text:
LaTeX/Command Glossary

This is a glossary of LaTeX commands—an alphabetical listing of LaTeX commands with the summaries of their effects. (Brackets "[]" are optional arguments and braces "{}" are required arguments.)

#

 * / : see slash marks
 * \@ : following period ends sentence
 * \\[*][extra-space] : new line
 * \, : thin space, math and text mode
 * \; : thick space, math mode
 * \: : medium space, math mode
 * \! : negative thin space, math mode
 * \- : hyphenation; tabbing
 * \= : set tab, see tabbing
 * \> : tab, see tabbing
 * \< : back tab, see tabbing
 * \+ : see tabbing
 * \' : accent or tabbing
 * \` : accent or tabbing
 * \| : double vertical lines, math mode
 * \( : start math environment
 * \) : end math environment
 * \[ : begin displaymath environment
 * \] : end displaymath environment

A

 * \addcontentsline{file}{sec_unit}{entry} : adds an entry to the specified list or table
 * \addtocontents{file}{text} : adds text (or formatting commands) directly to the file that generates the specified list or table
 * \addtocounter{counter}{value} : increments the counter
 * \address{Return address}
 * \addtolength{len-cmd}{len} : increments a length command, see Length
 * \addvspace : adds a vertical space of a specified height
 * \alph : causes the current value of a specified counter to be printed in alphabetic characters
 * \appendix : changes the way sectional units are numbered so that information after the command is considered part of the appendix
 * \arabic : causes the current value of a specified counter to be printed in Arabic numbers
 * \author : declares the author(s). See Document Structure

B

 * \backslash : prints a backslash
 * \baselineskip : a length command (see Lengths), which specifies the minimum space between the bottom of two successive lines in a paragraph
 * \baselinestretch : scales the value of \baselineskip
 * \bfseries : Boldface typeface
 * \bibitem : generates a labeled entry for the bibliography
 * \bigskipamount
 * \bigskip : equivalent to \vspace{\bigskipamount}
 * \boldmath : bold font in math mode
 * \boldsymbol : bold font for symbols

C

 * \cal : Calligraphic style in math mode
 * \caption : generate caption for figures and tables
 * \cdots : Centered dots
 * \centering : Used to center align LaTeX environments
 * \chapter : Starts a new chapter. See Document Structure.
 * \circle
 * \cite : Used to make citations from the provided bibliography
 * \cleardoublepage
 * \clearpage : Ends the current page and causes any floats to be printed. See Page Layout.
 * \cline : Adds horizontal line in a table that spans only to a range of cells. See \hline and ../Tables/ chapter.
 * \closing : Inserts a closing phrase (e.g. \closing{yours sincerely}), leaves space for a handwritten signature and inserts a signature specified by \signature{}.  Used in the Letter class.
 * \color : Specifies color of the text. ../Colors
 * \copyright : makes © sign. See Formatting.

D

 * \dashbox
 * \date
 * \ddots : Inserts a diagonal ellipsis (3 diagonal dots) in math mode
 * \documentclass[options]{style} : Used to begin a latex document
 * \dotfill
 * \dfrac

E

 * \em : Toggles italics on/off for the text inside curly braces with the command. Such as {\em This is in italics \em but this isn't \em and this is again}. This command allows nesting.
 * \emph : Toggles italics on/off for the text in curly braces following the command e.g. \emph{This is in italics \emph{but this isn't} and this is again}.
 * \ensuremath (LaTeX2e) : Treats everything inside the curly braces as if it were in a math environment. Useful when creating commands in the preamble as they will work inside or out of math environments.
 * \epigraph : Adds an epigraph. Requires epigraph package.
 * \euro : Prints euro € symbol. Requires eurosym package.

F

 * \fbox
 * \flushbottom
 * \fnsymbol
 * \footnote : Creates a footnote.
 * \footnotemark
 * \footnotesize : Sets font size. See Text Formatting.
 * \footnotetext
 * \frac : inserts a fraction in mathematics mode. The usage is \frac{numerator}{denominator}.
 * \frame
 * \framebox : Like \makebox but creates a frame around the box. See Boxes.
 * \frenchspacing : Instructs LaTex to abstain from inserting more space after a period (´.´) than is the case for an ordinary character. In order to untoggle this functionality resort to the command \nonfrenchspacing.

H

 * \hfill : Abbreviation for \hspace{\fill}.
 * \hline : adds a horizontal line in a tabular environment. See also \cline, Tables chapter.
 * \href : Add a link, or an anchor. See Hyperlinks
 * \hrulefill
 * \hspace : Produces horizontal space.
 * \huge : Sets font size. See Text Formatting.
 * \Huge : Sets font size. See Text Formatting.
 * \hyphenation{word list}: Overrides default hyphenation algorithm for specified words. See Hyphenation

I

 * \include : This command is different from \input in that it's the output that is added instead of the commands from the other files. For more see LaTex/Basics
 * \includegraphics : Inserts an image. Requires graphicx package.
 * \includeonly
 * \indent
 * \input : Used to read in LaTex files. For more see LaTex/Basics.
 * \itshape : Italicizes the text which is inside curly braces with the command. Such as {\itshape This is in italics}. \em is generally preferred since it allows nesting.
 * \item : Creates an item in a list. Used in list structures.

K

 * \kill : Prevent a line in the tabbing environment from being printed.

L

 * \label : Used to create label which can be later referenced with \ref. See Labels and Cross-referencing.
 * \large : Sets font size. See Text Formatting.
 * \Large : Sets font size. See Text Formatting.
 * \LARGE : Sets font size. See Text Formatting.
 * \LaTeX : Prints LaTeX logo. See Formatting.
 * \LaTeXe : Prints current LaTeX version logo. See Formatting.
 * \ldots : Prints sequence of three dots. See Formatting.
 * \left
 * \lefteqn
 * \line
 * \linebreak : Suggests LaTeX to break line in this place. See Paragraph Formatting.
 * \linethickness
 * \linewidth
 * \listoffigures : Inserts a list of the figures in the document. Similar to TOC
 * \listoftables : Inserts a list of the tables in the document. Similar to TOC
 * \location

M

 * \makebox : Defines a box that has a specified width, independent from its content. See Boxes.
 * \maketitle : Causes the title page to be typeset, using information provided by commands such as \title{} and \author{}.
 * \markboth \markright
 * \mathcal
 * \mathop
 * \mbox : Write a text in roman font inside a math part
 * \medskip
 * \multicolumn
 * \multiput

N

 * \newcommand : Defines a new command. See New Commands.
 * \newcolumntype : Defines a new type of column to be used with tables. See Tables.
 * \newcounter
 * \newenvironment : Defines a new environment. See New Environments.
 * \newfont
 * \newlength
 * \newline : Ends current line and starts a new one. See Paragraph Formatting.
 * \newpage : Ends current page and starts a new one. See Page Layout.
 * \newsavebox
 * \newtheorem
 * \nocite : Adds a reference to the bibliography without an inline citation. \nocite{*} causes all entries in a bibtex database to be added to the bibliography.
 * \noindent
 * \nolinebreak
 * \nonfrenchspacing : Setting the command untoggles the command \frenchspacing and activates LaTeX standards to insert more space after a period (´.´) than after an ordinary character.
 * \normalsize : Sets default font size. See Text Formatting.
 * \nopagebreak : Suggests LaTeX not to break page in this place. See Page Layout.
 * \not

O

 * \onecolumn
 * \opening : Inserts an opening phrase when using the letter class, for example \opening{Dear Sir}
 * \oval
 * \overbrace : Draws a brace over the argument. Can be used in displaystyle with superscript to label formulae. See Advanced Mathematics.
 * \overline : Draws a line over the argument.

P

 * \pagebreak : Suggests LaTeX breaking page in this place. See Page Layout.
 * \pagenumbering : Defines the type of characters used for the page numbers. Options : arabic, roman, Roman, alph, Alph, gobble (invisible).
 * \pageref : Used to reference to number of page where a previously declared \label is located. See Floats, Figures and Captions.
 * \pagestyle : See Page Layout.
 * \par : Starts a new paragraph
 * \paragraph : Starts a new paragraph. See Document Structure.
 * \parbox : Defines a box whose contents are created in paragraph mode. See Boxes.
 * \parindent : Normal paragraph indentation. See Lengths.
 * \parskip
 * \part : Starts a new part of a book. See Document Structure.
 * \protect
 * \providecommand (LaTeX2e) : See Macros.
 * \put

Q

 * \quad : Similar to space, but with the size of a capital M
 * \qquad : double \quad

R

 * \raggedbottom : Command used for top justified within other environments.
 * \raggedleft : Command used for right justified within other environments.
 * \raggedright : Command used for left justified within other environments.
 * \raisebox : Creates a box and raises its content. See LaTeX/Boxes.
 * \ref : Used to reference to number of previously declared \label. See Labels and Cross-referencing.
 * \renewcommand
 * \right
 * \rmfamily : Roman typeface.
 * \roman : Causes a counter to be printed in roman numerals.
 * \rule : Creates a line of specified width and height. See LaTeX/Rules and Struts.

S

 * \savebox : Makes a box and saves it in a named storage bin.
 * \sbox : The short form of \savebox with no optional arguments.
 * \scshape : Small caps.
 * \scriptsize : Sets font size. See Text Formatting.
 * \section : Starts a new section. See Document Structure.
 * \setcounter
 * \setlength
 * \settowidth
 * \sffamily : Sans serif.
 * \shortstack
 * \signature : In the Letter class, specifies a signature for later insertion by \closing.
 * \slshape : Slanted.
 * \slash : See slash marks
 * \small : Sets font size. See Text Formatting.
 * \smallskip
 * \sout : Strikes out text. Requires ulem package. See Text Formatting.
 * \space : force ordinary space
 * \sqrt : Creates a root (default square, but magnitude can be given as an optional parameter).
 * \stackrel : Takes two arguments and stacks the first on top of the second.
 * \stepcounter : Increase the counter.
 * \subparagraph : Starts a new subparagraph. See Document Structure.
 * \subsection : Starts a new subsection. See Document Structure.
 * \subsubsection : Starts a new sub-subsection. See Document Structure.

T

 * \tableofcontents : Inserts a table of contents (based on section headings) at the point where the command appears.
 * \telephone : In the letter class, specifies the sender's telephone number.
 * \TeX : Prints TeX logo. See Text Formatting.
 * \textbf{} : Sets bold font style. See Text Formatting.
 * \textcolor{}{} : Creates colored text. See Entering colored text.
 * \textit{} : Sets italic font style. See Text Formatting.
 * \textmd{} : Sets medium weight of a font. See Text Formatting.
 * \textnormal{} : Sets normal font. See Text Formatting.
 * \textrm{} : Sets roman font family. See Text Formatting.
 * \textsc{} : Sets font style to small caps. See Text Formatting.
 * \textsf{} : Sets sans serif font family. See Text Formatting.
 * \textsl{} : Sets slanted font style. See Text Formatting.
 * \texttt{} : Sets typewriter font family. See Text Formatting.
 * \textup{} : Sets upright shape of a font. See Text Formatting.
 * \textwidth
 * \textheight
 * \thanks
 * \thispagestyle
 * \tiny : Sets font size. See Text Formatting.
 * \title
 * \today : Writes current day. See Text Formatting.
 * \ttfamily
 * \twocolumn
 * \typeout
 * \typein

U

 * \uline : Underlines text. Requires <tt>ulem</tt> package. See Formatting.
 * \underbrace
 * \underline
 * \unitlength
 * \usebox
 * \usecounter
 * \uwave : Creates wavy underline. Requires <tt>ulem</tt> package. See Formatting.

V

 * \value
 * \vbox{text} : Encloses a paragraph's text to prevent it from running over a page break
 * \vcenter
 * \vdots : Creates vertical dots. See Mathematics.
 * \vector
 * \verb : Creates inline verbatim text. See Formatting.
 * \vfill
 * \vline
 * \vphantom
 * \vspace

title: LaTeX/Command Glossary


text:
Robotics/Computer Control/The Interface/SBC and multichip modules

SBC: Single Board Computers
Single Board Computers are a complete computer on a single printed circuit board. These usually require only a single power supply. SBCs commonly provide all standard PC I/O support like keyboard, mouse, SVGA, serial and parallel ports, ethernet, IDE, SCSI and USB. Some provide a PCMCIA connector. Late model SBCs are also replete with multiple CPU/Pentium 4/Xeon/AMD configurations.

SBC are commonly used in the industry in process control. Although they are quite expensive and hard to find (in retail), they can be a great way to control a larger robot. For small robots their power consumption would be a problem.

Stacking modular connector boards
Many robots include a "stack" of boards, typically with a processor on one board, H bridge motor driver on another board, and a wireless communication on another board.

Many people prefer to build rapid prototypes out of many single-purpose boards that can be disassembled and re-used for the next prototype, rather than making a single big specialized PCB prototype that is used once for testing and then thrown away. There are many standards for such electronic pieces.

 * PC/104
 * "PlugaPodS"
 * gumstix and gumstix packs and more gumstix packs
 * Stackable USB (USB is smaller and faster than the ISA bus used in the original PC/104)
 * Virtual Cogs uses a stacking connector. Virtual Cogs wiki.
 * ( Modular interface extension (MIX) stacking and communications interface )
 * "pass-through 40-Pin OOPic expansion connectors"
 * R-Dev-Ino is a Robotic Development Arduino compatible board, easily stackable.
 * the JeeNode Arduino-compatible board and JeeLabs modules that plug into it: a b c d
 * The Tower System
 * Bug Labs
 * Xadow
 * The Grove system:  "Cluster mode" and "Jigsaw mode"
 * Microsoft .NET Gadgeteer
 * DaisyLink interface
 * gobus ports
 * TinyDuino stacking connector
 * Wouter van Ooijen's Dwarf Boards have 10 pin shrouded header connected by IDC ribbon cable connectors (GND, +5V, and 8 GPIO pins).
 * "Stacking Arduino Shields" (compatibility between shields can be a little tricky)
 * ... (Add to me)
 * ... (Add to me)

(If I think the stacking idea is good, but my robot is too small for PC/104, do you have any tips for picking an appropriate stacking connector, and arranging which electrical signal/power goes where?)

The "stackable headers" are one way to stack boards together. What other options do we have for stacking connectors?

Multichip Module Boards

 * Is there a better name for this sort of thing? See Talk:Robotics.

Multichip Module boards are lighter versions of the SBC. These boards provide less I/O abilities than a full fledged SBC, but are considerably less expensive. For example the Acme Foxboard provides a 100Mips processor with 16MB RAM and 4MB Flash running Linux. This board has IDE, SCSI, USB, Ethernet, I2C and more on a surface of aprox. 6x7cm. It consumes about 280mA and costs around €170. While this particular board is designed for embedded internet-enabled applications, it's a great board for controlling your robot. Another alternative is to use a Linksys router and install OpenWRT on it. You can usually pick these up for around $50. If you spend some time shopping around you may find similar boards that are better or cheaper.

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


text:
Georgia Water/Best Practices/Planning/Goals

Envisioning Desired Futures
The purpose of planning is to identify a "best" set of actions to attain a more desirable future for someone(s). A public participation program may developed to identify the "someones" and to enable them and other affected parties to collaboratively define their desired future, which then becomes the target future condition (the goal) for the planning process. For example, workshops to define the desired future for the Georgia Basin in Canada, using GB-QUEST model, were organized as part of the Georgia Basin Futures Project.

Use of Goals in Planning
In a comprehensive multipurpose formulation approach, full consideration is given to all planning objectives and constraints in formulating alternative plans to achieve the multiple purposes. Formulation Approaches

Purposes

 * Flood damage reduction (+)
 * Navigation (+)
 * Ecosystem restoration (+)
 * Water quality
 * Water supply
 * Recreation
 * Hydropower generation
 * Hurricane and storm damage prevention
 * Stormwater management

(+) For a Water Resources Directory/U.S. Army Corps of Engineers' project, "a Stand alone project purpose may only consist of one of the Corps' high priority project purposes: flood damage reduction, navigation, or ecosystem restoration."


text:
User talk:Naiyenea~enwikibooks

Naiyenea, thanks for helping out with the EQ wikibook. Much appreciated! /bow --Kajolus 12:55, 6 March 2006 (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 Naiyenea. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Naiyenea~enwikibooks 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 23:31, 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) 05:17, 19 April 2015 (UTC)

title: User talk:Naiyenea~enwikibooks


text:
Talk:C Sharp Programming/Data structures

age example
with code like I get Hello World! twice followed by You become a teenager at an age of Teenager. I would have expected 13 instead of Teenager. Have I made an error in my program? Thanks. Sorry about messing up the syntax of the code block, but I can't figure it out -- take a look at the edit source. —The preceding unsigned comment was added by 70.182.153.38 (talk • contribs).

 * That's because  is an enumeration, so   returns the enumeration value's name.  To show the underlying integer (13), use this instead:
 * Rodasmith 19:13, 9 May 2007 (UTC)
 * Rodasmith 19:13, 9 May 2007 (UTC)

Errors in "person" example
There are some mistakes in definition of "person" struct and it's constructor. —the preceding unsigned comment is by 194.29.160.251 (talk • contribs) 2006-03-06 14:01:47  (UTC)
 * I have corrected the sample. Rodasmith 17:02, 7 March 2006 (UTC)
 * In order for the comparison dana.birthDate < DateTime.Now to work, does the birthDate (field?) need to be declared public? —The preceding unsigned comment was added by 70.182.153.38 (talk • contribs).
 * Yes, you're right. In fact, all the field should be public (or internal) for that sample to compile.  Rodasmith 20:05, 10 May 2007 (UTC)

Missing word
Structs are really only used for performance reasons and/or if you intend to it by value. Intend to what? Verb is missing here!


text: Talk:False Friends of the Slavist/Lower Sorbian-Upper Sorbian


text:
User talk:Soviet Dolphin~enwikibooks

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. Kellen T 15:40, 6 March 2006 (UTC)
 * Please also check out the Cookbook policy page and the Cookbook talk pages.

Cookbook naming policy & Templates
Hi, the (current) correct way to name recipes is in title case, as specified by Cookbook:Policy, including for the "(Vegan)" denotation. This might change in the future, but that should be discussed on Talk:Cookbook. Also you may wish to bring up (what i think are) your vegan/vegetarian templates on Talk:Cookbook. Kellen T 15:40, 6 March 2006 (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 Soviet Dolphin. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Soviet Dolphin~enwikibooks 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 23:43, 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) 05:31, 19 April 2015 (UTC)

title: User talk:Soviet Dolphin~enwikibooks


text:
Selling Property/Introduction

My name is Andrew Sylvia, and I am a licensed Real Estate agent in the American state of New Hampshire.

At first glance, the world of Real Estate can seem like a path to easy money, but this is definitely not the case, it takes the ability to withstand multiple and repeated failures because it takes many, many steps for someone to buy a home, and you need to make sure all of them are correct or you'll jeopardize your chances at a sale.

However, the best thing to know is that you're not alone in this, almost 2/3rds of new agents quit within the first year, as long as you have patience and a good corps of people around you, you'll succeed.

My goal with this book is to take the lessons I am currently learning as a new agent both for a reference to myself and future newly minted agents so myself and others can make it into that 1/3rd that sticks with the job and makes a large annual salary.

Please feel free to add any experience or information where it fits, just make sure that you clarify who you are, I don't want to take credit for your work.

title: Selling Property/Introduction


text:
Selling Property/Licensing

This chapter deals with everything you'll need to know to get your license, more or less, and you can't be an agent unless you have a license.

You have far more to learn after this, but in order to represent anyone other than yourself in real estate transactions, you need to be a licensed real estate agent or have power of attorney.

/United States/
These sections are geared towards what you'll need to know for the individual states.
 * Indiana
 * New Hampshire

Other books
Modern Real Estate Practice, Sixteenth Edition by Filmore W. Galaty, Wellington J. Allaway and Robert C. Kyle, ISBN 0-7931-4428-0

Principles of Real Estate Practice, 5th Edition by Stephen Mettling and David Cusic, ISBN-10: 1500569399. Principles of Real Estate Practice website

title: Selling Property/Licensing


text:
User:Funkychic

How Macbeth has changed as a character between Act 2 scene 2 and 3 - Act 5 scenes 3,4 and 5.

Macbeth is a very complex character, who has many layers. He changes a lot throughout the play;

 How he relates to his wife.  The choices he makes.

Macbeth’s thoughts and feelings are portrayed through all of these subjects, however the change that is most prominent is the relationship between Macbeth and Lady Macbeth. In Act 2, Macbeth is undecided on weather to kill Duncan, his confusion is shown in a monologue in Act 1 scene 7. Where he decides not to kill Duncan. “He’s here in double trust: First I am his Kinsman and his subject, Strong both against deed; then, as his host. This shows that Macbeth feels he should not kill Duncan because he has been kind to him the past few days. We can now tell that Macbeth is very compassionate for the people in his life and feels for them strongly. He also has high morals because he believes killing a relative is wrong and a king is even worse because God makes people Kings and if you disrupt the harmony then bad thing’s will happen to you. In Macbeth’s whole speech he shows that love is stronger than power.

However Lady Macbeth is the more ambitious and powerful character from the both of them and soon persuades him to kill Duncan. We know that Macbeth loves Lady Macbeth very much because on the success of his battle he wrote to tell her the good news. In Act 1 scene 7 Lady Macbeth uses this love to emotionally blackmail him into the murder. “From this time, such I account my love.” This is showing that Lady Macbeth is willing to do anything to get into a position of more power.

In Act 5 there position of power changes and their relationship is much weaker. Lady Macbeth has been driven mad by the guilt of Duncan’s death, even though she said, “Go get some water and wash this filthy witness from your hands.” This is showing that she believes anything can wash right of someone and that there is no need to lose sleep over this particular deed. Whereas in Act 5 she is sleepwalking and trys to get the blood of her hands. “Out damned spot! Out, I say!” This is a hallucination but it symbolises, the guilt she is experiencing and feels that Duncan should not have been killed. Overall Shakespeare is showing how she thought she was strong but it became to much to handle.

Macbeth however was contemplating over his first murder. When he realised how far the death of one person had got him, he started to kill other close friends. He did this because he was covering up for his first murder. However his next few murders were barely spared a thought and he did not confide them to Lady Macbeth. This shows how far a part they have grown and that Macbeth’s compassion has been replaced by power. To reinforce this Shakespeare has directed Lady Macbeth to die so he could show Macbeth’s reaction. Even though she is his wife he is to preoccupied with the forthcoming battle that he can barely spare her a thought. “should she have died hereafter, there would have been time for such a word.”

Overall Macbeth and Lady Macbeth have switched roles and his compassion has been replaced by power, so he no longer cares when it is time for him to grieve his wife’s death. Will anybody be mourning him when his time comes? Rebecca Smith

title: User:Funkychic


text:
User talk:Funkychic

Chapter One- A rather interesting tale

She may have been a twenty year old woman, but she still had the face of innocence. An inquisitive face that wanted to know the wisdom’s of the world, but as her deep hazel eyes reached into mine, I couldn’t help but let the light in my soul, flicker on. She had a pleasant warmth to her, like a flame in the distanced of a menacing night. As her eyes search mine, her cheeks turned a welcoming pink and she seemed to light up the room with her hope. Her smile was like the sweet smell of spring when the flowers were at there prime. Her auburn hair looked windswept and messy, showing just how much of a struggle her journey was. All to see me. I could only feel gratitude beyond all belief as her fragile hand reached into her pocket and withdrew the reason of her visit. See was beauty…..At least that’s how I hoped it would be.

Back in the real world, things were much different. Including this particular girl’s journey.

It all started when I took up the interest of finding my family tree. I always new my family had an interesting life. Many hours of my young childhood was spent by Grandma’s cosy fire, listening intensively to the stories of long forgotten family members. If anyone new history and law, it was Grandma. Unfortunately she was not with me to embark on this truly incredible adventure. As much as my heart wished she was here, I heaved on with my research, trying in my Grandmothers name, to find the most accurate information on long gone family members.

Things got plenty interesting when I stumbled along the most curious sounding person, in my family tree. Daniel Wood. My great-great-great-great-grandfather. A carpenter by day, but after working hours he had the most fascinating hobby, of invention. That was the only part of the website I understood entirely. Then it waffled on about patents and conspiracy theories.

I thought this was a good time to bring in, my very best friend (and true love) ,Tasha. A very talented law student, who had a un-canning passion for conspiracies of the past. All too perfect. Was it a coincidence.

There was a hammering knock on the flimsy front door, that wanted to break due to a hand smacking hard on it’s mud splattered face. The woman who was so furiously banging on the door, heard someone storming down the stairs. She was windswept as the man inside the house threw the door open with the greatest urgency. There before her was an unmistakably, overworked and underpaid, but gorgeous young man. His name was Michael Jaymolethue Wood. Also known as Mike. Light, wispy hair, entrancing blue eyes, cute button nose and welcoming smile. That was Mike.

There before him was a successful, independent young woman. auburn hair, tied into a lose ponytail with blonde bangs, hanging out. Deep hazel eyes and a deadly smile. She was an ornament of her sex. Freethinking and free living. The way she stood in her vintage clothes, standing gracefully on the door step. “ Come in, tea, coffee?” Asked Mike in awe. “Thank you for the offer but I’m trying to cut out coffee, I’ll have some tea with milk and no sugar though.” Replied Tasha, while striding through the front door. “Been thinking. That family tree I started, well I have a great-great-great-great grandfather who used to be an inven…” Tasha cut in. “tor, so you thought you would ask me if I could make sense of the website.” Mike busied himself with the tea, feeling slightly embarrassed. He found it incredible how Tasha could make assumption from the smallest amount of information. “Shall we go up stairs” said Tasha, while being handed the tea.

Chapter 2- The truth of the patent

Tasha cautiously walked into the study, hoping to find it clean and tidy like she liked it, however that was clearly not the case as the door handle pulled down and creaked the door open. What lay beyond there was anything but a clean and tidy working area. It was the reason she didn’t have a boyfriend. Mess! Piles of it, on the desk, on the floor, on the windowsill. She was going to have to do something about this, so she cleared an area for her tea, as she called out to Mike. “Go get a bin liner.” “What for?” Inquired Mike. “We’re going to clean this hell hole up, now go and get that bin liner.” Slowly half the day slipped between their fingers as they “chucked” and ‘kept” numerous belongings to Mike.

At 2 o’clock the study was immaculate. It had been tidied, cleaned and vacuumed, until at last it was a suitable working area for Tasha. After a quick lunch of peanut butter sandwiches, the work began. Mike flicked on the computer screen and took Tasha to the website. She started to read, it felt like hours, when eventually, Tasha started to explain the meaning of the words, splattered on the page.

“Basically, your great-great-great-great-grandfather invented the telephone, but then didn’t patent it because he didn’t have the money. So Henry Thatcher gave him a large fortune of fifty thousand pounds, to get your relative to say Henry invented it.” Shocked at the news Mike managed to splutter out a question. “How much is fifteen thousand pounds worth now?” asked mike, cautiously. “About two million pounds.” Explained Tasha. “So where is the money now?” “That’s the problem, he gave it to a friend to look after because many people wanted the money, but he never saw it again.” “Does that mean it’s gone?” Asked mike apprehensively. “ Far from it. Now, Harry Thatcher owns the money and he’s not what you’d call a nice fellow”

So the conversation carried on, they talked long into the night, about Daniel Wood and his telephone to what they would do with two million pounds.

Chapter 3- The problem with information

Information is a curious thing. You may find out a piece of interesting information but then out of the blue, want to know more. This can cause great adventures of mild peril for some people, but for Mike, it would only cause massive peril. All because of his need for more information.

For the next few days, Mike tried to continue with his normal life. However this was a lot harder when you have obtained a piece of information that tells you that your family rightfully owns millions of pounds. Whatever he did, no matter how normal he could not tame the twinge that was forever in his stomach. A twinge that needed information.

Life suddenly became a lot more difficult for Tasha as well. It may have been none of her business, but the thought that someone had a fortune that wasn’t even theirs, made her cringe. Yet no matter how much information she acquired on the problem at hand, she still felt that it was her business to put it right. After all she was a girl of action.

Chapter 4 The city really wasn’t big enough for the both of them.

He was cruel and malevolent. Whatever he did he wanted more, and as his thin nimble hands curled around his cigar he felt no guilt towards his family name. As his dark and entrancing eyes stared into the mirror he knew he would not let his guard down. As his fat cigar grazed his thin lips he felt no dread for what he was going to do.

Harry Thatcher. He was one of those people everyone knew. Even though they weren’t in movies or wrote songs. He was the kind of person who was born rich and lived the rich lifestyle. Knew the right people. If you know what I mean.

MORE TO COME Rebecca Smith

title: User talk:Funkychic


text:
Talk:Romanian/Pronunciation and alphabet

Untitled
Romanian pronunciation is very phonetic

'All pronunciation is phonetic! Is this not perhaps, rather, a reference to the "phonetic" (i.e. near-phonemic) spelling of Romanian? -- 81.158.0.123 18:30, 6 March 2006 (UTC)

a lot of foreigners find it hard to speak it, especially English speakers

Is there really any evidence that English-speakers are more likely than, say, Mandarin-speakers, Hungarian-speakers, or Arabic-speakers to find Romanian hard to speak? -- 81.158.0.123 18:26, 6 March 2006 (UTC)

No, there's not. For one thing, "English-speakers" is not the same thing as "native English-speakers" and certainly not the same thing as "native English speakers who speak Romanian non-natively". Some people are even native in both languages. In addition, I don't think this is an objective claim at all, and evidence obviously has not been provided in over two years. Removed. Tlaxcalli (talk) 04:03, 10 July 2008 (UTC)

 * ... And if it were so hard for English speakers then I'm not sure what this "Category I: Romanian" is on about (Language_Learning_Difficulty_for_English_Speakers). Perhaps a better wording would have been "it may appear hard/different, but ..." (followed by encouragement of sorts, particularly linking to the aforementioned phonetic spelling). Ceigered (talk) 10:01, 13 July 2010 (UTC)

oa
What about the diphthonge oa as in the word dumneavoastră? How to spell? --80.223.182.232 10:57, 22 October 2006 (UTC)

ău
Is this sound [@u] identical to the Received Pronunciation treatement of a long "o" in English (slope), and to a lesser extent similar to the long "o" in Australian/NZ/SA accents? This might help English speakers familiar with these sounds better approximate the sound if it is indeed identical/similar I suppose Ceigered (talk) 10:01, 13 July 2010 (UTC)


text:
Selling Property/Properties

This chapter is geared towards all the things that you'll need to know to be a real estate agent that wasn't on your licensure test. Basically getting your feet wet in the big bad world of selling property.

 * /Residential/
 * /Commercial/
 * /Industrial/
 * /Special Use/
 * /Mixed Use/

title: Selling Property/Properties


text:
User talk:205.204.242.21

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:205.204.242.21


text: User talk:201.247.27.124

title: User talk:201.247.27.124


text:
Talk:Selling Property/Properties

Miscellaneous to put in later
As a Real Estate Agent, You are an independent contractor officially, but technically you're a business onto yourself. This chapter is designed to help with with Self-Marketing, The Roles of Fellow Agents and Brokers, Brand Names versus Mom n' Pops, and probably some other things. Just don't get the impression that you need to wear one of those "open" signs as a necklace.

title: Talk:Selling Property/Properties


text:
User talk:68.106.167.248

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you.

title: User talk:68.106.167.248


text:
User talk:Whiteunggoy

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional help.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Take a look at Naming policy
 * See list of templates which can save your time
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 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page.

Good luck!--Derbeth talk 19:52, 6 March 2006 (UTC)

title: User talk:Whiteunggoy


text:
User talk:Cathyhsu

Welcome
Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You can sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * Check out our help page if you need additional help.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Take a look at Naming policy
 * See list of templates which can save your time
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page.

Good luck!--Derbeth talk 19:53, 6 March 2006 (UTC)

title: User talk:Cathyhsu


text:
User talk:Dandaya~enwikibooks

Copyright problem with Image:IslandRose.jpg
--Derbeth talk 20:04, 6 March 2006 (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 Dandaya. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Dandaya~enwikibooks 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 23:04, 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) 04:51, 19 April 2015 (UTC)

title: User talk:Dandaya~enwikibooks


text:
Selling Property/Glossary

Z
=References= Balaster and Balustrade Definition at About.com

title: Selling Property/Glossary


text:
What You Should Know About Medicines/Suppository

A suppository is a method of giving medicines into the rectum. The medicine is mixed with a fat or wax. Traditionally cocoa butter (theobroma oil) was used, but synthetic bases are more common today. The important thing is that the base should melt at temperatures above normal room temperature, but below body temperature. This gives us a narrow band between roughly 30 and 35 degrees celsius for the melting point of the base.

There are also suppositories based on gelatin. These need to be dampened before insertion, because they dissolve rather than melting.

The same technology used for suppositories applies to female pessaries, but pessaries tend to be larger. Suppositories typically come in 1g, 2g or 4g sizes, while pessaries may be 4g, 8g or 15g. The size of the suppository depends on the size of the recipient - 1g for infants, 2g for children and 4g for adults being a general rule.

The drugs used in suppositories are either chosen for their local effect - medicines for use in haemorrhoids, for example - or because this route avoids the need to swallow. Diazepam may be given rectally in cases of epilepsy because a person undergoing fits may not be able to take medicines by mouth at that time.


text:
Talk:Geometry/Chapter 2

greek lettters
shouldn't you use greek letters to name angles, like a theta, alpha, because everybody does? 08:28, 28 October 2009 (UTC)08:28, 28 October 2009 (UTC)08:28, 28 October 2009 (UTC)~

When attempting to math the given of problem 4 it failed and gave this error: Failed to parse (PNG conversion failed; check for correct installation of latex, dvips, gs, and convert): \overleftrightarrow{GH} || \overrightarrow{DK} The noted line segement GH will need to be corrected to line GH at a future time. --Kinglag 20:44, 6 March 2006 (UTC)

wtf
How do students do the exercises if they don't know the postulates/theorems of the transversals?FlashingYoshi (discuss • contribs)

title: Talk:Geometry/Chapter 2


text:
Talk:OpenGL Programming

smaller screen shots?
Would it make sense to have smaller screen shots? I'm thinking of icon-size instead of small image size. That would make the layout a lot smaller and would provide a better overview of the table of contents (which is the whole point of a table of contents :) and it would require less scrolling. --Martin Kraus (discuss • contribs) 13:07, 29 August 2011 (UTC)
 * Thanks for the suggestion. I rearranged the page with smaller screenshots and double-columns - but I didn't go as small as icon-sized :) Beuc (discuss • contribs) 20:07, 29 August 2011 (UTC)
 * That's better. Maybe you could also remove the numbers to the left of the images? -Martin Kraus (discuss • contribs) 11:27, 30 August 2011 (UTC)
 * Hmmm, I think I like it better with the digits. I did a test without - it doesn't convey the same "everything you'll want to know in N steps" feeling :) Beuc (discuss • contribs) 22:15, 30 August 2011 (UTC)

TODO / WIP illustrations
I copy these two illustrations here, so we can easily copy/paste the code when we need them on the wikibook front page.

OpenGL 2.1 - big picture missing
It seems the OpenGL 2.1 ("modern") part jumps directly to code and vertex/fragment shaders. I think a big picture (what stages does the pipeline consist of, what data is passed from what stage to what stage, etc.) is missing there. See for an example. -- NotInventedHere (discuss • contribs) 08:40, 6 December 2011 (UTC)

 * The overview that you cite is given in an appendix of the OpenGL Programming book. Thus, it is certainly not missing. Would it be a good idea to start with that overview instead of putting it into an appendix? Here are some reasons against this approach:
 * It's very difficult to understand what the stages of the pipeline are good for before you see any application of the pipeline. It's easier to start with some simple examples and later introduce the pipeline, once its main features and uses are known.
 * Many modern learners prefer to learn from tutorials that teach useful stuff instead of books that talk about abstract concepts (e.g. the OpenGL pipeline) that cannot be used for anything without a lot of other information.
 * For some learners (in particular with a strong technical background), it is very helpful to know the pipeline. Presenting the pipeline in an appendix and linking to it at appropriate places in the tutorials allows these learners to read about the pipeline at the best possible time: when they already have an idea how the pipeline fits into the rendering process and they are curious how it works exactly.
 * I understand that there are also reasons in favor of a more prominent introduction to the pipeline but I think the current version is a quite good solution. --Martin Kraus (discuss • contribs)

 * The overview has been written by me a while back, basically filling in the (in my eyes crucial) information my OpenGL ES tutorial book ("OpenGL ES 2.0 Programming Guide") was missing, making it hard to comprehend. So it's been written from a learner's perspective. Anyways, I agree that no long-winded pipeline introduction is needed, but some advance words about it (some paragraphs) would be good. The problem with my text is that it's too long and applies to OpenGL ES. I would rework it if I had the time and knowledge about OpenGL 2.0 (non-ES). -- NotInventedHere (discuss • contribs) 22:59, 28 December 2011 (UTC)

Sides labelled wrongly
In the topic that adds the cube I notice that at least in my implementation (and also from what I can tell by thinking through the code) the index's that are listed as making up some of the sides are labelled as making up different sides. For example // left 4, 5, 1,   1, 0, 4,

Looks to me like it makes up the BOTTOM of the cube, not the left. Can anyone clarify? 62.49.19.234 (discuss) 13:02, 4 March 2012 (UTC)

Copyright of these tutorials?
What is the license of these tutorials? Is it ok to use these kinds of code (and e.g. Wikipedia's code examples) in closed source projects? For example, in the GLSL_Programming/Introduction there is a box that says "Unless stated otherwise, all example source code on this page is granted to the public domain." at the bottom of the page. --88.148.251.200 (discuss) 10:39, 16 December 2012 (UTC)

 * Without such a notice, any code in Wikibooks is by default under the Creative Commons Attribution-ShareAlike 3.0 license, which makes it difficult to use it in closed source projects. Thus, you have to ask the author for permission. (For code from the GLSL Programming wikibook you don't have to ask because that box grants the code to the public domain.) --Martin Kraus (discuss • contribs) 18:55, 17 December 2012 (UTC)

GLFW
I don't use it myself, but many newer applications are using GLFW ( https://www.glfw.org/ ) instead of libraries like GLUT to get an OpenGL application up and running on a variety of platforms. GLFW handles creating windows and receiving input from users. Think it would be useful to mention somewhere on the wiki.

TinyGL and forks
For systems that don't have a full OpenGL implementation, TinyGL offers a way to run some older OpenGL (approx. 1.1) functions on the machine. It does CPU rendering. It runs very well on handheld devices such as gaming consoles. It's also been used on operating systems like Amiga, BEOS and Syllable that may not normally offer OpenGL support. There are several forks of TinyGL including TinySDGL (which works with SDL), PicoGL (which supports SDL, nano-x, vesa and X11 backends) and TinyGLES (used by glshim). Some forks include an alternative floating point library for devices that don't support floating point calculations efficiently. There's even a tinygl.js implementation that uses emscripten to run TinyGL with JavaScript at web sites. If one wants to use OpenGL on platforms that don't have OpenGL implementations or don't have the GPU/hardware support to run them efficiently, TinyGL and its forks are a good alternative. Most demos and some applications targeting OpenGL 1.1 work fine with TinyGL or some of its forks. (I'm currently working on a fork of PicoGL that takes some of the additions from various TinyGL forks and incorporates them as well as other useful features so that it's easier to port older OpenGL applications and get them working.) One can also use TinyGL or a fork to supply missing OpenGL functionality on systems that only support OpenGLES. For instance, one can port a demo or game using SDL and a TinyGL fork to an Android device.

Drawing text
I've been looking for resources on how to draw text (using TrueType fonts). Have not found much information on it other than to use someone else's library. Would love to see some documentation added to the wiki. Most references say it's difficult and gloss over the problem. So far, I've found out that there are two main libraries typically used to access the TrueType fonts, Freetype2 ( https://www.freetype.org/ ) and stb_truetype.h ( https://github.com/nothings/stb ). From what I've read from others, the opinion is that Freetype typically has better rendering quality than stb_truetype.h. The best example library I could find for showing different methods of getting fonts to the screen using Freetype was oglft ( http://oglft.sourceforge.net/ ) which demos using techniques such as glBitmap, glDrawPixels, texture mapping and others. Most, but not all font libraries that work later versions of OpenGL seem to use texture mapping and a texture alias. Freetype2 or stb_truetype.h generate pixmaps at the size requested and several pixmaps are stored together as a texture using glTexImage2D. A texture atlas is used to limit the amount of data one needs to transfer from the CPU to the GPU. glTexSubImage2D is used to update parts of the texture atlas as needed. fontstash is one example of a texture atlas ( https://github.com/memononen/fontstash ). There are a few other tutorials on the Internet. Would love to see more detailed information on design pros and cons for this. There are other methods of drawing fonts such as tessellation. The texture atlas method seems to be the easiest method to use on both older and newer versions of OpenGL if you need to support working with more than one version.

If some knows more details on the subject, it would be great to see a section added that details how to draw TrueType fonts, pros and cons of various approaches, what to do and what not to do when rendering fonts. Thanks.

Thanks
Hey there, I just wanted to jump in and thank you guys, your tutorials are being invaluably useful to me. Happy hacking, and have the best luck! Martin.

title: Talk:OpenGL Programming


text:
User:ArnTracks

'''

ArnTracks
'''

Programming Languages: C/C++, C#

title: User:ArnTracks


text:
Non-nerd's Guide to Computers

Table of Contents

 * About This Wikibook
 * What is a Computer?
 * The Essential Components
 * The Motherboard (From Whence All Connections Came)
 * The Hard Drive (Talkin' 'Bout a Revolution)
 * The CPU (At the Heart of the Process)
 * Operating Systems
 * GNU/Linux, and all its variants
 * Windows
 * Apple Mac OS
 * Mobile OSes
 * Appendices
 * Further Reading
 * Thanks

title: Non-nerd's Guide to Computers


text:
Non-nerd's Guide to Computers/About

The Non-nerd's Guide to Computers book guarantees that

 * By the end of reading this text, you will know enough about computers to be considered a nerd, and
 * You will be able to understand everything in this book, thanks to analogies and examples!

About "Explanation Entries"
If there is something regular people would not understand in this book, it is usually followed by (some explanation of definition).

Contributors to this book include

 * CherryT 22:07, 6 March 2006 (UTC)
 * Christopher Woods, from the 24th of August 2011
 * Heimerslinger, from the 28th of November, 2023

Improving the Wikibook
If you feel that this book needs help and you would like to contribute: by all means, edit it! We need all the help we can get so don't be afraid to change things!

title: Non-nerd's Guide to Computers/About


text:
Maple/Graphic functions

Simple plots
To plot a funtion you use the plot(function) command. You need to tell Maple what variable it needs to plot against the value function. This is done by plot(funtion, variable=a..b). This will plot the value of the function as the variable changes from a to b. Example: >plot(x^2, x=0..1);    #Image on the left >plot(1/3*x^3, x=-1..1);    #Image on the right

You can also get Maple to plot a function that you have entered previously. >2/3*x^2+x; >plot(%, x=-2..1);

Maple will also accept variables in the range option if it can equate the function to those extremes. This is particularly useful if you are plotting trigonometric functions as you can then make use of multiples of pi. >plot(cos(x), x=0..2*Pi);    #Image on the left >a:=Pi:    #Affecting the variable a to equal pi >plot(sin(x), x=-a..a);     #Image on the right

There are many other options you can apply to a plot. >plot(x^3+3*x^2+x-1, x=-3..1, colour=blue, style=point, title="This is a title");    #Image on the left >plot(-x^3-3*x^2-x+1, x=-3..1, colour=green, thickness=2, labels=["X axis label", "Y axis label"], labeldirections=[horizontal, vertical]);    #Image on the right

Saving of plots
For using (storing, publishing), the figures should be prepared in an appropriate format (gif, jpg, pdf, eps) and saved to disk. Such a convertion can be achieved by setting the device with the command plotssetup. Example:

> plotsetup(ps)

This command specifies that the graphic should be prepared in the EncapsulatedPostscript format. However, after such a command, while all other setting required is well arranged the plot command may cause errors. Therefore, after such a command, the command

> plotsetup(default)

can be very useful; especially while the user tries all the options one by one trying to catch the combination of commands which writes the picture into a file.

However, there exist also a way of saving pictures by use of the menu. The user should click on the figure ("mark it"), then find the option plot at the top menu bar and open the second-order menu "export" at its bottom, where the user has to choose the file-format to export to. This work should be repeated for each picture saved or updated.

Display multiple graphs in single plot
t2 := plot(g2(y), y = 1 .. 10, color = red): t4 := plot(g4(y), y = 1 .. 8, color = blue): t6 := plot(g6(y), y = 1 .. 8): display({t2, t4, t6});

Rotation and reflection of plot
>K2 := plot(g2, y = 0 .. 10,color=red): plottools:-reflect(plottools:-rotate(K2, (1/2)*Pi), [[0, 0], [0, 1;

K4:= plot(g4, y = 0 .. 10,color=blue): plottools:-reflect(plottools:-rotate(K4, (1/2)*Pi), 0, 0], [0, 1);

>K6 := plot(g6, y = 0 .. 10, color = black); plottools:-reflect(plottools:-rotate(K6, (1/2)*Pi), 0, 0], [0, 1);

Animation
$$f:=2*k^2/cosh(k*(x-4*k^2*t))^2$$

with(plots); animate(subs(k = .5, f), x = -30 .. 30, t = -10 .. 10, numpoints = 200, frames = 50, color = red, thickness = 3);
 * Bellsoliton2.gif

animate3d(cos(t*x)*sin(3*t*y), x = -Pi .. Pi, y = -Pi .. Pi, t = 1 .. 2)

title: Maple/Graphic functions


text:
A-level Physics/Wave Properties

Contents

 * Reflection and Refraction
 * Waves
 * Superposition

title: A-level Physics/Wave Properties


text:
University of Alberta Guide/STAT/222/Uncatagorized

University of Alberta Guide > STAT > 222

 * Biased means $$E\left[\hat{\Theta}\right] \ne \Theta\,$$
 * $$\hat{\Theta}_{1} = E\left[\Theta|X(1)\right]\,$$ cannot be biased.


text:
Category Theory

 * /Definition, examples/
 * /Monoidal categories/
 * /Enriched categories/
 * /Natural transformations/
 * /Representable functors and Yoneda's lemma/
 * /(Co-)cones and (co-)limits/
 * /Adjoint functors/
 * /Subcategories/
 * /Categories of sets/
 * /Categories of ordered sets/
 * /Categories of graphs/
 * /Additive categories/
 * /Abelian categories/

Introduction
This Wikibook is an introduction to category theory. It is written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. The book contains many examples drawn from various branches of math. If you are not familiar with some of the kinds of math mentioned, don’t worry. If all the examples are unfamiliar, it may be wise to research a few before continuing.

What is a category?
A category is a mathematical structure, like a group or a vector space, abstractly defined by axioms. Groups were defined in this way in order to study symmetries (of physical objects and equations, among other things). Vector spaces are an abstraction of vector calculus.

What makes category theory different from the study of other structures is that in a sense the concept of category is an abstraction of a kind of mathematics. (This cannot be made into a precise mathematical definition!) This makes category theory unusually self-referential and capable of treating many of the same questions that mathematical logic treats. In particular, it provides a language that unifies many concepts in different parts of math.

In more detail, a category has objects and morphisms or arrows. (It is best to think of the morphisms as arrows: the word “morphism” makes you think they are set maps, and they are not always set maps. The formal definition of category is given in the chapter on categories.)
 * The category of groups has groups as objects and homomorphisms as arrows.
 * The category of vector spaces has vector spaces as objects and linear maps as arrows.

The maps between categories that preserve structure are called functors.
 * The underlying set of a group determines a functor from the category of groups to the category of sets.
 * The fundamental group of a pointed space determines a functor from the category of pointed topological spaces to the category of groups. The fact that it is a functor means that a continuous point-preserving map from a pointed space S  to a pointed space T induces a group homomorphism from the fundamental group of S to the fundamental group of T.

Categories form a category as well, with functors as arrows. Most fundamentally, functors between specific categories form a category: its morphisms are called natural transformations. The fact that category theory has natural transformations is arguably the single feature that makes category theory so important.

History
Category theory was invented by Samuel Eilenberg and Saunders Mac Lane in the 1940s as a way of expressing certain constructions in algebraic topology. Category theory was developed rapidly in the subsequent decades. It has become an autonomous part of mathematics, studied for its own sake as well as being widely used as a unified language for the expression of mathematical ideas relating different fields.

For example, algebraic topology relates domains of interest in geometry to domains of interest in algebra. Algebraic geometry, on the other hand, goes in the opposite direction, associating, for example, with each commutative ring its spectrum of prime ideals. These fields were among the earliest to be studied using tools of category theory. Later applications came to abstract algebra, logic, computing science and physics, among others.

Aspects of category theory
Because the concept of a category is so general, it is to be expected that theorems provable for all categories will not usually be very deep. Consequently, many theorems of category theory are stated and proved for particular classes of categories.
 * Homological algebra is concerned with Abelian categories, which exhibit features suggested by the category of Abelian groups.
 * Logic is studied using topos theory: a topos is a category with certain properties in common with the category of sets but which allows the logic of the topos to be weaker than classical logic. It is characteristic of the malleability of category theory that toposes were originally developed to study algebraic geometry.

Categorical reasoning can identify particular arguments or results as consequences of more general theory. For example, in the study of the theory of the GCD, the fact that it is essentially unique simply follows from the uniqueness of the product in any category and is thus merely one example of a more general result. On the other hand, the fact that the GCD of the integers A and B can be expressed as a linear combination of A and B with integer coefficients—GCD(a, b) = ma + nb, for some integers m and n—is a much deeper fact that is special to a much more restricted situation.

Note on terminology
Most variations in terminology are discussed in the place where the terminology is defined. Here it is important to point out one annoying terminological problem: The adjective corresponding to “category” is “categorical”. Since “categorical” in logic means having only one model up to isomorphism, this can cause cognitive dissonance; in any case, the use of “categorical” in this book has nothing to do with the idea of having only one model.

Some authors use “categorial” instead. Unfortunately, this means something else in linguistics. This book follows majority usage with “categorical”.

title: Category Theory


text:
Advanced Mathematics for Engineers and Scientists

An all-in-one /Printable Version/ is available. Partial differential equations may hurt your eyes and a computer monitor doesn't help, so printing is recommended.

Table of Contents
/The Front Cover/

/Introduction to Partial Differential Equations/

Introductory Topics and Techniques

 * /Parallel Plate Flow: Easy IC/
 * /Parallel Plate Flow: Realistic IC/
 * /Change of Variables/
 * /The Laplacian and Laplace's Equation/

Fundamentals

 * /Introduction and Classifications/
 * /Vector Spaces: Mathematic Playgrounds/
 * /Nondimensionalization/
 * /Details and Applications of Fourier Series/

Moving On
 * /Using the Rayleigh Quotient/

Numeric Methods

 * /Finite Difference Method/
 * /Method of Lines/

Other Topics

 * /Scale Analysis/
 * /Eigenfunction Expansion/


text:
Topology/Countability

Bijection
A set is said to be countable if there exists a one to one correspondence between that set and the set of integers.

Examples
The Even Integers: There is a simple bijection between the integers and the even integers, namely $$f:\mathbf{Z}\rightarrow\mathbf{Z}$$, where $$f(n)=2n$$. Hence the even integers are countable.

A 2 - Dimensional Lattice: Let $$\mathbf{Z}^2$$ represent the usual two dimensional integer lattice, then $$\mathbf{Z}^2$$ is countable.

Proof: let $$f:\mathbf{Z}\rightarrow\mathbf{Z}$$ represent the function such that $$f(0)=(0,)$$ and $$f(n)= (x,y)$$, where $$(x,y)$$ is whichever point:

 * not represented by some $$f(m)$$ for $$m<n$$

 * $$(x,y)$$ is the lattice point 1 unit from $$f(n-1)$$ nearest to the origin. In the case where there are two such points, an arbitrary choice may be made.

Because $$f$$ exists and is a bijection with the integers, The 2 - dimensional integer lattice is countable.

Definition
A topological space $$X$$is said to satisfy the First Axiom of Countability if, for every $$x\in X$$ there exists a countable collection $$\mathcal{U}$$of neighbourhoods of $$x$$, such that if $$N$$ is any neighbourhood of $$x$$, there exists $$U\in\mathcal{U}$$ with $$U\subseteq N$$.

A topological space that satisfies the first axiom of countability is said to be First-Countable.

All metric spaces satisfy the first axiom of countability because for any neighborhood $$N$$ of a point $$x$$, there is an open ball $$B_r(x)$$ within $$N$$, and the countable collection of neighborhoods of $$x$$ that are $$B_{1/k}(x)$$ where $$k\in\mathbb{N}$$, has the neighborhood $$B_{1/n}(x)$$ where $$\tfrac{1}{n}<r$$.

Theorem
If a topological space satisfies the first axiom of countability, then for any point $$x$$ of closure of a set $$S$$, there is a sequence $$\{ a_i\}$$ of points within $$S$$ which converges to $$x$$.

Proof
Let $$\{ A_i\}$$ be a countable collection of neighborhoods of $$x$$ such that for any neighborhood $$N$$ of $$x$$, there is an $$A_i$$ such that $$A_i\subset N$$. Define $$B_n=\bigcap_{i=1}^{n} A_n$$.

Then form a sequence $$\{ a_i\}$$ such that $$a_i\in B_i$$. Then obviously $$\{ a_i\}$$ converges to $$x$$.

Theorem
Let $$X$$ be a topological space satisfying the first axiom of countability. Then, a subset $$A$$ of $$X$$ is closed if an only if all convergent sequences $$\{ x_n\}\subset A$$ converge to an element of $$A$$.

Proof
Suppose that $$\{ x_n\}$$ converges to $$x$$ within $$X$$. The point $$x$$ is a limit point of $$\{ x_n\}$$ and thus is a limit point of $$A$$, and since $$A$$ is closed, it is contained within $$A$$. Conversely, suppose that all convergent sequences within $$A$$ converge to an element within $$A$$, and let $$x$$ be any point of contact for $$A$$. Then by the theorem above, there is a sequence $$\{ x_n\}$$ which converges to $$x$$, and so $$x$$ is within $$A$$. Thus, $$A$$ is closed.

Theorem
If a topological space $$X$$ satisfies the first axiom of countability, then $$f:X\to Y$$ is continuous if and only if whenever $$\{ x_n\}$$ converges to $$x$$, $$\{ f(x_n)\}$$ converges to $$f(x)$$.

Proof
Let $$X$$ satisfy the first axiom of countability, and let $$f:X\to Y$$ be continuous. Let $$\{ x_n\}$$ be a sequence which converges to $$x$$. Let $$B$$ be any open neighborhood of $$f(x)$$. As $$f$$ is continuous, there exists an open neighbourhood $$A\subset f^{-1}(B)$$ of $$x$$. Since $$\{ x_n\}$$ to $$x$$, then there must exist an $$N\in\mathbb{N}$$ such that $$A$$ must contain $$x_n$$ when $$n>N$$. Thus, $$f(A)$$ is a subset of $$B$$ which contains $$f(x_n)$$ when $$n>N$$. Thus, $$\{ f(x_n)\}$$ converges to $$f(x)$$.

Conversely, suppose that whenever $$\{ x_n\}$$ converges to $$x$$, that $$\{ f(x_n)\}$$ converges to $$f(x)$$. Let $$B$$ be a closed subset of $$Y$$. Let $$x_n\in f^{-1}(B)$$ be a sequence which converges onto a limit $$x$$. Then $$f(x_n)$$ converges onto a limit $$f(x)$$, which is within $$B$$. Thus, $$x$$ is within $$f^{-1}(B)$$, implying that it is closed. Thus, $$f$$ is continuous.

Definition
A topological space is said to satisfy the second axiom of countability if it has a countable base.

A topological space that satisfies the second axiom of countability is said to be Second-Countable.

A topological space satisfies the second axiom of countable is first countable, since the countable collection of neighborhoods of a point can be all neighborhoods of the point within the countable base, so that any neighborhood $$N$$ of that point must contain at least one neighborhood $$A$$ within the collection, and $$A$$ must be a subset of $$N$$.

Theorem
If a topological space $$X$$ satisfies the second axiom of countability, then all open covers of $$X$$ have a countable subcover.

Proof
Let $$\mathcal{G}$$ be an open cover of $$X$$, and let $$\mathcal{B}$$ be a countable base for $$X$$. $$\mathcal{B}$$ covers $$X$$. For all points $$x$$, select an element of $$\mathcal{G}$$, $$C_x$$ which contains $$x$$, and an element of the base, $$B_x$$ which contains $$x$$ and is a subset of $$C_x$$ (which is possible because $$\mathcal{B}$$ is a base). $$\{ B_x\}$$ forms a countable open cover for $$X$$. For each $$B_x$$, select an element of $$\mathcal{G}$$ which contains $$B_x$$, and this is a countable subcover of $$\mathcal{G}$$.

Definition
A topological space $$X$$ is separable if it has a countable proper subset $$A$$ such that $$\mathrm{Cl}(A)=X$$.

Example: $$\mathbb{R}^n$$ is separable because $$\mathbb{Q}^n$$ is a countable subset and $$\mathrm{Cl}(\mathbb{Q}^n)=\mathbb{R}^n$$.

Definition
A topological space $$X$$ is seperable if it has a countable dense subset.

Example: The set of real numbers and complex numbers are both seperable.

Theorem
If a topological space satisfies the second axiom of countability, then it is separable.

Proof
Consider a countable base of a space $$X$$. Choose a point from each set within the base. The resulting set $$A$$ of the chosen points is countable. Moreover, its closure is the whole space $$X$$ since any neighborhood of any element of $$X$$ must be a union of the bases, and thus must contain at least one element within the base, which in turn must contain an element of $$A$$ because $$A$$ contains at least one point from each base. Thus it is separable.

Corollary
In any topological space, second countability implies seperable and first countable. Prove of this is left for the reader.

Theorem
If a metric space is separable, then it satisfies the second axiom of countability.

Proof
Let $$X$$ be a metric space, and let $$A$$ be a countable set such that $$\mathrm{Cl}(A)=X$$. Consider the countable set $$B$$ of open balls $$\{ B_{1/k}(p)|k\in N, p\in A\}$$. Let $$O$$ be any open set, and let $$x$$ be any element of $$O$$, and let $$N$$ be an open ball of $$x$$ within $$O$$ with radius r. Let $$r'$$ be a number of the form $$1/n$$ that is less than $$r$$. Because $$\mathrm{Cl}(A)=X$$, there is an element $$x'\in A$$ such that $$d(x',x)<\tfrac{r'}{4}$$. Then the ball $$B_{r'/2}(x')$$ is within $$B$$ and is a subset of $$O$$ because if $$y\in B_{r'/2}(x')$$, then $$d(y,x)\leq d(y,x')+d(x',x)<\tfrac{3}{4}r'<r$$. Thus $$B_{r'/2}\subseteq O$$ that contains $$x$$. The union of all such neighborhoods containing an element of $$O$$ is $$O$$. Thus $$B$$ is a base for $$X$$.

Corollary (Lindelöf covering theorem)
If a metric space is separable, then it satisfies the second axiom of countability, and thus any cover of a subset of that metric space can be reduced to a countable cover.

Example: Since $$\mathbb{R}^n$$ is a separable metric space, it satisfies the second axiom of countability. This directly implies that any cover a set in $$\mathbb{R}^n$$ has a countable subcover.

Definition
A subset $$A$$ of a topological space $$X$$ is said to be Countably Compact if and only if all countable covers of $$A$$ have a finite subcover.

Clearly all compact spaces are countably compact.

A countably compact space is compact if it satisfies the second axiom of countability by the theorem above.

Theorem
A topological space $$X$$ is countably compact if and only if any infinite subset of that space has at least one limit point.

Proof
($$\Rightarrow$$)Let $$\{ x_i\}$$, $$(i=1,2,3,...)$$ be a set within $$X$$ without any limit point. Then this sequence is closed, since they are all isolated points within the sequence. Let $$S_n=\{ x_i\}$$ for $$(i=n, n+1, n+2, ...)$$. The $$X\setminus S_n$$ are all open sets, and so is a countable cover of the set, but any finite subcover $$\{ X\setminus S_{n_i}\}$$ of this cover does not cover $$X$$ because it does not contain $$S_{n_{max\{ i\} }}$$. This contradicts the assumption that $$X$$ is countably compact.

($$\Leftarrow$$)Let $$\{ S_n\}$$ be open subsets of $$X$$ such that any finite union of those sets does not cover $$X$$. Define:

$$B_n=\bigcup_{i=1}^{n} S_n$$,

which does not cover $$X$$, and is open. Select $$x_n$$ such that $$x_n\notin B_n$$. There is a limit point $$x$$ of this set of points, which must also be a limit point of $$X\setminus B_n$$. Since $$X\setminus B_n$$ is closed, $$x\in X \setminus B_n$$. Thus, $$x\notin B_n$$ and thus is not within any $$S_n$$, so $$S_n$$ is not an open cover of X. Thus, $$X$$ is countably compact.

Relative Countable Compactness
Since there is relative compactness, there is an analogous property called relative countable compactness.

Definition
A subset S of a topological space X is relatively countably compact when its closure Cl(S) is countably compact.

Definition
A set $$N\subseteq X$$ is an $$\varepsilon$$-net of a metric space $$X$$ where $$\varepsilon>0$$ if for any $$b$$ within $$X$$, there is an element $$x\in N$$ such that $$d(b,x)<\varepsilon$$.

Definition
A metric space $$X$$ is totally bounded when it has a finite $$\varepsilon$$-net for any $$\varepsilon>0$$.

Theorem
A countably compact metric space is totally bounded.

Proof
Any infinite subset of a countably compact metric space $$X$$ must have at least one limit point. Thus, selecting $$x_1,x_2,x_3,\ldots$$ where $$x_n$$ is at least $$\varepsilon$$ apart from any $$x_d$$ where $$d<n$$, one must eventually have formed an $$\varepsilon$$-net because this process must be finite, because there is no possible infinite set with all elements more than $$\varepsilon$$ apart.

Theorem
A totally bounded set is separable.

Proof
Take the union of all finite $$1/n$$-nets, where $$n$$ varies over the natural numbers, and that is a countable set such that its closure is the whole space $$X$$.

Urysohn's Metrizability Theorem
The following theorem establishes a sufficient condition for a topological space to be metrizable.

Theorem
A second countable normal T1 topological space is homeomorphic to a metric space.

Proof
We are going to use the Hilbert cube, which is a metric space, in this proof, to prove that the topological space is homeomorphic to a subset of the Hilbert cube, and is thus a metric space.

First, since all T1 normal spaces are Hausdorff, all single points are closed sets. Therefore, consider any countable base of the topological space X, and any open $$O_n$$ set of it. Select a point $$x_n$$ within this open set. Since the complement of the open set is closed, and since a point within the open set is also closed, and since these two closed sets are disjoint, we can apply Urysohn's lemma to find a continuous function $$f_n: X \rightarrow [0,1]$$ such that:

$$f_n(x_n)=0$$

$$f_n(X/O_n)=1$$

It is easy to see from the proof of Urysohn's lemma that we have not only constructed a function with such properties, but that such that $$f_n(O_n)<1$$, meaning that the function value of any point within the open set is less than 1.

Now define the function $$g: X \rightarrow H$$ from X to the Hilbert cube to be $$g(x)=(f_1(x),\frac{f_2(x)}{2},\frac{f_3(x)}{4},...)$$.

To prove that this is continuous, let $$a_n \rightarrow a$$ be a sequence that converges to a. Consider the open ball $$B_\epsilon(f(a))$$ where $$\epsilon>0$$. There exists an N such that

$$\sum_{i=N}^\infty(\frac{1}{2^i})^2<\frac{\epsilon^2}{2}$$.

Moreover, since $$f_n$$ is a continuous function from X to [0,1], there exists a neighborhood of $$a$$, and therefore an open set $$S_n$$ of the base within that neighborhood containing a such that if $$y\in S_n$$, then

$$|f_n(y)-f_n(z)|<\frac{2^n\epsilon}{\sqrt{2N}}$$

or

$$(\frac{f_n(y)-f_n(z)}{2^n})^2<\frac{\epsilon^2}{2N}$$.

Let

$$S=\bigcap_{i=1}^{N-1} S_i$$.

In addition, since $$a_n\rightarrow a$$, there exists an $$M_i$$ (i=1,2,3,...,M-1) such that when $$n>M_i$$, that $$a_n\in S_i$$, and let M be the maximum of $$M_i$$ so that when n>M, then $$a_n\in S$$.

Let n>M, and then the distance from $$g(a_n)$$ to g(a) is now

$$\sum_{i=1}^\infty (\frac{f_i(a_n)-f_i(a)}{2^i})^2 = $$ $$\sum_{i=1}^{N-1}(\frac{f_i(a_n)-f_i(a)}{2^i})^2 + $$ $$\sum_{i=N}^\infty(\frac{f_i(a_n)-f_i(a)}{2^i})^2 \le $$ $$\frac{N-1}{2N}\epsilon^2+\sum_{i=N}^\infty(\frac{f_n(y)-f_n(z)}{2^n})^2 \le $$ $$\frac{N-1}{2N}\epsilon^2+\frac{\epsilon^2}{2} < \epsilon^2.$$

This proves that it is continuous.

To prove that this is one-to-one, consider two different points, a and b. Since the space is Hausdorff, there exists disjoint open sets $$a\in U_a$$ and $$b\in U_b$$, and select an element of the base $$O_n$$ that contains a and is within $$U_a$$. It follows that $$f_n(a)<1$$ whereas $$f_n(b)=1$$, proving that the function g is one-to-one, and that there exists an inverse $$g^{-1}$$.

To prove that the inverse $$g^{-1}$$ is continuous, let $$O_n$$ be an open set within the countable base of X. Consider any point x within $$O_n$$. Since $$f_n(x)<1$$, indicating that there exists an $$\epsilon_n>0$$ such that when

$$|f_n(z)-f_n(x)|<2^n\epsilon_n$$

then $$z\in O_n$$.

Suppose that $$g(z)\in g(X)\cap B_{\epsilon_n}(g(y))$$. Then

$$(\frac{f_n(z)-f_n(x)}{2^n})^2\le\sum_{i=1}^\infty(\frac{f_i(z)-f_i(x)}{2^i})^2\le \epsilon_n^2$$

Implying that $$|f_n(z)-f_n(x)|\le 2^n\epsilon^n$$ indicating that $$z\in O_n$$.

Now consider any open set O around x. Then there exists a set of the base $$x\in O_n\subseteq O$$ and an $$\epsilon_n>0$$ such that whenever $$g(z)\in g(X)\cap B_{\epsilon_n}(g(y))$$, then $$z\in O_n$$, meaning that $$z\in O$$. This proves that the inverse is continuous.

Since the function is continuous, is one-to-one, and has a continuous inverse, it is thus a homeomorphism, proving that X is metrizable.

Note that this also proves that the Hilbert cube thus contains any second-countable normal T1 space.

Hahn-Mazurkiewicz Theorem
The Hahn-Mazurkiewicz theorem is one of the most historically important results of point-set topology, for it completely solves the problem of "space-filling" curves. This theorem provides the necessary and sufficient condition for a space to be 'covered by curve', a property that is widely considered to be counter-intuitive.

Here, we present the theorem without its proof.

Theorem
A Hausdorff space is a continuous image of the unit interval $$[0,1]$$ if and only if it is a compact, connected, locally connected and second-countable space.

Exercise
If a Hausdorff space is a continuous image of the unit interval, then it is compact, connected, locally-connected and second countable.
 * 1) Prove that a separable metric space satisfies the second axiom of countability. Hence, or otherwise, prove that a countably compact metric space is compact.
 * 2) Prove the sufficiency condition of the Hahn-Mazurkiewicz theorem:

title: Topology/Countability


text:
Non-nerd's Guide to Computers/definition

What is a Computer?
If you are not reading this from printed paper, you will – without a shadow of a doubt – be using a computer (most likely taking the form of a desktop, laptop or portable mobile device) to read this WikiBook. Pretty much everything around you that's mechanical is a computer. You may say, "No way! My old wooden grandfather clock is not a computer," but you would be wrong — computers are 'general purpose machines that process data according to a set of (temporarily or permanently) internally stored instructions.'

A computer (or computing device) is, fundamentally, 'a programmable general purpose electronic device capable of performing multiple functions.' Or, in non-nerd terms, 'anything that performs defined functions automatically according to instructions it has already been given.'

So, that clock is indeed a computer: its 'set of instructions' is its internal timekeeping mechanism, cogs, springs, weights and all. The fact that its program happens to be one which is predictable in its expected output makes no difference (the gradual rotation of the hands around the clock face every twenty-four hours, or the fact that it self-regulates its output – the hands' movement – to once per second).

Whilst the example of a clock may be more reminiscent of the very first computer (Charles Babbage's Difference Engine) the concepts employed are identical. Practically anything electromechanical could be considered a 'computer'.

This Book's definition of a Computer
When most people talk about 'computers', they are implicitly referring to Personal Computers (PCs) - those wondrous devices that allow us to communicate, read, write and learn with the help of about a dozen common components all working harmoniously to send, receive, process and display information of every type imaginable. For consistency, whenever this Book mentions a 'computer', it is referring to a Personal Computer (to avoid any confusion possibly arising from the more specialist 'computing systems' or 'computational devices'.)

But what's in a computer? Read on to find out...


text:
Non-nerd's Guide to Computers/basic components

What's in a Computer?
Ask a pedant, or nerd (most are both) what the 'computer' is, and they will reply 'the Central Processing Unit' (CPU) - and the rest of the machine is considered 'peripheral'. However, as a lowest common denominator, every computer contains half a dozen essential components (plus a few more to enhance and add new functionality). Take one of those away, and the machine simply won't turn on (or if it does, you won't get very far with it).

Here's a quick list of what you absolutely need:

 * The motherboard (or 'mainboard') - the core component onto which all other components and peripherals connect;
 * The hard drive (or 'hard disk') - on which the computer's data, operating system (Windows, Mac OS X or Linux) and your personal files are stored;
 * The RAM (Random Access Memory) - the computer's temporary storage; this is where the computer 'parks' data whilst it's working with it;
 * The CPU (or Central Processing Unit, aka the 'Processor') - the brain of the computer, usually obscured by a large fan and heatsink as they generate a lot of heat during operation;
 * The video card (or 'graphics card') - this creates all the graphics you see on-screen, be it a spreadsheet, this WikiBook, a game or a film;
 * The sound card - this outputs every sound you hear from your computer, as well as 'digitising' incoming sounds from a microphone;
 * The optical drive (DVD, Blu-Ray etc) and various other 'peripherals' like memory card readers and any specialist equipment like TV cards;
 * The power supply - the substation providing continuous, regulated power to every component inside your computer; and
 * The connecting cables - most computers contain several dozen power, data and monitoring cables, all colour coded and with specific connectors to avoid inadvertent misconnections.

This Book could go on and on listing every connector and screw (and there are many hundreds of permutations of memory, processors, hard drives and motherboards – it is not 'one size fits all') but these are the fundamental components of any working computer. We'll discuss these parts, one by one, in the following subsections, starting with the very first part: the ../motherboard/.


text:
Non-nerd's Guide to Computers/motherboard

The Motherboard: From Whence All Connections Came
What exactly IS a motherboard? Let's take a quick example through a figure of speech. Think about mail service. Who delivers and picks up the mail? The mail carrier of course! He or she is given mail and drives around putting someone's mail in its appropriate mailbox, allowing people to communicate, and picks up mail already in the mailbox. The mail carrier is the equivalent of a motherboard. The motherboard is basically a mail carrier which allows all the components of a computer to communicate through exchanging data. The motherboard directs all this data, sending it to the appropriate places to be taken care of. Without a motherboard, computers would be lost, sending letters without an address. Since there is no way for each component to discern where data goes, it would be a mess and would not work.


text: User:Adamwg~enwikibooks

title: User:Adamwg~enwikibooks


text:
University of Alberta Guide/STAT/222/Downloadable Resources

University of Alberta Guide > STAT > 222

Exam Material and Solutions

 * Winter 2006

Assignment Solutions

 * Winter 2006
 * 3.2.3, 3.2.6 (mistake found - Please use [a_i,b_i] instead of [0,1]), 3.2.7, 3.3.3 (ans: 2ln(4/3)), 3.3.4 (hint: see Stat 221 Notes on line), 3.3.5, 3.3.6, 3.4.1, 3.4.4, 3.4.5
 * [[Media:Uofa_stat222_Sol2-06.pdf|Assignment 2]]
 * 3.5.2, 3.5.4 (ans: 0.696735), 3.5.5, 3.5.6, 3.6.3, 3.6.4 (ans: 0.062), 3.6.9, 3.6.11, 3.7.1, 3.7.4 (ans: 0.696665)
 * 3.8.2, 3.8.6, 3.8.7, 4.2.1, 4.2.2, 4.2.3 (There are typos in the errors. I always wanted to say that.), 4.2.4, 4.3.4, 4.3.5, 4.3.6
 * 4.4.4, 4.4.8, 4.4.9, 4.5.1, 4.5.2, 4.5.4, 4.6.1, 4.6.4, 4.6.5, 4.6.6
 * 5.2.2 (Ans: 930), 5.2.3, 5.2.6, 5.2.7 (Hint: Read section 5.3 first), 5.3.2, 5.3.3, 5.3.4, 5.4.2, 5.4.3, 5.4.7 (Computers)
 * 5.5.3, 5.5.4, 5.6.1, 5.6.2, 5.6.3, 6.2.6, 6.2.9, 6.3.1, 6.3.2, 6.4.3, 6.4.5


text:
Template:Merge section

Adds page to Category:Books to be merged.

title: Template:Merge section


text:
Cookbook talk:Onion Chutney

what is channa dahl

title: Cookbook talk:Onion Chutney


text:
French/Lessons/Vocabulary to be added

Dans la salle de jeux
Préposition :

Misc

 * qui
 * la ville (principale)
 * un fois
 * une école
 * excellent(e)(s)
 * un pays (francophone)
 * La langue (officielle) (maternelle)
 * riche(s)
 * beaucoup de (noun)
 * la vie
 * le jeune
 * Juste un peu.
 * mais
 * aussi
 * tous
 * plus vite
 * de jour en jour
 * N’est-ce pas?
 * C’est pas vrai!
 * la capitale
 * il y a
 * dans
 * même
 * combien de
 * la banlieue
 * libre(e)(s) / librement
 * tout le monde
 * pendant
 * pratiquement
 * entre
 * célèbre
 * commencer
 * passer la journée
 * comme
 * retrouver
 * gagner
 * l’argent.
 * par semaine
 * l'adieu
 * eh bien
 * la musique
 * même (adj)
 * parler au téléphone
 * écouter la radio
 * le monde (entier)
 * une journée
 * tout le monde
 * autour de (d’)
 * passer du temps
 * en très peu de temps

 * toujours.
 * souvent.
 * quelquefois.
 * très peu.

 * la reine
 * le roi
 * le grand palais à Versailles
 * l’époque révolutionnaire.

/Lessons

title: French/Lessons/Vocabulary to be added


text:
French/Lessons/Science

The indirect object pronoun  means to him or to her:

Likewise, the indirect object pronoun means to them:

Lui replaces à [person]:

Likewise, leur replaces à [people]:

Lui and leur usually only refer to people; they will sometimes also be used in reference to things.

The expression means there is … or there are …:

The interrogative form of il y a is. That is, il y a is inverted to y a-t-il, meaning is there? or are there?, within questions:

Both How much … and How many … (quantity) are translated as.

If the person or thing it refers to is countable, combien de is always followed by a plural noun:

However, with uncountable nouns, such as and, the singular form is used:

Inversion
Nouns and verbs are often inverted within questions. The inverted words are connected by a dash:

is used to connect vowels in inverted phrases (called an euphonic or pleasing to the ear):

For example:

Conjunctions in french function in the same way as english.

In addition to, , and , there are several common prepositions in French.

title: French/Lessons/Science


text:
User:Hairy Dude

Active on the English Wikipedia (wikipedia:User:Hairy Dude)

title: User:Hairy Dude


text:
Adventist Youth Honors Answer Book/Health and Science/Health and Healing

1. Be in at least the eighth grade.
== 2. Through the Bible and/or Spirit of Prophecy learn how Jesus healed the sick and the procedure for church elders to use to anoint the sick and ask God for healing. Write a 250-word report or give a two-minute oral report on what you learned. ==

Spirit of Prophecy texts

 * The Ministry of Healing Chapter 16: Prayer for the Sick.
 * Desire of Ages Chapter 36: The Touch of Faith

Procedure for Anointing the Sick
The procedure for anointing the sick is outlined in the Minister's Manual. The anointing service is performed for anyone who is seriously ill. While it should not be used for minor ailments, it should also not be reserved only for those who are dying.

"Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord.  And the prayer of faith will save the sick, and the Lord will raise him up.  And if he has committed sins, he will be forgiven." (James 5:14, 15).

Note that the verse asks, "Is anyone among you sick?" rather than "Is anyone among you dying?"

The service is performed by a pastor or in his absence, by an elder (but with the pastor's approval). The person officiating should be accompanied by a few elders, and anyone who has a special gift for prayer. It can be performed in a home, at the church, in a nursing home, or in a hospital. If it is done in a hospital or nursing home, it should not interfere with the medical work being done there.

Normally, non-Christian friends and family are not invited to the service, but they should not be asked to leave if they are present already.

Before the service, the recipient should be prepared by a careful examination of his or her own heart. This should include a confession of any sins to the Lord. "If I regard iniquity in my heart, the Lord will not hear" (Psalm 66:18). The recipient may also be encouraged to read the chapter "Prayer for the Sick" in Ellen White's The Ministry of Healing. (see the Spirit of Prophecy references above).

The service begins when the pastor explains the purpose of the service to all present, and how the service will be performed. The recipient may be asked to give a testimony. If the recipient is not too sick, time should be taken to read passages from the Scriptures explaining the prerequisites for divine healing:

 * 1) Belief that God can and does heal.
 * 2) The confession of sin.
 * 3) Commitment to healthful living.  It is presumptuous to ask God to heal us if the person intends to continue the behavior that caused the illness in the first place.
 * 4) Willingness to use human means.  God does work miracles, but sometimes he chooses to do this through human agents.  He may already have chosen a doctor through whom the afflicted person may be healed.  It is not a sign of faithlessness to seek healing through human effort.  "Every good gift and every prefect gift is from above" (James 1:17)
 * 5) Trust God's answer. Sometimes God answers quickly, sometimes slowly, and sometimes He answers "No."  If the sick person is not healed immediately (or is not healed at all) it is not a sign that God was unwilling to heal or that the person lacked faith or spirituality.  The scripture reading should end with the assurance that everything has been placed in God's hands and that God can be trusted.

Everyone then kneels, and prayer begins. The anointed may pray first, followed by the elders. The pastor prays last as he dips his finger into a vial of olive oil and rubs a small amount on the recipient's forehead. The oil symbolizes the Holy Spirit touching the sick person in a special way. Seventh-day Adventists do not follow the practice of applying oil to the part of the body that is afflicted.

As soon as the prayer is ended, the anointing party leaves. If fellowship is desired, it should take place before the anointing service. The party should leave while the spirit of reverence and the presence of God prevail.

3. What is continuing education as related to health careers?
Once health professionals are certified or licensed to practice, they are required to keep their educations current by enrolling in "Continuing Professional Education" or CPE. They must complete a specific number of hours of coursework every year. During these courses, the professionals review current practices and are exposed to the latest techniques. These courses are often sponsored by their employers, and often involve overnight trips taught at resorts or spas. Employers provide this "perk" because they wish to retain their employees.

== 4. Interview at least two people who work in a medical health career. One of the two must be someone other than a doctor or nurse, such as someone working in dentistry, physical therapy, respiratory therapy, radiology, nutrition, etc. In your interview ask the following questions ==
 * a. Why did you choose your profession?
 * b. What education is necessary to enter your profession?
 * c. After education, what amount of time does it take to become certified or proficient in your field?
 * d. What part of your job do you like the best? The least?
 * e. What day of the week and hours per day do you work at your job?
 * f. What advancement is available in your field?
 * g. What course of study in college would complement your chosen profession?
 * h. List local schools that offer training in your profession?

The interview should take about 20–30 minutes to complete. Interviewing a respiratory therapist can also meet a requirement for the Voyager AY curriculum, so if you choose this option, be sure to ask these questions as well:

 * 1) What are the benefits of regular exercise?
 * 2) Explain the treadmill test.

You may need to set up an appointment with these professionals, and they may ask that you come to their facilities for the interview. Be prompt. It is also courteous to send your interviewees a card or a gift as a thank you. If the interview is conducted at the medical facility, you may be able to meet much of requirement 5b as well.

b. Visit a medical or dental office and do the following

 * (1) Observe the areas of operation, such as the business office, laboratory, examining rooms, x-ray room, etc.
 * (2) Be introduced to the equipment used in the office.
 * (3) Learn the steps of an office visit from when a patient comes into the waiting room until the time he leaves the office.
 * (4) Learn how the doctor does an examination from the taking of the patient's history to the diagnosis.

c. Go on a visit with a home nurse and do the following

 * (1) Learn the steps of a home visit from when the nurse finds out about the patient to when the nurse reports to a doctor.
 * (2) Observe the nurse taking the vital signs.
 * (3) Observe the nurse giving instructions and medication.

d. Visit an outpatient department of a hospital, such as physical therapy, x-ray, laboratory, etc. Do the following

 * (1) Observe the areas of operation in the department.
 * (2) (Be introduced to the equipment used in the department and how it works.)
 * (3) Learn the steps a patient takes when visiting the department.
 * (4) How many people does it take to staff the department?
 * (5) Does the department operate at night?


text:
University of Alberta Guide/STAT/222/Combining Continuous Random Variables

Convolution

 * $$f_{X + Y}(z) = \int_{-\infty}^{\infty}f_{X}(y - z)f_{Y}(z)\delta z = \int_{-\infty}^{\infty}f_{X}(z)f_{Y}(y - z)\delta z$$

Example
$$f_{X}(x) = \begin{cases}\frac{3x^{2}}{2}& x \in [-1,1]\\ 0& else \end{cases} \qquad f_{Y}(y) = \begin{cases}\frac{y}{9}& y \in [4,5]\\ 0& else \end{cases} \qquad X \mbox{ and } Y \mbox{ are independent RVs, find } f_{X + Y}(z)$$
 * Start by converting the pdf's to indicator functions
 * $$f_{X}(x) = \frac{3x^{2}}{2}\cdot 1_{[-1,1]}(x) \qquad f_{Y}(y) = \frac{y}{9}\cdot 1_{[4,5]}(y)$$
 * Now $$f_{X}(x)\,$$ is defined only when $$x \in [-1,1]\,$$ and $$f_{Y}(y)\,$$ is defined only when $$y \in [4,5]\,$$
 * Use the convolution formula above to write out the integral
 * $$\int_{-\infty}^{\infty}f_{X}(z)f_{Y}(y - z)\delta z = \int_{-\infty}^{\infty}\frac{3z^{2}}{2}\cdot 1_{[-1,1]}(z)\frac{y - z}{9}\cdot 1_{[4,5]}(y - z)\delta z$$
 * Factor out any constants, in this case, a multiplier
 * $$\frac{3}{18}\int_{-\infty}^{\infty}z^{2}\cdot 1_{[-1,1]}(z)(y - z)\cdot 1_{[4,5]}(y - z)\delta z = \frac{1}{6}\int_{-\infty}^{\infty}z^{2}\cdot 1_{[-1,1]}(z)(y - z)\cdot 1_{[4,5]}(y - z)\delta z$$
 * Factor out the indicator function for $$(z)\,$$ into the integral bounds
 * $$\frac{1}{6}\int_{-1}^{1}z^{2}(y - z)\cdot 1_{[4,5]}(y - z)\delta z$$
 * Note that $$4 \leq y - z \leq 5, (\mbox{ try to isolate } z) \rightarrow 4 - y \leq -z \leq 5 - y \rightarrow y - 5 \leq z \leq y - 4$$
 * Now that have isolated the indicator for z, we can combine the entire integral for that indicator
 * $$\frac{1}{6}\int_{-1}^{1}\left(z^{2}(y - z)\right)\cdot 1_{[y-5,y-4]}(z)\delta z = \frac{1}{6}\int_{-1}^{1}\left(z^{2}y - z^{3}\right)\cdot 1_{[y-5,y-4]}(z)\delta z$$
 * Finally, split the integral into the separate cases based on the remaining indicator function
 * $$f_{X + Y}(z) = \frac{1}{6} \begin{cases}0& y < 3\\ \int_{-1}^{y-4}(z^{2}y - z^{3})\delta z& 3 \leq y < 4\\ \int_{y-5}^{y-4}(z^{2}y - z^{3})\delta z& 4 \leq y < 5\\ \int_{y-5}^{1}(z^{2}y - z^{3})\delta z& 5 \leq y < 6\\ 0& y \geq 6\\ \end{cases} \qquad = \begin{cases}0\\ -\frac{255}{4} + 43z + \frac{z^{4}}{12} - 8z^{2}\\ \frac{369}{4} - \frac{122z}{3} + \frac{9z^{2}}{2}\\ 156 - 83z - \frac{z^{4}}{12} + \frac{25z^{2}}{2}\\ 0\\ \end{cases}$$
 * When $$y < 3\,$$ the integral has no bounds since $$(y<3) - 4 < -1\,$$ so the upper bound would be less than $$-1\,$$ which would be $$0\,$$.
 * When $$3 \leq y < 4\,$$ the integral is bound between $$-1\,$$ and $$y - 4\,$$since $$y - 4\,$$ will be at least $$-1\,$$ but less than $$0\,$$
 * As you can see there is a pattern here, it goes as follows:
 * Given $$\int_{a}^{b}(\cdot)1_{[c,d]}\delta z\,$$ you will have $$\begin{cases}y < (d - a = 0)\\ (d - a = 0) \leq y < (c - a = 0)\\ (c - a = 0) \leq y < (d - b = 0)\\ (d - b = 0) \leq y < (c - b = 0)\\ y \geq (c - b = 0)\\ \end{cases}$$


text: French/Grammar/Moods/Imperative

title: French/Grammar/Moods/Imperative