text:
User talk:Boltzelius

 Hello Boltzelius, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 15:16, 7 June 2011 (UTC)

title: User talk:Boltzelius


text:
User talk:RogueKnight

 Hello RogueKnight, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 15:20, 7 June 2011 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User talk:RogueKnight


text:
User talk:Tashif

 Hello Tashif, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 15:21, 7 June 2011 (UTC)

title: User talk:Tashif


text:
User talk:Jeyashree

 Hello Jeyashree, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 15:22, 7 June 2011 (UTC)

title: User talk:Jeyashree


text:
User talk:Rahulrsharma

 Hello Rahulrsharma, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Juan de Vojníkov 16:52, 7 June 2011 (UTC)

Hi, I am glad too, you are in here.--Juan de Vojníkov 16:52, 7 June 2011 (UTC)

title: User talk:Rahulrsharma


text:
User:Alainawegiel

'''מיכאל לייטמן, סגנון חיים, משנתו כמו גם את החמלה כלפי הקבלה '''

כפי שאתה מקושר הכיבוש על ההוראה, אז יכול להיות שיש את האפשרויות שיש לך רק להתקל עם תלמיד כזה מדהים אשר מחפשים פתרונות על שאלות אחדות, כאשר הרגל של תלמיד זה הפרט מייצר אתה כועס, אז יש סיכויים מעטים כי תגלו כי תלמיד זה בטח יהיה לרכוש עם אורח החיים שלו. קרה בדיוק אותו יפה על הסטודנט באוניברסיטה בשם מיכאל לייטמן מי היה כל כך עמוק בתוך מדווח כי הוא התעלם לחלוטין מחיי היומיום של אנשים שלך כל הסובבים אותו, ובדרך זו בפרט, הוא היה לגמרי למראה כי היום אנשים בסופו של דבר ואילו בשלב של התעלמות ממנו, אבל לטווח ארוך אמר לנו כי זה סטודנט גדל להיות אחד החלק החשוב ביותר של הקבלה, ועכשיו הוא נקרא מיכאל לייטמן.

כאשר תלמיד מכללה ברמה הזו מגיע מול מהמורה, זה באמת אורגני כי המורה יהיה לגמרי מתעלמים אחד קטן, ובדרך זו בפרט, סטודנט ברמה הזו יגיעו כדי להבין את החיוניים ביותר חלק של חיי היומיום על תורתו של אשר היה גילוי. ללימוד הקבלה הפכה חלק מבנה גוף ומחשבות של התלמיד הספציפי, ובדרך זו בפרט, תלמידת קולג 'יהיה הרבה יותר לחפש את התשובה האידיאלית שלך הצרות שלך.

מחפשים את הפתרון שלך אם אתה בהפקת גישות גדול צריך לגלות נוספת היא בין אלה שאתה הפקת די הפונקציה טוב שיש את התשובה עם. לפיכך, כאשר אתה לבצע את ההפעלה הגדולה, אז אתה בהחלט דורשים לדעת מה את חיי היומיום הצרכים מאיתנו, במהלך הדרך הזו, היום אנשים שאולי מחפשים שיטות חדשות יותר של דרכים להפוך את הבעיות מעולה יפה עובד בשבילך, תוכל לנסות לעשות את זה. במקרה זה, זו תהיה ככל הנראה של הפעלה נפלאה דרך שיטות על מיכאל לייטמן.

הקבלה היא לא רק את משנתו קל, כדי להבין את זה, יהיה עליך ראש פנטסטי, כך שאתה יכול לעשות את לעשות את העבודה, וכאשר אתה מרוויח על עובד נהדר שלך, אז קליבר וגם האינטלקטואלית של מיכאל לייטמן הוא בין אלה ניתן לחשוב על להיות על איך לעשות את החיים היומיומית שלך טוב שלך, כמו גם עבור אנשים אחרים שלך.

title: User:Alainawegiel


text:
COMT

Catechol-O-methyltransferase (COMT) is an enzyme that degrades catecholamines such as dopamine, epinephrine, and norepinephrine.

The Val108/158Met polymorphism
In addition to coding for multiple isoforms, the COMT gene itself is also polymorphic. There is a common single nucleotide polymorphism (SNP) located on codon 108 of the soluble form and codon 158 of the membrane bound form (Val108/158Met). This polymorphism results in the substitution of Valine (Val) for Methionine (Met). Individuals who are homozygous for the Met allele exhibit preserved levels of dopamine compared to individuals who are homozygous for the Val allele.

Associations have been reported between the Val108/158Met polymorphism and performance on the Wisconsin Card Sorting Test (WCST) in healthy adults. Individuals who have more copies of the Met allele make fewer preservative errors on the Wisconsin Card Sorting Test but are more likely to suffer from borderline personality disorder. 9% of Kenyans, 31% of Caucasians and 27% of South-west Asians are homozygous for the Met allele.

title: COMT


text:
User:Buaidh

Please feel free to leave me a message at w:User talk:Buaidh or e-mail me at w:Special:EmailUser/Buaidh. Yours aye, Buaidh

title: User:Buaidh


text:
User:Shashankpjha

Shashank Jha [full name Shashank Pareshkumar Jha] (born on 15 June 1992) is a brahmin by birth. He has taken his graduate degree from Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, in India. He is Editor in Chief in a Maninagar based print and publishing company Orient SP-Age Publications, and is also a Team Leader - Content Writing in Black iD Solutions Pvt. Ltd., Vadodara, India. He has written more than 9000 articles and proposals and letters as a part of his career, and has also published a few of his creative writings including poetry in different magazines and newspapers.

His research includes translation of The Little Prince from English to Maithili and many dissertations.

title: User:Shashankpjha


title: User:Kylephoto760


text:
Talk:Assistant teacher course/Collaborative action research

Analysis of Former Learning Assistants’ Views on Cooperative Learning
"Broadly speaking, by this he meant that we teach the way we are taught. The data presented here suggests that the former LAs were apprenticed under a different model of teaching than the non-LAs. For example, the LAs discussed the value of argumentation, building a learning community, and coaching their own students in assisting other students in the process of learning. Based on the data presented here, the other teachers in the study (non-LAs) tended to put students in groups to solve logistical problems (such as not having enough equipment) rather than as a mechanism for facilitating learning and argumentation. The LA program is, by design, an experiential learning program in which content is learned through the practice (or experience) of helping others learn. Argumentation and learning communities are explicitly valued and promoted throughout the Learning Assistant experience. The LAs experienced a non-traditional way of learning leading them to teach their students in a non-traditional way. If classroom practice is to become more student-centered and aligned with contemporary research, the way our future teachers are taught truly matters." (Source: Analysis of Former Learning Assistants’ Views on Cooperative Learning)


text:
User talk:Joseph Godes

 Hello Joseph Godes, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 12:19, 8 June 2011 (UTC)

title: User talk:Joseph Godes


text:
User talk:Alainawegiel

 Hello Alainawegiel, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 12:21, 8 June 2011 (UTC)

title: User talk:Alainawegiel


text:
User talk:Dgeary

 Hello Dgeary, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 12:23, 8 June 2011 (UTC)

title: User talk:Dgeary


text:
Talk:Emergency medical responder (EMR)/Primary survey

 Hello EMR primary survey, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 12:27, 8 June 2011 (UTC)


text:
User talk:Pelter~enwikiversity

 Hello Pelter, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 12:29, 8 June 2011 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Pelter. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Pelter~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:40, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:17, 19 April 2015 (UTC)

title: User talk:Pelter~enwikiversity


text: Template:Music symbols

title: Template:Music symbols


text:
Template:Music symbols/doc

Music symbols renders Western music notation of various types into Wikipedia and improves cross-browser support for music symbols.

1    2     3     4     5     6     7     8

Accidentals
The template correctly renders Unicode sharps, flats , and natural signs in Internet Explorer which would otherwise display empty squares unless a full Unicode font is chosen in its Preferences. The choice of fonts also improves the rendering in other browsers on Microsoft Windows such as Mozilla Firefox. See the tables below to compare the results in your current browser. The template makes use of SVG to display double flat, double sharp , and microtonal signs since the corresponding Unicode characters are not widely supported.

The C crops up very early in Beethoven's Symphony No. 3 in E.
 * Sample text

Notes and rests
Some browsers and typefaces support  (♩) and   (♪) for quarter and eighth notes, as well as   (♫) and   (♬) for beamed eighth-note and sixteenth-note pairs respectively, but since the display of these characters does not match any of the other (non-supported) notes and rests, this template does not use these characters.

In place of the single whole note, Chopin writes   , completely changing the profile of the music.
 * Sample text

Clefs
Note that there is no graphical distinction between treble clef and G-clef; alto clef, tenor clef and C-clef; bass clef and F-clef. The names preserve a difference in meaning and make the caption text (for screen readers) different.

Time signatures
For a general time signature, use. This makes use of Template:Time signature, which should not be used on its own.

Scale degrees
Scale degrees are often represented as Arabic numerals with a hat on them and thus the root of a scale is undefined.

A descending tetrachord could be written as undefined-undefined-undefined-undefined.
 * Sample text

Chord symbols
vii becomes vii in B minor by raising the G to G.
 * Sample text

III becomes III in G minor by raising the F to F.

The F7 is used to great effect in the last measure of the piece.

Key signatures
Key signatures must be typed in using the names of the articles themselves on keys. Note that there is no visual difference between the major and minor key signatures, but the alt text is different.

title: Template:Music symbols/doc


text:
User talk:Jamesbzr

Your editing experiment
Thank you for experimenting with Wikiversity. Your test was recorded, and it has been reverted or removed. Please use the sandbox for further testing. You may wish to learn more about what Wikiversity is to help you contribute. If you haven't done it yet, consider registering if you are keen on our project. --Gaidheal1 14:17, 8 June 2011 (UTC)

title: User talk:Jamesbzr


text: File:Probability.djvu

title: File:Probability.djvu


text:
User:Luísa Ourique Lau/Canabinóides

Cannabinóides

Diversas pesquisas, mostraram que os efeitos farmacológicos da maconha são mediados por dois receptores, CB1 e CB2. Ambos ativam mecanismos de transdução similares, incluindo a inibição da adenilate ciclase e de canais de Ca2+ do tipo N. O CB1 ocorre no cérebro, onde é responsável por efeitos característicos da cannabis (relaxação, bem-estar, analgesia, aumento da percepção audio-visual, depressão da atividade motora, analgesia e catalapsia) e também no sistema nervoso periférico. Aí, os receptores CB1 são localizados pressinapticamente e sua ativação pode produzir uma supressão da liberação de neurotransmitores. Os principais sintomas da ativação destes receptores são a estimulação do apetite, vasodilatação (particularmente dos vasos conjuntivos), taquicardia e inibição da mobilidade instestinal. Os receptores CB2, até agora, somente foram localizados fora do SNC (sistema nervoso central), principalmente em células do sistema imunológico. Muitos autores relacionam a ativação destes receptores com imunosupressão, efeitos anti-inflamatórios e analgesia associada a processos inflamatórios. Ao contrário dos receptores CB1, pouco se sabe, ainda, sobre este grupo de receptores. Tão logo se fez a descoberta dos receptores cannabinóides e dos cannabinóides endógenos, cientistas do mundo todo passaram a brincar de química orgânica e sintetizar os mais variados agonistas e antagonistas cannabinóides possíveis, para estudar as suas atividades biológicas. Embora o número seja imenso, os agonistas cannabinóides (incluindo os sintéticos) podem ser separados em 4 grandes grupos: não-clássicos, clássicos, aminoalquilindols e eicosanóides. O grupo clássico são os derivados do dibenzopirano - tal como o THC. O grupo não-clássico consiste em substâncias bicíclicas ou tricíclicas, similares ao THC, mas sem o anel pirano. O mais comum é o agonista sintético CP55940. Os demais grupos têm estruturas bastante distintas da do THC.

Endocanabinóides

A existência dos receptores CB1 revelou que no próprio cérebro existe um conjunto de mecanismos especificamente desenvolvidos durante a evolução para interagir com substâncias semelhantes aos canabinóides da maconha, mas de origem endógena. A descoberta desses receptores revelou que o sistema nervoso produz suas próprias "maconhas" para serem utilizadas em circunstâncias e locais cerebrais especificamente precisamente controlados pelo organismo. Em 1992, William Devane e outros pesquisadores na Universidade Hebraica de Jerusalém isolaram do cérebro de porco um composto lipídico que se ligava especificamente aos receptores de CB1 e que produzia efeitos fisiológicos semelhantes ao THC e outros canabinóides sintéticos. Essa molécula recebe o nome convencional de araquidonoiletanolamida em função de sua estrutura química, mas foi batizada por seus descobridores como anadamida, em referencia à palavra anand, que em sânscrito significa "êxtase". A anandamida foi, portanto, o primeiro endocanabinóide identificado. Em 1997, um segundo composto com características semelhantes foi isolado do cérebro de rato, o 2-araquidonoilglicerol, também conhecido como 2-AG. Estudos posteriores demonstraram que a anandamida, embora se ligasse com maior afinidade do que o 2-AG ao CB1 era um ativador apenas parcial deste receptor, assim como o TCH, enquanto que a 2-AG, embora possuísse menor afinidade pelo receptor, existia no cérebro em concentrações até 170 vezes maiores do que a anandamida e atuava como um ativador (agonista) completo de CB1. Isso sugeriu que, em algumas circunstâncias, a anandamida possa funcionar para substituir o 2-AG nos receptores CB1, fazendo um ajuste fino de sua ativação. Ambos endocanabinóides são derivados do ácido araquidônico e de lipídios (gorduras) que constituem a membrana celular. Ao contrário dos outros neurotransmissores, os endocanabinóides não são armazenados em vesículas para serem liberados nas sinapses. Quando sua síntese é estimulada na membrana plasmática dos neurônios, eles ganham acesso ao espaço extracelular e aos receptores CB1 presentes nas membranas de outros neurônios. Uma molécula presente na membrana celular de neurônios limita a permanência dos endocanabinóides no espaço extracelular, transportando-os de volta a interior das células, onde são degradadas. No final da década de 1990 e no início dos anos 2000, descobriu-se que, quando neurônios pré-sinápticos do hipocampo liberam glutamato causando a despolarização de neurônios pós-sinápticos, esses últimos respondiam produzindo endocanabinóides que se ligavam a outros neurônios pré-sinápticos inibitórios, interrompendo ou reduzindo a quantidade de GABA que recebiam. Essa forma de controle de atividade sináptica de neurônios inibitórios existe em outros circuitos do cérebro, e foi denominada tecnicamente "supressão de inibição induzida por despolarização". Nesse processo, os endocanabinóides funcionam como mensageiros retrógrados, já que fazem o caminho oposto ao dos mensageiros normais, ou seja, eles saem dos neurônios pós-sinápticos para afetarem a atividade de neurônios pré-sinápticos. Descobriu-se que um processo semelhante envolvendo ação retrógrada de endocanabinóides causava inibição de neurônios glutamatérgicos pré-sinápticos. Esse mecanismo foi denominado "supressão de excitação induzida por despolarização" Além dos receptores pós-sinápticos de glutamato que funcionam como canais que permitem a passagem de íons, existem também receptores aos quais o glutamato se liga para desencadear seqüências de reações bioquímicas intracelulares que culminam na alteração da atividade sináptica. Esses receptores são chamados receptores metabotrópicos de glutamato e são normalmente localizados no mesmo terminal pré-sináptico de onde o glutamato é liberado. Quando grandes quantidades de glutamato são liberadas, esses receptores são ativados para diminuir a atividade pré-sináptica. Em alguns circuitos, a ativação de receptores metabotrópicos de glutamato também causa a liberação de endocanabinóides, contribuindo para o estabelecimento da depressão de longa depressão.

Regulação hormonal de endocanabinóides no cérebro A liberação de endocanabinóides no cérebro também é controlada por dois tipos de hormônios produzidos na periferia, glicocorticóides e leptina, os quais informam ao cérebro o estado nutricional e fisiológico do organismo. Glicocorticóides são uma classe de hormônios produzidos na glândula adrenal (cortisol no homem, corticosterona nos ratos) que, quando elevados, informam ao SNC que está em curso uma adaptação do organismo a algum tipo de estresse físico, incluindo hemorragia, grande esforço físico, ferimentos ou falta de nutrientes. A percepção pelo cérebro de risco de dano físico, a constatação de uma derrota na disputa de um parceiro sexual, conflitos sociais ou a antecipação de tais problemas são formas de estresse psicológico que também causam aumento nos níveis de glicocorticóides. O outro hormônio envolvido no controle de endocanabinóides no hipotálamo é a leptina, cujos níveis circulantes são reduzidos quando o animal se encontra em jejum. Essa redução funciona como um sinal permissivo para que o SNC desencadeie uma série de adaptações que otimizam o uso das reservas endógenas de energia (gordura e glicogênio) e estimulam a busca por alimentos. Os glicocorticóides e a leptina exercem efeitos opostos sobre a síntese de endocanabinóides no hipotálamo, regulando o equilíbrio fisiológico do organismo (homeostase). Os hormônios glicocorticóides causam a liberação retrógrada de endocanabinóides, suprimindo a excitação pré-sináptica sobre neurônios do hipotálamo. Esse mecanismo de controle sináptico foi denominado "supressão de excitação induzida por glicocorticóides". A leptina, por outro lado, quando em níveis elevados, impede que os glicocorticóides estimulem a síntese de endocanabinóides. Essa interação foi demonstrada em circuitos hipotalâmicos envolvidos na regulação da saciedade e dos níveis sanguíneos de diversos hormônios, incluindo os próprios glicocorticóides, os hormônios da glândula tireóide e os hormônios vasopressina e oxitocina, que participam da regulação do balanço hídrico e do metabolismo. O diálogo entre os glicocorticóides e a leptina funciona, portanto, como um mecanismo sensível ao estado nutricional que coordena a regulação dos hormônios que, por sua vez, regulam a homeostase energética, o balanço de fluidos e a adaptação a diferentes formas de estresse físico e psicológico. Tal coordenação favorece a liberação hipotalâmica de endocanabinóides durante o jejum, o que, em tese, colaboraria para a adaptação ao déficit calórico e ao retardamento da saciedade. Posteriormente demonstrou-se que a oxitocina e hormônio estimulador de melanócito também causam a liberação retrógrada de endocanabinóides no hipotálamo.

A relevância evolutiva do sistema endocanabinóide O sistema endocanabinóide está presente em todos os invertebrados e vertebrados. Nos vertebrados regula funções orgânicas por meio do receptor periférico CB2 e funções neurais através de receptor CB1, que é um dos receptores mais abundantes no cérebro. Estes fatos revelam que do ponto de vista evolutivo o aparecimento do sistema endocanabinóide pode ter sido de extrema importância para o desenvolvimento e viabilidade das espécies. Pode-se dizer que a obtenção de nutrientes, a manutenção da integridade física e do equilíbrio funcional do organismo, bem como a produção de uma prole viável, são as condições mais fundamentais para a preservação da vida. Os animais, precisam aprender a encontrar seus alimentos, seu pares de acasalamento e a fugir de predadores e outros perigos. Dependendo das condições ambientais e das demandas do corpo, ajustes funcionais e comportamentais (que requerem reaprendizado) são necessários para aumentar as chances de cumprir com sucesso essas demandas. Para tanto, é imperativo o engajamento coordenado do SNC com as funções dos órgãos e o metabolismo. A presença ampla dos receptores de canabinóides no organismo e as evidências de que os endocanabinóides são influenciados por hormônios indicam que o sistema endocanabinóide funciona como um dos principais maestros na orquestração das funções vitais, conforme o contexto em que o organismo se encontre. Isso explica porquê a maconha produz efeitos tão complexos e indica o fantástico potencial do sistema endocanabinóide como alvo de novos remédios. Mas também fica evidente quão desafiadora é a tarefa de direcionar os efeitos dos remédios para aspectos específicos do funcionamento do sistema endocanabinóide, de forma a utilizá-los seletivamente.

title: User:Luísa Ourique Lau/Canabinóides


title: File:Eml5526.s11.mtg2.pic1.svg


title: File:Eml5526.s11.mtg4.pic1.svg


title: File:Eml5526.s11.mtg6.pic1.svg


title: File:Eml5526.s11.mtg6.pic2.svg


title: File:Eml5526.s11.mtg6.pic3.svg


text: File:Eml5526.s11.team5.JA.mtg12.pic1 (2).svg


text: File:Eml5526.s11.team5.JA.mtg14True.pic1.svg


text:
User talk:Bhudjo

 Hello Bhudjo, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 00:53, 9 June 2011 (UTC)

title: User talk:Bhudjo


text: File:Eml5526.s11.team5.JA.mtg14.pic1.svg


text:
Category:Egm5526.s11.arunas

Egm5526.s11 even slide numbers categories

title: Category:Egm5526.s11.arunas


text:
User talk:Jamiewgabriel

 Hello Jamiewgabriel, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 00:59, 9 June 2011 (UTC)

title: User talk:Jamiewgabriel


text:
Research Wikiversity: DIVISION ALGORITHM POLYNOMIALQUOTIENTS

The mathematical topic: DIVISION ALGORITHM POLYNOMIAL QUOTIENTS already exists and has been comprehensively typed out on a Talk Page. Resulting symmetrical and antisymmetrical polynomial quotients have been tabulated from the integer unity [1], the degenerate case, then for the series of Q's : [3, 5, 7, 9, ... 33]. The polynomials continue to any uneven integer however large but always finite.

The derivation is rather lengthy but the principle is that any uneven integer: Q[N] = 2.n + 1, identically, can be divided by two [2] in such a way that the remainder depends only on Q[N] and is either + 1 or - 1. The integer: [N] is such that: 2**{N} < Q[N] < 2**{N + 1}. The two inequalities set limits on the integer: [n] where [n] takes values: [0, 1, 2, ...]. This division by two invariably yields a quotient that is also an uneven integer.

The two extreme values of the integer [n] that satisfy the above inequalities are: n[minimum] = 2**{N - 1} and n[maximum] = 2**{N} - 1, for N equal or greatr than unity..

Iteration of the Division Algorithm as above, starting with Q[N] = 2.Q[N - 1] + r[N - 1] down to iterations of the form: 1 = 2.1 - 1 and similar for - Q[N] with proper counting of the iterations yields polynomials. The integer: [N] counts down.

The general remainder: r[j - 1] = [i]**{1 + Q[j]}. " i " satisfies: i^2 = - 1, using the more conventional " ^ " here rather than " ** " to represent exponentiation. This is generalized to:

r[j - 1] = Z**{1 + Q[j]}

Negative Q[j] given by - Q[j] gives the remainder: - r[j - 1] = [i]**{1 - Q[j]} This is generalized to: - r[j - 1] = Z**{1 - Q[j]}

Irrespective of whether Q[N] or - Q[N] is divided by two iteratively, the divisor is always plus two [ + 2].

The iteration: 1 = 2.1 - 1 is repeated integer: L times and this produces the constant: L[n], that can have any fixed value in the final polynomial equations. There is another integer L[2] involved in the iterations of - Q[N], but L[2] disappears in the algebra.

The iterations are algebraically " condensed " so eliminating every Q[j] with the exception of Q[N, n] and the exception of the final Q[j] of value unity. For each value of Q[N, n], there are two primitive asymmetrical polynomials which when combined either by addition or by subtraction produce the primitive polynomials below. The primitive equation leading to symmetrical quotient polynomials is:

[2**{N + L[n]} - 2**{N}].Z**{Q[N, n] + 1} + [2**{N + L[n]} - 2**{N}].Z**{Q[N, n] - 1} + Σ [2**{N - j}.[Z**{Q[N, n] + Q[j]}]] + Σ [2**{N - j}.[Z**{Q[N, n] - Q[j]}]] = 0

and the primitive equation leading to antisymmetrical quotient polynomials is:

[2**{N + L[n]} + 2**{N} - 2.Q{N, n]].Z**{Q[n, N] - 1} + [2**{N + L[n]} - 2**{N}].Z**{Q[N, n] + 1} + Σ [2**{N - j}.[Z**{Q[n, N] + Q[j]}]] - Σ [2**{N - j}.[Z**{Q[n, N] - Q[j]}]] = 0

The integer: j in the summations runs j = 1, ... N inclusive. Q[N, n] is identifiable with Q[N].

For particular values of Q[N, n] that are consistent with the integer N [see the above lower and upper limits on the integer [n]], the above two primitive equations are easily divisible by the divisor: [Z**{2} + 1], with remainder zero. In either case, a quotient polynomial equation results.

Unlike the primitive polynomials, there does not appear to be a general form of the quotient polynomial for a non-specific Q[N, n].

The next stage would be to solve the tabulated quotient polynomials taking values of Q: [3, 5, ... 33] using a suitable polynomial solver computer program, for simple values of L[n] such as L[n] = 0, noting that the substitution: z = Z**{2} halves the degree of the quotient polynomial in every case.

A plot of the labeled zeros of the quotient polynomial equations may produce a further insight into prime and non-prime uneven integers that have two or more prime factors.

[TO BE CONTINUED] SHAWWPG19410425 11:20, 9 June 2011 (UTC)SHAWWPG19410425 21:18, 24 July 2011 (UTC)SHAWWPG19410425 (talk) 20:55, 15 June 2012 (UTC)


text:
Category:EGM6341.s11.TEAM1.WILKS

See the Wiki Commons category EGM6341.s11.TEAM1.WILKS for all figures by Dave Wilks.

title: Category:EGM6341.s11.TEAM1.WILKS


text:
Isoforms

The word “isoforms” has two distinct but related meanings. If you have linked to this page from another page, then the word isoform is probably being used to refer to two different proteins coded for by a single gene. This is the result of alternative splicing of messenger RNA (mRNA). Eukaryote genes are a sequence of exons and introns coded as a sequence of nucleotide base pairs of DNA. Before a gene can be expressed as a protein, that gene must be transcribed into mRNA. Introns are then spliced out of the mRNA before the mRNA is translated into protein. If the mRNA can be spliced in different ways, or if the mRNA is translated before it is spliced, then it gives rise to different proteins. As a consequence of alternative splicing, a single gene can give rise to both soluble proteins and membrane bound proteins.

See isoform for alternative meanings of the word “isoform”.

title: Isoforms


text:
User talk:Luísa Ourique Lau

 Hello Luísa Ourique Lau, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 19:52, 9 June 2011 (UTC)

Your article
Canabinóides is not in English. I'm moving it to your user space, should you want to use it to work on an English version, this is the English Wikiverity. Thanks. --Abd 19:52, 9 June 2011 (UTC)

The article also appears to be copyright violation, appearing word-for-word, at least a part that I checked, elsewhere. I am proposing it for deletion, therefore. Please respond if there is some reason why this should not be deleted. --Abd 19:55, 9 June 2011 (UTC)

title: User talk:Luísa Ourique Lau


text:
User talk:Guitarsandcars76

 Hello Guitarsandcars76, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 19:59, 9 June 2011 (UTC)

title: User talk:Guitarsandcars76


text:
User talk:Leighblackall/Networked learning a biomass heat transfer system

Peeragogy
12 October via Google Chat, Steven Parker pointed me to the Peeragogy Handbook Leighblackall (discuss • contribs) 03:44, 14 October 2013 (UTC)

A gap in the literature?
I have a feeling I might have found a "gap in the literature" of Networked Learning.

There is a leap from the idea of networked learning in the 1970s, to when computers came in the 80s, and I haven't been able to find challenges or discussion in the 'canon' about this leap. It seems, like so many things, computing has overwhelmed this field, and marginalised those interested in a wider understanding of human networks across media and social systems, such as was the case in the 70s. The discussion of this is largely taking place on the Wikipedia entry for Networked Learning.

Additionally, in private emails with Downes and others, I don't have difficulty in finding agreement that Networked Learning is about more than computer network mediated learning, yet it seems that authoritative academe has not/can not consider it. At least those in the UK/Europe, associated with the Networked Learning conference since 1998. See comments from Chris Jones on the Wikipedia discussion, and my blog post on the matter.

And so, I think this Wikipedia exercise becomes part of my literature review, where as Keith suggests, we agree to differ, and I set to work designing research around my understanding of networked learning, and attempt to introduce it into the 'canon' of Networked Learning literature as a new form of understanding and studying the field more widely.

So, my hunt becomes more focused, have I really found a gap in the research and literature.. back to Illich again, to see who did anything with his "Learning Webs" idea, and the present day Free University Movement

Publication outlets

 * 1) Learning Analytics and Knowledge, 2012: http://lak12.sites.olt.ubc.ca/cfp/ The conference will be hosted in Vancouver, BC at the end of April 2012.
 * 2) The last Networked Learning Conference hosted a series of Hot Seat discussions and the plan is to do something similar in the run in to NLC 2012 in Maastricht (NL). Perhaps the readers of this blog could join in on these discussions. Still a bit vague but the planning is underway now. See http://www.networkedlearningconference.org.uk/

Alternative Publication Idea (Data)
Leigh, I like the idea that you DONT publish your papers. In saying so, please consider this - the dynamic state of your work is what rings true for me as publication. Have you considered 'data' as publication ? Perhaps compose an abstract that points to the dynamic status of your work (data) ie. Figshare. This then allows your freedom of collaboration and provides a bridge for those who are not dynamically networking their publication alexanderhayes 01:23, 30 January 2013 (UTC)


text:
Genetics/DRD2

The DRD2 gene codes for the dopamine receptor D2. This polymorphic gene is located on chromosome 11. Point mutations in and near the coding region of the DRD2 gene which have a major impact on personality.

Basal personality endophenotypes
Four basal personality endophenotypes are associated with polymorphisms in the ANKK1 gene and D2 receptor response to dopamine: calm, anxious, impulsive, and dissocial.

Personality phenotypes
A number of distinct personality phenotypes have been associated with polymorphisms in and near the DRD2 gene.

The –141C ins/del polymorphism
The –141C ins/del polymorphism is located in the promoter region of the DRD2 gene 141 base pairs upstream of the coding region. This polymorphism has been associated with a detached personality type. The –141C ins/del polymorphism may be associated with a blunted expression of DRD2 receptors in response to dopamine.

The C957T polymorphism
The C957T polymorphism is a synonymous mutation located within the coding region of the DRD2 gene. This mutation affects the conformation and stability of DRD2 messenger RNA. The C957T polymorphism might not influence the intensity of the initial expression of DRD2 receptors in response to dopamine. However, it may influence the duration of that response. In any event, the T allele appears to be associated with decreased D2 receptor expression compared to the C allele. The C957C genotype is associated with a reward-related impulsivity endophenotype in response to acute psychosocial stress. The C957C genotype is also associated with schizophrenia.

The TaqI-A polymorphism
Although the TaqI-A polymorphism is traditionally associated with the DRD2 gene itself, it is actually a single nucleotide polymorphism (Glu713Lys) located 9.4 Kb downstream of the DRD2 gene in the coding region of the ANKK1 gene. This gene controls the synthesis of dopamine. Phenotypic expression of the TaqI-A polymorphism differs according to gender. Results of studies of this polymorphism involving males should be interpreted with caution when being applied to females.

A1 allele
The TaqI-A A1 allele is associated with a reduced expression of D2 receptors, an increased susceptibility to Neuroleptic malignant syndrome  and posttraumatic stress disorder. The C957T CC genotype and the TaqI-A A1 allele are epistatically associated with dissocial personality disorder among alcoholics.

A2 allele
The TaqI-A A2 allele is associated with smoking.

Height and Body Mass
In addition to the three point mutations discussed above, two additional single nucleotide polymorphisms within the DRD2 gene have been associated with height and body mass. These two mutations may reduce the binding affinity of the D2 receptors. L-tyrosine, a metabolic precursor to dopamine has been proposed as a treatment for obesity.

Avoidant personality disorder
A detached personality is associated with the –141C ins/del polymorphism in the promoter region of the DRD2 gene, and avoidant attachment is associated with a polymorphism of the 5HT2A serotonin receptor gene. Avoidant personality disorder has also been associated with Taq A1 allele.

Also see
DSM-5 Personality Disorders

title: Genetics/DRD2


text:
User:Mietchen/Q & A

If I am giving presentations using wikis that require registration, people in the audience hesitate to actually post their questions there. The subpages of this page (listed below the line) are meant to ease that situation by providing an opportunity for feedback without the need to register.

title: User:Mietchen/Q & A


text:
User:Mietchen/Q & A/OKCon 2011

This page is a supplement to this presentation and meant to allow for easy feedback. Please type your question, suggestion or comment below the line. I would appreciate if you state your identity but that is not necessary for me to address the issue you brought up. Thanks for your feedback.

Sample question
Please click the [edit] link, copy this section and modify your copy as needed, then save the page, preferably along with some keywords in the Summary window. Thank you! --Daniel Mietchen (talk) 23:09, 9 June 2011 (UTC)

title: User:Mietchen/Q & A/OKCon 2011


text:
User:Mietchen/Q & A/e-publishing 2011

This page is a supplement to this presentation and meant to allow for easy feedback. Please type your question, suggestion or comment below the line. I would appreciate if you state your identity but that is not necessary for me to address the issue you brought up. Thanks for your feedback.

Sample question
Please click the [edit] link, copy this section and modify your copy as needed, then save the page, preferably along with some keywords in the Summary window. Thank you! --Daniel Mietchen (talk) 23:09, 9 June 2011 (UTC)

title: User:Mietchen/Q & A/e-publishing 2011


text:
C957T

The C957T gene polymorphism is a single nucleotide synonymous mutation located within the coding region of the DRD2 gene. Rather than being ‘silent’ the C allele influences mRNA stability and translation. As a result, the C allele alters dopamine-induced up-regulation of the D2 receptor. Individuals with the CC genotype make a greater number of preservative errors on the Wisconsin Card Sorting Test and exhibit a reward-related impulsivity endophenotype in response to acute psychosocial stress. The CC genotype interacts with the COMT Val158Met polymorphism and is associated with schizophrenia. The CC genotype also interacts with the TaqI-A polymorphism of the ANKK1 gene and is associated with dissocial personality disorder.

title: C957T


text:
User talk:Gzc6064

Mtg6

title: User talk:Gzc6064


text:
User talk:A.Thomas

hi folks,i am new to this site-activity......just getting started up  A.ThomasA.Thomas 01:41, 10 June 2011 (UTC)

title: User talk:A.Thomas


text:
Acids and bases/Litmus paper

Many vegetable inks contain compounds which can be used for indicator paper.

Simple recipe for litmus paper:
 * 1) Chop up some red cabbage
 * 2) Add water to cover
 * 3) Bring to a boil
 * 4) Soak some blotting paper in the colored solution
 * 5) Let the paper dry

Experiment with dipping the paper into a variety of common acids and bases. The paper will change color. Other intensely colored vegetables can also be used to make litmus paper.

See also:
 * Acids and bases

title: Acids and bases/Litmus paper


text:
User:Vickismith

-
 * vicki smith
 * educator [ How Haka Tells a Story ]

 * w : http://westnet.vln.school.nz/
 * e : vickismith@paradise.net.nz
 * s : +64 3 753 3012  [static]
 * t :  +64 21 778 067 [travelling]

 * artist
 * http://www.avatarbodycollision.org
 * http://upstage.org.nz/blog
 * http://www.flickr.com/photos/upstage

---

title: User:Vickismith


text:
Organometallic chemistry/Cone Angles

When a ligand is attached to a central metal atom, it is generally free to rotate. As it does so, the ligand sweeps out a region of space that is shaped like a cone, and the cone angle refers to the angle at its apex.

Exact Cone Angle
If the geometry of a ligand is known, either through crystallography or computations, an exact cone angle (θ°) can be calculated. No assumptions about the geometry are made–as in the Tolman method–since the structure can be obtained for a ligand in any environment by several experimental and theoretical methods. A Mathematica script is freely available which will compute the cone angle for any ligand with known Cartesian coordinates. Calculating the cone angle for specific instances, rather than applying a universal value, opens up the possibility to track the change in sterics over the course of a reaction.

title: Organometallic chemistry/Cone Angles


text:
User:KYPark/DIKW

Against DIKW

The hierarchy of DIKW is largely built on helpless and hopeless category mistakes, and perhaps mainly used to underrate cognitive (user-centered) information science and overrate such parodies as materialist tall librarianship in disguise of awkward LIS (library and information science), emphasizing the best store of recorded knowledge, and cognitivist digitall librarianship in disguise of reworked KM (knowledge management), e.g., CiteSeer.

No doubt, computing makes progress in enhancing both human and dehumanizing brains! Both should complement rather than compete so as to do good to us at last. Meanwhile, it should be frankly admitted that the on-going information revolution mainly owes to cognitive, user-centered, "direct-manipulating" human-computer interaction rather than cognitivist, computer-centered, dehumanizing augmentation of AI. Wikipedia and Google are marvelous examples of such a close cognitive interaction.

Either information or knowledge implied in books, encyclopedias and libraries does not readily manifest itself of itself, but only varying from person to person from context to context in terms of meaning, significance, utility, etc. Without the user in context, the mere messy mass of library holdings could not make sense of useful information at all, but perhaps a dull body of knowledge at best. Therefore, it is no use grading and gracing knowledge as a whole of context over information as a "snippet out of context" [sic], as defined by Gorman (2004), the then president-elect of ALA. He was speaking, if not thinking, of a different kind of context, hence perhaps an evil sophistry! Poor philosophical tradition always remain most responsible for poor scholarship as well as poor worldview, as may be more shown in the following.

Taking information seriously

 * A parody of the title of Dworkin (1977) of interpretivist jurisprudence

Matter M, Energy E, and Information I make up Universe MEI. Each element is known and used by virtue of the last, I, to be wise or foolish. The following color mixing may suggest the relationship among them.

Category mistaking
It is often said that to teach is to learn. This is a shorter way of saying. A longer way may be such that before you teach, you have to learn. Or, before you speak or inform, in everyday life, you have to know. To inform is to help or let know at all after all. Or, to teach is to help or let learn at all after all.

In parallel, informing is (to) teaching, while knowing is (to) learning. Then, to say that informing is worse than knowing is to say that teaching is worse than learning. Hence, either way of saying is a fallacy or sophistry relying heavily on the category mistake. Either informing & knowing or teaching & learning do not compete at all but complement after all. It appears as evil to subordinate informing to knowing, as teaching to learning.

Sadly, the hierachy of DIKW looks like a total fallacy or sophistry relying heavily on various category mistakes such that information and knowledge compete, and so do knowledge and wisdom.

Know and inform
To know and inform, or to learn and teach may be one of the social responsibilities of the learned. The following would be problematic in this perspective:

He who knows does not speak, he who speaks does not know.

In the opening passage of their book (1923), Ogden & Richards quote the above skeptical cases from Lao-Tzu. The following 2x2 contingency table would reflect the wider perspective, where inform just replaces speak above:

You do know (DK) --- and do inform (DI). \ /                     or                \ / \                     do not know (NK) --- and not inform (NI).

Then, between the lefthand and righthand sides of the table, there are:

1. two parallel, rational paths, DK-DI and NK-NI, 2. two diagonal, skeptical paths, DK-NI and NK-DI.

In analogy, you may consider the following cases as well:

You do learn (DL) --- and do teach (DT). \ /                    or                 \ / \                    do not learn (NL) --- and not teach (NT).

Triangle of reference
While our body walks on two body's legs, our mind does on two mind's ones. That is to say, our mind's eyes alternatingly see facts or forms on the one leg, and artefacts or norms on the other. For example, we see through the sight, situation or realism on the one leg, often by virtue of the sign, narration or symbolism on the other. This biped stance of the mind may be well illustrated as the triangle of reference below by Ogden & Richards (1923), or as the parody further below by Blackburn (1984).

Besides Blackburn (1984), there are various signs of the biped mind:

Contrary to the wide-spread and deep-rooted belief in academia and elsewhere, the two mental legs relate to each other only indirectly indeed, necessarily via the mind on top, hence the dotted bottom of the triangle. Korzybski (1933) put forward the dictum "The map is not the territory." Ogden & Richards (1923) required that this indirect, imputed relationship or truism be taken most seriously in theory of meaning, hence logic as well. In effect, they were undermining not only the biblical tradition but also the logical tradition of philosophy and science, especially the analytic doctrine as an alternative to idealism around the mind.

Their thesis was too devastating a revolution indeed to be readily received in Western tradition. In addition to Dewey and Sapir, it prompted Russell to write two reviews (1923, 1926), which in turn prompted Skinner to decide to major in psychology, as witnessed by Skinner (1976). However, it was not original but originating in modernism and even romanticism since the 19th century. The Roman Catholic Church had rigidly enforced the Oath Against Modernism during the period 1910-1967.

title: User:KYPark/DIKW


text:
Tongue Twisters

Tongue Twisters written by Igor Status (The Netherlands) To get the full effect of a tongue twister you should try to repeat it several times, as quickly as possible, without stumbling or mispronouncing.

Asia providers provide casual clothes worldwide.

Rose has sewn a bloody beautiful blue blouse with black and red roses.

Clammy clams clamber along a can camber to get to the clabber.

Languorous regulators angrily and regularly regulated regulators.

He thinks his intense thoughts should bring to the brilliant results. He says what he thinks, but he does not think what he says.

If you charge non-rechargeable batteries, you’d better mind a flutter; do it not floppy but properly without cutter - a result does not matter.

In a sense, the consequence of the consentient pretense gives sense in talking nonsense when fencing the constituency to mend your fences before the elections.

Jack from Jacksonville has a knack to make cracklings.

Once lived eleven lively elves in a little littoral village.

Several external extensive territories are terribly and extraordinarily extended.

The instructor used an extractor to extract some extraction for insects.

The pirates` private property was probably promptly and properly roped with a rope and put on board by Bob and Rob.

When toting a tote, do not totter so that the tote bought would be brought.

Which of these benevolent pet animals does benefit: black-beetle, rat, bat or elephant?

Mr. Write is in a desperate plight, trying to write right. He is right that he has no fright to write not right enough. He is inclined to keep fighting for right writing.

William was willing to make his will in favour of Willy, Winnie and Will.

title: Tongue Twisters


text:
Computer Essentials/Top PC, Term 3, 2011

CPU - Intel Xeon X5670 (14,336 CPUs) Memory - 262 TB Power supply - Unknown, but it sucks up 4.04 MW Case - 112 separate cases, 12 storage cabinets, 6 comm. cabinets, 8 I/O cabinets HDD - Unknown, Totalling 2 PB Video card - NVIDIA Tesla M2050 (7,168 GPUs) Network - Proprietary, running at 160 Gbps Total price - 88 million USD (bare price) + 20 million USD/year for electrical/maintenance


text:
User talk:Igor Status

 Hello Igor Status, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:48, 10 June 2011 (UTC)

title: User talk:Igor Status


text:
User talk:Shikhardua

 Hello Shikhardua, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:49, 10 June 2011 (UTC)

title: User talk:Shikhardua


text:
User talk:Vickismith

 Hello Vickismith, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:49, 10 June 2011 (UTC)

title: User talk:Vickismith


text:
User talk:Xlnt~enwikiversity

 Hello Xlnt, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:50, 10 June 2011 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Xlnt. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Xlnt~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:12, 18 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:25, 19 April 2015 (UTC)

title: User talk:Xlnt~enwikiversity


text:
User talk:MNrykein

 Hello MNrykein, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:51, 10 June 2011 (UTC)

title: User talk:MNrykein


text:
User talk:TopHats

 Hello TopHats, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Gaidheal1 20:51, 10 June 2011 (UTC)

title: User talk:TopHats


text:
Wikiversity:Wikiversity Day/2011

Plans for this Wikiversity Day (15.8.2011) are: Happy Birthday
 * review past Wikiversity Days
 * (develop outreach) review of Colloquium

title: Wikiversity:Wikiversity Day/2011


text: Category:Wikiversity Day 2011

title: Category:Wikiversity Day 2011


title: Category:2011


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg1

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 1: Tue, 25 Aug 09

[[media: Egm6321.f09.mtg1.djvu | Page 1-1]]
1-1 defined as (Meeting Number) - (Slide Number) German Transrapid Emsland 500 km/h, youtube, Uploaded by TransrapidSupporter on Feb 14, 2007 Vu-Quoc & Olson (1989) CMAME The magnet (i.e vehicle) and structure (i.e. guideway) interaction is shown below. Where: $$ y^1(t)= \ $$ nominal motion $$ u^1(s,t)= \ $$ axial displacement of guideway $$ u^2(s,t)= \ $$ transversal displacement of guideway

[[media: Egm6321.f09.mtg1.djvu | Page 1-2]]
$$ f(y^1(t),t) \ $$ Total time derivative of f is given as: Where $$ \dot y^1(t)=\frac{d}{dt}y^1(t) \ $$ $$ \frac{d}{dt}f=f_{,s}(y^1,t) \dot y^1+f_{,t}(y^1,t) $$ Where $$ \dot y^'= \dot y^2 $$ Coriolis forces - Dynamics

Material time derivative - Continuum Mechanics

Reynolds transport theorem - Continuum Mechanics is an example of a nonlinear ordinary differential equation (ODE)


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg5

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 5: Thur, 03 Sept 09

[[media: Egm6321.f09.mtg5.djvu | Page 5-1]]
Note: [[media: Egm6321.f09.mtg4.djvu | Eq.(2)p.4-2 ]] and [[media: Egm6321.f09.mtg4.djvu | Eq.(4)p.4-2 ]] $$ y'(x)=p(x) \ $$ Integrate from a to x: $$ \int_{s=a}^{s=x} y'(s)\, ds = \int_{s=a}^{s=x} p(s)\, ds $$ $$ \left [ y(s) \right ]_{s=a}^{s=x} = y(x)-y(a) $$, where $$ y(a) = constant \ $$, $$ y(x)=\int_{s=a}^{s=x} p(s)\, ds +y(a)= \int_{}^{x} p(s)\, ds = \int_{}^{} p(x)\, dx+k $$ another way: $$ y(x)=\int_{}^{} p(x)\, dx +k $$ Where $$ \int_{}^{} p(x)\, dx = F(x) $$ and $$ k=constant \  $$ $$ \Rightarrow \ y(a)=F(a)+k \ $$ $$ \Rightarrow \ k=y(a)-F(a) \ $$ $$ \Rightarrow \ y(x)=F(x)-F(a)+y(a) \ $$

[[media: Egm6321.f09.mtg5.djvu | Page 5-2]]
But $$ F(x)-F(a)=\int_{s=a}^{s=x} p(s)\, ds \ $$ [[media: Egm6321.f09.mtg4.djvu | Eq.(3)p.4-2 ]]: Why this form of nonlinear 1st order ODE? Most general form:

Application:

Where $$ x^2y^5+6(y')^2 \ $$ is defined as $$ F(x,y,y') \ $$ HW: Show that $$ F(x,y,y')=0 \ $$ in Eq(3) is a nonlinear 1st order ODE. Hint: Define the differential operator $$ D(.) \ $$ associated with Eq(3).

[[media: Egm6321.f09.mtg5.djvu | Page 5-3]]
Form for exact nonlinear 1st order ODE: $$ F(x,y,y')=0 \ $$ is exact if $$ \exists \ $$ a function $$ \phi\ (x,y) $$ such that

where:

$$ \exists \ $$ is defined as "there exists"

$$ \phi\ _x = M(x,y) $$

$$ \phi\ _y = N(x,y) $$

Multiply Eq1) thru by $$ dx \ $$ to get:

[[media: Egm6321.f09.mtg4.djvu | Eq.(3)p.4-2 ]] : $$ M(x,y)dx + N(x,y)dy=0 \ $$

NOTE: If $$ F(X,y,y')=0 \ $$ does not have the form:

Then $$ F(.) \ $$ cannot be exact.

Application: [[media: Egm6321.f09.mtg5.djvu | Eq.(3)p.5-2 ]] is not exact because of the nonlinear term $$ (y')^2 \ $$

[[media: Egm6321.f09.mtg5.djvu | Page 5-4]]
Exactness test (continued)

p5-3 Eq(1):

$$ M(x,y)= \phi\ _x(x,y) \ $$

$$ N(x,y)= \phi\ _y(x,y) \ $$

Since $$ \phi\ _{xy} = \phi\ _{yx} \ $$

and $$ \phi\ _{xy} = \frac{\partial ^2 \phi\ }{\partial x \partial y} \ $$

and $$ \phi\ _{yx} = \frac{\partial ^2 \phi\ }{\partial y \partial x} \ $$

and $$ \frac{\partial ^2 \phi\ }{{\partial x} {\partial y} } = (\phi\ _{x})_y \ $$

and $$ \frac{\partial ^2 \phi\ }{{\partial y} {\partial x} } = (\phi\ _{y})_x \ $$

Application: [[media: Egm6321.f09.mtg4.djvu | Eq.(1)p.4-3 ]] Not Exact

$$ M(x,y)=2x^2 + \sqrt{y} \Rightarrow \ M_y= \frac{1}{2 \sqrt{y}} \ $$

$$ N(x,y)=x^5y^3 \Rightarrow \ N_x= 5x^4y^3 \ $$

$$ M_y \ne \ N_x \ $$


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg9

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 9: Thur, 10Sept09

[[media: Egm6321.f09.mtg9.djvu | Page 9-1]]
Note: Symbol notations: $$ \Delta\ $$ defined as equal by definition Non-symmetric notation $$ := $$ means equal by definition as well, better notation than $$ \Delta\ $$ Goal: Derive mathematical structure of a class of exact N1_ODEs Exact L1_ODE_VC: Application: Just invent any $$ a(x),b(x) \ $$ Let $$ a(x)=x^4 \ $$ $$ b(x)=x \Rightarrow \ \bar b \ (x)=\frac{1}{2}x^2 \ $$ $$ k=10 \ $$

[[media: Egm6321.f09.mtg9.djvu | Page 9-2]]
HW: Show that Eq(3) L1_ODE_VC is "exact". See Note [[media: Egm6321.f09.mtg10.djvu | P.10-1 ]] Question: How about N1_ODEs? Eq.(2)P.6-4 N1 means Nonlinear, 1st Order Where $$ \int_{}^{x} b(s) = \bar b \ (x) \ $$ [[media: Egm6321.f09.mtg6.djvu | Eq.(2) P.6-4]]: $$ \frac{1}{N}(N_x-M_y)=\frac{1}{ \bar b \ (x) c(y)} \left [ b(x)c(y)-a(x)c(y) \right ]=-f(x) \ $$

[[media: Egm6321.f09.mtg9.djvu | Page 9-3]]
[[media: Egm6321.f09.mtg9.djvu | Eq.(4) P.9-2 ]] $$ M(x,y)=a(x)\int_{}^{y} c(s) \ $$ Where $$ \int_{}^{y} c(s)= \bar c \ (y) \ $$ From [[media: Egm6321.f09.mtg9.djvu | Eq.(6) P.9-3 ]], [[media: Egm6321.f09.mtg9.djvu  | Eq.(4) P.9-2 ]] and [[media: Egm6321.f09.mtg4.djvu  | Eq.(3) P.4-2 ]] obtain: Application: Consider the following $$ a(x)=5x^3+2 \ $$ $$ b(x)=x^2 \Rightarrow \ \bar b \ (x)=\frac{1}{3}x^3 \ $$ $$ c(y)=y^4 \Rightarrow \ \bar c \ (y)=\frac{1}{5}y^5 \ $$ HW: Show Eq(8) is "exact" N1_ODE. Note [[media: Egm6321.f09.mtg10.djvu | P.10-1 ]]

[[media: Egm6321.f09.mtg9.djvu | Page 9-4]]
L2_ODE_VC with missing dependant variable $$ P(x)y''+Q(x)y'+R(x)y=S(x) \ $$ Where $$ R(x) \rightarrow \ 0 \ $$ due to missing dependant variable y. [[media: Egm6321.f09.mtg2.djvu | Eq.(1)P.2-3]] $$ p:=y' \rightarrow \ P(x)p'+Q(x)p=S(x) \ $$ is a L1_ODE_VC Solution: [[media: Egm6321.f09.mtg8.djvu | Eq.(4)P.8-2]] Exact N2_ODEs: General N2_ODEs: $$ F(x,y,y',y'')=0 \ $$ Application: $$ (x^3+2x^5y^2)y''+(x^{\frac{3}{2}}+10) \sqrt{y} y'+y^{100}=0 \ $$ $$ F=0 \ $$ is exact means $$ \exists \phi\ (x,y,y') \ $$ such that $$ F(x,y,y',y'')=\frac{d}{dx} \phi\ (x,y,y') \ $$


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg13

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 13: Tues, 22Sept09

[[media: Egm6321.f09.mtg13.djvu | Page 13-1]]
Euler integrating factor method [[media: Egm6321.f09.mtg12.djvu | Eq.(1) P.12-3 ]] Where: $$ (x^wy^n)=h(x,y) \ $$ HW: Find (m,n) such that Eq(1) is exact. Result: A first integration is: Where $$ p=y' \ $$ and $$ k_1 \ $$ and $$ k_2 \ $$ are constants HW: Solve Eq(2) for $$ y(x) \ $$ HINT: L1_ODE_VC (integrating factor) A class of exact L2_ODE_VC (how to invent more exact L2_ODE_VC) HW: Find mathematical structure of $$ \phi\ \ $$ that yields the above class

[[media: Egm6321.f09.mtg13.djvu | Page 13-2]]
$$ F=\frac{d \phi\ }{dx}= \phi\ _x(x,y,p)+ \phi\ _yp+ \phi\ _pp'=P(x)y''+Q(x)y'+R(x)y \ $$ Where $$ p=y' \ $$ and $$ p'=y'' \ $$ and $$ P(x)= \phi\ _p \ $$ and $$ Q(x)= \phi\ _y \ $$ and $$ R(x)y= \phi\ _x \ $$ Answer: [[media: Egm6321.f09.mtg13.djvu | Eq.(2) P.13-1 ]] : $$ P(x)=x \ $$ and $$ T(x)=2x^{\frac{3}{2}}-1 \ $$ and $$ k=k_1 \ $$ Exact Nn_ODE's, where N means nonlinear and n means nth order Where $$y^{(0)}=y \ $$ and $$y^{(1)}=y' \ $$ and $$y^{(n)}= \frac{d^ny}{dx^n} \ $$

[[media: Egm6321.f09.mtg13.djvu | Page 13-3]]
Condition 1 for exactness: Where $$ \phi\ _x+ \phi\ _{y(0)}y^{(1)}+...+ \phi\ _{y(n-1)}y^{(n)} \ $$ is related term by term to $$ x,y^{(0)},...,y^{n-1} \ $$ Condition 2 of exactness: $$ f_i:= \frac{\partial F}{\partial y^{(i)}} \ $$, where $$ i=1,...,n \ $$ HW: Case $$ n=1 \ $$ (N1_ODE) $$ F(x,y,y')=0=\frac{d}{dx} \phi\ (x,y) \ $$ $$ f_0-\frac{df_1}{dx}=0 \Leftrightarrow \phi\ _{xy}= \phi\ _{yx} \ $$ HINT: $$ f_1= \phi\ _y \ $$

[[media: Egm6321.f09.mtg13.djvu | Page 13-4]]
Case $$ n=2 \ $$ (N2_ODE) $$ f(x,y,y',y'')=0=\frac{d \phi\ }{dx}(x,y,y') \ $$ $$ f_0-\frac{df_1}{dx}+\frac{d^2f_2}{dx^2}=0 \ $$


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg15

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 15: Thur, 24Sept09

[[media: Egm6321.f09.mtg15.djvu | Page 15-1]]
[[media: Egm6321.f09.mtg14.djvu | Ex.1 P.14-4 ]] : $$ N_J(x)= \ $$ finite element basis function associated with node J = "hat" function. $$ N_J \in C^0 \ $$, but $$ N_J \notin C^1 \ $$ [[media: Egm6321.f09.mtg14.djvu | Ex.1 P.14-4 ]]: Cubic Spline (Bexler, cubic Hermitian)

[[media: Egm6321.f09.mtg15.djvu | Page 15-2]]
Cubic $$ \Rightarrow \ \ $$ 4 Coefficients $$ \Rightarrow \ \ $$ 4 degrees of freedom per element $$ \Rightarrow \ \ $$ 2 degrees of freedom per node (each element has 2 nodes) HW: $$ N_J^{ \alpha\ }(x) \in C^1 \ $$, but $$ N_J^{ \alpha\ } \notin C^2 \ $$, for $$ \alpha\ =1,2 \ $$

[[media: Egm6321.f09.mtg15.djvu | Page 15-3]]
$$ L_2(y_H^{ \alpha\ })=0 \ $$, $$ \alpha\ =1,2 \ $$ $$ L_2(y_P)=f(x) \ $$ $$ y=Ay_H^1+By_H^2+y_P \ $$, where A and B are constants Where this can be rewritten for x as: $$ x=Ax_H^1+Bx_H^2+x_P \ $$, where A and B are constants $$ L_2(y)=f \Leftrightarrow y=L_2(f) \ $$

[[media: Egm6321.f09.mtg15.djvu | Page 15-4]]
Euler Equations: Special Homogeneous Ln_ODE_VC $$ a_nx^ny^{(n)})+a_{n-1}x^{n-1}y^{n-1}+...+a_1xy'+a_0y=0 \Leftrightarrow \sum_{i=0}^n a_ix^iy^{(i)}=0 \ $$ Where $$ y'=y^{(1)} \ $$ and $$ y=y^{(0)} \ $$ Two methods of solution: Method 1: Transfer of variables $$ x=e^t \ $$ Method 2: Method of undetermined coefficients $$ y=x^r \ $$ (Or Trial Solution) [[media: http://books.google.com/books?id=9Cg3HWCnCjAC&printsec=frontcover&dq=differential+equations+billingham&ei=pGR4SpPVLojSMpb07Qw#v=onepage&q=&f=false | K.etal(2003) ]]


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg17

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 17: Thur, 10Oct09

[[media: Egm6321.f09.mtg17.djvu | Page 17-1]]
Linearity $$ \Rightarrow \ \ $$ superposition $$ y=y_H+y_P \ $$ Homogeneous Solution $$ y_H \ $$ - Euler Equations - Trial solution (undefined coefficient) - Reduction of order method 2: Undetermined factor Homogeneous L2_ODE_VC: cf. [[media: Egm6321.f09.mtg3.djvu | Eq.(1) P.3-1 ]] Where $$ a_0(x) \ $$ can be substituted for $$ a_1(x) \ $$ or $$ a_0y \ $$ in Eq(1) Given one homogeneous solution $$ u_1(x) \ $$ known Find second homogeneous solution $$ u_2(x) \ $$ such that Where$$ k_1,k_2 \ $$ are constants Assume full homogeneous solution Where$$ U(x) \ $$ is an unknown to be determined Where$$ u_1(x) \ $$ is known

[[media: Egm6321.f09.mtg17.djvu | Page 17-2]]
"Full" = includes $$ u_2(x) \ $$ Add the following: $$ a_0(x) \left [ y=Uu_1 \right ] \ $$ and $$ a_1(x) \left [ y'=Uu_1'+U'u_1 \right ] $$ and $$ \left [ y=Uu_1+2U'u_1'+U''u_1 \right ] $$ To get $$ a_0y+a_1y'+y=U \left [ a_0u_1+a_1u_1'+u_1 \right ] + U'\left [ a_1u_1+2u_1' \right ]+U''u_1=0 \ $$ by Eq(1) p17-1 Reduce to $$ u_1''+a_1u_1'+a_0u_1=0 \ $$ Since $$ u_1 \ $$ is a homogeneous solution $$ \Rightarrow \ 0=U'(a_1u_1+2u_1')+U''u_1 \ $$, NOTE missing dependent variable U in front of $$ U' \ $$ term Let $$ Z:=U' \Rightarrow \ \ $$ homogeneous L1_ODE_VC for Z

[[media: Egm6321.f09.mtg17.djvu | Page 17-3]]
Solve for Z, - integration factorial method (HW) - Direct integration (because Eq(1) is homogeneous) $$ \Rightarrow \ \frac{Z'}{Z}+(a_1+\frac{2u_1'}{u_1})=0 \ $$ Where $$ a_1, \frac{2u_1'}{u_1} \ $$ are known Integrate $$ \log \left | Z \right \vert +2 \log \left | u_1 \right \vert+ \int_{}^{x} a_1(s)\, ds=k $$, where k is a constant where $$ c=e^k \ $$ $$ \Rightarrow \ U(x)=\int_{}^{x} \frac{c}{(u_1(t))^2}e^ \, dt+\tilde{c} \ $$ where $$ \bar a \ _1(t)=\int_{}^{t} a_1(s)\, ds \ $$

[[media: Egm6321.f09.mtg17.djvu | Page 17-4]]
Homogeneous solution where $$ \tilde{c}=k_1 \ $$ and $$ c=k_2 \ $$ HW: obtain [[media: Egm6321.f09.mtg17.djvu | Eq.(2) P.17-3 ]] $$ Z(x) \ $$ using the integrating factor method


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg19

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 19: Tues, 5Oct09

[[media: Egm6321.f09.mtg19.djvu | Page 19-1]]
HW: Legendre differential [[media: Egm6321.f09.mtg14.djvu | Eq.(1) P.14-2 ]] with $$ n=0 \ $$, such that homogeneous solution $$ u_1(x)=1 \ $$. Use reduction of order method 2 (undetermined factor) to find $$ u_2(x) \ $$, second homgenous solution HW: [[media: http://books.google.com/books?id=9Cg3HWCnCjAC&printsec=frontcover&dq=differential+equations+billingham&ei=pGR4SpPVLojSMpb07Qw#v=onepage&q=&f=false | K. p28, pb. 1.1.b. ]] Variation of parameters (continued)  P.18-4

Use expression for $$ y' \ $$  Eq.(2) P.18-4  and $$ y'' \ $$   Eq.(3) P.18-4  in non-homogeneous L2_ODE_VC [[media: Egm6321.f09.mtg3.djvu  | Eq.(1) P.3-1 ]]

Where $$ u_1''+a_1u_1'+a_0u_1 \Rightarrow 0 \ $$, because $$ u_1 \ $$ is a homogeneous solution Where $$ u_2''+a_1u_2'+a_0u_2 \Rightarrow 0 \ $$, because $$ u_2 \ $$ is a homogeneous solution

[[media: Egm6321.f09.mtg19.djvu | Page 19-2]]
2 equations Eq.(1) P.18-4  and  Eq.(1) P.19-1  for two unknowns $$ \begin{Bmatrix} c_1' \\ c_2' \end{Bmatrix} \ $$ In matrix form: $$ \begin{bmatrix} u_1 & u_2 \\ u_1' & u_2' \end{bmatrix}  \begin{Bmatrix} c_1' \\ c_2'\end{Bmatrix} = \begin{Bmatrix} 0 \\ f \end{Bmatrix} \ $$ Where $$ \begin{bmatrix} u_1 & u_2 \\ u_1' & u_2' \end{bmatrix} \ $$ is the Wronskian matrix designated as $$ \underline{W} \ $$ The Wronskian, W, is the determinant of $$ \underline{W} \ $$ $$ W= det \underline{W} \ $$ If $$ W \ne \ 0 \ $$, then $$ \underline{W}^{-1} \ $$ exists and $$ \begin{Bmatrix} c_1' \\ c_2'\end{Bmatrix} =  \underline{W} ^{-1}  \begin{Bmatrix} 0 \\ f \end{Bmatrix} \ $$ Theorem: $$\forall \!\,$$ $$ u_1, u_2 \ $$ (function of x) are linearly independant if $$ \underline{W} \ne \ 0  \ $$, where $$ 0= \ $$ zero function.

[[media: Egm6321.f09.mtg19.djvu | Page 19-3]]
Where $$ \begin{Bmatrix} -u_2f \\ u_1f \end{Bmatrix} \ $$ are known Where $$ \int_{}^{x} \frac{u_2(s)f(s)}{W_s}\, ds = d_1(x) \ $$ Where $$ \int_{}^{x} \frac{u_1(s)f(s)}{W_s}\, ds= d_2(x) \ $$


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg21

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 21: Thurs, 8Oct09

[[media: Egm6321.f09.mtg21.djvu | Page 21-1]]
P.20-4 (continued) $$ \Rightarrow ax^{-1} \ $$ is a homgenous solution $$ \forall \!\, a\ $$ $$ u_1(x)=c_1x^{-1} \ $$ 2) $$ b=2 \Rightarrow ax^2 \ $$ is another homogeneous solution since $$ b^2-b-2=0 \ $$ $$ u_2(x)=c_2x^2 \ $$ (Verify $$ u_1 \ $$ and $$ u_2 \ $$ are linearly independant components of $$ W \ $$ 3) $$ b=6, a=\frac{1}{4} \Rightarrow \ $$ left hand side of Eq(1) p20-4 $$ =7x^4 \ $$, where $$ =7x^4 \ $$  is the 1st term on the right hand side for $$ b=6, a=\frac{1}{4} \Rightarrow  \frac{1}{4}x^6 \ $$  4) $$ b=5, a=\frac{1}{6} \Rightarrow \ $$ left hand side of Eq(1) p20-4  $$ =3x^3 \ $$ , where $$ =3x^3 \ $$  is the 2nd term on the right hand side for $$ b=5, a=\frac{1}{6} \Rightarrow \frac{1}{6}x^5 \ $$

[[media: Egm6321.f09.mtg21.djvu | Page 21-2]]
Llinearity of ordinary differential equation $$ \Rightarrow \ $$ superposition $$ y_P(x)=\frac{1}{4}x^6+\frac{1}{6}x^5 \ $$ $$ y(x)=c_1x^{-1}+c_2x^2+y_P(x) \ $$, where  $$  c_1x^{-1}+c_2x^2=y_H(x) \ $$ Alternative method to obtain full solution for non-homogeneous L2_ODE_VC knowing only one homogeneous solution (e.g. obtained by trial solution) (bypassing reduction of order method2-undertermined factor for $$ u_2 \ $$ and variation of parameter method) [[media: Egm6321.f09.mtg3.djvu | Eq.(1) P.3-1 ]] =    $$ y''+a_1(x)y'+a_0(x)y=f(x) \ $$ Assume having found $$ u_1(x) \ $$, a homogeneous solution: $$ u_1''+a_1(x)u_1'+a_0(x)u_1=0 \ $$ Consider: $$ y(x)=U(x)u_1(x) \ $$, where $$ U(x) \ $$ is an undetermined factor

[[media: Egm6321.f09.mtg21.djvu | Page 21-3]]
Follow the same argument as on [[media: Egm6321.f09.mtg17.djvu | P.17-2 ]] to obtain: NOTE: this equation is missing the dependant variable $$ U \ $$ in front of $$ U' \ $$ term due to reduction of order method $$ \phi\ \ $$ where $$ u_1(x) \ $$ and $$ \left [ a_1(x)u_1(x)+2u_1'(x) \right ] \ $$ are known Non-homogeneous L1_ODE_VC solution for $$ Z(x) \ $$ : [[media: Egm6321.f09.mtg8.djvu |  Eq.(4) P.8-2 ]] ref: [[media: http://books.google.com/books?id=9Cg3HWCnCjAC&printsec=frontcover&dq=differential+equations+billingham&ei=pGR4SpPVLojSMpb07Qw#v=onepage&q=&f=false | K p.28, problem 1.1ab ]] a) $$ u_1(x)=e^x \ $$, $$ (x-1)y''-xy'+y=0 \ $$ Trial solution $$ y(x)=e^{rx} \ $$ , where $$ r= \ $$ constant

[[media: Egm6321.f09.mtg21.djvu | Page 21-4]]
Find $$ r_1,r_2 \ $$ How many valid homogeneous solutions to $$ u_1=e^{r_1x} \ $$, find $$ u_2 \ $$ using undetermined factor method


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg25

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
[tp://upload.wikimedia.org/wikiversity/en/e/e5/Egm6321.f09.mtg25.djvu Mtg 25:] Tues, 20Oct09

[[media: Egm6321.f09.mtg25.djvu | Page 25-2]]
Generate non-exact L2_ODE_VC that can be made exact by intergral factor method: $$ x^a \left [ x^{2-a}y''+x^{1-a}(2+x^3)y'+4x^{3-a}y \right ]=0 \ $$ Where $$ x^a \ $$ is the integrating factor $$ h(x,y)=x^my^n\ $$ and $$ \left [ x^{2-a}y''+x^{1-a}(2+x^3)y'+4x^{3-a}y \right ]=0 \ $$ is L2_ODE_VC, not necessarily exact "$$ a \ $$" can be any number, $$ a=1, \frac{3}{2},5... \ $$


text:
User:EGM6321.F10.TEAM1.WILKS/EGM6321.F10.TEAM1.WILKS/Mtg31

=EGM6321 - Principles of Engineering Analysis 1, Fall 2009= Mtg 31: Tues, 3Nov09

[[media: Egm6321.f09.mtg31.djvu | Page 31-1]]
HW: Circular cylindrical coordinates

$$ x=r \cos \theta\ = \xi\ _1 \cos \xi\ _2 \ $$

$$ y=r \sin \theta\ = \xi\ _1 \sin \xi\ _2 \ $$

$$ z= \xi\ _3 \ $$

1) Find $$ \left \{ dx_i \right \} = \left \{ dx_1, dx_2, dx_3 \right \} \ $$ in terms of $$ \left \{ \xi\ _j \right \} = \left \{ \xi\ _1, \xi\ _2, \xi\ _3 \right \}  \ $$ and $$ \left \{ d \xi\ _k \right \}  \ $$

2) Find $$ ds^2 = \sum_{i} (dx_i)^2 = \sum_{k} (h_k)^2(d \xi\ _k)^2 \ $$. Identify $$ \left \{ h_i \right \} \ $$ in terms of $$ \left \{ \xi\ _j \right \}  \ $$

3) Find Laplacian in this curviture coordinate

Note: Prelude to Bessel functions; Bessel Differential Equation

HW: Spherical coordinates. Repeat 1), 2) and 3) above steps. See [[media: Egm6321.f09.mtg29.djvu |  P.29-3 ]], use astronautical convention

[[media: Egm6321.f09.mtg31.djvu | Page 31-2]]
Conventions:

Astronomy: $$ \left ( r, \varphi, \theta\ \right ) \ $$ [[media: Egm6321.f09.mtg29.djvu  |  P.29-3 ]]

Math/Physics: $$ \left ( r, \varphi, \bar \theta\ \right ) \ $$, where $$ \bar \theta\ = \frac{ \pi\ }{2} - \theta\ \ $$, [[media: http://books.google.com/books?id=9Cg3HWCnCjAC&printsec=frontcover&dq=differential+equations+billingham&ei=pGR4SpPVLojSMpb07Qw#v=onepage&q=&f=false  | K p39 ]]

HW: Find Laplacian in Math/Physics convention. $$ \left ( r, \varphi, \bar \theta\ \right ) \ $$

Continued from [[media: Egm6321.f09.mtg30.djvu |  P.30-4]] : Heat problem in sphere

From [[media: Egm6321.f09.mtg30.djvu | Eq.(2) P.30-4]] and [[media: Egm6321.f09.mtg30.djvu  | Eq.(5) P.30-2]] :

Where:

and

HW: Solve Eq(1) (quadratic equation)

[[media: Egm6321.f09.mtg30.djvu | Eq.(3) P.30-2]] : $$ R(r)=A_nr^n+B_nr^{-(n+1)}  \ $$

One of two homogeneous solutions of Legendre differential equations, [[media: Egm6321.f09.mtg30.djvu | Eq.(1) P.30-4]] is the Legendre ppolynomial $$ P_n( \mu\ ) \ $$. How...given later

[[media: Egm6321.f09.mtg31.djvu | Page 31-3]]
HW: show that Eq(6) = Eq(7)

$$ \left [ \frac{n}{2} \right ] = \ $$ integer part of  $$ \frac{n}{2} \ $$

HW: Verify that Eq(1) thru Eq(5) can be written as Eq(6) or Eq(7)


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg33

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 33: Thurs, 5Nov09

[[media: Egm6321.f09.mtg33.djvu | Page 33-1]]
Where: $$ \sin \theta\ = \mu\ \ $$ and $$ d \theta\ \ $$ becomes $$ d \mu\ \ $$ Similarly for $$ \left \langle P_n, P_m \right \rangle $$ Orthogonality of Legendre polynomial Where $$ \delta\ _{mn} = \ $$ kronecker delta

[[media: Egm6321.f09.mtg33.djvu | Page 33-2]]
$$ \Rightarrow \ \underline{ \Gamma\ } (F) \ $$ is diagonal with diagonal coefficient: F is complete, i.e. any continuous function, f, can be expressed as an infinite series of function in F:     Eq(4) is an equality due to the completeness of F p29-5: $$ f( \theta\ )= T_0 \cos ^4 \theta\ = T_0(1- \mu\ ^2)^2\sum_{u=0}^\infty A_nP_n( \mu\ ) \ $$ Where $$ \mu\ = \sin |theta\ \ $$ Where n=0,1,2...n

[[media: Egm6321.f09.mtg33.djvu | Page 33-3]]
HW: $$ f= \sum_{i} g_i \ $$ Show that if $$ \left \{ g_i \right \} \ $$ is odd, then f is odd Show that if $$ \left \{ g_i \right \} \ $$ is even, then f is even HW: Show that $$ P_{2k} \ $$ is even for k=0,1,2... and $$ P_{2k+1} \ $$ is odd [[media: Egm6321.f09.mtg33.djvu | Eq.(5) P.33-2]] $$ A_n=\frac{ \left \langle f, P_n \right \rangle }{ \left \langle P_n, P_n \right \rangle } \ $$, f even $$ \Rightarrow \ A_n=0 \ $$ for  $$  n=2k+1 \ $$, since $$  P_{2k+1}(x) \ $$ is odd $$ A_1=A_3=A_5=...=0 \ $$ It turns out that $$ A_n=0 \ $$ for all $$ n \ge 5 \ $$ due to linear independance of $$ F= \left \{ P_n \right \} \ $$ and the orthogonality of $$ F \ $$

[[media: Egm6321.f09.mtg33.djvu | Page 33-4]]
Linear independance of $$ F \ $$ $$ P_n(x) \ $$ is a polynomial of order n $$ P_n \in \Rho\ _n  \ $$ set of all polynomials of degree (order)  $$ \le \ n \ $$ HW: $$ q \in \Rho\ _4 \ $$ $$ q(x) = \sum_{i=0}^4 c_ix^i \ $$ Given $$ c_0=3, c_1=10, c_2=15, c_3=-1, c_4=5 \ $$ Find $$ \left \{ a_i \right \} \ $$ such that $$ q(x) = \sum_{i=0}^4 a_iP_i \ $$ Plot $$ q = \sum_{i} c_ix^i = \sum_{i} a_iP_i \ $$ Where $$ \sum_{i} c_ix^i = \ $$ figure 1 and $$ \sum_{i} a_iP_i= \ $$ figure 2 Othogonality of $$ F= \left \{ P_k \right \} \ $$ [[media: Egm6321.f09.mtg33.djvu | Eq.(3) P.33-1]]


text:
University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg35

EGM6321 - Principles of Engineering Analysis 1, Fall 2009
Mtg 35: Thurs, 12Nov09

[[media: Egm6321.f09.mtg35.djvu | Page 35-1]]
Gauss Legendre quadrature (numerical integration} Quadrature; QUAD-->quadrilateral-->Greek: measuring areas Area $$ = \sum $$ Quadrilaterals Cubature; CUBE; Volume $$ = \sum  $$ cubes $$ I(f):=\int_{-1}^{1} f(x)\, dx \ $$ $$ I_n(f):=\sum_{j=1}^n w_jf(x_j)\, dx \ $$ with $$ \left \{ x_j \right \} \ $$ the roots for $$ P_n(x)=0 \ $$, where n is the degree of $$ P_n(x) \ $$ and $$ w_j \ $$ being the weight $$ -1[[media: Egm6321.f09.mtg35.djvu | Page 35-2]]
where j=1,2,...,n for $$ \eta\ \in \left [ -1,+1 \right ] \ $$ Ex: $$ n=2 \ $$ (2 point interpolation) [[media: Egm6321.f09.mtg31.djvu | Eq.(3) P.31-3]]  $$ P_2(x)=\frac{1}{2}(3x^2-1) \ $$ $$ \Rightarrow \ x_{1,2}= \pm \ \frac{1}{ \sqrt{3} } \ $$ [[media: Egm6321.f09.mtg31.djvu | Eq.(4) P.31-3]] $$ P_2'(x)=3x, P_3(x)=\frac{1}{2}(5x^3-3x) \ $$ $$ W_1=\frac{2}{(2+1)(3)(\frac{-1}{ \sqrt{3} }) \frac{1}{2} \left [ 5 (\frac{-1}{\sqrt{3}}) ^3-3(\frac{-1}{\sqrt{3}}) \right ] }=1 \ $$

[[media: Egm6321.f09.mtg35.djvu | Page 35-3]]
$$ W_2=1 \ $$ HW: verify table for Gauss Legendre quadrature in wikipedia, analytical expression of $$ \left \{ x_j \right \} \ $$ and $$ \left \{ w_j \right \}, j=1,...,n \ $$ and  $$ n=1,...,5 \ $$ (n=integration points) after verifying the expression for  $$ P_n(x) \ $$ with $$ n=1,...,6 \ $$; (see [[media: Egm6321.f09.mtg31.djvu  | HW p31-3]] ) Evaluate numerically $$ \left \{ x_j \right \} \ $$ and $$ \left \{ w_j \right \} \ $$ and compute results with Abram & Stegum (see lecture plan) Question: How does Gauss Legendre quadrature compare to other quadrature methods, e.g. trapezoidal rule? Answer: Look at $$ E_n(f) \ $$, [[media:Egm6321.f09.mtg35.djvu | Eq.(3) P.35-2]]. Consider  $$ f \in \Rho\ _{2n-1} \ $$...