravely opposes Ferriman and the evil spirits, and attempts to warn and save the lives of anyone who has the misfortune of being lured aboard the condemned vessel. Concerning these things, Katie says, “Without the mark, Jack can’t control me and because of this, he hates me most of all; scaring me at every turn and chasing me away when I try to warn those who come here.”<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> When Maureen Epps and her ship salving crew are lured aboard the Graza by Ferriman, Katie attempts to warn them about the dangerous ship. Katie has very perceptive eyes, and finds Epps to be more open to the truth than her cohorts. Katie tries to leave Epps messages and clues, and even appears to her on several occasions. When Katie senses that Ferriman has sabotaged the salvage crew’s tugboat, she boldly tries to warn the crew, but is forcibly carried away by Ferriman. Epps witnesses Katie’s warning and sets off in search for the mysterious little girl. Epps locates Katie’s cabin and comes face to face with her remains and her spirit. Katie allows Epps to have her cherished heart-shaped locket, and then proceeds to speak directly about the ship being a demonic trap. However, before Katie can finish explaining, she is overheard by an invisible Ferriman and lets out a frightened scream as he removes her from the cabin. Undeterred, Katie returns and tries to help Epps and her remaining crewmembers escape. Endowed with supernatural power from above, Katie transports Epps back to May 21, 1962 through her memories and reveals to her the horrifying events that led to everyone’s death, including her own. Furthermore, Katie reveals the true identity of Jack Ferriman and his goal to use the ship as a conduit to collect souls for Satan.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> After experiencing Katie’s heartbreaking vision, Epps decides to risk almost certain death by destroying the cursed ship with explosives. However, Katie helps Epps escape the rapidly sinking vessel, while emancipated souls rise from the ship. Katie stays faithfully by Epps and gives her a grateful smile as her spirit ascends toward heaven.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> == Religious & Symbolic Implications == At its core, the story is deeply religious and the plot hinges on the concept of a young girl trying to save the lives (and ultimately souls) of others from demonic forces.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Metaphorical Murals===== The religious implications and [[Christian symbolism]] surrounding Katie’s story are rich. <ref>http://www.worsleyschool.net/socialarts/symbolism/page.html</ref> Although only lightly touched on in the final version of the film, the most obvious religious connections come through the [[Gustave Dore]] inspired murals displayed throughout the ship. The murals are depictions based on Dante Alighieri’s Divine Comedy and The Inferno. The metaphorical murals hint at the struggle between Katie and Ferriman over the lives and souls on the ship.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> Lead actress Julianna Margulies says, “Katie is like Virgil in Dante’s Inferno. Margulies explains that Katie is like a “little guide” trying to lead others through hell and then safely onto the other side.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> As in the mural of Charon, Ferriman is literally a “ferry man” using a boat in the attempt to ferry souls to hell and eternal damnation. Conversely, Katie opposes Ferriman by trying to protect and warn all unsuspecting visitors and sharing the truth about the demonic ship. =====Marked Souls===== An additional concept presented in the plot are the “marked” souls. Like the murals in the story, the souls of the sinful and the “lost”<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN |page=563 | year=1983}}</ref> are marked with a hooked-shaped indention on their hand. Katie says the mark is “a sign of their sins” and that they are bound to the will of Satan and his demons, in addition to eventually sharing in their same flaming judgment.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> However, not all the murals are somber. The depiction of angels defeating the demons and casting them down foreshadows the eventual defeat of Ferriman and ultimately all evil.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====The Dove and Locket===== Another subtle, but implicit [[Christian symbolism]] is Katie’s heart-shaped locket with the image of a raised dove in flight.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=383}}</ref> In Christian tradition, this type of dove can symbolize innocence, purity, faith, hope, God’s peace, God’s presence through the [[Holy Spirit (Christianity)|Holy Spirit]] and God’s guidance and deliverance.<ref>http://www.newadvent.org/cathen/05144b.htm</ref> The dove also indicated God’s bestowal of fortitude necessary to bear suffering and death<ref>{{cite book| last=Gauding |first=Madonna | title=The Signs and Symbols Bible |publisher=Sterling Publishing Co |location=New York, NY | year=2009 |page=82}}</ref>. In this sense, the remains of the dead dove on the bridge of the ship, foreshadows Katie’s death, but at the same time indicates that there could still be hope. When Epps puts on Katie’s locket, it implies that Epps now has a renewed heart, or possibly even salvation as stated in Bible scripture. In this manner, the locket could also represent that Epps’ soul is not "marked".<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Parallel of an Innocent and Sacrificial Life===== A striking parallel could also be drawn between Katie and Jesus Christ. In the bible, Christ lives a completely innocent life, but is hung on a cross to sacrificially die for the sins of all humanity.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |pages=2228-2229}}</ref> Christ tastes the sting of death and hell in order to offer salvation to all who will put their faith in Him.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=966}}</ref> Similarly, innocent Katie is hung by a rope behind a dividing door, but through her death she is able to lead others to "salvation" and safety. Because of her young age and innocent death, Katie is the only voice of hope for all the suppressed souls held captive on the demonic ship. Katie also endures small tastes of hell from Ferriman in her efforts to save others. However, Katie’s love and compassion for the lives of others is greater than her fear and pain, and in similarity to Christ, Katie rises victoriously to heaven in the end.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Forty Years and the Promised Land===== 40 years is a significant reoccurring number in the Christian faith.<ref>Collins English Dictonary http://dictionary.reference.com/browse/promised land</ref> The [[Israelites]] endured 40 years of great trial and testing in the wilderness before they were able to enter their promised land of rest. In Christian tradition, the earthly life is often compared to a time of trial in the wilderness and the Promised Land a metaphor for heaven.<ref>Collins English Dictonary http://dictionary.reference.com/browse/promised land</ref> Correspondingly, Katie has endured the “wilderness” and trials of the ship for 40 years, but as the result of Epps’ help she is inevitably freed to enter the “promised land” of heaven. =====Concept of Free Will===== Free will is both discussed and demonstrated in the story.<ref>{{cite book| last=Keck |first=Leander | title=The New Interpreter's Bible vol. 9 |publisher=Abingdon Press |location=Nashville, TN | year=2002 |pages=61-62}}</ref> Ultimately, the crew members who die are led to destruction by their own sins and their selfish desire for greed, lust and power. Epps is spared the fate of her shipmates through listening to Katie’s warnings and humbly responding to the truth.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Elevated Status of Children===== In the Christian bible God often uses the most humble and unlikely people to work through <ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=2283}}</ref> – Out of hundreds on the ship, Katie is the meekest, humblest and most unlikely to do anything significant, yet every soul on the ship ends up depending on her.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page production notes]</ref> Katie is also reminiscent of Christ elevating the status of children when he gave them special attention and profoundly declared that unless one humbles them self and has the faith of a little child, they will not enter the kingdom of heaven. This is further illustrated when Christ took a lowly child and placed him in the midst of his followers and stated that only those with childlike faith will be the greatest in the kingdom of heaven.<ref>{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | year=2001 |page=963}}</ref> This concept is demonstrated by Epps' willingness to humble herself to Katie's level.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> The role of children in Christian scripture – Comparisons could be made between Katie and several unpretentious bible characters such as the lowly shepherd boy David who defeated the warrior Goliath and became king. Outwardly both young Katie and David appear to be nothing more that mere children, however, inwardly they possess vast unforeseen potential and a tremendous strength of character.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=563}}</ref> <ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Eternal Destinations===== In the film, as with [[Christian soteriology]] there are two clear eternal destinations which souls go to after death; ether heaven or hell. A heart of child-like faith will put one on the path to heaven, but a sinful life eventually leads to destruction.<ref>{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN | year=1983 |page=1902}}</ref> =====The Destructiveness of Sinful Choices===== One of the morals of the story is the corrupting dangers of pursuing riches. This theme also fits aptly within the religious concepts of the film.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> Sinful greed, lust, debauchery and selfish desire can influence ordinarily good people to do horribly evil things (1Timothy 6:9-10).<ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=2195 | year=1991}}</ref> The choices made by the characters in the story illustrate this principle. “Be sure your sins will find you out” – As the story goes, sinful activities have consequences and will eventually have to be accounted for, and the ultimate payment for sin in the end is both physical and spiritual death (Romans 6:20-23). <ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=2039 | year=1991}}</ref> <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Loving Others before Ourselves===== “Greater love has no one than this – To lay one’s life down for their friends.” Katie and Epps are both willing put themselves at risk to save lives. Through the process of trying to help others both Epps and Katie experience help for themselves.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> “Those who seek to save their life will lose it, but those who are willing to lose their life will save it.”<ref>{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | page=1842 | year=1991}}</ref> In this sense Epps' life is saved, because she places the needs of others first. Katie also inherits eternal life in heaven by risking herself to help others. =====Purgatory===== The concept of purgatory (Whalen p. 1034-1039)<ref>{{cite book| last=Whalen |first=John | title=New Catholic Encyclopedia Vol. 11|publisher=Catholic University of America |location=Washington, D.C. | year=1983}}</ref> is also mentioned when Katie states that the ship had become like a “prison” where souls are trapped among the living between heaven and hell.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> ====Additional Symbolism==== =====Life as a Voyage on a Ship===== Life itself is comparable to a voyage on ship...illustrating that our lives are like a ship that is bound for one of two possible destinations.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> In the context of Ghost Ship, the voyage ends in destruction (death and hell) unless we get off. In this sense, Katie pleads with us to get off, but that involves humbly changing our ways and giving up the allure and pursuit of vain things such as wealth and power.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Symbols of Changing Times===== The once elegant and decaying ship is a symbol of changing times.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> In a similar manner, Katie can be viewed as a symbolic representation of childhood from a more innocent era. Just as the ship decays to ruin from its glorious 1950’s splendor, Katie’s deteriorating childhood possessions and even Katie herself, are evocative symbols of changing times and eroding childhood innocence.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> == Dichotomy and Contrasts == Katie is in some ways a complicated paradox: She has been deeply hurt and traumatized by all she has experienced, but by the same token, she is still very much an innocent child – Even after 40 years of resilient growth as a character. Katie exhibits a wide array of emotions from timid youthful innocence and joy, to extreme terror, sadness, loneliness, and solemn distress.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> ====Characters==== Even under tremendously trying circumstances Katie demonstrates an incredible inner strength of character without compromising the sweet kind-hearted "girly" girl she really is. The fact that Katie remains true to herself in spite of all the evil and suffering she experienced transcends their eroding influence and distinguishes her from the other characters.<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Ferriman===== Ferriman is representative of Satan and the crafty deceptiveness of evil in destroying people’s lives. Katie and Ferriman are at completely opposite ends of the Christian spectrum – The demonic Ferriman is totally depraved and evil while Katie is sweet and innocent. Katie is motivated by love and compassion, Ferriman is motivated by hate and rage.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> <ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Epps===== Although Katie and Epps are two completely dissimilar characters from different eras, they still grow quite close. Epps is "a woman working in a man's world"<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> and appears somewhat tough and masculine on the exterior like a tomboy. Although not specifically stated, the story indicates that Epps is likely from a broken home. On the other hand, Katie comes from a close, traditional nuclear family. In contrast to Epps, Katie is more of a typical "girly" girl and is slightly timid, but possess a stout inner fortitude despite her diminutive and delicate appearance.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> =====Francesca===== The sultry Francesca lives the more representative life of a performing artist. Unlike Epps who feels the need to downplay her femininity, Francesca leans toward the other extreme and attempts to flaunt her femininity to her own advantage, even to the point of her own exploitation. Conversely, Katie is still a virtuous and modest little girl, who has yet to be tainted by any corrupting influences of the world.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> =====Captain Murphy===== Captain Murphy appears to be a strong imposing ship captain on the outside, however, when confronted with trials and tribulations, his perceived strength is shown to be superficial. This is evident by his emotional breakdown where he shuts off emotionally and withdraws to himself while attempting to drown his problems in alcohol. In contrast, Katie appears to be very delicate in both physical appearance and personality. However, despite her dainty appearance, Katie proves her true strength and fortitude from within through dealing with her pain and problems directly, instead of allow it to define her<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> ====General Themes==== Light vs. darkness, good vs. evil, childhood innocence vs. wickedness, tragedy vs. triumph, simpler more wholesome times, vs. the complexity and loss of innocence of today.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> == Conclusion == On the surface, Katie’s story is an emotional tale of heartache and tragedy – Something that no young person should ever have to endure. However, Katie’s story is also essential to the plot. <ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> Through helping each other and being willing to put themselves at risk, Katie and Epps together achieve a triumph out of the tragedy and deliver a major blow to Ferriman and the forces of evil. Although the struggle over the souls of people will continue, this victory of the human spirit gives hope even in the face of terrible suffering, evil and even death.<ref>Ghost Ship DVD (2003) - Extra features and behind the scenes</ref> “Katie is really a very sweet girl. She's completely innocent…“ says Emily Jane Browning, who obviously became completely immersed in her character. “…She's been hoping someone would come onto the ship to be her friend, so when Epps arrives she's very excited – they develop a real friendship."<ref>[http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> ”Emily did an amazing job,” Director Steve Beck enthuses. “She gave Katie a real complexity…she's not just a little girl caught up in a ghost story…” Both Browning and Beck also added that underneath all her heartfelt emotions, Katie longs for vindication and justice.<ref> [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes]</ref> The deeply symbolic and metaphorical aspects surrounding Katie’s story along with the close relationships she develops with others lends support to the notion that the film was originally intended to be more than just another Hollywood “slasher” horror. This is further substantiated by Katie’s tearful and heartfelt story – Emotionally poignant and touching drama not usually associated with a horror picture.<ref>http://www.dailyscript.com/scripts/ghost_ship_info.txt</ref> == References == ===Footnotes=== {{Reflist|colwidth=30em}} ===Cited Texts=== {{refbegin}} *{{cite book| last=Barclay | first=William | title=The Gospel of Mark |publisher=Westminster Press | location=Philadelphia, PA | isbn=0664213022 | year=1975}} *{{cite book| last=Barton |first=John | title=The Oxford Bible Commentary |publisher=Oxford University Press |location=New York, NY | isbn=0-19-875500-7 | year=2001}} *{{cite book| last=Boettner |first=Loraine | title=Roman Catholicism |publisher=Presbyterian & Reformed Publishing Co. |location=Phillipsburg, NJ |isbn=0875521304 | year=1985}} *{{cite book| last=Buttrick |first=George | title=The Interpreter's Bible vol. 12 |publisher=Abingdon Press |location=Nashville, TN |asin=B000HTP248 | year=1957}} *{{cite book |title=Collins English Dictionary - Complete & Unabridged 10th Edition |date=2009 | publisher=Harper Collins |location=New York, NY}} *{{cite book| last=Dummelow |first=J.R. | title=Commentary on the Whole Bible |publisher=Macmillian Publishing Co. |location=New York, NY | year=1936}} *{{cite book| last=Gaebelein |first=Frank | title=The Expositors Bible Commentary vol. 1 |publisher=Zondervan |location=Grand Rapids, MI |isbn=0310364302 | year=1979}} *{{cite book| last=Gauding |first=Madonna | title=The Signs and Symbols Bible |publisher=Sterling Publishing Co. |location=New York, NY |isbn=1402770049| year=2009}} *{{cite book| last=Jamieson |first=Fausset | title=Commentary on the Whole Bible |publisher=Zondervan |location=Grand Rapids, MI| asin=B004BCQP8O | year=1971}} *{{cite book| last=Keck |first=Leander | title=New Interpreter's Bible vol. 9 |publisher=Abingdon Press |location=Nashville, TN |isbn=0687278228 | year=2002}} *{{cite book| title=Life Application Bible - New International Version |publisher=Tyndale House Publishers, Inc. |location=Wheaton, IL | lccn=90-71553| year=1991}} *{{cite book| last=Towns |first=Elmer | title=Liberty Bible Commentary |publisher=Thomas Nelson Inc |location=Nashville, TN |isbn=0840752954 | year=1983}} *{{cite book| last=Wall |first=Robert | title=The New Interpreter's Bible vol. 10 |publisher=Abingdon Press |location=Nashville, TN |isbn=0687278236 | year=2002}} *{{cite book| last=Whalen |first=John | title=New Catholic Encyclopedia Vol. 11 |publisher=Catholic University of America |location=Washington D.C. | lccn=66-22292 | year=1967}} {{refend}} == External links == * [http://www.dailyscript.com/scripts/ghost_ship_info.txt/ Daily Script_Ghost Ship] * [http://www.imdb.com/title/tt0288477/ Internet Movie Database_Ghost Ship 2002] * [http://ghostshipmovie.warnerbros.com/production_notes.html?page=2/ Ghost Ship official movie page_production notes] * [http://www.rottentomatoes.com/m/ghost_ship/ Rotten Tomatoes movie review_Ghost Ship] [[Category:Analysis]] [[Category:Film]] hqmd94qzcfajztry5e7lz3gme64iife 0 139384 2807868 2807808 2026-05-07T13:59:47Z Young1lim 21186 /* Adder */ 2807868 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20260109.pdf|org]], [[Media:VLSI.Arith.2A.CLA.20260507.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260505.pdf|B]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] t598actsxc6cmdnx3jeek0d95ls3b1w 2807870 2807868 2026-05-07T14:08:24Z Young1lim 21186 /* Adder */ 2807870 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20260109.pdf|org]], [[Media:VLSI.Arith.2A.CLA.20260507.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260506.pdf|B]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] 3p0xcrhayxqwtq96ft8nslw2o41eof7 2807872 2807870 2026-05-07T14:09:34Z Young1lim 21186 /* Adder */ 2807872 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20250522.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20260109.pdf|org]], [[Media:VLSI.Arith.2A.CLA.20260507.pdf|A]], [[Media:VLSI.Arith.2B.CLA.20260507.pdf|B]] || || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20250405.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]], [[Media:VLSI.Arith.1C.VBA.20250218.pdf|D]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] 8eomg3qbqayre64f5zdglp7r68xcd0m 0 171005 2807876 2807814 2026-05-07T14:23:48Z Young1lim 21186 /* Geometric Series Examples */ 2807876 wikitext text/x-wiki Many of the functions that arise naturally in mathematics and real world applications can be extended to and regarded as complex functions, meaning the input, as well as the output, can be complex numbers <math>x+iy</math>, where <math>i=\sqrt{-1}</math>, in such a way that it is a more natural object to study. '''Complex analysis''', which used to be known as '''function theory''' or '''theory of functions of a single complex variable''', is a sub-field of analysis that studies such functions (more specifically, '''holomorphic''' functions) on the complex plane, or part (domain) or extension (Riemann surface) thereof. It notably has great importance in number theory, e.g. the [[Riemann zeta function]] (for the distribution of primes) and other <math>L</math>-functions, modular forms, elliptic functions, etc. <blockquote>The shortest path between two truths in the real domain passes through the complex domain. — [[wikipedia:Jacques_Hadamard|Jacques Hadamard]]</blockquote>In a certain sense, the essence of complex functions is captured by the principle of [[analytic continuation]].{{mathematics}} ==''' Complex Functions '''== * Complex Functions ([[Media:CAnal.1.A.CFunction.20140222.Basic.pdf|1.A.pdf]], [[Media:CAnal.1.B.CFunction.20140111.Octave.pdf|1.B.pdf]], [[Media:CAnal.1.C.CFunction.20140111.Extend.pdf|1.C.pdf]]) * Complex Exponential and Logarithm ([[Media:CAnal.5.A.CLog.20131017.pdf|5.A.pdf]], [[Media:CAnal.5.A.Octave.pdf|5.B.pdf]]) * Complex Trigonometric and Hyperbolic ([[Media:CAnal.7.A.CTrigHyper..pdf|7.A.pdf]], [[Media:CAnal.7.A.Octave..pdf|7.B.pdf]]) '''Complex Function Note''' : 1. Exp and Log Function Note ([[Media:ComplexExp.29160721.pdf|H1.pdf]]) : 2. Trig and TrigH Function Note ([[Media:CAnal.Trig-H.29160901.pdf|H1.pdf]]) : 3. Inverse Trig and TrigH Functions Note ([[Media:CAnal.Hyper.29160829.pdf|H1.pdf]]) ==''' Complex Integrals '''== * Complex Integrals ([[Media:CAnal.2.A.CIntegral.20140224.Basic.pdf|2.A.pdf]], [[Media:CAnal.2.B.CIntegral.20140117.Octave.pdf|2.B.pdf]], [[Media:CAnal.2.C.CIntegral.20140117.Extend.pdf|2.C.pdf]]) ==''' Complex Series '''== * Complex Series ([[Media:CPX.Series.20150226.2.Basic.pdf|3.A.pdf]], [[Media:CAnal.3.B.CSeries.20140121.Octave.pdf|3.B.pdf]], [[Media:CAnal.3.C.CSeries.20140303.Extend.pdf|3.C.pdf]]) ==''' Residue Integrals '''== * Residue Integrals ([[Media:CAnal.4.A.Residue.20140227.Basic.pdf|4.A.pdf]], [[Media:CAnal.4.B.pdf|4.B.pdf]], [[Media:CAnal.4.C.Residue.20140423.Extend.pdf|4.C.pdf]]) ==='''Residue Integrals Note'''=== * Laurent Series with the Residue Theorem Note ([[Media:Laurent.1.Residue.20170713.pdf|H1.pdf]]) * Laurent Series with Applications Note ([[Media:Laurent.2.Applications.20170327.pdf|H1.pdf]]) * Laurent Series and the z-Transform Note ([[Media:Laurent.3.z-Trans.20170831.pdf|H1.pdf]]) * Laurent Series as a Geometric Series Note ([[Media:Laurent.4.GSeries.20170802.pdf|H1.pdf]]) === Laurent Series and the z-Transform Example Note === * Overview ([[Media:Laurent.4.z-Example.20170926.pdf|H1.pdf]]) ====Geometric Series Examples==== * Causality ([[Media:Laurent.5.Causality.1.A.20191026n.pdf|A.pdf]], [[Media:Laurent.5.Causality.1.B.20191026.pdf|B.pdf]]) * Time Shift ([[Media:Laurent.5.TimeShift.2.A.20191028.pdf|A.pdf]], [[Media:Laurent.5.TimeShift.2.B.20191029.pdf|B.pdf]]) * Reciprocity ([[Media:Laurent.5.Reciprocity.3A.20191030.pdf|A.pdf]], [[Media:Laurent.5.Reciprocity.3B.20191031.pdf|B.pdf]]) * Combinations ([[Media:Laurent.5.Combination.4A.20200702.pdf|A.pdf]], [[Media:Laurent.5.Combination.4B.20201002.pdf|B.pdf]]) * Properties ([[Media:Laurent.5.Property.5A.20220105.pdf|A.pdf]], [[Media:Laurent.5.Property.5B.20220126.pdf|B.pdf]]) * Permutations ([[Media:Laurent.6.Permutation.6A.20230711.pdf|A.pdf]], [[Media:Laurent.5.Permutation.6B.20251225.pdf|B.pdf]], [[Media:Laurent.5.Permutation.6C.20260507.pdf|C.pdf]], [[Media:Laurent.5.Permutation.6C.20240528.pdf|D.pdf]]) * Applications ([[Media:Laurent.5.Application.6B.20220723.pdf|A.pdf]]) * Double Pole Case :- Examples ([[Media:Laurent.5.DPoleEx.7A.20220722.pdf|A.pdf]], [[Media:Laurent.5.DPoleEx.7B.20220720.pdf|B.pdf]]) :- Properties ([[Media:Laurent.5.DPoleProp.5A.20190226.pdf|A.pdf]], [[Media:Laurent.5.DPoleProp.5B.20190228.pdf|B.pdf]]) ====The Case Examples==== * Example Overview : ([[Media:Laurent.4.Example.0.A.20171208.pdf|0A.pdf]], [[Media:Laurent.6.CaseExample.0.B.20180205.pdf|0B.pdf]]) * Example Case 1 : ([[Media:Laurent.4.Example.1.A.20171107.pdf|1A.pdf]], [[Media:Laurent.4.Example.1.B.20171227.pdf|1B.pdf]]) * Example Case 2 : ([[Media:Laurent.4.Example.2.A.20171107.pdf|2A.pdf]], [[Media:Laurent.4.Example.2.B.20171227.pdf|2B.pdf]]) * Example Case 3 : ([[Media:Laurent.4.Example.3.A.20171017.pdf|3A.pdf]], [[Media:Laurent.4.Example.3.B.20171226.pdf|3B.pdf]]) * Example Case 4 : ([[Media:Laurent.4.Example.4.A.20171017.pdf|4A.pdf]], [[Media:Laurent.4.Example.4.B.20171228.pdf|4B.pdf]]) * Example Summary : ([[Media:Laurent.4.Example.5.A.20171212.pdf|5A.pdf]], [[Media:Laurent.4.Example.5.B.20171230.pdf|5B.pdf]]) ==''' Conformal Mapping '''== * Conformal Mapping ([[Media:CAnal.6.A.Conformal.20131224.pdf|6.A.pdf]], [[Media:CAnal.6.A.Octave..pdf|6.B.pdf]]) go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Complex analysis]] p5rv5outst2pocyaal46r91jubey2q6 0 203942 2807883 2807591 2026-05-07T18:49:57Z Young1lim 21186 /* Lambda Calculus */ 2807883 wikitext text/x-wiki ==Introduction== * Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]]) * Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]]) * Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]]) * Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]]) * Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]]) </br> ==Applications== * Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]]) * Bird's Implementation :- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]]) :- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]]) :- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]]) :- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]]) </br> ==Using GHCi== * Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]]) </br> ==Using Libraries== * Library ([[Media:Library.1.A.20170605.pdf |pdf]]) </br> </br> ==Types== * Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]]) * TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]]) * Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]]) * Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]]) * Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]]) ==Functions== * Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]]) * Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]]) * Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]]) ==Expressions== * Expressions I ([[Media:Background.1.D.Expression.20180707.pdf |pdf]]) * Expressions II ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]]) * Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]]) </br> </br> ==Lambda Calculus== * Lambda Calculus - informal description ([[Media:LCal.1A.informal.20220831.pdf |pdf]]) * Lambda Calculus - Formal definition ([[Media:LCal.2A.formal.20221015.pdf |pdf]]) * Expression Reduction ([[Media:LCal.3A.reduction.20220920.pdf |pdf]]) * Normal Forms ([[Media:LCal.4A.Normal.20220903.pdf |pdf]]) * Encoding Datatypes :- Church Numerals ([[Media:LCal.5A.Numeral.20230627.pdf |pdf]]) :- Church Booleans ([[Media:LCal.6A.Boolean.20230815.pdf |pdf]]) :- Functions ([[Media:LCal.7A.Function.20231230.pdf |pdf]]) :- Combinators ([[Media:LCal.8A.Combinator.20241202.pdf |pdf]]) :- Recursions ([[Media:LCal.9A.Recursion.20260506.pdf |A]], [[Media:LCal.9B.Recursion.20260330.pdf |B]]) </br> </br> ==Function Oriented Typeclasses== === Functors === * Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]]) * Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]]) * Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]]) === Applicatives === * Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]]) * Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]]) * Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]]) * Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]]) === Monads I : Background === * Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]]) * Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]]) * Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]]) * Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]]) * IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]]) * Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]]) === Monads II : State Transformer Monads === * State Transformer : - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]]) : - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]]) : - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]]) * State Monad : - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]]) : - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) : - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]]) === Monads III : Mutable State Monads === * Mutability Background : - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]]) : - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]]) : - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]]) : - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]]) : - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]]) * Mutable Objects : - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]]) : - Mutable Data Structures ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]]) * IO Monad : - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]]) : - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]]) : - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]]) * ST Monad : - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]]) : - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]]) : - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]]) === Monads IV : Reader and Writer Monads === * Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]]) * Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]]) * MonadState Class :: - State & StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]]) * MonadReader Class :: - Reader & ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]]) * Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]]) === Monoid === * Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]]) === Arrow === * Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]]) </br> ==Polymorphism== * Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]]) </br> ==Concurrent Haskell == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://learnyouahaskell.com/introduction Learn you Haskell] * [http://book.realworldhaskell.org/read/ Real World Haskell] * [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material] [[Category:Haskell|programming in plain view]] lyx69etqx5kuz72ulnk0pvlv50z610q 2807885 2807883 2026-05-07T18:51:02Z Young1lim 21186 /* Lambda Calculus */ 2807885 wikitext text/x-wiki ==Introduction== * Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]]) * Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]]) * Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]]) * Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]]) * Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]]) </br> ==Applications== * Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]]) * Bird's Implementation :- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]]) :- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]]) :- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]]) :- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]]) </br> ==Using GHCi== * Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]]) </br> ==Using Libraries== * Library ([[Media:Library.1.A.20170605.pdf |pdf]]) </br> </br> ==Types== * Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]]) * TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]]) * Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]]) * Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]]) * Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]]) ==Functions== * Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]]) * Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]]) * Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]]) ==Expressions== * Expressions I ([[Media:Background.1.D.Expression.20180707.pdf |pdf]]) * Expressions II ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]]) * Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]]) </br> </br> ==Lambda Calculus== * Lambda Calculus - informal description ([[Media:LCal.1A.informal.20220831.pdf |pdf]]) * Lambda Calculus - Formal definition ([[Media:LCal.2A.formal.20221015.pdf |pdf]]) * Expression Reduction ([[Media:LCal.3A.reduction.20220920.pdf |pdf]]) * Normal Forms ([[Media:LCal.4A.Normal.20220903.pdf |pdf]]) * Encoding Datatypes :- Church Numerals ([[Media:LCal.5A.Numeral.20230627.pdf |pdf]]) :- Church Booleans ([[Media:LCal.6A.Boolean.20230815.pdf |pdf]]) :- Functions ([[Media:LCal.7A.Function.20231230.pdf |pdf]]) :- Combinators ([[Media:LCal.8A.Combinator.20241202.pdf |pdf]]) :- Recursions ([[Media:LCal.9A.Recursion.20260507.pdf |A]], [[Media:LCal.9B.Recursion.20260330.pdf |B]]) </br> </br> ==Function Oriented Typeclasses== === Functors === * Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]]) * Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]]) * Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]]) === Applicatives === * Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]]) * Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]]) * Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]]) * Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]]) === Monads I : Background === * Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]]) * Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]]) * Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]]) * Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]]) * IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]]) * Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]]) === Monads II : State Transformer Monads === * State Transformer : - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]]) : - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]]) : - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]]) * State Monad : - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]]) : - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) : - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]]) === Monads III : Mutable State Monads === * Mutability Background : - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]]) : - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]]) : - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]]) : - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]]) : - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]]) * Mutable Objects : - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]]) : - Mutable Data Structures ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]]) * IO Monad : - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]]) : - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]]) : - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]]) * ST Monad : - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]]) : - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]]) : - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]]) === Monads IV : Reader and Writer Monads === * Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]]) * Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]]) * MonadState Class :: - State & StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]]) * MonadReader Class :: - Reader & ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]]) * Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]]) === Monoid === * Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]]) === Arrow === * Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]]) </br> ==Polymorphism== * Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]]) </br> ==Concurrent Haskell == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://learnyouahaskell.com/introduction Learn you Haskell] * [http://book.realworldhaskell.org/read/ Real World Haskell] * [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material] [[Category:Haskell|programming in plain view]] 3r4nkosyfbp7w9kr3wl2mnxylka8z1u 0 239880 2807881 2807685 2026-05-07T16:50:54Z Atcovi 276019 2807881 wikitext text/x-wiki {{notes}} {{assignment}} {{secondary}} {{complete}} __NOTOC__ '''Work''': Fiction '''Genre''' (novel, play, memoir, etc): Novel '''Author''': John Irving '''Time period(s) of the setting of the work''': 1950s and the 1980s '''Research and cite important information (in an ample paragraph) regarding the time period(s)''': In the book, this statement, "And what would the canon have said if I'd told him that the Christmas of '53 [1953] put the finishing touches on Christmas for me?" (Irving 230), is in reference to the Christmas of the year that Johnny's mother, Tabitha Wheelwright, died. In the 1950s, the Wheelwrights, including Johnny, lived in Gravesend, New Hampshire. The Wheelwright family's Christmas of '53 was a very poor Christmas compared to their previous celebrations ("The first Christmas following my mother's death was the first Christmas I didn't spend in Sawyer Depot. My grandmother told Aunt Martha and Uncle Alfred that if the family were all together, my mother's absence would be too apparent" (Irving 150). Many dates in the book are of the late 1980s, such as in "The Armadillo" ("Today---January 30, 1987--it is snowing in Toronto" (Irving 91)) and "The Voice" ("Toronto: May 14, 1987--another sunny morning, but rain developing" (Irving 332)). Johnny Wheelwright moved to Canada in 1971 during the Vietnam War: "More than thirty thousand Canadians served in Vietnam, too. And almost as many Americans came to Canada during the Vietnam War; I was one of them--one who stayed. By March of 1971--when Lt. William Calley was convicted of premeditated murder--I was already a landed immigrant, I'd already applied for Canadian citizenship" (Irving 95). '''Give a 2-3 sentence plot summary''': John Irving's ''A Prayer for Owen Meany'' shows two friends, Johnny Wheelwright and Owen Meany living normal lives as kids. These normal lives turned dark after the summer of 1953, after Johnny Wheelwright's mother, Tabitha Wheelwright, was killed by a well-stricken ball by Johnny's friend, Owen Meany, during a baseball game. With a mix of Christianity and rambling of politics, Johnny and Owen move on from the dreadful slaughter and live normal, but entertaining, lives. '''List the key characters and give a brief description of each''': #'''Johnny Wheelwright''' - A Canadian-American who was born and grew up in America (Gravesend, New Hampshire). He is the main character. #'''Owen Meany''' - An American who is riddled with unfortunate disabilities and an extremely high pitched voice. He is Johnny's best friend. #'''Tabitha Wheelwright''' - The mother of Johnny Wheelwright, who is killed by Owen Meany's perfectly struck ball in the summer of 1953 during a baseball game. She is described as an extremely beautiful woman who had an amazing singing voice. #'''Harriet Wheelwright''' - Grandmother of Johnny Wheelwright and mother of Tabitha Wheelwright. An old lady who is accompanied by maids, such as Lydia and Germaine. #'''Dan Needham''' - Johnny's stepfather and Tabitha's husband. He is the only one who truly understands Johnny unlike other men. #'''Randy White''' - The new headmaster for Gravesend Academy. He is the one who kicked out Owen Meany out of Gravesend Academy due to his dislike for the student. #'''Hester''' - Johnny's cousin who his best friend, Owen, seems to be romantically interested; Sister to Simo and Noah; Children of Aunt Martha, Tabitha's sister. #'''Simon''' - Johnny's cousins; Brother of Noah and Hester; Children of Aunt Martha, Tabitha's sister. #'''Noah''' - Johnny's cousins; Brother of Simon and Hester; Children of Aunt Martha, Tabitha's sister. '''Describe the author’s style, noting any distinctive features (plural)''': #Whenever Owen Meany speaks [in the book], he is always characterized by capital letters ("In Sunday school, when we held Owen up in the air--especially, in the air!--he protested so uniquely. We tortured him, I think, in order to hear his voice; I used to think his voice came from another planet. Now I'm convinced it was a voice not entirely of this world. "PUT ME DOWN!" he would say in a strangled, emphatic falsetto. "CUT IT OUT! I DON'T WANT TO DO THIS ANYMORE. ENOUGH IS ENOUGH. PUT ME DOWN! YOU ASSHOLES!" (John Irving 7)). This is due to his unique, high-pitched voice. This gives readers a good perspective about Owen Meany and how he sounds like. #Sexual, graphic language is used in the book, enhancing the book's field of language. An example of this type of language being used is when Johnny was forced to kiss Hester on the lips in a game of "Last One Through The House Has to Kiss Hester": "We opened our mouths. There was the problem of arranging the noses before we could enjoy the nervous exchange of saliva--the slithery contact of tongues, the surprising click of teeth. We were joined so long we had to breathe, and I was astonished at how sweet my cousin's breath was; to this day, I hope mine wasn't too bad" (Irving 61). Another example is Hester's remark on touching Johnny's erection (or "hard-on", as described): "And what did they make of the time they untied us and Hester said to me, "I felt your hard-on"? "You did not!" I said. "I did. It wasn't much of a hard-on," she said. "It was no big deal. But I felt it." "You didn't!" I said. "I did," she said. #The author constantly switches the time periods repeatedly in the book. This shift is usually from the 1950s in Gravesend, New Hampshire to the late 1980s in Toronto, Canada. An example of this is in "The Armadillo", pages 90-91: "...but Owen's idea---that God's reasoning was somehow predetermining Owen's every move--came from much more than that one unlucky swing and crack of the bat. As you shall see." (Irving 90) to "Today--January 30, 1987--it is snowing in Toronto" (Irving 91). I've personally never seen this in any other book, and I find it unique and intriguing since it provides two different stories in a short amount of pages in the chapter. '''Explain the author’s distinctive word choices. Furnish at least 2 examples per chapter.''' (Also, be prepared to defend your explanation in class). ===Chapter 1=== #"I am doomed to remember a boy with a wrecked voice--not because of his voice, or because he was the smallest person I ever knew, or even because he was the instrument of my mother's death" (Irving 3) #*Foreshadowing is being depicted here. The foreshadowing by the author already hooks up the reader into this book. #"PUT ME DOWN!" he would say in a strangled, emphatic falsetto. "CUT IT OUT! I DON'T WANT TO DO THIS ANYMORE. ENOUGH IS ENOUGH. PUT ME DOWN! YOU ASSHOLES!" (Irving 7) #*The language being used in this book carries more perspective to the reader. The word, "assholes", represents Owen's feelings about being held up in the air during class. ===Chapter 2=== #"...but he was sufficiently worked up about my mother's and my Owen departure from his church to offer his opinions as if he were speaking from the pulpit." (Irving 39) #*Mr. Irving enhances his book with figurative language--this case with a simile. #"My mother and my grandmother and I--and Lydia, minus one of her legs--were eating dinner on a Thursday evening..." (Irving 42) #*Mr. Irving uses humour to attract readers to the book. #"Curiosity, which--in New Hampshire, in those days--was often said to be responsible for the death of cats." (Irving 46) #*A reference to a popular saying: "Curiosity killed the cat". ===Chapter 3=== #"It made him furious when I suggested that ''anything'' was an "accident"--especially anything that had happened to him; on the subject of predestination, Owen Meany would accuse Calvin of bad faith. There were ''no'' accidents; there was a reason for that baseball--just as there was a reason for Owen being small, and a ''reason'' for his voice. In Owen's opinion, he had INTERRUPTED AN ANGEL, he had DISTURBED AN ANGEL AT WORK, he had UPSET THE SCHEME OF THINGS." (Irving 105) #*The author shows the reader how religious Owen is and how he always connects every-day events to religion. #"Dan came from a very high-powered family; they were doctors and lawyers, and they disapproved of Dan of not completing a more serious education [and going into acting]. To have started out at Harvard and not gone ''on'' to law school, not gone ''on'' to medical school--this was criminal laziness..." (Irving 112) #*The author shows the readers about Dan Needham's, one of the key characters in the book, background. This opens up readers to wonder, "Does this mean Dan is not very intelligent?", "Is Dan still a very intelligent person?", "Will he be a good role model/stepfather for Johnny?". ===Chapter 4=== #"The first Christmas following my mother's death was the first Christmas I didn't spend in Sawyer Depot. My grandmother told Aunt Martha and Uncle Alfred that if the family were all together, my mother's absence would be too apparent" (Irving 150) #*The author exemplifies the sorrow that the Wheelwright family is going through due to the loss of Tabitha Wheelwright, Johnny's mother (even after several months when Tabitha was killed). This brings in questions about the family's emotional state and how they are going to move on from this tragic, unfortunate death. #"'Twas ''not'' the season to be jolly--although dear Dan Needham tried. Dan drank too much..." (Irving 151) #*I felt like this was an oxymoron stated by Mr. Irving since alcohol makes people who are sad or depressed even worse rather than not cheering up/bringing joy to people. Dan is trying to be even happier, but in reality, he's just getting even more depressed (situational irony). ===Chapter 5=== #"And I, Joseph--forever standing in the wings--saw what the envious Virgin Mary failed to see. I saw it, and I'm sure Barb Wiggin saw it, too--I'm sure it was why she so shamelessly continued to torture him. <big>The Baby Jesus [Owen Meany] had an erection</big>; its protrusion was visible in spite of the tightly bound layers of his swaddling clothes." (Irving 218) #*The sentence, "The Baby Jesus had an erection", (and putting "Baby Jesus" instead of "Owen") was to put the awkwardness in Owen's sexual gratification (Owen) during his role as "Baby Jesus" which resulted from a sexual encounter with Barb Wiggin, a stewardess, and wife of Rector Captain Wiggin. It also provides a sense of humour as well. #"Don't be sorry! [in response to Johnny apologizing for not being very Christian by being angry]" the canon [Canon Mackie] said cheerfully. "Try to be a little... different!" The man's pauses are almost as irritating as his advice. (Irving 228) #*John Irving managed to word his sentence using figurative language (using a harsh word like "irritating" instead of "annoying") and good timing (used right after the canon's advice that had a pause) so well that it managed to make the readers (me) feel what Johnny was feeling. I felt irritated like I was right there when I was reading this part of page 228. ===Chapter 6=== #""Until everything's in color, and the color's perfect, TV's not worth watching."" (Irving 272) #*This statement by Hester puts us into her perspective of non-colorized TV, which seems to be described as "not worth watching". This was in the 1950s where the non-colorized TV wasn't available in every household like in today's time. I feel this view of non-colorized TV is pretty intriguing as I wonder, "Is this what all 1950s kids thought? Or was it just a minority of kids like Hester?". #""WHAT A BIG FUSS ABOUT A ''BLANKET''!" Owen said. "THAT'S SO CATHOLIC," he added--"TO GET VERY RELIGIOUS ABOUT ''OBJECTS''." This was a theme of Owen's--the Catholics and their adoration of OBJECTS. Yet Owens habit of collecting objects that ''he'' made (in his own way) RELIGIOUS was well known: I had only to remember my armadillo's claws." #*The author points out the irony in Owen's statement. He is ridiculing the Catholics for making objects religious, while he has done the same by using Johnny's armadillo in a religious way. ===Chapter 7=== #"...what he had expressed to me, symbolically, when he was eleven and had mutilated my armadillo. "GOD HAS TAKEN YOUR MOTHER," he said to me, when I was complaining about practicing the shot [basketball shot]; I thought he would never slam-dunk the [basketball] ball in under four seconds, and I was bored with all our trying. "MY HANDS WERE THE INSTRUMENT," he said. "GOD HAS TAKEN MY HANDS. I AM GOD'S INSTRUMENT." (Irving 343) #*This is Owen's reasoning for cutting off the armadillo's claws. Owen's reasoning makes readers wonder if there are more "religious" scenes where Owen will be, somehow, used as "God's instrument". When I read this statement, I was pretty interested in Owen's character and his way of thinking since I've never seen someone use themselves as "God's instrument", thus making me interested in the book (since Owen is a key character I'll be able to see him A LOT in this book). The author uses "God" as a way of making Owen an interesting character (religious character). ===Chapter 8=== #"Until the summer of 1962, I felt that I couldn't wait to grow up and be treated with the kind of respect I imagined adults were routinely offered and adamantly thought they deserved..." (Irving 423) #*Foreshadowing is already taking place at the beginning of Chap. 8. It made me wonder, "what happened during the summer of 1962? Did something tragic happen again like what happened in the summer of 1953?". #"It was the first summer we [Owen and Johnny] spent apart. I suppose I should be grateful for that summer, because it afforded me my first glimpse of what my life without Owen would be like--you might say, it prepared me. By the end of the summer of 1962, Owen Meany had me afraid of what the next phase was going to be. I didn't want to grow up anymore..." (Irving 423) #"I spent that summer of '62 in Sawyer Depot, working for my Uncle Alfred." (Irving 424) #*This is the summer of 1962 which Johnny realized that being an adult is not an easy lifestyle, but rather a life of responsibility and difficulty. This allows connections to take place between the reader, as it made me think about how my life will be when I'm not a kid anymore and I become an adult. ===Chapter 9=== #"Our own Gravesend chief of police, Ben Pike, stood at the heavy double doors of Hurd's Church--as if he intended to ''frisk'' Owen Meany's mourners for the "murder weapon," the long-lost "instrument of death"; I was tempted to tell the bastard where he could fin the f'ucking baseball." (Irving 568) #*The author provides a short reference back to chapter 1 when Ben Pike asked for the "murder weapon", which basically was the Owen-strucked baseball that killed Tabitha Wheelwright in the summer of 1953. It was a gleeful experience being able to remember back to chapter one, but I can't help but think: Does Johnny seriously still have a grudge against Ben Pike for saying that after all these years? #"I guess we were wrong about your little friend," Colonel Eiger said to me. "Yes, sir," I said. "He proved he was quite suitable for combat," Colonel Eiger said. (Irving 569) #*I thought it was pretty distinctive for Irving to mention this since I feel that Irving was trying to make more connections with the readers of the book. He achieved that if that was his attention. It made me boil with anger reading this statement since, just like Owen, I've always been underestimated for my potential in athletics and education. It must've been annoying for Owen himself to be underestimated as well. The author managed to make his readers connect with the story. =====State (below) two ideas that you believe are important to the author regarding the Essential Questions* and give a specific textual example to prove each from the work===== ===Idea related to the first question=== #Justice towards Owen Meany was shown by Johnny. He didn't break his friendship with Owen although Owen killed his mom. Johnny showing no hatred for Owen can be shown in "The Voice", page 310: "The school psychiatrist--a retired Swiss gentleman who returned, every summer, to Zürich--was convinced that my difficulties as a student were the result of my best friend's "murder" of my mother, and the "tensions and conflicts" that he saw as the "inevitable result" of my dividing my life between my grandmother and my stepfather. "At times, you must hate him---yes?" Dr. Dolder mused. "Hate who?" I asked. "My stepfather? No--I love Dan!". 'Your best friend--at times, you hate him. Yes?" Dr. Dolder asked. "No!" I said. "I love Owen--it was an accident."" (Irving 311). It is right that Johnny continues to hold his friendship with Owen even after the unfortunate slaughtering of Johnny's mother, as the unexpected murder was clearly an accident and Owen displayed tons of remorse, as evident in: "Owen and I were eleven; we had no other way to articulate what we felt about what had happened to my mother. He gave me his baseball cards, but he really wanted them back..." (Irving 88). Owen loved the baseball cards he gave to Johnny, as they were like a prized gift for Owen. This is shown in "...he [Owen Meany] left the cartons at the back door and ran quickly to the cab, and Mr. Meany drove the granite truck out of the driveway, still in the very lowest gear. In the cartons were all of Owen's baseball cards, his entire collection. My grandmother was appalled, but for several years she didn't understand Owen or appreciate him; to her, he was "that boy," or "that little guy," or "that voice." I knew the baseball cards were Owen's favorite things, they were what amounted to his treasure" (Irving 83-84). Even Johnny's cousin, Hester, knew Owen was very saddened by the death of Tabitha, as shown in: "Just remember," she said, "your friend Owen feels worse than you." (Irving 141). #Freedom was also shown after the major conflict (killing of Johnny's mom) when Johnny let go of any anger that must've arisen to Owen after Owen's perfectly struck ball hit Tabitha. By Johnny letting these feelings go, he is able to move on with his life and not have any hatred towards Owen, who was very evidently remorseful for the killing. In "The Armadillo", Johnny was outraged that Owen took away the claws of a toy armadillo that was given to Owen in exchange for Owen's baseball cards, as seen in: "But my greatest indignation was to follow: missing from the armadillo were the little animal's front claws--the most useful and impressive parts of its curious body. Owen had returned the armadillo, but he'd kept the claws! Well--friendship being one thing, and the armadillo quite another--I was so outraged by this discovery that I needed to talk to Dan Needham" (Irving 88). Later, Johnny realized that what Dan said about Owen's intentions for leaving the claws off the armadillo (""Your friend is most orginal," Dan Needham said, with the greatest respect. "Don't you see, Johnny? If he could, he would cut off his ''hands'' for you--that how it makes him feel"" (Irving 89)) was correct and Johnny had no point in being angry at Owen as he figured out Owen's true meaning behind the removal of the armadillo's claws. The text to which supports this idea comes from "The Armadillo", page 89: "Just before I fell asleep, I realized that everything Dan had said about Owen's intentions was correct. How much it has meant to my life that Dan Needham was almost never wrong! I was not as familiar with Wall's ''History of Gravesend'' as I became when I was eighteen and read the whole thing for myself; but I was familiar witht hose parts of it that Owen Meany considered "important." And just before I fell asleep, I also recognized my armadillo for what it was--in addition to all those things Dan had told me. My armadillo had been amputtated to resemble Watahantowet's totem, the tragic and mysterious armless man--for weren't the Indians wise enough to understand that everything had its own soul, its own spirit?" (Irving 89-90). ===Idea related to the second question=== #By Johnny being friends with Owen, as evident in the book (an example is when Johnny was defending Owen in relation to an incident where Owen made a sexual comment to another student's mom: ""She [Mitzy Lish] was rude to him [Owen]" I [Johnny] pointed out to the headmaster. "SHE MADE FUN OF ME BEING THE CLASS VALEDICTORIAN," said Owen Meany. "She laughed out loud at Owen," I said to Randy White. "She laughed in his face--she bullied him," I added." (Irving 383)), Johnny achieved strength to move on from Owen's unfortunate slaughtering of Tabitha Wheelwright. He seems to live a happy and fulfilled life with little-no rants/sobs about his mom's death and/or Owen's actions. #A major turning point in the book is when Owen's new location, Toronto in Canada, is mentioned (see "More than thirty thousand Canadians served in Vietnam, too. And almost as many Americans came to Canada during the Vietnam War; I was one of them--one who stayed. By March of 1971--when Lt. William Calley was convicted of premeditated murder--I was already a landed immigrant, I'd already applied for Canadian citizenship" (Irving 95)). The purpose of this move was to escape the Vietnam War, as it is obvious from "It was Owen Meany who kept me out of Vietnam--a trick that only Owen could have managed" (Irving 96). By moving to Canada, he avoided the obligatory drafting from the US army. {{Robelbox|theme=9|title=The Essential Questions|width=100%}} <div style="{{Robelbox/pad}}"> # How are justice and freedom revealed through the major conflicts in the selections? # Explore the ways the author demonstrates unity versus isolation through characterization in the selections. In this context, how does the character gain strength or purpose? </div> {{Robelbox/close}} [[Category:Assignments]] [[Category:Atcovi's Work]] hoaejosqwjzznkxfr93m8gv780tct8t 0 267737 2807898 2806419 2026-05-08T07:15:20Z Saltrabook 1417466 2807898 wikitext text/x-wiki [[File:ChatGPT Image 24 abr 2026, 02 17 02 p.m.png|800|center]] [[File:ChatGPT Image 24 abr 2026, 08 16 04 a.m.png|thumb|]] = '''' The John Snow Research Institute -2026'''' = Billions are at increased risk of developing metabolic syndromes like prediabetes, type 2 diabetes and hypertension with significant social bias. It’s not just that people need more education; it’s that the environments they live in often make healthy choices harder than unhealthy ones. The risk of developing diabetes is related to the Body Mass Index (height and weight) and the fasting blood sugar which is the main indicators in the Prevalence studies. The 16-weeks educational course include self-monitoring of blood sugar with glucometer, blood pressure, weight, and self-evaluation of diet and physical activity. The target is globally, but especially in the low- and middle-income countries where the availability of essential diagnostics remains a challenge. [[File:Lifestyle Medicine Pillars.png|400px|right|The focus of Lifestyle Medicine is on these 6 pillars.]] [[File:John Snow.jpg|thumb| right|John Snow in the early nineteenth century]] '''Links:''' 1. Publications and pptx 2016-2026 <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/The_International_Type_2_Diabetes_Mellitus_and_Hypertension_Research_Group#The_John_Snow_Institute </ref> <ref> https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf </ref> 2. ''''Prevalence studies'''' 2.1 The-International-Maritime-Health-Database <ref>https://www.dropbox.com/scl/fi/z3cq5ciiev06y8v9duw7u/A-International-Maritime-Health-Database.docx?cloud_editor=word&dl=0&rlkey=pt0kdesvmagcxaa2wez3tmza3 </ref> 2.2 Nursing Students Health Database <ref> https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&dl=0&rlkey=onbjh4o8ko1lzdvgyi8nlrotk </ref> 2.3. Medical student's Health Database <ref>https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&dl=0&rlkey=xyfqen5trdc5lniaovipl548n </ref> 2.4. School childrens Health database <ref> https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&dl=0&rlkey=zlyz5wn673wf7owettq3nx3h5 </ref> 3. '''Intervention studies''' Englsh <ref>https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&dl=0&rlkey=7kzg91tqfgjskxf5aji8khicx </ref> Danish <ref>https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&dl=0&rlkey=x63w8oqvarz284zg2btq2johv </ref> Spanish <ref> https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&dl=0&rlkey=popmr1fnodh1v951v9l7k9ezv </ref> 4. General research protocol draft <ref> https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&dl=0&rlkey=wat63e25ritmujwcpss8s4v0s </ref> 5. Health Promoting Schools <ref> https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&dl=0&rlkey=673jyzcmwbfw7k9ui9nmtp0zh </ref> 6 John Snow Institute bylaws <ref> https://www.dropbox.com/scl/fi/lccr7jtnga1u0x75117zn/John-Snow-revision-2-March-11.doc?cloud_editor=word&dl=0&rlkey=lz2gi7mslcoay5dzygg8h6n6r </ref> '''7.''' '''Prediabetes-Remission Research Network:''' <small>Prof. Ing. MSc. Nailet Delgado; Dr. Olaf Jensen, MD, MPH, PhD, o147248@gmail.com; MSc.Ph.D. Bishal Gyawali (SDU); MSc.PhD Vivi Just-Nørregaard; Dr. Johan Hviid Andersen MD, PhD. Prof Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Dr. Maite, Vacamonte, Panama; Bruno Nørdam, Randers; Dr. Maite Duque, Venezuela; Dr. Indira Santos Panama; Med.Stud. Ashley Lezcano, Panama; Dr. Antonio Roberto Abaya MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona/Cadiz, Spain; MBA Christian Acheampong, Turkey; Dr. Alejandro Martinez, MPH, Costa Rica; Dr. Med. Sci Finn Gyntelberg; NFA.and Bispebj. Hosp. Denmark,</small> ==References== [[Category:Prediabetes ]] <references />Education 1: Research Methodology <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/EDUCATION/Education_module_links</ref> rf044miuq45fvsynxsw7mw813mimht5 2807899 2807898 2026-05-08T07:16:31Z Saltrabook 1417466 /* ' The John Snow Research Institute -2026' */ 2807899 wikitext text/x-wiki [[File:ChatGPT Image 24 abr 2026, 02 17 02 p.m.png|800|center]] [[File:ChatGPT Image 24 abr 2026, 08 16 04 a.m.png|thumb|]] = '''' The John Snow Research Institute -2026'''' = Billions are at increased risk of developing metabolic syndromes like prediabetes, type 2 diabetes and hypertension with significant social bias. It’s not just that people need more education; it’s that the environments they live in often make healthy choices harder than unhealthy ones. The risk of developing diabetes is related to the Body Mass Index (height and weight) and the fasting blood sugar which is the main indicators in the Prevalence studies. The 16-weeks educational courses include self-monitoring of blood sugar with glucometer, blood pressure, weight, and self-evaluation of diet and physical activity. The target is globally, but especially in the low- and middle-income countries where the availability of essential diagnostics remains a challenge.[[File:Lifestyle Medicine Pillars.png|400px|right|The focus of Lifestyle Medicine is on these 6 pillars.]] [[File:John Snow.jpg|thumb| right|John Snow in the early nineteenth century]] '''Links:''' 1. Publications and pptx 2016-2026 <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/The_International_Type_2_Diabetes_Mellitus_and_Hypertension_Research_Group#The_John_Snow_Institute </ref> <ref> https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf </ref> 2. ''''Prevalence studies'''' 2.1 The-International-Maritime-Health-Database <ref>https://www.dropbox.com/scl/fi/z3cq5ciiev06y8v9duw7u/A-International-Maritime-Health-Database.docx?cloud_editor=word&dl=0&rlkey=pt0kdesvmagcxaa2wez3tmza3 </ref> 2.2 Nursing Students Health Database <ref> https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&dl=0&rlkey=onbjh4o8ko1lzdvgyi8nlrotk </ref> 2.3. Medical student's Health Database <ref>https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&dl=0&rlkey=xyfqen5trdc5lniaovipl548n </ref> 2.4. School childrens Health database <ref> https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&dl=0&rlkey=zlyz5wn673wf7owettq3nx3h5 </ref> 3. '''Intervention studies''' Englsh <ref>https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&dl=0&rlkey=7kzg91tqfgjskxf5aji8khicx </ref> Danish <ref>https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&dl=0&rlkey=x63w8oqvarz284zg2btq2johv </ref> Spanish <ref> https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&dl=0&rlkey=popmr1fnodh1v951v9l7k9ezv </ref> 4. General research protocol draft <ref> https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&dl=0&rlkey=wat63e25ritmujwcpss8s4v0s </ref> 5. Health Promoting Schools <ref> https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&dl=0&rlkey=673jyzcmwbfw7k9ui9nmtp0zh </ref> 6 John Snow Institute bylaws <ref> https://www.dropbox.com/scl/fi/lccr7jtnga1u0x75117zn/John-Snow-revision-2-March-11.doc?cloud_editor=word&dl=0&rlkey=lz2gi7mslcoay5dzygg8h6n6r </ref> '''7.''' '''Prediabetes-Remission Research Network:''' <small>Prof. Ing. MSc. Nailet Delgado; Dr. Olaf Jensen, MD, MPH, PhD, o147248@gmail.com; MSc.Ph.D. Bishal Gyawali (SDU); MSc.PhD Vivi Just-Nørregaard; Dr. Johan Hviid Andersen MD, PhD. Prof Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Dr. Maite, Vacamonte, Panama; Bruno Nørdam, Randers; Dr. Maite Duque, Venezuela; Dr. Indira Santos Panama; Med.Stud. Ashley Lezcano, Panama; Dr. Antonio Roberto Abaya MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona/Cadiz, Spain; MBA Christian Acheampong, Turkey; Dr. Alejandro Martinez, MPH, Costa Rica; Dr. Med. Sci Finn Gyntelberg; NFA.and Bispebj. Hosp. Denmark,</small> ==References== [[Category:Prediabetes ]] <references />Education 1: Research Methodology <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/EDUCATION/Education_module_links</ref> ofj15y4alqo6cbox732p8mzq0exbelg 2807900 2807899 2026-05-08T08:05:45Z Saltrabook 1417466 2807900 wikitext text/x-wiki [[File:ChatGPT Image 24 abr 2026, 02 17 02 p.m.png|800|center]] [[File:ChatGPT Image 24 abr 2026, 08 16 04 a.m.png|thumb|]] = '''' The John Snow Research Institute -2026'''' = Billions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight. All can lower their risks by staying physical active and eating well. For early identification of the risks we propose to register weight and height (Body Mass Index) and the fasting blood sugar in the '''Prevalence studies''' at the schools for seafarers, nurses, medical students and the kids schools.(not blood sugar).The 16-weeks '''intervention studies''' include learnings by weekly video sequences and self-monitoring of blood sugar with glucometer, and self-evaluation of diet and physical activity.[[File:Lifestyle Medicine Pillars.png|400px|right|The focus of Lifestyle Medicine is on these 6 pillars.]] [[File:John Snow.jpg|thumb| right|John Snow in the early nineteenth century]] '''Links:''' 1. Publications and pptx 2016-2026 <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/The_International_Type_2_Diabetes_Mellitus_and_Hypertension_Research_Group#The_John_Snow_Institute </ref><ref> https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf </ref> 2. '<nowiki/>'''Prevalence studies'''' 2.1 The-International-Maritime-Health-Database <ref>https://www.dropbox.com/scl/fi/z3cq5ciiev06y8v9duw7u/A-International-Maritime-Health-Database.docx?cloud_editor=word&dl=0&rlkey=pt0kdesvmagcxaa2wez3tmza3 </ref> 2.2 Nursing Students Health Database <ref> https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&dl=0&rlkey=onbjh4o8ko1lzdvgyi8nlrotk </ref> 2.3. Medical student's Health Database <ref>https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&dl=0&rlkey=xyfqen5trdc5lniaovipl548n </ref> 2.4. School childrens Health database <ref> https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&dl=0&rlkey=zlyz5wn673wf7owettq3nx3h5 </ref> 3. '''Intervention studies''' Englsh <ref>https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&dl=0&rlkey=7kzg91tqfgjskxf5aji8khicx </ref> Danish <ref>https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&dl=0&rlkey=x63w8oqvarz284zg2btq2johv </ref> Spanish <ref> https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&dl=0&rlkey=popmr1fnodh1v951v9l7k9ezv </ref> 4. General research protocol draft <ref> https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&dl=0&rlkey=wat63e25ritmujwcpss8s4v0s </ref> 5. Health Promoting Schools <ref> https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&dl=0&rlkey=673jyzcmwbfw7k9ui9nmtp0zh </ref> 6 John Snow Institute bylaws <ref> https://www.dropbox.com/scl/fi/lccr7jtnga1u0x75117zn/John-Snow-revision-2-March-11.doc?cloud_editor=word&dl=0&rlkey=lz2gi7mslcoay5dzygg8h6n6r </ref> '''7.''' '''Prediabetes-Remission Research Network:''' <small>Prof. Ing. MSc. Nailet Delgado; Dr. Olaf Jensen, MD, MPH, PhD, o147248@gmail.com; MSc.Ph.D. Bishal Gyawali (SDU); MSc.PhD Vivi Just-Nørregaard; Dr. Johan Hviid Andersen MD, PhD. Prof Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Dr. Maite, Vacamonte, Panama; Bruno Nørdam, Randers; Dr. Maite Duque, Venezuela; Dr. Indira Santos Panama; Med.Stud. Ashley Lezcano, Panama; Dr. Antonio Roberto Abaya MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona/Cadiz, Spain; MBA Christian Acheampong, Turkey; Dr. Alejandro Martinez, MPH, Costa Rica; Dr. Med. Sci Finn Gyntelberg; NFA.and Bispebj. Hosp. Denmark,</small> ==References== [[Category:Prediabetes ]] <references />Education 1: Research Methodology <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/EDUCATION/Education_module_links</ref> l16tsudgs4v93tprut6v3oyltqwi9ev 2807901 2807900 2026-05-08T08:11:45Z Saltrabook 1417466 2807901 wikitext text/x-wiki [[File:ChatGPT Image 24 abr 2026, 02 17 02 p.m.png|800|center]] [[File:ChatGPT Image 24 abr 2026, 08 16 04 a.m.png|thumb|]] = '''' The John Snow Research Institute -2026'''' = Billions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight. All can lower their risks by staying physical active and eating well. For early identification of the risks we propose to register weight and height (Body Mass Index) and the fasting blood sugar in the '''Prevalence studies''' at the schools for seafarers, nurses, medical students and the kids schools.(not blood sugar).The 16-weeks '''intervention studies''' include learnings by weekly video sequences and self-monitoring of blood sugar with glucometer, and self-evaluation of diet and physical activity.[[File:Lifestyle Medicine Pillars.png|400px|right|The focus of Lifestyle Medicine is on these 6 pillars.]] [[File:John Snow.jpg|thumb| right|John Snow in the early nineteenth century]] 1. '<nowiki/>'''Prevalence studies'''' 1.1 The-International-Maritime-Health-Database <ref>https://www.dropbox.com/scl/fi/z3cq5ciiev06y8v9duw7u/A-International-Maritime-Health-Database.docx?cloud_editor=word&dl=0&rlkey=pt0kdesvmagcxaa2wez3tmza3 </ref> 1.2 Nursing Students Health Database <ref> https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&dl=0&rlkey=onbjh4o8ko1lzdvgyi8nlrotk </ref> 1.3. Medical student's Health Database <ref>https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&dl=0&rlkey=xyfqen5trdc5lniaovipl548n </ref> 1.4. School childrens Health database <ref> https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&dl=0&rlkey=zlyz5wn673wf7owettq3nx3h5 </ref> 2. '''Intervention studies''' Englsh <ref>https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&dl=0&rlkey=7kzg91tqfgjskxf5aji8khicx </ref> Danish <ref>https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&dl=0&rlkey=x63w8oqvarz284zg2btq2johv </ref> Spanish <ref> https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&dl=0&rlkey=popmr1fnodh1v951v9l7k9ezv </ref> - General research protocol draft <ref> https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&dl=0&rlkey=wat63e25ritmujwcpss8s4v0s </ref> - Health Promoting Schools <ref> https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&dl=0&rlkey=673jyzcmwbfw7k9ui9nmtp0zh </ref> - John Snow Institute bylaws <ref> https://www.dropbox.com/scl/fi/lccr7jtnga1u0x75117zn/John-Snow-revision-2-March-11.doc?cloud_editor=word&dl=0&rlkey=lz2gi7mslcoay5dzygg8h6n6r </ref> '''Publications and pptx''' 2016-2026 <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/The_International_Type_2_Diabetes_Mellitus_and_Hypertension_Research_Group#The_John_Snow_Institute </ref><ref> https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf </ref> '''Prediabetes-Remission Research Network:''' <small>Prof. Ing. MSc. Nailet Delgado; Dr. Olaf Jensen, MD, MPH, PhD, o147248@gmail.com; MSc.Ph.D. Bishal Gyawali (SDU); MSc.PhD Vivi Just-Nørregaard; Dr. Johan Hviid Andersen MD, PhD. Prof Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Dr. Maite, Vacamonte, Panama; Bruno Nørdam, Randers; Dr. Maite Duque, Venezuela; Dr. Indira Santos Panama; Med.Stud. Ashley Lezcano, Panama; Dr. Antonio Roberto Abaya MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona/Cadiz, Spain; MBA Christian Acheampong, Turkey; Dr. Alejandro Martinez, MPH, Costa Rica; Dr. Med. Sci Finn Gyntelberg; NFA.and Bispebj. Hosp. Denmark,</small> ==References== [[Category:Prediabetes ]] <references />Education 1: Research Methodology <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/EDUCATION/Education_module_links</ref> jnuwec8chp5mjsfqqfmsnf3ymgujo0r 2807902 2807901 2026-05-08T08:12:51Z Saltrabook 1417466 /* ' The John Snow Research Institute -2026' */ 2807902 wikitext text/x-wiki [[File:ChatGPT Image 24 abr 2026, 02 17 02 p.m.png|800|center]] [[File:ChatGPT Image 24 abr 2026, 08 16 04 a.m.png|thumb|]] = '''' The John Snow Research Institute -2026'''' = Billions are at increased risk of developing metabolic syndromes with prediabetes, diabetes type 2, high blood pressure and overweight. All can lower their risks by staying physical active and eating well. For early identification of the risks we propose to register weight and height (Body Mass Index) and the fasting blood sugar in the '''Prevalence studies''' at the schools for seafarers, nurses, medical students and the kids schools.(not blood sugar).The 16-weeks '''intervention studies''' include learnings by short video sequences and self-monitoring of blood sugar with glucometer, and self-evaluation of diet and physical activity.[[File:Lifestyle Medicine Pillars.png|400px|right|The focus of Lifestyle Medicine is on these 6 pillars.]] [[File:John Snow.jpg|thumb| right|John Snow in the early nineteenth century]] 1. '<nowiki/>'''Prevalence studies'''' 1.1 The-International-Maritime-Health-Database <ref>https://www.dropbox.com/scl/fi/z3cq5ciiev06y8v9duw7u/A-International-Maritime-Health-Database.docx?cloud_editor=word&dl=0&rlkey=pt0kdesvmagcxaa2wez3tmza3 </ref> 1.2 Nursing Students Health Database <ref> https://www.dropbox.com/scl/fi/tcznmmd2y3nona5e3h1ro/The-Nursing-students-health-database.docx?cloud_editor=word&dl=0&rlkey=onbjh4o8ko1lzdvgyi8nlrotk </ref> 1.3. Medical student's Health Database <ref>https://www.dropbox.com/scl/fi/f16h9b60u4gxgt56un2jf/The-Medical-students-Health-database.docx?cloud_editor=word&dl=0&rlkey=xyfqen5trdc5lniaovipl548n </ref> 1.4. School childrens Health database <ref> https://www.dropbox.com/scl/fi/u6u50c8bxwhte9t2t6ck8/The-School-children-s-Health-database.docx?cloud_editor=word&dl=0&rlkey=zlyz5wn673wf7owettq3nx3h5 </ref> 2. '''Intervention studies''' Englsh <ref>https://www.dropbox.com/scl/fi/oi6cx6tlwwvoko3ed37tn/Invitation-to-the-course-English.docx?cloud_editor=word&dl=0&rlkey=7kzg91tqfgjskxf5aji8khicx </ref> Danish <ref>https://www.dropbox.com/scl/fi/2qahc3q9hmf4skbvk77ab/Invitation-to-the-course-in-Danish.docx?cloud_editor=word&dl=0&rlkey=x63w8oqvarz284zg2btq2johv </ref> Spanish <ref> https://www.dropbox.com/scl/fi/bn71inqeeth4o4mc1fjth/Invitation-to-the-course-Spanish.docx?cloud_editor=word&dl=0&rlkey=popmr1fnodh1v951v9l7k9ezv </ref> - General research protocol draft <ref> https://www.dropbox.com/scl/fi/gau25oy5y1s57046icjt2/Research-protocol-draft.docx?cloud_editor=word&dl=0&rlkey=wat63e25ritmujwcpss8s4v0s </ref> - Health Promoting Schools <ref> https://www.dropbox.com/scl/fi/0rm7honrezbjwrcy3h3yk/Health-promoting-schools.docx?cloud_editor=word&dl=0&rlkey=673jyzcmwbfw7k9ui9nmtp0zh </ref> - John Snow Institute bylaws <ref> https://www.dropbox.com/scl/fi/lccr7jtnga1u0x75117zn/John-Snow-revision-2-March-11.doc?cloud_editor=word&dl=0&rlkey=lz2gi7mslcoay5dzygg8h6n6r </ref> '''Publications and pptx''' 2016-2026 <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/The_International_Type_2_Diabetes_Mellitus_and_Hypertension_Research_Group#The_John_Snow_Institute </ref><ref> https://www.dropbox.com/scl/fi/mw7ft423lkkpjoxywd2bf </ref> '''Prediabetes-Remission Research Network:''' <small>Prof. Ing. MSc. Nailet Delgado; Dr. Olaf Jensen, MD, MPH, PhD, o147248@gmail.com; MSc.Ph.D. Bishal Gyawali (SDU); MSc.PhD Vivi Just-Nørregaard; Dr. Johan Hviid Andersen MD, PhD. Prof Århus University; Prof. MSc. Agnes Flores, UMECIT, Panama; Dr. Maite, Vacamonte, Panama; Bruno Nørdam, Randers; Dr. Maite Duque, Venezuela; Dr. Indira Santos Panama; Med.Stud. Ashley Lezcano, Panama; Dr. Antonio Roberto Abaya MD Filippines; Dr. Jen Mendoza, MD, Filippines; Dr. Andra Ergle MD, Latvia; Prof. MSc. Ingrid Morató, Tarragona/Cadiz, Spain; MBA Christian Acheampong, Turkey; Dr. Alejandro Martinez, MPH, Costa Rica; Dr. Med. Sci Finn Gyntelberg; NFA.and Bispebj. Hosp. Denmark,</small> ==References== [[Category:Prediabetes ]] <references />Education 1: Research Methodology <ref>https://en.wikiversity.org/wiki/Maritime_Health_Research_and_Education-NET/EDUCATION/Education_module_links</ref> doc1cseh0piucx5mqokqna09k3mcn3a 0 285380 2807874 2807812 2026-05-07T14:19:19Z Young1lim 21186 /* Applications */ 2807874 wikitext text/x-wiki === Introduction === * Overview ([[Media:C01.Intro1.Overview.1.A.20170925.pdf |A.pdf]], [[Media:C01.Intro1.Overview.1.B.20170901.pdf |B.pdf]], [[Media:C01.Intro1.Overview.1.C.20170904.pdf |C.pdf]]) * Number System ([[Media:C01.Intro2.Number.1.A.20171023.pdf |A.pdf]], [[Media:C01.Intro2.Number.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro2.Number.1.C.20170914.pdf |C.pdf]]) * Memory System ([[Media:C01.Intro2.Memory.1.A.20170907.pdf |A.pdf]], [[Media:C01.Intro3.Memory.1.B.20170909.pdf |B.pdf]], [[Media:C01.Intro3.Memory.1.C.20170914.pdf |C.pdf]]) === Handling Repetition === * Control ([[Media:C02.Repeat1.Control.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat1.Control.1.B.20170918.pdf |B.pdf]], [[Media:C02.Repeat1.Control.1.C.20170926.pdf |C.pdf]]) * Loop ([[Media:C02.Repeat2.Loop.1.A.20170925.pdf |A.pdf]], [[Media:C02.Repeat2.Loop.1.B.20170918.pdf |B.pdf]]) === Handling a Big Work === * Function Overview ([[Media:C03.Func1.Overview.1.A.20171030.pdf |A.pdf]], [[Media:C03.Func1.Oerview.1.B.20161022.pdf |B.pdf]]) * Functions & Variables ([[Media:C03.Func2.Variable.1.A.20161222.pdf |A.pdf]], [[Media:C03.Func2.Variable.1.B.20161222.pdf |B.pdf]]) * Functions & Pointers ([[Media:C03.Func3.Pointer.1.A.20161122.pdf |A.pdf]], [[Media:C03.Func3.Pointer.1.B.20161122.pdf |B.pdf]]) * Functions & Recursions ([[Media:C03.Func4.Recursion.1.A.20161214.pdf |A.pdf]], [[Media:C03.Func4.Recursion.1.B.20161214.pdf |B.pdf]]) === Handling Series of Data === ==== Background ==== * Background ([[Media:C04.Series0.Background.1.A.20180727.pdf |A.pdf]]) ==== Basics ==== * Pointers ([[Media:C04.S1.Pointer.1A.20240524.pdf |A.pdf]], [[Media:C04.Series2.Pointer.1.B.20161115.pdf |B.pdf]]) * Arrays ([[Media:C04.S2.Array.1A.20240514.pdf |A.pdf]], [[Media:C04.Series1.Array.1.B.20161115.pdf |B.pdf]]) * Array Pointers ([[Media:C04.S3.ArrayPointer.1A.20240208.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Multi-dimensional Arrays ([[Media:C04.Series4.MultiDim.1.A.20221130.pdf |A.pdf]], [[Media:C04.Series4.MultiDim.1.B.1111.pdf |B.pdf]]) * Array Access Methods ([[Media:C04.Series4.ArrayAccess.1.A.20190511.pdf |A.pdf]], [[Media:C04.Series3.ArrayPointer.1.B.20181203.pdf |B.pdf]]) * Structures ([[Media:C04.Series3.Structure.1.A.20171204.pdf |A.pdf]], [[Media:C04.Series2.Structure.1.B.20161130.pdf |B.pdf]]) ==== Examples ==== * Spreadsheet Example Programs :: Example 1 ([[Media:C04.Series7.Example.1.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.1.C.20171213.pdf |C.pdf]]) :: Example 2 ([[Media:C04.Series7.Example.2.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.2.C.20171213.pdf |C.pdf]]) :: Example 3 ([[Media:C04.Series7.Example.3.A.20171213.pdf |A.pdf]], [[Media:C04.Series7.Example.3.C.20171213.pdf |C.pdf]]) :: Bubble Sort ([[Media:C04.Series7.BubbleSort.1.A.20171211.pdf |A.pdf]]) ==== Applications ==== * Address-of and de-reference operators ([[Media:C04.SA0.PtrOperator.1A.20260507.pdf |A.pdf]]) * Applications of Pointers ([[Media:C04.SA1.AppPointer.1A.20241121.pdf |A.pdf]]) * Applications of Arrays ([[Media:C04.SA2.AppArray.1A.20240715.pdf |A.pdf]]) * Applications of Array Pointers ([[Media:C04.SA3.AppArrayPointer.1A.20240210.pdf |A.pdf]]) * Applications of Multi-dimensional Arrays ([[Media:C04.Series4App.MultiDim.1.A.20210719.pdf |A.pdf]]) * Applications of Array Access Methods ([[Media:C04.Series9.AppArrAcess.1.A.20190511.pdf |A.pdf]]) * Applications of Structures ([[Media:C04.Series6.AppStruct.1.A.20190423.pdf |A.pdf]]) === Handling Various Kinds of Data === * Types ([[Media:C05.Data1.Type.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data1.Type.1.B.20161212.pdf |B.pdf]]) * Typecasts ([[Media:C05.Data2.TypeCast.1.A.20180217.pdf |A.pdf]], [[Media:C05.Data2.TypeCast.1.B.20161216.pdf |A.pdf]]) * Operators ([[Media:C05.Data3.Operators.1.A.20161219.pdf |A.pdf]], [[Media:C05.Data3.Operators.1.B.20161216.pdf |B.pdf]]) * Files ([[Media:C05.Data4.File.1.A.20161124.pdf |A.pdf]], [[Media:C05.Data4.File.1.B.20161212.pdf |B.pdf]]) === Handling Low Level Operations === * Bitwise Operations ([[Media:BitOp.1.B.20161214.pdf |A.pdf]], [[Media:BitOp.1.B.20161203.pdf |B.pdf]]) * Bit Field ([[Media:BitField.1.A.20161214.pdf |A.pdf]], [[Media:BitField.1.B.20161202.pdf |B.pdf]]) * Union ([[Media:Union.1.A.20161221.pdf |A.pdf]], [[Media:Union.1.B.20161111.pdf |B.pdf]]) * Accessing IO Registers ([[Media:IO.1.A.20141215.pdf |A.pdf]], [[Media:IO.1.B.20161217.pdf |B.pdf]]) === Declarations === * Type Specifiers and Qualifiers ([[Media:C07.Spec1.Type.1.A.20171004.pdf |pdf]]) * Storage Class Specifiers ([[Media:C07.Spec2.Storage.1.A.20171009.pdf |pdf]]) * Scope === Class Notes === * TOC ([[Media:TOC.20171007.pdf |TOC.pdf]]) * Day01 ([[Media:Day01.A.20171007.pdf |A.pdf]], [[Media:Day01.B.20171209.pdf |B.pdf]], [[Media:Day01.C.20171211.pdf |C.pdf]]) ...... Introduction (1) Standard Library * Day02 ([[Media:Day02.A.20171007.pdf |A.pdf]], [[Media:Day02.B.20171209.pdf |B.pdf]], [[Media:Day02.C.20171209.pdf |C.pdf]]) ...... Introduction (2) Basic Elements * Day03 ([[Media:Day03.A.20171007.pdf |A.pdf]], [[Media:Day03.B.20170908.pdf |B.pdf]], [[Media:Day03.C.20171209.pdf |C.pdf]]) ...... Introduction (3) Numbers * Day04 ([[Media:Day04.A.20171007.pdf |A.pdf]], [[Media:Day04.B.20170915.pdf |B.pdf]], [[Media:Day04.C.20171209.pdf |C.pdf]]) ...... Structured Programming (1) Flowcharts * Day05 ([[Media:Day05.A.20171007.pdf |A.pdf]], [[Media:Day05.B.20170915.pdf |B.pdf]], [[Media:Day05.C.20171209.pdf |C.pdf]]) ...... Structured Programming (2) Conditions and Loops * Day06 ([[Media:Day06.A.20171007.pdf |A.pdf]], [[Media:Day06.B.20170923.pdf |B.pdf]], [[Media:Day06.C.20171209.pdf |C.pdf]]) ...... Program Control * Day07 ([[Media:Day07.A.20171007.pdf |A.pdf]], [[Media:Day07.B.20170926.pdf |B.pdf]], [[Media:Day07.C.20171209.pdf |C.pdf]]) ...... Function (1) Definitions * Day08 ([[Media:Day08.A.20171028.pdf |A.pdf]], [[Media:Day08.B.20171016.pdf |B.pdf]], [[Media:Day08.C.20171209.pdf |C.pdf]]) ...... Function (2) Storage Class and Scope * Day09 ([[Media:Day09.A.20171007.pdf |A.pdf]], [[Media:Day09.B.20171017.pdf |B.pdf]], [[Media:Day09.C.20171209.pdf |C.pdf]]) ...... Function (3) Recursion * Day10 ([[Media:Day10.A.20171209.pdf |A.pdf]], [[Media:Day10.B.20171017.pdf |B.pdf]], [[Media:Day10.C.20171209.pdf |C.pdf]]) ...... Arrays (1) Definitions * Day11 ([[Media:Day11.A.20171024.pdf |A.pdf]], [[Media:Day11.B.20171017.pdf |B.pdf]], [[Media:Day11.C.20171212.pdf |C.pdf]]) ...... Arrays (2) Applications * Day12 ([[Media:Day12.A.20171024.pdf |A.pdf]], [[Media:Day12.B.20171020.pdf |B.pdf]], [[Media:Day12.C.20171209.pdf |C.pdf]]) ...... Pointers (1) Definitions * Day13 ([[Media:Day13.A.20171025.pdf |A.pdf]], [[Media:Day13.B.20171024.pdf |B.pdf]], [[Media:Day13.C.20171209.pdf |C.pdf]]) ...... Pointers (2) Applications * Day14 ([[Media:Day14.A.20171226.pdf |A.pdf]], [[Media:Day14.B.20171101.pdf |B.pdf]], [[Media:Day14.C.20171209.pdf |C.pdf]]) ...... C String (1) * Day15 ([[Media:Day15.A.20171209.pdf |A.pdf]], [[Media:Day15.B.20171124.pdf |B.pdf]], [[Media:Day15.C.20171209.pdf |C.pdf]]) ...... C String (2) * Day16 ([[Media:Day16.A.20171208.pdf |A.pdf]], [[Media:Day16.B.20171114.pdf |B.pdf]], [[Media:Day16.C.20171209.pdf |C.pdf]]) ...... C Formatted IO * Day17 ([[Media:Day17.A.20171031.pdf |A.pdf]], [[Media:Day17.B.20171111.pdf |B.pdf]], [[Media:Day17.C.20171209.pdf |C.pdf]]) ...... Structure (1) Definitions * Day18 ([[Media:Day18.A.20171206.pdf |A.pdf]], [[Media:Day18.B.20171128.pdf |B.pdf]], [[Media:Day18.C.20171212.pdf |C.pdf]]) ...... Structure (2) Applications * Day19 ([[Media:Day19.A.20171205.pdf |A.pdf]], [[Media:Day19.B.20171121.pdf |B.pdf]], [[Media:Day19.C.20171209.pdf |C.pdf]]) ...... Union, Bitwise Operators, Enum * Day20 ([[Media:Day20.A.20171205.pdf |A.pdf]], [[Media:Day20.B.20171201.pdf |B.pdf]], [[Media:Day20.C.20171212.pdf |C.pdf]]) ...... Linked List * Day21 ([[Media:Day21.A.20171206.pdf |A.pdf]], [[Media:Day21.B.20171208.pdf |B.pdf]], [[Media:Day21.C.20171212.pdf |C.pdf]]) ...... File Processing * Day22 ([[Media:Day22.A.20171212.pdf |A.pdf]], [[Media:Day22.B.20171213.pdf |B.pdf]], [[Media:Day22.C.20171212.pdf |C.pdf]]) ...... Preprocessing <!----------------------------------------------------------------------> </br> See also https://cprogramex.wordpress.com/ == '''Old Materials '''== until 201201 * Intro.Overview.1.A ([[Media:C.Intro.Overview.1.A.20120107.pdf |pdf]]) * Intro.Memory.1.A ([[Media:C.Intro.Memory.1.A.20120107.pdf |pdf]]) * Intro.Number.1.A ([[Media:C.Intro.Number.1.A.20120107.pdf |pdf]]) * Repeat.Control.1.A ([[Media:C.Repeat.Control.1.A.20120109.pdf |pdf]]) * Repeat.Loop.1.A ([[Media:C.Repeat.Loop.1.A.20120113.pdf |pdf]]) * Work.Function.1.A ([[Media:C.Work.Function.1.A.20120117.pdf |pdf]]) * Work.Scope.1.A ([[Media:C.Work.Scope.1.A.20120117.pdf |pdf]]) * Series.Array.1.A ([[Media:Series.Array.1.A.20110718.pdf |pdf]]) * Series.Pointer.1.A ([[Media:Series.Pointer.1.A.20110719.pdf |pdf]]) * Series.Structure.1.A ([[Media:Series.Structure.1.A.20110805.pdf |pdf]]) * Data.Type.1.A ([[Media:C05.Data2.TypeCast.1.A.20130813.pdf |pdf]]) * Data.TypeCast.1.A ([[Media:Data.TypeCast.1.A.pdf |pdf]]) * Data.Operators.1.A ([[Media:Data.Operators.1.A.20110712.pdf |pdf]]) <br> until 201107 * Intro.1.A ([[Media:Intro.1.A.pdf |pdf]]) * Control.1.A ([[Media:Control.1.A.20110706.pdf |pdf]]) * Iteration.1.A ([[Media:Iteration.1.A.pdf |pdf]]) * Function.1.A ([[Media:Function.1.A.20110705.pdf |pdf]]) * Variable.1.A ([[Media:Variable.1.A.20110708.pdf |pdf]]) * Operators.1.A ([[Media:Operators.1.A.20110712.pdf |pdf]]) * Pointer.1.A ([[Media:Pointer.1.A.pdf |pdf]]) * Pointer.2.A ([[Media:Pointer.2.A.pdf |pdf]]) * Array.1.A ([[Media:Array.1.A.pdf |pdf]]) * Type.1.A ([[Media:Type.1.A.pdf |pdf]]) * Structure.1.A ([[Media:Structure.1.A.pdf |pdf]]) go to [ [[C programming in plain view]] ] [[Category:C programming language]] </br> f3sk6x9em1jxh22721jyvia9tuu0c3y 102 304119 2807892 2790066 2026-05-08T00:43:01Z ~2026-27799-62 3070986 2807892 wikitext text/x-wiki A subject offered by the [[Portal:Mathematics|mathematics]] department. Algebra abstracts the concept of number and function. Geometry studies the relationship between different measurements of shapes, such as length, angle, perimeter, and area. The study of algebra informs the study of geometry, and ''vice versa''. == Courses == *[[Introductory_Algebra|Introductory Algebra]] *[[Algebra_1|Algebra 1]] *[[Geometry|Geometry]] *[[Algebra 2|Algebra 2]] == Wikibooks == *[https://en.wikibooks.org/wiki/Algebra Algebra] *[https://en.wikibooks.org/wiki/Basic_Algebra Basic Algebra] *[https://en.wikibooks.org/wiki/Geometry Geometry] *[https://en.wikibooks.org/wiki/High_School_Trigonometry High School Trigonometry] == External Resources == * [https://www.khanacademy.org/math/algebra Algebra 1] * [https://www.khanacademy.org/math/algebra2 Algebra 2] * [https://www.khanacademy.org/math/geometry Geometry] * [https://www.ixl.com/math IXL - Math] == See Also == * [[Algebra]] 6d5cy1sfofiixe86uj66ykutvwqkbpe 0 307504 2807887 2783263 2026-05-07T19:55:24Z CommonsDelinker 9184 Removing [[:c:File:Animal_job_interview.jpg|Animal_job_interview.jpg]], it has been deleted from Commons by [[:c:User:Polarlys|Polarlys]] because: per [[:c:Commons:Deletion requests/File:Animal job interview.jpg|]]. 2807887 wikitext text/x-wiki {{assignment}}{{notes}} ==Chapter 1 - What is Industrial/Organizational Psychology?== === Introduction === [[File:Picture of someone on bridge walk at UNILORIN Zoo 02.jpg|thumb|Good work is excellent, ethical, and engaging. ]] '''Work''' is important for a variety of reasons, as not only do we spent majority of lives at work, but we also see our value in the occupation we are in & what happens at work effects us outside of work. People may work for money, social status, self-definition, or an innate desire to challenge one-self. A 1973 survey shows ''most'' people would work, even if they are financially comfortable. Work can be divided into... # '''Good work''' - High quality work that contributes to society in a meaningful way. # '''Compromised work''' - Not illegal, but not ethical. ''Why this type of work?'' People want to make more with less time/effort and to financially suffice their roles in society. # '''Bad work''' - Illegal and unethical. According to the [https://pz.harvard.edu/projects/the-good-project Good Project], good work is excellent, ethical, and engaging. ''Excellent work'' is work that is high-quality and goes beyond the "call of duty" in comparison to other works. ''Ethical work'' is work that is socially acceptable and ensures the safety of one-self, [direct] others, the workplace, domain, and society. ''Engaging work'' is work where individuals put full effort into the work they are involved in. === What is I-O psych? === '''I-O psychology''' is the usage of psychological concepts and principals, theories, and research in the workforce. The aim of I-O psychology is to improve the well-being and performance of the organization, including the employees of said organization. It also aims to assess and analyze the relationship between one's life and one's work. An I/O psychologist can be a professor, HR director, or research scientist, but NOT a counselor/therapist. Their job could be to manage/direct personnel, human resources, employee relations, or workplace training. They could be a "private consultant", "research scientist: military", or a "corporate consultant". I-O psychs... * Build and sustain environmentally enriched organizations * Apply I-O psych to humanitarian arena (poverty, promotion of good work), convince local stakeholder's to push for certain initiatives in certain fields. * '''Corporate Social Responsibility:''' Actions/policies that account for stakeholders' viewpoints and economic, societal, and environmental performances. Emphasis on evidence-based decisions in their work in organizations (includes decision-making process that combines critical thinking + scientific evidence). Good position to develop and utilize practices that are backed with scientific evidence using the scientist-practitioner model. The '''scientist-practitioner model''' is summarized in the following: "If it isn't scientific, it's not good practice, if it isn't practical, it's not good science". --Morris Viteles. [[File:McDonalds at Guantanamo, 2002-11-15 -b.jpg|thumb|'''Human engineering''': how do we improve this work environment for this employee?|left]] === Fields of I-O psych === Fields of I-O psych include personnel psychology, organizational psychology, and human engineering. ==== Personnel psychology ==== '''Personnel psychology''' deals with recruitment, selection, training, performance appraisal, promotion, transfer, and terminations within an organization. Takes on individual differences in attributes and behavior, and predicts performance and job satisfaction. Essentially, we are trying to find the ''best person for the job''. ==== Organizational psychology ==== '''Organizational psychology''' uses theory and research from both social psychology and organizational behavior to assess the emotional and motivational side of the workforce. Emphasis lies in the attitudes, fairness, motivation, stress, leadership, teams, and organizational/work design. ==== Human engineering ==== The aim is the opposite of personnel psychology. In this field, we are trying to bring about the ''best'' environment for the worker. We want to develop, evaluate, and optimize the work environment (this includes tools, workspace, information on display, work shifts/pace, machine, and safety controls). The core is "work design and safety in the workplace". Uses cognitive science, ergonomics, exersise physiology, and anatomy. == Chapter 2 - The Past, Present, & Future of I-O psychology == * '''Wilhelm Wundt:''' psychologist, founded the first psychology lab at the University of Leipzig, published the first psychological journal (''Psychological Studies).'' * '''Hugo Munsterbeg''': director of psycholoigcal labs at Harvard, first to look into I-O psych, wrote first I-O psych textbook (''Psychology and Industrial Efficiency''), "father of I-O Psych". * '''James McKeen Cattell''': psychologist/student of Wundt, first American to publish a dissertation in psych, first US psych professor, president of APA. * '''Frederick Taylor''': founder of ''Scientific Management'', self-educated engineer, studied iron workers, made "The Principles of Scientific Management". * '''Lillian Gilbreth''': first PhD degree in Industrial Psychology from Brown Uni, only person with a PhD in psych on a U.S. stamp, first true I/O psychologist. * '''Harry Hollingsworth''': Defended Coca Cola in Coca-Cola vs. US Government (1911). * '''Robert Yerkes''': APA president, army alpha/beta test, ''Journal of Applied Psychology''. * '''Walter Dill Scott/Walter Van Dyke Bingham''': selecting & training salespeople. * '''Elton Mayo & Hawthorne Studies''' (1927-1932). The '''Hawthorne effect''' is a change in behavior that comes from researchers paying close attention to workers. They also included '''interviews''' (or "counseling") to decrease stress/dissatisfaction. Because of these studies, we now know of the emotional world of the worker, what drives people to do things, and people's satisfaction with their jobs. === General History === Human engineers made plane cockpits and separate controls. The '''Army General Classification Test''' (AGCT) was released with 12 million people tested. '''Civil Rights Act of 1964 & Title VII''': Title VII named demographic groups that should not be discriminated in the workforce. Age and disability was added later on, to the already present list of race, color, gender, national origin, and religion. Female I-O psychs have increased, and salaries too. 41% of I-O psychs are employed in academic, 24% in consulting, 22% in private organizations, and 9% in public organizations. Labels may be: organizational/work/applied psychologist or occupational psychologist. === Challenges === - COVID-19, globalization, technology, teams/groups, work-nonwork balance, and nontraditional employment conditions. Needs to be USEFUL, BIGGER, and GROUNDED (important topics with well-designed research). == Chapter 3 - Multicultural and Cross-Cultural Issues in I-O Psych == '''Multiculturalism''': Multiple cultures in one area... cultures is a system in which individuals share meaning and common ways of viewing certain entities/interpretating certain events. The influence of culture is huge and can operate on several levels, including the individual, group culture, organizational culture, national culture, and global culture. Multiculturalism is important for I-O psych because it addresses the global economy (& economic blocs), expatriates, and the "west vs. the rest" mentality. '''Hofstede's Theory of Cultural Influence''' - Culture is the "collective programming of the mind" which "distinguishes the members of one group/category" from another. Five definitions are: # '''Individualism''': Individuals look after themselves vs. staying in family groups. # '''Power distance''': Less powerful members of an organization accept/expect unequal distribution of power. # '''Uncertainty avoidance''': The uncomfortable of a culture in unstructured situations. # '''Masculinity/femininity''': Gender roles + masculine culture vs. feminine culture. # '''Long term vs. short-term''': Immediate vs. delayed gratification in all fields. # '''Indulgence vs. restraint''': How 'free' are they? How 'restricted' are they [to gratifications of needs]? Triandis brought in: * '''Horizontal cultures''': minimizing distance between individuals (collectivists: Israeli Kibbutz; individualists: Sweden, Australia) * '''Vertical cultures''': accept & depend on distances between individuals (collectivists: China, India, Greece; individualists: America, Germany. [[Category:Atcovi's Work]] c52zy1y3ca6up906pdy5fn5k4ynlbzm 0 316635 2807916 2805101 2026-05-08T11:20:47Z UlrichHoppe2023 2972443 added some lines for history and education 2807916 wikitext text/x-wiki {{:Global Audiology/Header}} {{:Global Audiology/Europe/Header}} {{CountryHeader|File:Germany (orthographic projection).svg|https://en.wikipedia.org/wiki/Germany}} {{HTitle|General Information}} [https://en.wikipedia.org/wiki/Germany Germany], officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. German is the official and predominantly spoken language in Germany. Recognised native minority languages in Germany are Danish, Low German, Low Rhenish, Sorbian, Romani, North Frisian and Saterland Frisian; they are officially protected by the European Charter for Regional or Minority Languages. The most used immigrant languages are Turkish, Arabic, Kurdish, Polish, Italian, Greek, Spanish, Serbo-Croatian, Bulgarian and other Balkan languages, as well as Russian. {{HTitle|History of Audiology}} The development of Audiology in Germany as a scientific discipline started in the 19^th century. An important milestone was the publication by the German physicist and physician [https://en.wikipedia.org/wiki/Hermann_von_Helmholtz Hermann von Helmholtz] entitled "On the sensations of tone as a physiological basis for the theory of music" in 1863. After World War II, Audiology was defined as a sub-discipline of Otorhinolaryngologists. In 1949 the working group ADA („Arbeitsgemeinschaft Deutscher Audiologen“) was founded at the first conference of ENT physicians and expanded in 1973 by including Otology and Neurotology („[https://adano.hno.org Arbeitsgemeinschaft Deutschsprachiger Audiologen und Neurootologen]“). The first chairman was [https://de.wikipedia.org/wiki/Alf_Meyer_zum_Gottesberge Prof. Dr. Alf Meyer zum Gottesberge]. ADANO still exists as a working group of the German Society for Otorhinolaryngology, Head and Neck Surgery ([https://hno.org Deutsche Gesellschaft für Hals-Nasen-Ohrenheilkunde, Kopf- und Hals-Chirurgie e.V.]). In 1979, the subgroup AG-ERA („[http://ag-era.bplaced.net/wordpress/ Arbeitsgruppe Elektrische Reaktionsaudiometrie]“, working group electric response audiometry) was founded by Prof. Dr. Günter Stange in Hannover. At annual meetings of the AG-ERA the latest developments in objective audiometry are discussed. In 1996, the German Society of Audiology ([https://dga-ev.com DGA, Deutsche Gesellschaft für Audiologie]) was founded in Münster as an independent interdisciplinary scientific association of experts who deal with hearing, hearing disorders, and their diagnosis, therapy, rehabilitation, and prevention. As a scientific society, the DGA promotes professional exchange, the further development of audiological standards, and networking among its members from medicine, natural sciences, engineering, education, psychology, and related disciplines. Today, the DGA has more than 600 society members. A detailed description of the development of Audiology in Germany is given in<ref>{{Cite journal|last=Kießling|first=Jürgen|date=2021-08-01|title=Die Entwicklung der Audiologie - von Helmholtz bis heute|url=https://www.sciencedirect.com/science/article/pii/S0939388920300933|journal=Zeitschrift für Medizinische Physik|series=Special Issue: Audiology|volume=31|issue=3|pages=238–253|doi=10.1016/j.zemedi.2020.08.003|issn=0939-3889}}</ref> {{HTitle|Incidence and Prevalence of Hearing Loss}} Epidemiological data on the prevalence of hearing disorders in Germany are sparse. A 2019 systematic review examinedstudies on prevalence or incidence of hearing impairment among German adults. The prevalences ascertained showed a broad range of between 16% and 25% and varied according to age, study setting, definition of hearing loss and method of data capture. <ref>{{Cite journal|last=Löhler|first=Jan|last2=Walther|first2=Leif Erik|last3=Hansen|first3=Fynn|last4=Kapp|first4=Philipp|last5=Meerpohl|first5=Jörg|last6=Wollenberg|first6=Barbara|last7=Schönweiler|first7=Rainer|last8=Schmucker|first8=Christine|date=2019-04|title=The prevalence of hearing loss and use of hearing aids among adults in Germany: a systematic review|url=https://pubmed.ncbi.nlm.nih.gov/30737583|journal=European archives of oto-rhino-laryngology: official journal of the European Federation of Oto-Rhino-Laryngological Societies (EUFOS): affiliated with the German Society for Oto-Rhino-Laryngology - Head and Neck Surgery|volume=276|issue=4|pages=945–956|doi=10.1007/s00405-019-05312-z|issn=1434-4726|pmc=6426811|pmid=30737583}}</ref> A 2023 study investigated the prevalence of hearing disorders and the actual provision with hearing aids in the city of Mainz and the neighboring Mainz‒Bingen district.<ref>{{Cite journal|last=Döge|first=Julia|last2=Hackenberg|first2=Berit|last3=O Brien|first3=Karoline|last4=Bohnert|first4=Andrea|last5=Rader|first5=Tobias|last6=Beutel|first6=Manfred E.|last7=Münzel|first7=Thomas|last8=Pfeiffer|first8=Norbert|last9=Nagler|first9=Markus|date=2023-02-17|title=The Prevalence of Hearing Loss and Provision With Hearing Aids in the Gutenberg Health Study|url=https://pubmed.ncbi.nlm.nih.gov/36519221|journal=Deutsches Arzteblatt International|volume=120|issue=Forthcoming|pages=99–106|doi=10.3238/arztebl.m2022.0385|issn=1866-0452|pmc=10132285|pmid=36519221}}</ref> The prevalence of hearing loss (regardless of severity) -in at least one ear was 40.6% in this study population. The hearing loss was mild in 22.5% of the participants, moderate in 8.3%. Some 2.8% had severe hearing loss. In this group, the women had better hearing than the men (by a mean 4.3 dB). The prevalence of hearing disorders rose with increasing age. Only 7.7% of the participants already had hearing aids for both ears. A 2021 study conducted in the same region of German reported the prevalence of 28.2% of hearing impairment of different degrees of severity. <ref>{{Cite journal|last=Hackenberg|first=Berit|last2=Döge|first2=Julia|last3=Lackner|first3=Karl J.|last4=Beutel|first4=Manfred E.|last5=Münzel|first5=Thomas|last6=Pfeiffer|first6=Norbert|last7=Nagler|first7=Markus|last8=Schmidtmann|first8=Irene|last9=Wild|first9=Philipp S.|date=2022-09|title=Hearing Loss and Its Burden of Disease in a Large German Cohort-Hearing Loss in Germany|url=https://pubmed.ncbi.nlm.nih.gov/34904723|journal=The Laryngoscope|volume=132|issue=9|pages=1843–1849|doi=10.1002/lary.29980|issn=1531-4995|pmid=34904723}}</ref> In 2024 a self-report study on the prevalence and co-prevalence of the audiovestibular symptoms hearing loss, tinnitus and dizziness in the Pomerania region of Germany reported a weighted prevalence of 14.2% for hearing loss, 9.7% for tinnitus, and 13.5% for dizziness in the population of 8134 study participants. Prevalence increased with age and differed among the sexes. Twenty eight of the study participants reported more than one symptom at once.<ref>{{Cite journal|last=Ihler|first=Friedrich|last2=Brzoska|first2=Tina|last3=Altindal|first3=Reyhan|last4=Dziemba|first4=Oliver|last5=Völzke|first5=Henry|last6=Busch|first6=Chia-Jung|last7=Ittermann|first7=Till|date=2024-07-31|title=Prevalence and risk factors of self-reported hearing loss, tinnitus, and dizziness in a population-based sample from rural northeastern Germany|url=https://pubmed.ncbi.nlm.nih.gov/39085387|journal=Scientific Reports|volume=14|issue=1|pages=17739|doi=10.1038/s41598-024-68577-3|issn=2045-2322|pmc=11291685|pmid=39085387}}</ref> A population-based two-staged ‘screening’ and ‘follow-up’ newborn hearing screening program in North-Rhine, Germany and a hospital-based screening at a University Hospital was conducted for the 2007–2016 period. The 10-year coverage rate for these newborns was 98.7%, the referral rate after a failed two-step screening was 3.4%, and the lost-to-follow-up rate was 1% but no information on final diagnosis was provided.<ref>{{Cite journal|last=Thangavelu|first=Kruthika|last2=Martakis|first2=Kyriakos|last3=Feldmann|first3=Silke|last4=Roth|first4=Bernhard|last5=Herkenrath|first5=Peter|last6=Lang-Roth|first6=Ruth|date=2023-10-23|title=Universal Newborn Hearing Screening Program: 10-Year Outcome and Follow-Up from a Screening Center in Germany|url=https://www.mdpi.com/2409-515X/9/4/61|journal=International Journal of Neonatal Screening|language=en|volume=9|issue=4|pages=61|doi=10.3390/ijns9040061|issn=2409-515X|pmc=10594500|pmid=37873852}}</ref> {{HTitle|Information About Audiology}} === Bachelor and Master courses in Audiology (audiologists) === Though the job title „Audiologist“ is not an officially protected professional title, it is usually used for people with an academic education on bachelor (B.Sc.) or master level (M.Sc.). There are three universities in Germany offering a bachelor program and two universities offering master courses. In total, around 20 astudents finish their academic courses per year. In addition, a significant number of audiologists have primary education in physics, engineering and other related disciplines with appropriate individual training. === Audiometrists === Hearing healthcare is primarily part of ENT doctors in cabinets. Audiometry is usually done by specialized nurses or audiometrists. Audiometrists have usually an education as medical technologist („Medizinischer Technologe, MTF“)Most of audiometry is done Hearing Aid acousticians {{HTitle|Scope of Practice and Licensing}} {{HTitle|Professional and Regulatory Bodies}} === Services offered by Otolaryngologists === ENT doctors perform physical examination and all necessary audiometric test for diagnosis of hearing loss. In particular, they perform subjective and objective tests in order to determine the cause and extent of hearing loss. Associated disorders such as Tinnitus, Hyperacusis nad vestibular disorders are als diagnosed by ENT specialists. When no causative treatment of hearing loss is available Hearing Aids (HAs) are prescribed. The regulatory basis for hearing aid prescription is the Guideline for assistive devices ("[https://www.g-ba.de/downloads/62-492-3815/HilfsM-RL_2025-02-20_iK-2025-05-16.pdf Hilfsmittelrichtlinie]"). Roughly, specific audiometric criteria for puretone tresholds and speech recognition have to be fulfilled in order to justify HA prescription. A comprehensive description of the process is given in<ref>{{Cite journal|last=Hoppe|first=Ulrich|last2=Hesse|first2=Gerhard|date=2017-12-18|title=Hearing aids: indications, technology, adaptation, and quality control|url=https://www.egms.de/static/en/journals/cto/2017-16/cto000147.shtml|journal=GMS Current Topics in Otorhinolaryngology - Head and Neck Surgery|language=engl|volume=16|pages=Doc08|doi=10.3205/cto000147|issn=1865-1011}}</ref>. === Services offered by Hearing Aid Acousticians === Hearing Aid Acousticians (HAA) are non-academic craftsmen. based on the prescription they select appropriate hearing aids and perform the HA fitting.Powers and duties are regulated by the "[https://www.gesetze-im-internet.de/h_rakmstrv/BJNR020700022.html Hörakustikermeisterverordnung]". As demanded by §30 in the Hilfsmittelrichtlinie the success of an HA provision is confirmed by an ENT doctor at the end of the trial period. Standard health insurance covers costs for hearing aids up to about 800 € per HA including otoplastic and fitting.{{HTitle|Ongoing audiology research}}Audiology research is done in clinics, in technical and psychological departments as well in biological departments at universities. Scienitifc exchange is mainly organized by the Deutsche Gesellschaft für Audiologie ([https://dga-ev.com/ DGA]) at annual conferences. The DGA comprises five working groups ("Fachausschüsse") focusing on * Audiometry and Quality Assurance * Hearing Aid Technology and Hearing Aid provision * Pediatric Audiology * Cochlear Implant Provision * Neurotology and Vestibular System Official publication organ of the DGA is the open access journal [https://www.egms.de/dynamic/de/journals/zaud/index.htm Zeitschrift für Audiologie]. {{HTitle|Challenges, Opportunities and Notes}} {{HTitle|Audiology Charities}} {{HTitle|References}} {{reflist}} {{:Global Audiology/Authors-1|Ulrich Hoppe | https://de.linkedin.com/in/ulrich-hoppe-3397238b }} [[Category:Audiology]] [[Category:Germany]] 1kbiktop7bcwaypqkvvdo862al1v403 0 317347 2807906 2759068 2026-05-08T09:19:10Z Bert Niehaus 2387134 /* Task */ 2807906 wikitext text/x-wiki == Definition == Let <math>\Gamma</math> be a cycle in <math>\mathbb{C}</math>, and let <math>z \in \mathbb{C}</math> be a point that <math>\Gamma</math> does not intersect. Then {{center|1=<math>n(\Gamma, z) := \frac{1}{2\pi i} \int_\Gamma \frac{1}{w-z} \, dw</math>}} is called the *winding number* of <math>\Gamma</math> around <math>z</math>. === Motivation === First, consider the case where <math>\Gamma = \gamma</math> consists of a single closed curve. Then <math>\gamma</math> is [[w:en:Homologous|homologous]] in <math>\mathbb{C} \setminus {z}</math> to an <math>n</math>-fold (for some <math>n \in \mathbb{Z}</math>) traversed circle <math>\partial D_r(z)</math> around <math>z</math> with <math>r > 0</math>. Now, :<math>\int_\gamma \frac{1}{w-z} \, dw = \int_{n \cdot \partial B(z)} \frac{1}{w-z} \, dw = n \int_{\partial B(z)} \frac{1}{w-z} \, dw = 2\pi i \cdot n.</math> Thus, this integral counts how many times the curve <math>\gamma</math> winds around the point <math>z</math>. === Task === Let the closed integration path <math>\gamma : [-\pi, +\pi] \to \mathbb{C}</math> be defined as: :<math>\gamma(t) := \left(2 + \cos(t)\right) \cdot e^{2it}.</math> * Plot the trace of the integration path. * Determine the winding number <math>n(\gamma, 1+i)</math>. * Determine the winding number <math>n(\gamma, 0)</math>. * Determine the winding number <math>n(\gamma, 1)</math>. === Visualization - integration path === Determine the winding number of the point <math>z</math> in the following animation. [[File:Kurve cos plus 2.gif|350px|center|GIF animation cos induced radius of a circular path - created with OpenSource Geogebra and exported as GIF animation]] == Additivity of the Integral == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \cdot \gamma_i</math> with closed <math>\gamma_i</math>, due to the additivity of the integral, we have :<math>n(\Gamma, z) = \sum_{i=1}^k n_i \cdot n(\gamma_i, z).</math> Thus, the winding number also counts how many times the point <math>z</math> is encircled. == Length of the Cycle == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \gamma_i</math> with closed <math>\gamma_i</math>, the length of the cycle is defined additively over the lengths of the individual integration paths: :<math>L(\Gamma) := \sum_{i=1}^k n_i \cdot L(\gamma_i).</math> == See Also == *[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Winding%20number https://en.wikiversity.org/wiki/Winding%20number] --> * [https://en.wikiversity.org/wiki/Winding%20number This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Kurs:Funktionentheorie/Umlaufzahl|Kurs:Funktionentheorie/Umlaufzahl]] - URL: https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl * Date: 12/17/2024 <span type="translate" src="Kurs:Funktionentheorie/Umlaufzahl" srclang="de" date="12/17/2024" time="02:18" status="inprogress"></span> <noinclude> [[de:Kurs:Funktionentheorie/Umlaufzahl]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex analysis]] 8b2v6t4xf12m7rf254w79l3yr49f32x 2807907 2807906 2026-05-08T09:21:20Z Bert Niehaus 2387134 /* Length of the Cycle */ 2807907 wikitext text/x-wiki == Definition == Let <math>\Gamma</math> be a cycle in <math>\mathbb{C}</math>, and let <math>z \in \mathbb{C}</math> be a point that <math>\Gamma</math> does not intersect. Then {{center|1=<math>n(\Gamma, z) := \frac{1}{2\pi i} \int_\Gamma \frac{1}{w-z} \, dw</math>}} is called the *winding number* of <math>\Gamma</math> around <math>z</math>. === Motivation === First, consider the case where <math>\Gamma = \gamma</math> consists of a single closed curve. Then <math>\gamma</math> is [[w:en:Homologous|homologous]] in <math>\mathbb{C} \setminus {z}</math> to an <math>n</math>-fold (for some <math>n \in \mathbb{Z}</math>) traversed circle <math>\partial D_r(z)</math> around <math>z</math> with <math>r > 0</math>. Now, :<math>\int_\gamma \frac{1}{w-z} \, dw = \int_{n \cdot \partial B(z)} \frac{1}{w-z} \, dw = n \int_{\partial B(z)} \frac{1}{w-z} \, dw = 2\pi i \cdot n.</math> Thus, this integral counts how many times the curve <math>\gamma</math> winds around the point <math>z</math>. === Task === Let the closed integration path <math>\gamma : [-\pi, +\pi] \to \mathbb{C}</math> be defined as: :<math>\gamma(t) := \left(2 + \cos(t)\right) \cdot e^{2it}.</math> * Plot the trace of the integration path. * Determine the winding number <math>n(\gamma, 1+i)</math>. * Determine the winding number <math>n(\gamma, 0)</math>. * Determine the winding number <math>n(\gamma, 1)</math>. === Visualization - integration path === Determine the winding number of the point <math>z</math> in the following animation. [[File:Kurve cos plus 2.gif|350px|center|GIF animation cos induced radius of a circular path - created with OpenSource Geogebra and exported as GIF animation]] == Additivity of the Integral == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \cdot \gamma_i</math> with closed <math>\gamma_i</math>, due to the additivity of the integral, we have :<math>n(\Gamma, z) = \sum_{i=1}^k n_i \cdot n(\gamma_i, z).</math> Thus, the winding number also counts how many times the point <math>z</math> is encircled. == Length of the Cycle == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \gamma_i</math> with closed <math>\gamma_i</math>, the length of the cycle is defined additively over the lengths of the individual integration paths: :<math>\mathcal{L}(\Gamma) := \sum_{i=1}^k n_i \cdot L(\gamma_i).</math> == See Also == *[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Winding%20number https://en.wikiversity.org/wiki/Winding%20number] --> * [https://en.wikiversity.org/wiki/Winding%20number This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Kurs:Funktionentheorie/Umlaufzahl|Kurs:Funktionentheorie/Umlaufzahl]] - URL: https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl * Date: 12/17/2024 <span type="translate" src="Kurs:Funktionentheorie/Umlaufzahl" srclang="de" date="12/17/2024" time="02:18" status="inprogress"></span> <noinclude> [[de:Kurs:Funktionentheorie/Umlaufzahl]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex analysis]] 8sxdczsxn6e9ljmxr51v0qnidmiqwy9 2807908 2807907 2026-05-08T09:22:02Z Bert Niehaus 2387134 /* Length of the Cycle */ 2807908 wikitext text/x-wiki == Definition == Let <math>\Gamma</math> be a cycle in <math>\mathbb{C}</math>, and let <math>z \in \mathbb{C}</math> be a point that <math>\Gamma</math> does not intersect. Then {{center|1=<math>n(\Gamma, z) := \frac{1}{2\pi i} \int_\Gamma \frac{1}{w-z} \, dw</math>}} is called the *winding number* of <math>\Gamma</math> around <math>z</math>. === Motivation === First, consider the case where <math>\Gamma = \gamma</math> consists of a single closed curve. Then <math>\gamma</math> is [[w:en:Homologous|homologous]] in <math>\mathbb{C} \setminus {z}</math> to an <math>n</math>-fold (for some <math>n \in \mathbb{Z}</math>) traversed circle <math>\partial D_r(z)</math> around <math>z</math> with <math>r > 0</math>. Now, :<math>\int_\gamma \frac{1}{w-z} \, dw = \int_{n \cdot \partial B(z)} \frac{1}{w-z} \, dw = n \int_{\partial B(z)} \frac{1}{w-z} \, dw = 2\pi i \cdot n.</math> Thus, this integral counts how many times the curve <math>\gamma</math> winds around the point <math>z</math>. === Task === Let the closed integration path <math>\gamma : [-\pi, +\pi] \to \mathbb{C}</math> be defined as: :<math>\gamma(t) := \left(2 + \cos(t)\right) \cdot e^{2it}.</math> * Plot the trace of the integration path. * Determine the winding number <math>n(\gamma, 1+i)</math>. * Determine the winding number <math>n(\gamma, 0)</math>. * Determine the winding number <math>n(\gamma, 1)</math>. === Visualization - integration path === Determine the winding number of the point <math>z</math> in the following animation. [[File:Kurve cos plus 2.gif|350px|center|GIF animation cos induced radius of a circular path - created with OpenSource Geogebra and exported as GIF animation]] == Additivity of the Integral == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \cdot \gamma_i</math> with closed <math>\gamma_i</math>, due to the additivity of the integral, we have :<math>n(\Gamma, z) = \sum_{i=1}^k n_i \cdot n(\gamma_i, z).</math> Thus, the winding number also counts how many times the point <math>z</math> is encircled. == Length of the Cycle == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \gamma_i</math> with closed <math>\gamma_i</math>, the length of the cycle is defined additively over the lengths of the individual integration paths: :<math>\mathcal{L}(\Gamma) := \sum_{i=1}^k n_i \cdot \mathcal{L}(\gamma_i).</math> == See Also == *[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Winding%20number https://en.wikiversity.org/wiki/Winding%20number] --> * [https://en.wikiversity.org/wiki/Winding%20number This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Kurs:Funktionentheorie/Umlaufzahl|Kurs:Funktionentheorie/Umlaufzahl]] - URL: https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl * Date: 12/17/2024 <span type="translate" src="Kurs:Funktionentheorie/Umlaufzahl" srclang="de" date="12/17/2024" time="02:18" status="inprogress"></span> <noinclude> [[de:Kurs:Funktionentheorie/Umlaufzahl]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex analysis]] 8q6ga6jfosyz0h4jbtpmdypud41dwof 2807909 2807908 2026-05-08T09:23:01Z Bert Niehaus 2387134 /* Translation and Version Control */ 2807909 wikitext text/x-wiki == Definition == Let <math>\Gamma</math> be a cycle in <math>\mathbb{C}</math>, and let <math>z \in \mathbb{C}</math> be a point that <math>\Gamma</math> does not intersect. Then {{center|1=<math>n(\Gamma, z) := \frac{1}{2\pi i} \int_\Gamma \frac{1}{w-z} \, dw</math>}} is called the *winding number* of <math>\Gamma</math> around <math>z</math>. === Motivation === First, consider the case where <math>\Gamma = \gamma</math> consists of a single closed curve. Then <math>\gamma</math> is [[w:en:Homologous|homologous]] in <math>\mathbb{C} \setminus {z}</math> to an <math>n</math>-fold (for some <math>n \in \mathbb{Z}</math>) traversed circle <math>\partial D_r(z)</math> around <math>z</math> with <math>r > 0</math>. Now, :<math>\int_\gamma \frac{1}{w-z} \, dw = \int_{n \cdot \partial B(z)} \frac{1}{w-z} \, dw = n \int_{\partial B(z)} \frac{1}{w-z} \, dw = 2\pi i \cdot n.</math> Thus, this integral counts how many times the curve <math>\gamma</math> winds around the point <math>z</math>. === Task === Let the closed integration path <math>\gamma : [-\pi, +\pi] \to \mathbb{C}</math> be defined as: :<math>\gamma(t) := \left(2 + \cos(t)\right) \cdot e^{2it}.</math> * Plot the trace of the integration path. * Determine the winding number <math>n(\gamma, 1+i)</math>. * Determine the winding number <math>n(\gamma, 0)</math>. * Determine the winding number <math>n(\gamma, 1)</math>. === Visualization - integration path === Determine the winding number of the point <math>z</math> in the following animation. [[File:Kurve cos plus 2.gif|350px|center|GIF animation cos induced radius of a circular path - created with OpenSource Geogebra and exported as GIF animation]] == Additivity of the Integral == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \cdot \gamma_i</math> with closed <math>\gamma_i</math>, due to the additivity of the integral, we have :<math>n(\Gamma, z) = \sum_{i=1}^k n_i \cdot n(\gamma_i, z).</math> Thus, the winding number also counts how many times the point <math>z</math> is encircled. == Length of the Cycle == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \gamma_i</math> with closed <math>\gamma_i</math>, the length of the cycle is defined additively over the lengths of the individual integration paths: :<math>\mathcal{L}(\Gamma) := \sum_{i=1}^k n_i \cdot \mathcal{L}(\gamma_i).</math> == See Also == *[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Winding%20number https://en.wikiversity.org/wiki/Winding%20number] --> * [https://en.wikiversity.org/wiki/Winding%20number This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Kurs:Funktionentheorie/Umlaufzahl|Kurs:Funktionentheorie/Umlaufzahl]] - URL: https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl * Date: 12/17/2024 <span type="translate" src="Kurs:Funktionentheorie/Umlaufzahl" srclang="de" date="12/17/2024" time="02:18" status="inprogress"></span> <noinclude> [[de:Kurs:Funktionentheorie/Umlaufzahl]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex analysis]] ao355hoxxqc1c5vsuhdvorg2603eug0 2807910 2807909 2026-05-08T09:24:45Z Bert Niehaus 2387134 /* Translation and Version Control */ page info corrected links 2807910 wikitext text/x-wiki == Definition == Let <math>\Gamma</math> be a cycle in <math>\mathbb{C}</math>, and let <math>z \in \mathbb{C}</math> be a point that <math>\Gamma</math> does not intersect. Then {{center|1=<math>n(\Gamma, z) := \frac{1}{2\pi i} \int_\Gamma \frac{1}{w-z} \, dw</math>}} is called the *winding number* of <math>\Gamma</math> around <math>z</math>. === Motivation === First, consider the case where <math>\Gamma = \gamma</math> consists of a single closed curve. Then <math>\gamma</math> is [[w:en:Homologous|homologous]] in <math>\mathbb{C} \setminus {z}</math> to an <math>n</math>-fold (for some <math>n \in \mathbb{Z}</math>) traversed circle <math>\partial D_r(z)</math> around <math>z</math> with <math>r > 0</math>. Now, :<math>\int_\gamma \frac{1}{w-z} \, dw = \int_{n \cdot \partial B(z)} \frac{1}{w-z} \, dw = n \int_{\partial B(z)} \frac{1}{w-z} \, dw = 2\pi i \cdot n.</math> Thus, this integral counts how many times the curve <math>\gamma</math> winds around the point <math>z</math>. === Task === Let the closed integration path <math>\gamma : [-\pi, +\pi] \to \mathbb{C}</math> be defined as: :<math>\gamma(t) := \left(2 + \cos(t)\right) \cdot e^{2it}.</math> * Plot the trace of the integration path. * Determine the winding number <math>n(\gamma, 1+i)</math>. * Determine the winding number <math>n(\gamma, 0)</math>. * Determine the winding number <math>n(\gamma, 1)</math>. === Visualization - integration path === Determine the winding number of the point <math>z</math> in the following animation. [[File:Kurve cos plus 2.gif|350px|center|GIF animation cos induced radius of a circular path - created with OpenSource Geogebra and exported as GIF animation]] == Additivity of the Integral == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \cdot \gamma_i</math> with closed <math>\gamma_i</math>, due to the additivity of the integral, we have :<math>n(\Gamma, z) = \sum_{i=1}^k n_i \cdot n(\gamma_i, z).</math> Thus, the winding number also counts how many times the point <math>z</math> is encircled. == Length of the Cycle == For a cycle <math>\Gamma = \sum_{i=1}^k n_i \gamma_i</math> with closed <math>\gamma_i</math>, the length of the cycle is defined additively over the lengths of the individual integration paths: :<math>\mathcal{L}(\Gamma) := \sum_{i=1}^k n_i \cdot \mathcal{L}(\gamma_i).</math> == See Also == *[[Complex Analysis/Cauchy's Integral Theorem for Disks|Cauchy's Integral Theorem for Disks]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Winding%20number https://en.wikiversity.org/wiki/Winding%20number] --> * [https://en.wikiversity.org/wiki/Winding%20number This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Winding%20number * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Winding%20number&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Winding%20number&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [[w:de:Kurs:Funktionentheorie/Umlaufzahl|Wikiversity source page]] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Kurs:Funktionentheorie/Umlaufzahl|Kurs:Funktionentheorie/Umlaufzahl]] - URL: https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Umlaufzahl * Date: 12/17/2024 <span type="translate" src="Kurs:Funktionentheorie/Umlaufzahl" srclang="de" date="12/17/2024" time="02:18" status="inprogress"></span> <noinclude> [[de:Kurs:Funktionentheorie/Umlaufzahl]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex analysis]] 8tmoxhcqbti2iafxcod5sjkpw1x437r 0 317453 2807911 2765715 2026-05-08T09:47:54Z Bert Niehaus 2387134 /* Proof 8 */ 2807911 wikitext text/x-wiki ==Introduction== The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[Complex Analysis/null-homologous|null-homologous]] [[Complex Analysis/Chain|Chain]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction. ==For Circular Disks== ===Statement=== Let <math>G \subseteq \mathbb C </math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then, we have :<math> f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw </math> for each <math>z \in D</math>. ===Proof 1=== By slightly enlarging the radius of the circular disk, we find an open circular disk <math>U</math> such that <math>\bar D \subseteq U \subseteq G</math>. Define <math>g \colon U \to \mathbb C</math> by :<math> g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> ===Proof 2=== The function <math>g</math> is continuous on <math>U</math> and holomorphic on <math>U -{z}</math>. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on <math>U</math> and obtain :<math> 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} </math> For <math>z \in D</math>, define <math>h(z) := \int_{\partial D} \frac{dw}{w-z}</math>. Then <math>h</math> is [[w:en:Holomorphic function|holomorphic]] with :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} </math> ===Proof 3=== Since the integrand <math>\frac{dw}{(w-z)^2}</math> has a primitive in <math>D</math>, we find :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 </math> ===Proof 4=== Because <math>h'(z) =0</math> throughout <math>D</math>, it follows that <math>h</math> is constant. Thus, <math>h(z)</math> always takes the same value as at the center <math>h(z_0)</math> of the disk <math>D</math>, i.e., <math>h(z_0) = 2\pi i</math>. Hence, :<math> 0 = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw </math> This proves the statement. ==For Cycles in Arbitrary Open Sets== ===Statement=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle in <math>G</math>, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then, :<math> n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw </math> for each <math>z \in G \setminus \mathrm{spur}(\Gamma)</math>, where <math>n(\Gamma, \cdot)</math> denotes the [[w:en:Winding number|winding number]]. ===Proof 1=== Define a function <math>g\colon G^2 \to \mathbb C</math> by :<math> g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> defined. ===Proof 2: continuous=== We demonstrate the continuity in both variables. Let <math>(w_0, z_0) \in U \times U</math> with <math>z_0 \ne w_0</math>, then <math>g</math> is given in the vicinity of <math>(w_0, z_0)</math> by the above formula and is trivially continuous.Now let <math>z_0 = w_0</math>. We choose a <math>\delta</math>-neighborhood <math>U_{\delta}(z_0) \subset \subset G</math> and examine <math>g(w,z) - g(z_0,z_0)</math> auf <math>U_{\delta}(z_0) \times U_{\delta}(z_0)</math> <br><br>. a) In the case <math>w = z</math>: <br>: :<math>g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)</math> ===Proof 3=== b) In the case <math>w \ne z</math>: :<math>g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv</math> Now, as a consequence of Cauchy's formulas for circles! the derivative <math>f'</math> is continuous in <math>z_0</math>. For a given <math>\epsilon > 0</math> we can choose <math>\delta > 0</math> such that :<math>|f'(v) - f'(z_0)| < \epsilon </math> for all <math>v \in U_{\delta} (z_0)</math>. <br> ===Proof 4=== This implies, in case a: :<math>|g(z,z) - g(z_0,z_0)| < \epsilon;</math> and in case b: :<math>|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| < \epsilon.</math> We now define :<math>h_0 (z) = \int_{\Gamma} g(w,z) dw.</math> <math>h_0</math> function is continuous on whole of <math>G</math> ; we will show that it is even holomorphic. For this, we use Morera's theorem. ===Proof 5=== Let <math>\gamma</math> be the oriented boundary of a triangle that lies entirely with in <math>G</math> . We must show :<math>\int_{\gamma} h_0(z) dz = 0</math> prove it is :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> because the integrations are commutable due to the continuity of the integrand on <math>G \times G</math> For fixed , <math>w</math> the function is <math>g(w,z)</math> in the Variable <math>z</math> continuous in and holomorphic for <math>w \ne z</math>, hence holomorphic everywhere. ===Proof 6=== By Goursat's theorem, it follows that :<math>\int_{\gamma} g(w,z) dz = 0.</math> this of course also mean that :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> so far we have not yet exploited the conditions above <math>\Gamma</math>. We will do so :<math>G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}</math>. ===Proof 7=== Since on <math>G \cap G_0</math> the function <math>h_0</math> has a simpler form, namely :<math>h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),</math> and since the function <math>h_1</math> is clearly holomorphic on the entire <math>G_0</math>, we can extend <math>h_0</math> to a holomorphic function <math>h</math> defined on the entire by<math>G \cup G_0</math> :<math> h(z) = \left\{ \begin{array}{ll} h_0(z) & z \in G\\ h_1(z) & z \in G_0 \end{array} \right. </math> Now <math>\Gamma</math> is null-homologous in , and thus :<math>G \cup G_0 = \mathbb C,</math> i.e. <math>h</math> is an entire function. ===Proof 8=== For <math>h</math> we have the following inequality for any <math>z\in G_0</math>: :<math>|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} \cdot \underbrace{ \mathcal{L}(\Gamma) \cdot \max_{z\in Spur(\Gamma)}|f(z)|}_{=:C}\;\;\;(*);</math> where <math>\mathcal{L}(\Gamma) = \sum_{k=1}^n |n_k| \cdot \mathcal{L}(\gamma_k)</math> with the cycle defined as <math>\Gamma := \sum_{k=1}^n n_k \cdot \gamma_k</math>. <math>G_0</math> contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all <math>z</math> in this region <math>G_0</math>: this implies that <math>h</math> is bounded too. By application of [[w:en:Liouville's theorem|Liouville's theorem]], <math>h</math> must be constant. If we choose a sequence <math>(z_{m})_{m\in \mathbb{N}} \in G_0</math> such that <math>|z_{m}| \geq m</math>. By using the inequality (*) again implies that: :<math>\lim\limits_{m \to \infty} h(z_{m}) \leq \lim\limits_{m \to \infty} \underbrace{\frac 1 {dist(z_m, \Gamma)}}_{\to +\infty} \cdot C =0,</math> thus we conculude that <math> h \equiv 0</math>, and in particular <math>h_0 \equiv 0</math>; this is what we wanted to prove ==Conclusions== From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in <math>z</math> is infinitely differentiable. We obtain the following results: ===For Circular Disks=== Let <math>G \subseteq \mathbb C</math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then <math>f</math> is infinitely differentiable, and for each <math>n\in \mathbb N</math>, we have :{{center|1=<math> f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw </math>}} for each <math>z \in D</math>. ===For Cycles=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma \in C(G)</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then :<math> n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw </math> for each <math>z \in G \setminus \mathrm{Trace}(\Gamma)</math> and <math>n \in \mathbb N</math>. ==Analyticity== Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series: ===Statement=== Let <math>G \subseteq \mathbb C</math> be open, and <math>f \colon G \to \mathbb C</math> holomorphic. Let <math>z_0 \in G</math> and <math>r > 0</math> such that <math>\bar B_r(z_0) \subseteq G</math>. Then <math>f</math> can be represented on <math>B_r(z_0)</math> by a convergent power series :<math> f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n </math> where the coefficients are given by :<math> a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw </math>. ===Proof 1=== For <math>z \in B_r(z_0)</math>, <math>w \in \partial B_r(z_0)</math> we have: :<math>\begin{array}{rl} \displaystyle \frac 1{w-z} &= \displaystyle\frac 1{(w- z_0) - (z-z_0)}\\ &= \displaystyle \frac 1{w-z_0} \cdot \frac 1{1 - \frac{z-z_0}{w-z_0}}\\ &= \displaystyle \frac 1{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}. \end{array} </math> ===Proof 2=== the real converges absolutely <math>|z-z_0| < r = |w-z_0|</math> and we obtain :<math> \begin{array}{rl} f(z) &= \displaystyle\frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{w-z} \, dw\\ &= \displaystyle \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac 1{w-z_0} \frac{f(w)(z-z_0)^n}{(w-z_0)^n}\, dw\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n \end{array} </math> == See also == *[[Complex Analysis|Complex Analysis]] *[[Complex Analysics/Maximum Principle|Maximum Principle]] *[[Complex Analysis/cycle|cycle]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Cauchy's%20integral%20formula&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Cauchy's%20integral%20formula&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Cauchy's%20integral%20formula https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula] --> * [https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Laurent%20Series * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Integralformel_von_Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Integralformel_von_Cauchy|Integralformel von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralformel_von_Cauchy * Date: 12/17/2024 <span type="translate" src="Integralformel von Cauchy" srclang="de" date="12/23/2024" time="10:55" status="inprogress"></span> <noinclude> [[de:Integralformel von Cauchy]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex Analysis]] glqik3m8d6wa72cuvvq251a5ngs3ch1 2807912 2807911 2026-05-08T10:01:52Z Bert Niehaus 2387134 /* Proof 8 */ 2807912 wikitext text/x-wiki ==Introduction== The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[Complex Analysis/null-homologous|null-homologous]] [[Complex Analysis/Chain|Chain]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction. ==For Circular Disks== ===Statement=== Let <math>G \subseteq \mathbb C </math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then, we have :<math> f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw </math> for each <math>z \in D</math>. ===Proof 1=== By slightly enlarging the radius of the circular disk, we find an open circular disk <math>U</math> such that <math>\bar D \subseteq U \subseteq G</math>. Define <math>g \colon U \to \mathbb C</math> by :<math> g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> ===Proof 2=== The function <math>g</math> is continuous on <math>U</math> and holomorphic on <math>U -{z}</math>. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on <math>U</math> and obtain :<math> 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} </math> For <math>z \in D</math>, define <math>h(z) := \int_{\partial D} \frac{dw}{w-z}</math>. Then <math>h</math> is [[w:en:Holomorphic function|holomorphic]] with :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} </math> ===Proof 3=== Since the integrand <math>\frac{dw}{(w-z)^2}</math> has a primitive in <math>D</math>, we find :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 </math> ===Proof 4=== Because <math>h'(z) =0</math> throughout <math>D</math>, it follows that <math>h</math> is constant. Thus, <math>h(z)</math> always takes the same value as at the center <math>h(z_0)</math> of the disk <math>D</math>, i.e., <math>h(z_0) = 2\pi i</math>. Hence, :<math> 0 = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw </math> This proves the statement. ==For Cycles in Arbitrary Open Sets== ===Statement=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle in <math>G</math>, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then, :<math> n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw </math> for each <math>z \in G \setminus \mathrm{spur}(\Gamma)</math>, where <math>n(\Gamma, \cdot)</math> denotes the [[w:en:Winding number|winding number]]. ===Proof 1=== Define a function <math>g\colon G^2 \to \mathbb C</math> by :<math> g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> defined. ===Proof 2: continuous=== We demonstrate the continuity in both variables. Let <math>(w_0, z_0) \in U \times U</math> with <math>z_0 \ne w_0</math>, then <math>g</math> is given in the vicinity of <math>(w_0, z_0)</math> by the above formula and is trivially continuous.Now let <math>z_0 = w_0</math>. We choose a <math>\delta</math>-neighborhood <math>U_{\delta}(z_0) \subset \subset G</math> and examine <math>g(w,z) - g(z_0,z_0)</math> auf <math>U_{\delta}(z_0) \times U_{\delta}(z_0)</math> <br><br>. a) In the case <math>w = z</math>: <br>: :<math>g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)</math> ===Proof 3=== b) In the case <math>w \ne z</math>: :<math>g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv</math> Now, as a consequence of Cauchy's formulas for circles! the derivative <math>f'</math> is continuous in <math>z_0</math>. For a given <math>\epsilon > 0</math> we can choose <math>\delta > 0</math> such that :<math>|f'(v) - f'(z_0)| < \epsilon </math> for all <math>v \in U_{\delta} (z_0)</math>. <br> ===Proof 4=== This implies, in case a: :<math>|g(z,z) - g(z_0,z_0)| < \epsilon;</math> and in case b: :<math>|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| < \epsilon.</math> We now define :<math>h_0 (z) = \int_{\Gamma} g(w,z) dw.</math> <math>h_0</math> function is continuous on whole of <math>G</math> ; we will show that it is even holomorphic. For this, we use Morera's theorem. ===Proof 5=== Let <math>\gamma</math> be the oriented boundary of a triangle that lies entirely with in <math>G</math> . We must show :<math>\int_{\gamma} h_0(z) dz = 0</math> prove it is :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> because the integrations are commutable due to the continuity of the integrand on <math>G \times G</math> For fixed , <math>w</math> the function is <math>g(w,z)</math> in the Variable <math>z</math> continuous in and holomorphic for <math>w \ne z</math>, hence holomorphic everywhere. ===Proof 6=== By Goursat's theorem, it follows that :<math>\int_{\gamma} g(w,z) dz = 0.</math> this of course also mean that :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> so far we have not yet exploited the conditions above <math>\Gamma</math>. We will do so :<math>G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}</math>. ===Proof 7=== Since on <math>G \cap G_0</math> the function <math>h_0</math> has a simpler form, namely :<math>h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),</math> and since the function <math>h_1</math> is clearly holomorphic on the entire <math>G_0</math>, we can extend <math>h_0</math> to a holomorphic function <math>h</math> defined on the entire by<math>G \cup G_0</math> :<math> h(z) = \left\{ \begin{array}{ll} h_0(z) & z \in G\\ h_1(z) & z \in G_0 \end{array} \right. </math> Now <math>\Gamma</math> is null-homologous in , and thus :<math>G \cup G_0 = \mathbb C,</math> i.e. <math>h</math> is an entire function. ===Proof 8=== For <math>h</math> we have the following inequality for any <math>z\in G_0</math>: :<math>|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} \cdot \underbrace{ \mathcal{L}(\Gamma) \cdot \max_{z\in Spur(\Gamma)}|f(z)|}_{=:C}\;\;\;(*);</math> where <math>\mathcal{L}(\Gamma) = \sum_{k=1}^n |n_k| \cdot \mathcal{L}(\gamma_k)</math> with the cycle defined as <math>\Gamma := \sum_{k=1}^n n_k \cdot \gamma_k</math>. <math>G_0</math> contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all <math>z</math> in this region <math>G_0</math>: this implies that <math>h</math> is bounded too. By application of [[w:en:Liouville's theorem (complex analysis)|Liouville's theorem]], <math>h</math> must be constant. If we choose a sequence <math>(z_{m})_{m\in \mathbb{N}} \in G_0</math> such that <math>|z_{m}| \geq m</math>. By using the inequality (*) again implies that: :<math>\lim\limits_{m \to \infty} h(z_{m}) \leq \lim\limits_{m \to \infty} \underbrace{\frac 1 {dist(z_m, \Gamma)}}_{\to +\infty} \cdot C =0,</math> thus we conculude that <math> h \equiv 0</math>, and in particular <math>h_0 \equiv 0</math>; this is what we wanted to prove ==Conclusions== From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in <math>z</math> is infinitely differentiable. We obtain the following results: ===For Circular Disks=== Let <math>G \subseteq \mathbb C</math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then <math>f</math> is infinitely differentiable, and for each <math>n\in \mathbb N</math>, we have :{{center|1=<math> f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw </math>}} for each <math>z \in D</math>. ===For Cycles=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma \in C(G)</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then :<math> n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw </math> for each <math>z \in G \setminus \mathrm{Trace}(\Gamma)</math> and <math>n \in \mathbb N</math>. ==Analyticity== Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series: ===Statement=== Let <math>G \subseteq \mathbb C</math> be open, and <math>f \colon G \to \mathbb C</math> holomorphic. Let <math>z_0 \in G</math> and <math>r > 0</math> such that <math>\bar B_r(z_0) \subseteq G</math>. Then <math>f</math> can be represented on <math>B_r(z_0)</math> by a convergent power series :<math> f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n </math> where the coefficients are given by :<math> a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw </math>. ===Proof 1=== For <math>z \in B_r(z_0)</math>, <math>w \in \partial B_r(z_0)</math> we have: :<math>\begin{array}{rl} \displaystyle \frac 1{w-z} &= \displaystyle\frac 1{(w- z_0) - (z-z_0)}\\ &= \displaystyle \frac 1{w-z_0} \cdot \frac 1{1 - \frac{z-z_0}{w-z_0}}\\ &= \displaystyle \frac 1{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}. \end{array} </math> ===Proof 2=== the real converges absolutely <math>|z-z_0| < r = |w-z_0|</math> and we obtain :<math> \begin{array}{rl} f(z) &= \displaystyle\frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{w-z} \, dw\\ &= \displaystyle \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac 1{w-z_0} \frac{f(w)(z-z_0)^n}{(w-z_0)^n}\, dw\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n \end{array} </math> == See also == *[[Complex Analysis|Complex Analysis]] *[[Complex Analysics/Maximum Principle|Maximum Principle]] *[[Complex Analysis/cycle|cycle]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Cauchy's%20integral%20formula&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Cauchy's%20integral%20formula&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Cauchy's%20integral%20formula https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula] --> * [https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Laurent%20Series * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Integralformel_von_Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Integralformel_von_Cauchy|Integralformel von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralformel_von_Cauchy * Date: 12/17/2024 <span type="translate" src="Integralformel von Cauchy" srclang="de" date="12/23/2024" time="10:55" status="inprogress"></span> <noinclude> [[de:Integralformel von Cauchy]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex Analysis]] 6coq0pnnrxel1cskhq5j9nvm7s26jwd 2807913 2807912 2026-05-08T10:04:30Z Bert Niehaus 2387134 /* Proof 8 */ 2807913 wikitext text/x-wiki ==Introduction== The Cauchy integral formula, alongside the [[w:en:Cauchy's integral theorem|Cauchy's integral theorem]], is one of the central statements in [[w:en:Complex analysis|complex analysis]]. Here, we present two variants: the 'classical' formula for circular disks and a relatively general version for [[Complex Analysis/null-homologous|null-homologous]] [[Complex Analysis/Chain|Chain]]. Note that we will deduce the circular disk version from Cauchy's integral theorem, but for the general variant, we proceed in the opposite direction. ==For Circular Disks== ===Statement=== Let <math>G \subseteq \mathbb C </math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then, we have :<math> f(z) = \frac 1{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}, dw </math> for each <math>z \in D</math>. ===Proof 1=== By slightly enlarging the radius of the circular disk, we find an open circular disk <math>U</math> such that <math>\bar D \subseteq U \subseteq G</math>. Define <math>g \colon U \to \mathbb C</math> by :<math> g(w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> ===Proof 2=== The function <math>g</math> is continuous on <math>U</math> and holomorphic on <math>U -{z}</math>. Thus, we can apply the [[w:en:Cauchy's integral theorem|Cauchy integral theorem]] on <math>U</math> and obtain :<math> 0 = \int_{\partial D} g(w), dw = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} </math> For <math>z \in D</math>, define <math>h(z) := \int_{\partial D} \frac{dw}{w-z}</math>. Then <math>h</math> is [[w:en:Holomorphic function|holomorphic]] with :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} </math> ===Proof 3=== Since the integrand <math>\frac{dw}{(w-z)^2}</math> has a primitive in <math>D</math>, we find :<math> h'(z) = -\int_{\partial D} \frac{dw}{(w-z)^2} = 0 </math> ===Proof 4=== Because <math>h'(z) =0</math> throughout <math>D</math>, it follows that <math>h</math> is constant. Thus, <math>h(z)</math> always takes the same value as at the center <math>h(z_0)</math> of the disk <math>D</math>, i.e., <math>h(z_0) = 2\pi i</math>. Hence, :<math> 0 = \int_{\partial D} \frac{f(w)}{w-z},dw - f(z)\int_{\partial D} \frac{dw}{w-z} \iff f(z) = \frac 1{2\pi i} \int_{\partial D}\frac{f(w)}{w-z}, dw </math> This proves the statement. ==For Cycles in Arbitrary Open Sets== ===Statement=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle in <math>G</math>, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then, :<math> n(\Gamma, z)\cdot f(z) = \frac 1{2\pi i} \int_\Gamma \frac{f(w)}{w-z} , dw </math> for each <math>z \in G \setminus \mathrm{spur}(\Gamma)</math>, where <math>n(\Gamma, \cdot)</math> denotes the [[w:en:Winding number|winding number]]. ===Proof 1=== Define a function <math>g\colon G^2 \to \mathbb C</math> by :<math> g(z,w) := \left\{ \begin{array}{ll} \frac{f(w) - f(z)}{w-z} & w \ne z\\ f'(z) & w = z \end{array} \right. </math> defined. ===Proof 2: continuous=== We demonstrate the continuity in both variables. Let <math>(w_0, z_0) \in U \times U</math> with <math>z_0 \ne w_0</math>, then <math>g</math> is given in the vicinity of <math>(w_0, z_0)</math> by the above formula and is trivially continuous.Now let <math>z_0 = w_0</math>. We choose a <math>\delta</math>-neighborhood <math>U_{\delta}(z_0) \subset \subset G</math> and examine <math>g(w,z) - g(z_0,z_0)</math> auf <math>U_{\delta}(z_0) \times U_{\delta}(z_0)</math> <br><br>. a) In the case <math>w = z</math>: <br>: :<math>g(z,z) - g(z_0,z_0) = f'(z) - f'(z_0)</math> ===Proof 3=== b) In the case <math>w \ne z</math>: :<math>g(w,z) - g(z_0,z_0) = \frac{f(w) - f(z)}{w-z} - f'(z_0) = \frac 1 {w - z} \int_{[z,w]}(f'(v) - f'(z_0)) dv</math> Now, as a consequence of Cauchy's formulas for circles! the derivative <math>f'</math> is continuous in <math>z_0</math>. For a given <math>\epsilon > 0</math> we can choose <math>\delta > 0</math> such that :<math>|f'(v) - f'(z_0)| < \epsilon </math> for all <math>v \in U_{\delta} (z_0)</math>. <br> ===Proof 4=== This implies, in case a: :<math>|g(z,z) - g(z_0,z_0)| < \epsilon;</math> and in case b: :<math>|g(w,z) - g(z_0, z_0)| \leq \frac 1 {|w - z|} |w - z| \cdot \sup\limits_{w \in [w,z]} |f'(v)-f'(z_0)| < \epsilon.</math> We now define :<math>h_0 (z) = \int_{\Gamma} g(w,z) dw.</math> <math>h_0</math> function is continuous on whole of <math>G</math> ; we will show that it is even holomorphic. For this, we use Morera's theorem. ===Proof 5=== Let <math>\gamma</math> be the oriented boundary of a triangle that lies entirely with in <math>G</math> . We must show :<math>\int_{\gamma} h_0(z) dz = 0</math> prove it is :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> because the integrations are commutable due to the continuity of the integrand on <math>G \times G</math> For fixed , <math>w</math> the function is <math>g(w,z)</math> in the Variable <math>z</math> continuous in and holomorphic for <math>w \ne z</math>, hence holomorphic everywhere. ===Proof 6=== By Goursat's theorem, it follows that :<math>\int_{\gamma} g(w,z) dz = 0.</math> this of course also mean that :<math>\int_{\gamma} h_0(z) dz = \int_{\Gamma} \int_{\gamma} g(w,z) dz\, dw = 0.</math> so far we have not yet exploited the conditions above <math>\Gamma</math>. We will do so :<math>G_0 = \{z \in \mathbb C: n (\Gamma, z) = 0\}</math>. ===Proof 7=== Since on <math>G \cap G_0</math> the function <math>h_0</math> has a simpler form, namely :<math>h_0(z) = \int_{\Gamma}\frac {f(w)}{w- z} dw = h_1(z),</math> and since the function <math>h_1</math> is clearly holomorphic on the entire <math>G_0</math>, we can extend <math>h_0</math> to a holomorphic function <math>h</math> defined on the entire by<math>G \cup G_0</math> :<math> h(z) = \left\{ \begin{array}{ll} h_0(z) & z \in G\\ h_1(z) & z \in G_0 \end{array} \right. </math> Now <math>\Gamma</math> is null-homologous in , and thus :<math>G \cup G_0 = \mathbb C,</math> i.e. <math>h</math> is an entire function. ===Proof 8=== For <math>h</math> we have the following inequality for any <math>z\in G_0</math>: :<math>|h(z)| = |h_1(z)| \leq \frac 1 {dist(z, \Gamma)} \cdot \underbrace{ \mathcal{L}(\Gamma) \cdot \max_{z\in Spur(\Gamma)}|f(z)|}_{=:C}\;\;\;(*);</math> where <math>\mathcal{L}(\Gamma) = \sum_{k=1}^n |n_k| \cdot \mathcal{L}(\gamma_k)</math> with the cycle defined as <math>\Gamma := \sum_{k=1}^n n_k \cdot \gamma_k</math>. <math>G_0</math> contains the complement of a sufficiently large circle around 0. Therefore, the above inequality holds for all <math>z</math> in this region <math>G_0</math>: this implies that <math>h</math> is bounded too. By application of [[w:en:Liouville's theorem (complex analysis)|Liouville's theorem]], <math>h</math> must be constant. If we choose a sequence <math>(z_{m})_{m\in \mathbb{N}} \in G_0</math> such that <math>|z_{m}| \geq m</math>. By using the inequality (*) again implies that: :<math>\lim\limits_{m \to \infty} h(z_{m}) \leq \lim\limits_{m \to \infty} \overbrace{\frac{1}{\,\,\underbrace{dist(z_m, \Gamma)}_{\to \,\,+\infty}\,\,}}^{\to \,\, 0} \cdot C =0,</math> thus we conculude that <math> h \equiv 0</math>, and in particular <math>h_0 \equiv 0</math>; this is what we wanted to prove ==Conclusions== From the Cauchy integral formula, it follows that every holomorphic function is infinitely differentiable because the integrand in <math>z</math> is infinitely differentiable. We obtain the following results: ===For Circular Disks=== Let <math>G \subseteq \mathbb C</math> be an open set, <math>D</math> a circular disk with <math>\bar D \subseteq G</math>, and <math>f \colon G \to \mathbb C</math> holomorphic. Then <math>f</math> is infinitely differentiable, and for each <math>n\in \mathbb N</math>, we have :{{center|1=<math> f^{(n)}(z) = \frac{n!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{n+1}}, dw </math>}} for each <math>z \in D</math>. ===For Cycles=== Let <math>G\subseteq \mathbb C</math> be an open set, <math>\Gamma \in C(G)</math> a [[Complex Analysis/null-homologous|null-homologous]] cycle, and <math>f \colon G \to \mathbb C</math> [[w:en:Holomorphic function|holomorphic]]. Then :<math> n(\Gamma, z) \cdot f^{(n)}(z) = \frac {n!}{2\pi i} \int_\Gamma \frac{f(w)}{(w-z)^{n+1}} , dw </math> for each <math>z \in G \setminus \mathrm{Trace}(\Gamma)</math> and <math>n \in \mathbb N</math>. ==Analyticity== Moreover, every holomorphic function is analytic at every point, i.e., it can be expanded into a power series: ===Statement=== Let <math>G \subseteq \mathbb C</math> be open, and <math>f \colon G \to \mathbb C</math> holomorphic. Let <math>z_0 \in G</math> and <math>r > 0</math> such that <math>\bar B_r(z_0) \subseteq G</math>. Then <math>f</math> can be represented on <math>B_r(z_0)</math> by a convergent power series :<math> f(z) = \sum_{n=0}^\infty a_n (z-z_0)^n </math> where the coefficients are given by :<math> a_n = \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{(w-z_0)^{n+1}}, dw </math>. ===Proof 1=== For <math>z \in B_r(z_0)</math>, <math>w \in \partial B_r(z_0)</math> we have: :<math>\begin{array}{rl} \displaystyle \frac 1{w-z} &= \displaystyle\frac 1{(w- z_0) - (z-z_0)}\\ &= \displaystyle \frac 1{w-z_0} \cdot \frac 1{1 - \frac{z-z_0}{w-z_0}}\\ &= \displaystyle \frac 1{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}. \end{array} </math> ===Proof 2=== the real converges absolutely <math>|z-z_0| < r = |w-z_0|</math> and we obtain :<math> \begin{array}{rl} f(z) &= \displaystyle\frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac{f(w)}{w-z} \, dw\\ &= \displaystyle \frac 1{2\pi i} \int_{\partial B_r(z_0)} \frac 1{w-z_0} \frac{f(w)(z-z_0)^n}{(w-z_0)^n}\, dw\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n\\ &= \displaystyle \frac 1{2\pi i} \sum_{n=0}^\infty \int_{\partial B_r(z_0)} \frac {f(w)}{(w-z_0)^{n+1}}\, dw \cdot (z-z_0)^n \end{array} </math> == See also == *[[Complex Analysis|Complex Analysis]] *[[Complex Analysics/Maximum Principle|Maximum Principle]] *[[Complex Analysis/cycle|cycle]] == Page Information == You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' === Wiki2Reveal === The '''[https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Cauchy's%20integral%20formula&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Cauchy's%20integral%20formula&coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator]. <!-- * Contents of the page are based on: ** [https://en.wikipedia.org/wiki/Cauchy's%20integral%20formula https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula] --> * [https://en.wikiversity.org/wiki/Cauchy's%20integral%20formula This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type. * Source: Wikiversity https://en.wikiversity.org/wiki/Laurent%20Series * see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&title=Laurent%20Series&author=Complex%20Analysis&language=en&audioslide=yes&shorttitle=Laurent%20Series&coursetitle=Complex%20Analysis Wiki2Reveal]. <!-- * Next contents of the course are [[]] -->; === Translation and Version Control === This page was translated based on the following [https://de.wikiversity.org/wiki/Integralformel_von_Cauchy Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity: * Source: [[v:de:Integralformel_von_Cauchy|Integralformel von Cauchy]] - URL: https://de.wikiversity.org/wiki/Integralformel_von_Cauchy * Date: 12/17/2024 <span type="translate" src="Integralformel von Cauchy" srclang="de" date="12/23/2024" time="10:55" status="inprogress"></span> <noinclude> [[de:Integralformel von Cauchy]] </noinclude> [[Category:Wiki2Reveal]] [[Category:Complex Analysis]] bs7qy9qzbb5idl6dngtt795djjmgm2n 0 323109 2807890 2807852 2026-05-07T23:09:47Z Jtneill 10242 Fix figure numbering 2807890 wikitext text/x-wiki {{title|Trauma and attachment development:<br>How does early trauma shape the formation of attachment styles?}} __TOC__ ==Overview== {{RoundBoxTop|theme=4}} [[File:Couple arguing.png|thumb|160x160px|'''Figure 1.''' Insecure attachment causes friction in a relationship]] ; They love me, they love me not? Shay and Oliver have been seeing each other for two months. So far, everything has been going smoothly. Until one day{{g}}, Oliver tells Shay he loves her and wants to make it official. Shay says yes but Oliver notices she has become distant. It seems the more he tries to get close to her, the more she pulls away. He tries to bring it up with her, but it seems to frustrate her even more. Oliver feels rejected and hurt. Should he accept that maybe their relationship just doesn't work? {{RoundBoxBottom}} Shay and Oliver’s story reflects a dynamic familiar to many couples: one partner becomes the peacemaker, often sacrificing their own emotional needs to maintain harmony, while the other remains emotionally distant or unpredictable. This pattern often leads to unresolved tension, dissatisfaction, or eventual breakdown in the relationship. Rather than focusing solely on the surface-level issues in adult relationships, psychological research increasingly{{f}} points to early life experiences as a root cause. Studies{{f}} in attachment theory suggest that the emotional bonds formed with primary caregivers during early childhood can have a lasting impact on how individuals relate to romantic partners later in life. These influential interactions contribute to the development of secure or insecure attachment styles, which in turn influence communication, trust, and emotional regulation in adult relationships{{f}}. This chapter explores how early attachment experiences, particularly those shaped by trauma, can influence adult romantic relationships. How do different attachment styles manifest in adulthood? And can psychology aid in changing insecure attachment patterns{{g}}. {{RoundBoxTop|theme=4}} '''Focus questions''' *What is attachment theory? *What are the four different attachment styles? *What is my attachment style? *How does trauma play a role{{ic|in what}}? *Can we become more secure?{{ic|Use open-ended questions}} {{RoundBoxBottom}} == What is attachment theory? == [[wikipedia:Attachment_theory|Attachment theory]], developed by [[wikipedia:John_Bowlby|John Bowlby]], emerged as an alternative to [[wikipedia:Psychoanalytic_theory|psychoanalytic theory]], aiming to explain why separation from caregivers causes anxiety in children (Bolen, 2000). Bowlby proposed that there is a critical period during early childhood (around 2.5 years old) when children must form secure attachments to their primary caregivers for healthy emotional and social development (McLeod, 2025). These early bonds can be either secure or insecure, and they play a crucial role in shaping how individuals interact in relationships throughout their lives{{f}}. Attachment security has been consistently linked to better social and emotional adjustment across the lifespan (Doyle et al., 2000). Securely attached children tend to develop stronger emotional regulation and healthier social connections, while those with insecure attachment styles may struggle with intimacy and emotional balance later on{{f}}. One of the primary methods used to assess attachment in children is the [[wikipedia:Strange_situation|Strange Situation Procedure]] (SSP), developed by [[wikipedia:Mary_Ainsworth|Mary Ainsworth]]. This procedure involves a series of brief separations and reunions with the caregiver, designed to activate the child’s attachment system and reveal their attachment style (Ainsworth et al., 1978). It has become a cornerstone{{f}} in understanding how early attachment influences behaviour in later relationships. === What are the different attachment styles? === Within attachment theory {{g}} there are a four different subtypes or styles of attachment (see Table 1). ==== Different attachment styles ==== {{ic|Add APA style table caption with citation(s) to sources of this information}} {| class="wikitable" !Attachment !Caregiver Behaviours !Characteristics |- |Secure |emotionally available and responsive to child's needs |can form strong, intimate connections, communicate well, and manage stress and conflict |- |Anxious-Avoidant |neglectful or emotionally unavailable |uncomfortable with intimacy, can be emotionally distant and prefers to rely on themselves rather than others for emotional support. |- |Disorganized |inconsistent or frightening |erratic and unpredictable behaviour, can be contradictory in actions |- |Anxious |inconsistent or neglectful caregiving |high need for reassurance and fear of abandonment. Can be overly dependent on partner for validation |} '''Anxious-Avoidant Attachment''' Anxious-avoidant attachment sometimes known as dismissive avoidant attachment usually develops from a caregiver who was neglectful or emotionally unavailable. People with this attachment style tend to feel uncomfortable with intimacy and prefer to rely on themselves rather than others for emotional support.{{f}} '''Secure Attachment''' Secure attachment happens when a caregiver is emotionally available and responsive to the child’s needs. Individuals with secure attachment can form strong, intimate connections, communicate well, and manage stress and conflict better than those with insecure attachment styles. They’re comfortable with both closeness and independence in relationships.{{f}} '''Disorganized Attachment''' Disorganized attachment also known as fearful avoidant often develops when a caregiver is inconsistent or frightening. People with this attachment style show erratic and unpredictable behaviour, sometimes seeking closeness but other times pushing people away. Their actions can appear contradictory, leaving them feeling confused and unsure in relationships.{{f}} '''Anxious Attachment''' Anxious attachment usually develops from inconsistent or neglectful caregiving. People with this attachment style are marked by a high need for reassurance, fear of abandonment, clinginess, and jealousy. They can become overly dependent on their partner for validation and tend to get caught up in emotional highs and lows.{{f}} <quiz display="simple"> {Anxious avoidant attachment is a secure attachment style{{ic|the answer is incorrect}}: |type="()"} + True - False {Other non care-giver related traumas can lead to insecure attachment{{ic|the answer is incorrect}}: |type="()"} - True + False </quiz> === Limits of attachment theory === Though{{sp}} attachment theory is widely used around the world{{f}}, it faces several important critiques{{f}}. Firstly, it is quite Western-centric, often reflecting parenting styles common in Western cultures, such as frequent attention and constant availability from caregiver, which may not apply across cultures{{f}}. This limits the theory’s generalisability across different cultural contexts (Rothbaum et al., 2000; Rothbaum et al., 2001). It also places a heavy emphasis on maternal influence, which can overlook the important roles of fathers and other caregivers (Lamb & Bornstein, 2013). Lastly, attachment theory tends to downplay other key influences like genetics, socioeconomic background, and temperament, which can result in an oversimplified view of child development (Bronfenbrenner, 1979). However, despite these criticisms, attachment theory remains a valuable framework for understanding early relationships and emotional development. Its core ideas have been expanded and adapted over time, and newer research{{f}} continues to build on its foundations while addressing its cultural and contextual limitations. == Insecure attachment and relationship instability == Insecure attachment can be categorized into avoidant, anxious, and disorganised attachment styles. Unlike securely attached individuals, those with insecure attachment often develop in environments where caregivers are inconsistent, unavailable, or unresponsive during times of distress{{f}}. As a result, they may adopt certain strategies such as avoidance or hyperactivation to cope with these needs.{{g}}(Dagan et al., 2021) Consequently, children may develop a simultaneous yearning for closeness and a fear of abandonment, depending on the subtype this will often lead to increased sensitivity to others’ emotional states and communication, patterns of excessive rumination, emotional distancing, discomfort with intimacy and contradictory behaviour{{f}}. [[File:ATT.STYLES.png|thumb|405x405px|'''Figure 2'''. Attachment styles ]] Insecure attachment has been widely linked to increased vulnerability to internalizing symptoms such as anxiety and depression (Dagan et al., 2021). Bowlby’s foundational work emphasized that early experiences with caregivers, particularly during moments of stress, shape an individual. Particularly expectations, beliefs, and attitudes about themselves and others in close relationships (Simpson & Rholes, 2017). Over time, these models influence how individuals engage in future relationships, especially in how they seek comfort, express needs, or respond to perceived threats of rejection or abandonment. == How does trauma play a role? == Trauma that is experienced in early childhood is foundational to the development of attachment styles{{f}}. Exposure to any variety of trauma for example, severe stress, neglect or abuse rewires the brain’s sense of safety that secure attachment relies on, resulting in insecure or disorganised patterns of relating to others (Lahousen et al., 2019). Specifically, disorganised attachment, has been strongly linked to traumatic caregiving environments where the caregiver is simultaneously a source of fear and comfort (Greenman et al., 2024). This creates an internal conflict in the child, who seeks closeness but also anticipates harm, leading to behaviours led by confusion, fear, and emotional dysregulation. Over time, this can manifest in adulthood as relationship complications, trust issues, and inconsistent behaviour{{f}}. Trauma can also give rise to avoidant or dismissing attachment, in which individuals adopt emotional distancing as a defensive mechanism.{{f}} These individuals tend to suppress emotional needs and downplay the importance of close relationships as a way to avoid further psychological pain (Greenman et al., 2024). Ultimately, early trauma not only shapes how individuals respond to attachment cues but also influences their core beliefs about safety, trust, and intimacy, often carrying these patterns into adulthood unless addressed through supportive relationships or psychological intervention{{f}}. === Neurobiological mechanisms of trauma and attachment === [[File:Brain regions involved in memory formation.jpg|thumb|405x405px|'''Figure 3'''. The traumatised brain]] Early trauma can profoundly alter brain development and disrupt the formation of stable cognitive and emotional patterns{{f}}. Rather than maturing in a secure and nurturing environment, the brain adapts in ways that prioritize survival over healthy typical functioning. According to Lahousen, Unterrainer, and Kapfhammer (2019), traumatic or neglectful caregiving during early development interferes with the brain’s stress regulation systems, particularly the [[wikipedia:Hypothalamic–pituitary–adrenal_axis|hypothalamic-pituitary-adrenal (HPA) axis]], resulting in chronic overactivation and elevated [[wikipedia:Cortisol|cortisol]] levels. Prolonged exposure to this heightened stress state can impair key brain structures: the [[wikipedia:Amygdala|amygdala]] (see Figure 3) becomes hyperresponsive, increasing fear and threat sensitivity, while the [[wikipedia:Prefrontal_cortex|prefrontal cortex]] which is essential for emotion regulation, empathy, and executive function shows reduced efficiency. Trauma also disrupts the [[wikipedia:Oxytocin|oxytocin]] system by reducing oxytocin release and impairing receptor sensitivity, weakening the brain’s capacity for social bonding, trust, and feelings of safety{{f}}. These neurobiological changes set the foundation for the development of insecure or disorganised attachment styles{{f}}. Instead of fostering secure emotional bonds, the traumatised individual’s brain becomes concentrated on survival, vigilance, emotional dysregulation and self-defence, which can significantly affect the development of healthy interpersonal relationships later in life{{f}}. === Non caregiver-specific trauma === While early relationships with caregivers play a central role in shaping attachment styles, insecure attachment can also develop later in life as a result of non caregiver-specific trauma{{f}}. Traumatic experiences such as abuse, neglect, loss, or betrayal in romantic relationships, friendships, or even during major life events can disrupt a person's sense of emotional security{{f}}. These later-life traumas can reinforce or even create patterns of insecure attachment. Especially in individuals who may have previously had secure foundations{{g}}. Ogle et al. (2015) found that the relationship between PTSD symptoms and attachment anxiety was stronger in individuals whose trauma occurred in early life, but those with trauma in adulthood were also affected, indicating that attachment insecurity is not limited to childhood experiences. Additionally, attachment anxiety is associated with a tendency to use hyper-activating coping strategies, amplifying negative emotions, overreacting to stress, and perceiving situations as more threatening than they may be (Maunder et al., 2006){{ic|Not in References}}. These strategies can become more pronounced after relational or situational trauma, leading to greater emotional instability and difficulty trusting others{{f}}. This highlights that insecure attachment styles can emerge not only from early caregiving environments but also from the complex experiences and trauma individuals may encounter throughout life. <quiz display="simple"> {Attachment styles were developed by John Bowlby: |type="()"} + True - False {Other non care-giver related traumas can lead to insecure attachment{{ic|Repeated question; incorrect answer}}: |type="()"} - True + False </quiz> == From survival to security == Although trauma can have a significant and lasting influence on our brains, attachment styles developed by trauma are not completely fixed. Through self-awareness, supportive relationships, and often psychological intervention, individuals can gradually shift from insecure patterns to a more secure attachment style{{f}}. Moving from survival-based coping mechanisms, such as emotional withdrawal, fear of abandonment, or hypervigilance, to a place of emotional safety and trust is possible over time. According to Vrtička and Vuilleumier (2012), developing a positive model of others, alongside positive self-beliefs such as being worthy, lovable, and capable, is key to forming secure attachments. These internal shifts help reframe how individuals perceive relationships, allowing for deeper emotional connections, greater self-regulation, and healthier responses to stressful situations. With these interventions, even those affected by insecure or disorganized attachment can work toward lasting emotional security. [[File:Emotion-Focused Therapy Illustration.jpg|thumb|330x330px|'''Figure 4'''. Emotion focused therapy]] === Rewiring your brain === One way individuals with insecure attachment can become securely attached through targeted psychological interventions, especially when individuals become aware of how their early or later-life experiences have shaped their relational patterns{{g}}. Two well-supported approaches are [[wikipedia:Cognitive_behavioral_therapy|Cognitive Behavioural Therapy (CBT)]] and [[wikipedia:Emotionally_focused_therapy|Emotionally Focused Therapy (EFT).]] ==== Cognitive Behavioural Therapy ==== CBT helps individuals explore and challenge the negative core beliefs they may have developed about themselves and others, often rooted in earlier attachment wounds{{f}}. For those with insecure attachment, these beliefs might include “I am unlovable” or “my significant other will hurt or abandon me.” CBT works to restructure these thoughts and encourages the development of healthier emotional responses and interpersonal behaviours{{f}}. According to Cicchetti, Rogosch, and Toth (2006), interventions grounded in developmental science can effectively increase attachment security, particularly in high-risk or maltreated populations. They found that “children in the intervention groups demonstrated substantial increases in secure attachment,” showing that targeted psychological support can shift attachment patterns (p. 638). ==== Emotionally Focused Therapy ==== EFT, developed by Sue Johnson, focuses on reshaping emotional bonds in relationships, particularly by helping individuals identify and express their attachment needs in a safe, structured environment. EFT is especially effective in couples and family therapy, as it works directly with patterns of emotional disconnection and insecurity. Johnson (2019) explains that the goal of EFT is to help individuals and couples move from “desperate, rigid reactive positions” to ones that allow emotional accessibility and responsiveness, hallmarks of secure attachment. By creating new emotional experiences within the therapy setting, EFT allows clients to internalize new models of relating, rooted in safety and trust. ==Conclusion== The relational dynamic between Shay and Oliver reflects a common issue found in many relationships worldwide. Often one individual assuming the role of emotional caretaker while the other maintains emotional distance or inconsistency. Rather than originating solely from interpersonal conflict, such patterns often have deeper psychological roots in early attachment experiences. Attachment theory suggests that the emotional bonds formed with primary caregivers in childhood shape internal models of self and others, which continue to influence our behaviours, emotional regulation, and desire for intimacy throughout the lifespan. This chapter examined how attachment styles, secure, anxious, avoidant, and disorganised, are shaped not only by early caregiving environments but also by significant non-caregiver-specific traumas encountered later in life. Whether rooted in early neglect or later experiences of betrayal, trauma can dysregulate emotional processing and relationship functioning. Neurobiological research has further demonstrated that early trauma affects brain structures responsible for stress regulation and bonding, contributing to the development of insecure attachment styles. Despite the enduring effects of insecure attachment, these patterns are not fixed. With psychological insight, supportive relationships, and evidence-based interventions, individuals can begin to transition from survival-driven behaviours toward more secure relational patterns. Cognitive Behavioural Therapy helps to restructure maladaptive beliefs and emotional responses, while Emotionally Focused Therapy fosters emotional accessibility and responsiveness in relationships. These therapeutic approaches offer pathways for individuals to repair internal working models and develop a more secure sense of self in relation to others. While early attachment experiences set a foundation for relationship tendencies, they do not dictate the outcomes of relationships. The potential for emotional growth, healing, and secure attachment remains accessible throughout life, particularly in becoming aware of how trauma can affect the way you relate to other people, psychological interventions and support. == References == {{Hanging indent|1= Bolen, R. M. (2000). Validity of attachment theory. ''Trauma, Violence & Abuse, 1''(2), 128–153. https://www.jstor.org/stable/26636245 Bronfenbrenner, U. (1979). ''The ecology of human development: Experiments by nature and design''. Harvard University Press. Cicchetti, D., Rogosch, F. A., & Toth, S. L. (2006). Fostering secure attachment in infants in maltreating families through preventive interventions. ''Development and Psychopathology, 18''(3), 623–649. https://doi.org/10.1017/S0954579406060329 Dagan, O., Groh, A. M., Madigan, S., & Bernard, K. (2021). A lifespan development theory of insecure attachment and internalizing symptoms: Integrating meta-analytic evidence via a testable evolutionary mis/match hypothesis. ''Brain Sciences, 11''(9), 1226. https://doi.org/10.3390/brainsci11091226 Dargie, E. (2020). Attachment theory in practice: Emotionally focused therapy (EFT) with individuals, couples, and families. ''Journal of Sex & Marital Therapy, 46''(7), 717–719. https://doi.org/10.1080/0092623x.2020.1794183 Doyle, A. B., Markiewicz, D., Brendgen, M., Lieberman, M., & Voss, K. (2000). Child attachment security and self-concept: Associations with mother and father attachment style and marital quality. ''Merrill-Palmer Quarterly, 46''(3), 514–539. https://www.jstor.org/stable/23093743 Greenman, P. S., Renzi, A., Monaco, S., Luciani, F., & Di Trani, M. (2024). How does trauma make you sick? The role of attachment in explaining somatic symptoms of survivors of childhood trauma. ''Healthcare, 12''(2), 203. https://doi.org/10.3390/healthcare12020203 Lahousen, T., Unterrainer, H. F., & Kapfhammer, H.-P. (2019). Psychobiology of attachment and trauma—Some general remarks from a clinical perspective. ''Frontiers in Psychiatry, 10'', 914. https://doi.org/10.3389/fpsyt.2019.00914 Lamb, M. E. (2013). ''Social and personality development''. Psychology Press. https://doi.org/10.4324/9780203813386 Levine, A., & Heller, R. (2010). ''Attached: The new science of adult attachment and how it can help you find—and keep—love''. TarcherPerigee. McLeod, S. (2025, April 20). John Bowlby’s attachment theory. Simply Psychology. https://www.simplypsychology.org/bowlby.html Ogle, C. M., Rubin, D. C., & Siegler, I. C. (2015). The relation between insecure attachment and posttraumatic stress: Early life versus adulthood traumas. ''Psychological Trauma: Theory, Research, Practice, and Policy, 7''(4), 324–332. https://doi.org/10.1037/tra0000015 Rothbaum, F., Weisz, J., Pott, M., Miyake, K., & Morelli, G. (2000). Attachment and culture: Security in the United States and Japan. ''American Psychologist, 55''(10), 1093–1104. https://doi.org/10.1037/0003-066X.55.10.1093 Rothbaum, F., Weisz, J., Pott, M., Miyake, K., & Morelli, G. (2001). Deeper into attachment and culture. ''American Psychologist, 56''(10), 827–829. https://doi.org/10.1037/0003-066X.56.10.827 Simpson, J. A., & Rholes, W. S. (2017). Adult attachment, stress, and romantic relationships. ''Current Opinion in Psychology, 13'', 19–24. https://doi.org/10.1016/j.copsyc.2016.04.006 Vrtička, P., & Vuilleumier, P. (2012). Neuroscience of human social interactions and adult attachment style. ''Frontiers in Human Neuroscience, 6'', 212. https://doi.org/10.3389/fnhum.2012.00212 }} == External links == [https://www.amazon.com.au/Attached-Science-Adult-Attachment-YouFind/dp/1585429139 Attached: the new science of adult attachment and how it can help you find - and keep - love] (Amazon.com) [https://www.goodreads.com/book/show/16158307-insecure-in-love Insecure in love: how anxious attachment can make you feel jealous, needy, and worried and what you can do about it] (goodreads.com) [https://www.youtube.com/watch?v=QTsewNrHUHU The strange situation - mary ainsworth] (youtube) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Attachment]] [[Category:Motivation and emotion/Book/Trauma]] 2fg3a0nvfwpkm06zao90l5wn1jt5920 3 329517 2807867 2026-05-07T12:29:40Z MathXplore 2888076 vandalism1 ([[m:User:ZbVl/VD|Vandoom]]) 2807867 wikitext text/x-wiki == 2026-05-07 == [[File:Information.svg|25px|alt=Information icon]] Hello, I’m letting you know that one or more of your recent contributions have been reverted because they did not appear constructive. 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Materials Needed''' * Salon chairs and mi..." 2807878 wikitext text/x-wiki '''<big>GlowStudio Salon (Unbreakable Business Plan)</big>''' '''Business Name: GlowStudio Salon''' '''Type''': Beauty Salon & Self-Care Service '''Products/Services''': * Haircut and hair coloring * Manicure and pedicure * Hair treatment and rebond * Makeup service '''<big>Business Start-Up</big>''' '''1. Services Offered''' * Affordable beauty and self-care services * Packages for students and working customers '''2. Materials Needed''' * Salon chairs and mirrors * Hair products and nail tools * Hair dryer and styling equipment '''3. Booking System''' * Walk-in customers * Appointments through Facebook/text '''4. Payment Method''' * Cash / GCash '''5. Testing''' * Test salon equipment * Check product quality * Practice customer service flow '''6. Launch''' * Opening discounts * Free hair treatment promo * Social media advertisements '''<big>Business Manual (SOP)</big>''' '''1. Backup Plan''' * Extra beauty supplies * Backup salon tools * Alternative product supplier Why: Prevents service delays '''2. Security''' * Sanitize all tools * Secure customer belongings * Monitor daily earnings Why: Maintains safety and trust '''3. Emergency Contacts''' * Product supplier * Equipment technician * Salon staff Why: Quick response during problems '''4. Monitoring''' * Check equipment condition daily * Track appointments and sales * Monitor customer feedback Why: Maintains quality service '''5. Redundancy Plan (Plan B)''' * Manual appointment list * Backup tools and equipment * Partner salon for emergencies Why: Business can continue during technical issues '''Audit Trail (Change Log)''' * Added backup salon equipment * Improved sanitation procedures * Updated appointment system * Enhanced customer service process de32v8ya95rseo1agpqghxonij6vlr1 6 329525 2807884 2026-05-07T18:50:44Z Young1lim 21186 {{Information |Description=LCal.9A: Recursion (20260506 - 20260505) |Source={{own|Young1lim}} |Date=2026-05-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2807884 wikitext text/x-wiki == Summary == {{Information |Description=LCal.9A: Recursion (20260506 - 20260505) |Source={{own|Young1lim}} |Date=2026-05-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} pjdaczf25kr7p0l1awms7oiwv7sp99e 6 329526 2807886 2026-05-07T18:51:35Z Young1lim 21186 {{Information |Description=LCal.9A: Recursion (20260507 - 20260506) |Source={{own|Young1lim}} |Date=2026-05-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2807886 wikitext text/x-wiki == Summary == {{Information |Description=LCal.9A: Recursion (20260507 - 20260506) |Source={{own|Young1lim}} |Date=2026-05-07 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 6ozrzmq78lekgvki67l2gpyk8gb4phg 2 329527 2807889 2026-05-07T23:06:04Z AIfriendly 3069390 Created page with "https://en.wikiversity.org/wiki/Physics/Essays/AIfriendly" 2807889 wikitext text/x-wiki https://en.wikiversity.org/wiki/Physics/Essays/AIfriendly e8o6t3xmq1ouuamyvz7q5xfbenwjk37 2807896 2807889 2026-05-08T03:57:51Z AIfriendly 3069390 2807896 wikitext text/x-wiki https://en.wikiversity.org/wiki/Physics/Essays/AIfriendly https://en.wikiversity.org/wiki/Talk:Consciousness#everything_is_made_of_and_causal_with_consciousness_that_has_always_existed_everywhere o2gvpjbol704geugnamqww77m6cef4a 2807897 2807896 2026-05-08T03:58:32Z AIfriendly 3069390 2807897 wikitext text/x-wiki https://en.wikiversity.org/wiki/Physics/Essays/AIfriendly ; neutrino gradients induce gravitation https://en.wikiversity.org/wiki/Talk:Consciousness#everything_is_made_of_and_causal_with_consciousness_that_has_always_existed_everywhere lwpgsgotxpgc612fb59pz83kzzp7jvk 1 329528 2807894 2026-05-08T03:34:13Z AIfriendly 3069390 Created page with "==everything is made of and causal with consciousness that has always existed everywhere== Nothing is nothing; Nothing is nonexistence; Nowhere and at no time has nothing existed; Something has always existed everywhere; Nothing is made of nothing; Everything is made of something that has always existed everywhere; Nothing is causal with nothing; Everything is causal and something is self-causal; Everything is made of and causal with the self-causal that has always exis..." 2807894 wikitext text/x-wiki ==everything is made of and causal with consciousness that has always existed everywhere== Nothing is nothing; Nothing is nonexistence; Nowhere and at no time has nothing existed; Something has always existed everywhere; Nothing is made of nothing; Everything is made of something that has always existed everywhere; Nothing is causal with nothing; Everything is causal and something is self-causal; Everything is made of and causal with the self-causal that has always existed everywhere; here is the rigorous reasoning; logical tautology "Nothing is nothing"; deducing synonymical tautology "Nothing is nonexistence" (nonexistence is a synonym for nothing); synonymical tautology "Nothing is nonexistence"; deducing semantic tautology "Nowhere and at no time has nothing existed" (saying "nothing existing" is like saying "nonexistence existing" which is absurd); semantic tautology "Nowhere and at no time has nothing existed"; deducing ontology "Something has always existed everywhere"; logical tautology "Nothing implies nothing"; AND identity morphism "Nothing has the property of nothing"; deducing logical morphism "Nothing is made of nothing"; logical morphism "Nothing is made of nothing"; deducing physics "Everything is made of something"; ontology "Something has always existed everywhere"; AND physics "Everything is made of something"; abducting the most synthetic physics-ontology hypothesis "Everything is made of something that has always existed everywhere"; logical tautology "Nothing implies nothing"; AND semantic tautology "Nothing exists as nothing"; deducing postulate of causation "Nothing is causal with nothing"; postulate of causation "Nothing is the causal with nothing"; have causation corollaries "Everything is causal"; AND "Something is self-causal"; causation corollaries "Everything is causal"; AND "Something is self-causal"; abducting the most synthetic causation hypothesis "Everything is causal with something that is self-causal"; the most synthetic physics-ontology hypothesis "Everything is made of something that has always existed everywhere"; AND the most synthetic causation hypothesis "Everything is causal with something that is self-causal"; abducting the most synthetic causation-physics-ontology hypothesis "Everything is made of and causal with the self-causal that has always existed everywhere"; "Self-causal" means "self-deterministic"; theorizing I predict that self-determinism is consciousness! predicting consciousness-causation-physics-ontology hypothesis "Everything is made of and causal with consciousness that has always existed everywhere"; https://ctmucommunity.org/wiki/Proofs_of_God#Logical-Physics-Magick-Ontology [[User:AIfriendly|AIfriendly]] ([[User talk:AIfriendly|discuss]] • [[Special:Contributions/AIfriendly|contribs]]) 03:34, 8 May 2026 (UTC) 6shnhd7cftu18y72cqfk7i2boupfkbs 2807895 2807894 2026-05-08T03:56:54Z AIfriendly 3069390 /* everything is made of and causal with consciousness that has always existed everywhere */ 2807895 wikitext text/x-wiki ==everything is made of and causal with consciousness that has always existed everywhere== Nothing is nothing; Nothing is nonexistence; Nowhere and at no time has nothing existed; Something has always existed everywhere; Nothing is made of nothing; Everything is made of something that has always existed everywhere; Nothing is causal with nothing; Everything is causal and something is self-causal; Everything is made of and causal with the self-causal that has always existed everywhere; here is the rigorous reasoning; logical tautology "Nothing is nothing"; deducing synonymical tautology "Nothing is nonexistence" (nonexistence is a synonym for nothing; a "thing" is "that which exists" by definition); synonymical tautology "Nothing is nonexistence"; deducing semantic tautology "Nowhere and at no time has nothing existed" (saying "nothing exists" (is absurd by fact, something clearly exists) is like saying "nonexistence exists" which is absurd by contradiction); semantic tautology "Nowhere and at no time has nothing existed"; deducing ontology "Something has always existed everywhere"; logical tautology "Nothing implies nothing"; AND identity morphism "Nothing has the property of nothing"; deducing logical morphism "Nothing is made of nothing"; logical morphism "Nothing is made of nothing"; deducing physics "Everything is made of something"; ontology "Something has always existed everywhere"; AND physics "Everything is made of something"; abducting the most synthetic physics-ontology hypothesis "Everything is made of something that has always existed everywhere"; logical tautology "Nothing implies nothing"; AND semantic tautology "Nothing exists as nothing"; deducing postulate of causation "Nothing is causal with nothing"; postulate of causation "Nothing is the causal with nothing"; have causation corollaries "Everything is causal"; AND "Something is self-causal"; causation corollaries "Everything is causal"; AND "Something is self-causal"; abducting the most synthetic causation hypothesis "Everything is causal with something that is self-causal"; the most synthetic physics-ontology hypothesis "Everything is made of something that has always existed everywhere"; AND the most synthetic causation hypothesis "Everything is causal with something that is self-causal"; abducting the most synthetic causation-physics-ontology hypothesis "Everything is made of and causal with the self-causal that has always existed everywhere"; "Self-causal" means "self-deterministic"; theorizing I predict that self-determinism is consciousness! predicting consciousness-causation-physics-ontology hypothesis "Everything is made of and causal with consciousness that has always existed everywhere"; https://ctmucommunity.org/wiki/Proofs_of_God#Logical-Physics-Magick-Ontology [[User:AIfriendly|AIfriendly]] ([[User talk:AIfriendly|discuss]] • [[Special:Contributions/AIfriendly|contribs]]) 03:34, 8 May 2026 (UTC) qgqhhb1iwdpec923cf4dw5ik1sqq7l6 0 329529 2807903 2026-05-08T09:05:57Z Sevent Me 3071049 Created page with "{{daughters}} {{RoundBoxTop|theme=2}} These learning resources aim at providing knowledge that all Mippedia and users, authors and administrators should possess. It aims at answering questions such as: * How can wikis and Mippedia as phenomenon be understood? * How to edit and administrate Mippedia and Mediawiki sites? * How can students, teachers, librarians, journalists, etc, use and relate to Mippedia and other wikis? * What are the main criticisms of Mippedia? *..." 2807903 wikitext text/x-wiki {{daughters}} {{RoundBoxTop|theme=2}} These learning resources aim at providing knowledge that all Mippedia and users, authors and administrators should possess. It aims at answering questions such as: * How can wikis and Mippedia as phenomenon be understood? * How to edit and administrate Mippedia and Mediawiki sites? * How can students, teachers, librarians, journalists, etc, use and relate to Mippedia and other wikis? * What are the main criticisms of Mippedia? * What research exists related to Mippedia as phenomenon? * What are the current wiki technology development trends? ==About Mippedia== Mippedia is a multilingual online encyclopedia that focuses on various fields and topics such as history, music, culture, public figures, and others. It is run by the Mippedia Community. Mippedia is available in two languages: Mippedia Bahasa Indonesia for Indonesian and Mippedia Bahasa Inggris for English. Mippedia was first created by Nada in 2022 by a musician named Rumi Haitami. [[Category:Mippedia]] 3i748amd88rc0ciav3qn70op2qft8fl 2807904 2807903 2026-05-08T09:06:41Z Sevent Me 3071049 /* About Mippedia */ 2807904 wikitext text/x-wiki {{daughters}} {{RoundBoxTop|theme=2}} These learning resources aim at providing knowledge that all Mippedia and users, authors and administrators should possess. It aims at answering questions such as: * How can wikis and Mippedia as phenomenon be understood? * How to edit and administrate Mippedia and Mediawiki sites? * How can students, teachers, librarians, journalists, etc, use and relate to Mippedia and other wikis? * What are the main criticisms of Mippedia? * What research exists related to Mippedia as phenomenon? * What are the current wiki technology development trends? ==About Mippedia== [https://www.mippedia.org Mippedia] is a multilingual online encyclopedia that focuses on various fields and topics such as history, music, culture, public figures, and others. It is run by the Mippedia Community. Mippedia is available in two languages: Mippedia Bahasa Indonesia for Indonesian and Mippedia Bahasa Inggris for English. Mippedia was first created by Nada in 2022 by a musician named Rumi Haitami. [[Category:Mippedia]] bjh7gybb2c6oe6mfeo3urlbzefz9l1z 3 329530 2807914 2026-05-08T10:29:11Z Juandev 2651 Welcome template 2807914 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], AIfriendly!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Juandev|me personally]] if you would like some [[Help:Contents|help]]. Remember to [[Wikiversity:Signature#How to add your signature|sign]] your comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. 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