text:
User talk:Babylace

Hello and Thanks
Hi Babylace,

Thanks for your contributions to the AY Honors Answer Book! I hope you don't mind, but I changed the formatting a little bit and turned some of your text into complete sentences. I also added a couple of "TODO" items.

But mostly, I just wanted to thank you for your input. It is really, Really, REALLY appreciated! Jim Thomas 19:16, 8 June 2006 (UTC)

SPD vs NAD
I have noticed that you have been adding (or changing) the requirements for various honors using the South Pacific Division's version. Until now, I have been changing the SPD requirements to the NAD version, but this really doesn't make a lot of sense. There's no reason the SPD shouldn't have a place in this answer book as well as the NAD. I'm trying to think of a structure that would accomodate multiple divisions, but it might take a while to work it out. We might have to fork the book at the top level kinda like this:

 * AY Honors Answer Book (top level)
 * SPD, NAD, EAD, EUD, etc at second level
 * Arts and Crafts, health and healing, etc at the third level
 * Individual Honors at the fourth level

Where the honor requirements are not different, we can use a common chapter. This is going to be a LOT of work to fix, but I think it needs to be done. There may be a few false starts and errors along the way, so I ask you to bear with me.

Thanks again for your work on this project. Jim Thomas 02:15, 28 July 2006 (UTC)

Historical Notes
Please do not delete the historical notes from the answers. Jim Thomas 02:19, 25 September 2006 (UTC)

title: User talk:Babylace


text:
Bartending/Cocktails/Eggnog

Ingredients

 * 8 eggs (separated into yolks/whites)
 * 1 cup sugar
 * 1 cup white rum
 * 3 cups whole milk
 * 3 cups whiskey
 * 2 cups heavy/whipping cream
 * ground nutmeg to taste

Glass

 * Punch Cup

Instructions
You are doing things gently and slowly to preserve the eggnog's fluffiness.

 * 1) Beat egg-yolks with 1/2 of sugar, set aside.
 * 2) Beat egg-whites until stiff, then mix in other 1/2 of sugar.
 * 3) Pour the yolks into the whites and mix together slowly.
 * 4) Stir in white rum slowly
 * 5) Stir in milk slowly
 * 6) Stir in whiskey slowly
 * 7) Stir in 1/2 of cream slowly
 * 8) Whip rest (1/2) of cream and fold in carefully.
 * 9) Serve at room temperature by ladling into cups and sprinkle nutmeg one top.

Makes 6 servings

Variations
Shake with ice, strain into highball glass.

Warnings

 * This recipe uses raw eggs. See the module Egg for possible health risks.

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

title: Bartending/Cocktails/Eggnog


text:
Puzzles/Non-scientific puzzles/Boy, Girl, and a Dog/Solution

Since the dog travels at 10 km/hr, in 1 hour it will cover 10 km.

The boy moves at 5km/hr the girl at 4km/hr. After 1 hour the distance between them is 1km. The dog is within 1km. The distance between the boy and girl will increase linearly over the one hour, to its maximum of 1km. During this time the dog has been running back and forth at 10km/hr.To calculate its exact position is a VERY scientific question.

The boy moves at 5km/hr the girl at 4km/hr, but we don´t know for how long they have being moving. They could have just started to move and there´s virtually no distance between them. So the dog, whatever his speed, could just had travel a couple meters. Also we dont know if he stops when he gets back to the boy or continues running, and for how long. Or if his speed is constant and movement linear. Maybe after a 100 meters he got tired and took a nap.


text:
Adventist Youth Honors Answer Book/Vocational/Shorthand

1. Be able to take dictation on new material at 80 words per minute for three consecutive minutes and transcribe accurately the notes taken.
There are many forms of shorthand, but the one most commonly used in the United States is Gregg Shorthand. This section presents the Century Edition.

Gregg Shorthand is a phonetic writing system, which means it records the sounds of the speaker, not the English spelling. It uses the f stroke for the f sound in funnel, telephone, and laugh. All silent letters are omitted. The image on the right shows the strokes of Gregg Shorthand Simplified. The sounds are represented in this image by the International Phonetic Alphabet. The system is written from left to right and the letters are joined.

 * Sh (and zh), Ch, and J (or Dzh) are written downward.
 * T and d are written upward.
 * X is expressed by putting a slight backward slant on the s, though the word beginning ex is just written es.
 * W, when in the middle of a word, is notated with a short dash under the next vowel.
 * Q is usually a k with a dash underneath the next vowel.

Many of the letters shown are also what are called "brief forms". For instance, "which" is written as ch. These brief forms are shown on the image to the right. There are several others not shown, however. For instance, "please" is written as simply pl, and "govern" as gv. These brief forms can make Gregg Shorthand much faster.

Another mechanism for increasing the speed of shorthand is phrasing. Based on the calculation that lifting the pen between words has a speed cost equivalent to one stroke, phrasing is the combination of several smaller distinct forms into one outline, for example "it may be that the" could be written in one outline, "(tm)ab(th)a(th)". "I have not been able" would be written, "avnba" (Note that to the eye of the reader this phrase written in shorthand looks like "I-have-not-been-able", and so phrasing is far more legible than a longhand explanation of the principle may lead one to believe).

The vowels in Gregg shorthand are divided into three main groups that very rarely require further notation. The a is a large circle, and can stand for the a in "apple", "father", and "ache". The e is a small circle, and can stand for the e in feed and help, the i in trim and marine, and the obscure vowel in her and learn. The ī represents the i in fine. The o is a small hook that represents the al in talk, the o in cone, jot, and order. The u is a tiny hook that expresses the three vowel sounds heard in the words who, up, and foot. It also expresses a w at the beginning of a word.

There are special vowel markings for certain diphthongs (two-sound vowels). The ow in how is just an a circle followed by a u hook. The io in lion is written with a small circle inside a large circle. The ia in piano and repudiate is notated as a large circle with a dot in its center. The u in united is notated with a small circle followed by an u hook above it.

Due to the very simple alphabet, Gregg shorthand is very fast in writing. It takes a great deal of practice, however, to master it. Speeds of 280 WPM (where a word is 1.4 syllables) have been reached with this simple system before, and those notes are still legible to anyone else who knows the system.

This is the Lord's Prayer written in several forms of shorthand. Gregg's is first (although it is an older version) followed by several others.

Historical Notes
Shorthand was introduced in 1929, discontinued in 1956, and reintroduced in 1986.


text:
Talk:Latin/Appendix E

Untitled
ŒÁÉþŻ!!

title: Talk:Latin/Appendix E


text:
Radiation Oncology/Head & Neck

Cancers of the Head & Neck
 * H&N Anatomy & Contouring
 * General Head and Neck
 * Concurrent Chemo-RT
 * Neoadjuvant Chemotherapy
 * Post-operative Head and Neck
 * By Site
 * Nasopharynx
 * Larynx
 * Hypopharynx
 * Oral cavity
 * Oropharynx
 * Nasal cavity and paranasal sinuses
 * Salivary gland
 * Thyroid
 * Unknown Primary
 * Ear
 * Mucosal melanoma
 * Esthesioneuroblastoma
 * /Ameloblastoma/
 * Temporal bone tumor
 * Recurrent disease
 * H&N Palliation
 * Second primary tumors / chemoprevention
 * See also: Esophagus for cervical esophagus
 * Technique
 * Treatment Technique
 * Altered Fractionation
 * Proton Therapy
 * Neutron Therapy
 * Brachytherapy
 * Hypoxia
 * Treatment toxicity & NTCP
 * Supportive care
 * Level I Evidence

title: Radiation Oncology/Head & Neck


text:
User:RockinRob

 • User page • Talk page • Toolset • To Do • Sandbox1/2 •  Leave a message  • Email'''

I'm Rob, and I'm an engineer. I grew up in Northeast Philadelphia, where I worked at Al's Hobby Shop in the Roosevelt Mall. After graduating Northeast High School in 1984, I went to Penn State Ogontz, and then moved to Penn State's main campus in 1986. I received my degree in Aerospace Engineering in 1990. After working at convenience stores, the IRS, and a department store, I landed my first job on SOHO in 1996, and moved to suburban DC in order to work at NASA Goddard.

I left SOHO after 3 years, and then I worked on NEAR at JHU/APL. After NEAR was landed on Eros, I returned to Goddard to work on Terra. After Terra, I worked on Aqua, doing GNC work before launch, and I became the Flight Software Engineer a year after launch, and also helped to support Aura pre-launch. I left Aqua and Aura in 2004 to jump at the chance to work on Swift, because it meant moving back to bucolic Happy Valley, otherwise known as State College, PA. I consider myself really fortunate to have the opportunity to live and work where I went to school.

What I might like to write about
I'd be interested in writing a wikibook about spacecraft design and operations. The emphasis would be on actual spacecraft engineering versus spacecraft of scientific fiction. I believe a large amount of spacecraft-related information already exists on Wikipedia and Wikibooks, and I'd like to begin to pull it together, but I think the subject is too large for a Wikipedia article or series of articles.

title: User:RockinRob


text:
Backgammon

Contents

 * /Introduction/
 * /History/
 * General Rules and Gameplay
 * Setup, Movement, and Doubling
 * Sample Game
 * Opening Moves
 * /Strategy/
 * The Social Chouette Play
 * /Authors/
 * /Glossary/

Literature

 * Backgammon (also called "The Backgammon Bible") by Paul Magriel and Renee Magriel (Harwich Port: Clock & Rose Press, 2004) is the acknowledged best book on the game, particularly for beginning and intermediate players.
 * Starting out in backgammon: An introduction to the gameplay and tactics for backgammon board game, Paul Lamford, 2001
 * Beginning backgammon: Strategy and tactics for winning play, J. Du C. Vere Monlyneux, 1984

title: Backgammon


text:
Backgammon/Chouette

Brief Overview
The Backgammon Chouette is a social, multi-player form of backgammon and was mostly played socially when you would have a number of players conversing and playing against each other on the same table. Now days with the broad reach of the internet this form of backgammon can be played across different countries and various platforms. It can be a tremendous amount of fun, with lots of cube turns, players taking different points of view, getting to rotate and play as a team-mate of another player one game and against him the next. However, if it’s not done right, especially online, it can get boring quickly. This page will give you an outline of what a chouette is and how to play.

Basic Terms and Rules of a Chouette
One player – the “box” – plays against a team. One member of the team is the “Captain.” This all takes place on one board. The Captain has final say over all checker plays, although he can ask his team-mates for help in some situations. However, each player has his own doubling cube. He can double regardless of what his team-mates do, and he can take or drop if doubled on his own. A chouette is played just like a money game. There is no “match score” – you play one game, win or lose points, then go on to the next game. Positions change every game. In general, if the box wins, he stays as the box; if the Captain wins he becomes the box. Whether the Captain wins or loses, the next player in line becomes the Captain.

The scoring is just points won or lost. Each player has a running score, of plus or minus a certain number of points, or even. If you were playing for money, you would multiply this by the stakes, and that’s how many dollars ahead or behind you would be. Naturally, the sum of all the scores is always zero. Online chouettes can be somewhat awkward to run. There is no special software for chouettes. What is required is someone to run the chouette who understands a chouette, whom I call a monitor. The monitor keeps track of the position of all cubes, and tallies the running score. When a chouette gets large, it gets to be a lot of work.

Listed below is everyone’s responsibilities. From experience you should know that if everyone doesn’t follow these, it can really ruin things for everyone. A chouette can be an awful lot of fun. For the team, there is the opportunity to gang up on one helpless victim (the box), to consult on checker plays, to show how much smarter you are than the others by, say, dropping a double and losing one point when everyone else goes on to lose a doubled gammon – or by taking and winning two points when most of your teammates dropped and lost one. There is the excitement of being the box and winning or losing 5 or 10 or 20 points at a time.

When you are the Captain

 * Turn on Board Notation so that you can understand the comments your team is making.
 * If you want advice on a move, type the move in the chat box at the bottom of the screen before moving. You do not have to ask for advice, or to follow it. But it will be very frustrating to your teammates if you don’t ask their advice and then make foolish moves. It is generally considered good practice that, if you are a relatively weak player, to ask advice from the strong players, and if you are the strongest player on the team to just move. The bottom line is that your teammates will forgive you anything if you win, but if you lose and they think you did so foolishly, you won’t become very popular! Remember too that everyone else wants to be involved in the game. If you just keep moving without ever asking for advice, even on close plays, you’re taking your teammates out of the game.
 * When you are in a position where anyone on the team might even be thinking of doubling, wait just a couple seconds before rolling. Give them the chance to say “double.” If anyone doubles, make sure to wait until the box has decided on all the cubes. But also, don’t wait forever to roll. If there has been any cube action, give the monitor a minute to record the results. Remember, he’s got a lot of paperwork to keep track of!
 * Never use the “double” button on the board. If you want to double, say “double.” It will be very frustrating if the box reflexively drops and the game ends.
 * A special situation arises if you drop but someone else on the team takes. Now, you are no longer allowed to participate in the game. In a real-life chouette, you would leave your seat and the person next in line to be Captain would take your place.

When you are the Box

 * If you are doubled by one or more players, wait until everyone has had a chance to double. You might ask “anyone else?” You do not have to decide to take or drop until everyone has doubled who wants to. If you’re going to drop, then of course everyone will suddenly want to double!
 * If you double, wait for everyone to decide to take or drop before rolling, and give the monitor time to record the results.

When you are the Team

 * Pay Attention. It’s easy to lose interest in the game if you’re not an active participant, but you are very much a part of the game. One of the most frustrating things is when the box says “Double all” and one or two players on the team don’t respond and you’re waiting.
 * Know the position of your cube. If you have doubled and the box has taken, don’t say “double.” You can’t double, and it will only slow the game down if the monitor has to tell you that you have already given your cube. (Of course, if you doubled to 2 and the box has redoubled to 4, you can now double to 8!) Likewise, if you doubled and the box dropped, you’ve already won this game. You’re out, you can’t win the same game twice!

For All Chouette Players

 * Take the game seriously. If a player always doubles at the first opportunity, takes every double, and immediately redoubles. That kind of play takes away from the game, because this is supposed to be fun, but it’s supposed to be a test of skill. Pretend you’re playing for $10 a point! If that were the case, you’d play your best; you’d certainly pay attention even when you’re on the team. And if you were Captain and had money on the line, you’d try to get the better players to help you win. If you pretend you’re playing for real money, you’ll find you have more fun!
 * Be patient. A real-life chouette goes almost as fast as a regular game, and when it slows down it's because people are discussing (or arguing!) over checker plays, which is part of the fun. Online, because the software doesn’t support chouettes, it can slow down a little. Try to be a little patient and keep focused on the game.
 * If you have to leave, leave. There’s no requirement that you stay in a chouette for any particular period of time. If you’re losing interest, then just say that you’re leaving and leave. It’s best if you stay to the end of the current game, though.

Rules for Chouettes

 * 1) Jacoby Rule, backgammon beavers but no backgammon raccoons. explanations to these terms can be found in the glossary.
 * 2) Players on the team can consult only after their cube has been turned. This means that the Captain is free to play the opening in peace, while getting help once the game has advanced.
 * 3) If any player drops, the Captain may buy his cube. What that means is that the player who drops pays the Captain the undoubled value of the cube, rather than the box. The Captain is now playing with two (or three or four or five) cubes against the box.
 * 4) If all players but one drop, that player must either drop or he must buy all the other cubes. This prevents one player from holding up the game. However, in this case it works a little differently. The box still gets the point from all the cubes. However, each player on the team pays the remaining player one additional point, and they now join the box. If you are doubled and drop, you are saying that you would rather pay one point to get out of the game than play on with a 2-cube. So if someone said “I think it’s better to play on with a 2-cube than drop” you should be willing to say “OK, I will pay you one point to take that inferior side of the board and play it with a 2-cube.” This way, if one player wants to play on, everyone is still involved in the game.
 * 5) Settlements are allowed. Lets look at a very simple example. Suppose you are in a last-roll position. The cube is at 4, and you have one checker on your 5-point and one on your one-point; your opponent has one checker on his one-point. You have 23 rolls that win the game and 13 that lose. On average in 36 games you will win 92 points and lose 52, for a net average of (92-52) / 36, or about 1.1 points. You might say “I’ll take one point.” Anyone who wants can now pay you one point and the game ends for them. Settlements can be proposed by either side at any time.

title: Backgammon/Chouette


text:
Talk:Backgammon/Chouette

Wikipedia AfD for backgammon chouette
As you might have noticed the article Wikipedia:Backgammon Chouette in wikipedia has an AfD and a discussion on it of weather it should be placed in wikibooks or in wikipedia. Currently what i think will happen is that the longer version of the article will be here if deemed to be good enough, and the short version of the article will hopefully be accepted in wikipedia, but i guess time will tell in the next 5 days of this AfD discussion about the article, where the main concern is that it is a game manual and is better suited for wikibooks. I partially disagree because a chouette is a form of backgammon play that people try to understand what it is about, thus a wikipedia definition is needed. Moreover, if a reader wants to find out more about the rules and gameplay of this chouette he will get a link to the wikibooks article in order to know about how to play this great game. Thanks for your time The-writer 04:38, 9 June 2006 (UTC)

Page Moved to Backgammon:Chouette
Page Moved to Backgammon:Chouette Sorry for the mess just makes more sense this way when linking from wikipedia

The-writer 05:57, 10 June 2006 (UTC)

Can someone help me with deleting this page? it is new and i know moved the content to a different link, there should be no problem in deleting this page because it is still a very much new page here. I am new here and i am really kean on making a backgammon book. Thanks and sorry for the mess.

The-writer 06:16, 10 June 2006 (UTC)

title: Talk:Backgammon/Chouette


text:
AP Biology/LABORATORY 1. Diffusion and Osmosis

 * Diffusion: the movement of molecules from an area of higher concentration to an area of lower concentration. For example, if a bottle of air freshener is sprayed on one side of a room, the fragrance would eventually be able to be smelled on the opposite side of the room. The air freshener diffused from an area of high concentration (where it was first sprayed) to an area of low concentration (the rest of the room). Eventually, an equilibrium will be reached, and the concentration will be uniform throughout the room, and there will be no net movement of molecules.

Water potential is the measure of free energy of water in a solution. Water will always move from an area of higher water potential (more water molecules) to an area of lower water potential (fewer water molecules). Water potential is affected by two factors, the addition of solute and physical pressure. In this lab, we will investigate the processes of diffusion and osmosis in a model membrane system, and investigate the effect of solute concentration on water potential as it relates to living plant tissues.
 * Osmosis: a special case of diffusion, in which water will diffuse across a selectively permeable (allows some but not all molecules to gow through) membrane. Water will diffuse from an area of higher water concentration (low solute concentration), to a lower water concentration (high solute concentration).

 * Water Potential
 * is the potential energy of water in proportion to dirty water. It is defined by the formula Ψ = Ψp + Ψs where
 * Ψ is the total water potential
 * Ψp is the pressure potential of the solution
 * Ψs is the solute potential of the solution

Osmosis and diffusion are two of the most important processes in the study of how organisms maintain homeostasis, particularly with regard to their electrolyte and water balances. This AP lab attempts to demonstrate the process of osmosis using dialysis bags.

=Expected Results and Analysis= From only having glucose and starch within the dialysis bag, the glucose diffuses and there is a presence of glucose inside the cup that was initially distilled water and the absence of starch. This is because the selectively permeable dialysis bag, cell membrane, only allows small molecules, such as glucose and water to pass, but not large polysaccharides like starch.

=Conclusions=

Diffusion is the movement of particles from an area of high concentration to an area of low concentration. One can see the effects of diffusion when one puts several balls tightly packed in a room and open the door to an adjacent room. The balls will gradually slide to the other room. Due to diffusion since the room had a high concentration of balls and the new room did not the balls diffused equally to both rooms. Another important piece of information to know about diffusion is that it is passive which means it requires no energy. Osmosis on the other hand is exactly like diffusion except that in osmosis the object that is being diffused is water, whereas diffusion implies no specific object. One example of osmosis can be seen in a plant when one pours water into a plant and the plant becomes turgid. This is because there is a lower concentration of water inside the plant so water diffuses into the plant. Osmosis like diffusion is also passive.


text:
Biology, Answering the Big Questions of Life

Contents

 * Cover
 * Foreword -
 * About the Book -

 * 1) Introduction to the Science of Biology -  [[Image:Leafgreen40.jpg]]
 * 2) What are living creatures made of? (Cells) -  [[Image:Leafgreen40.jpg]]
 * 3) How can you see things that are really small? (Microscopes)-  [[Image:Leafgreen40.jpg]]
 * 4) (organelles)-  [[Image:Leaforange40.jpg]]
 * 5) membranes-  [[Image:Leaforange40.jpg]]
 * 6) (osmosis)-  [[Image:Leaforange40.jpg]]
 * 7) How are living things named? (Taxonomy) -  [[Image:Leafgreen40.jpg]]
 * 8) What is everything made of? (Atoms and Molecules) -  [[Image:Leafgreen40.jpg]]
 * 9) How do plants make food? (Photosynthesis) -  [[Image:Leafgreen40.jpg]][[image:Audiobutton.png]]
 * 10)  How does Photosynthesis work? (Light and Dark Reactions) -  [[Image:Leaforange40.jpg]]
 * 11)  Tell me more about Photosynthesis. (Photosystems, C4 plants and CAM) -  [[Image:Leafpurple40.jpg]]
 * 12) What's really going on in there? (Metabolism) -  [[Image:Leafgreen40.jpg]]
 * 13) How are food molecules broken down to make energy? -  [[Image:Leaforange40.jpg]]
 * 14)  What are the steps in the breakdown of glucose for energy? -  [[Image:Leafpurple40.jpg]]
 * 15) How do living things grow? -
 * 16) Mitosis -  [[Image:Leaforange40.jpg]]
 * 17) Meiosis -  [[Image:Leaforange40.jpg]]
 * 18) How are babies made? (Human reproduction) - [[Image:Leafgreen40.jpg]]
 * 19) How are babies made? (Human reproduction) [[Image:Leafpurple40.jpg]]
 * 20) How do parents pass things on to their children? (Genetics) - [[Image:Leaforange40.jpg]]
 * 21) Exceptions to Mendel (Genetics) - [[Image:Leaforange40.jpg]]
 * 22) Human Genetics (Genetics) -  [[Image:Leaforange40.jpg]]
 * 23) What is DNA?  -  [[Image:Leafpurple40.jpg]]
 * 24) Why do species change over time? -  [[Image:Leaforange40.jpg]]
 * 25) How do viruses make people sick? -  [[Image:Leaforange40.jpg]]

Laboratory Manual

 * 0. Introduction to the Biology Laboratory - [[Image:Leafgreen40.jpg]]
 * 1. Cells and the Microscope - [[Image:Leafgreen40.jpg]]

 * 2. Osmosis lab - [[Image:Leafgreen40.jpg]]

 * 3. Organic Chemistry - [[Image:Leafgreen40.jpg]]

 * 4. Fermentation Lab - [[Image:Leafgreen40.jpg]]  [[Image:Leaforange40.jpg]]

 * 6. DNA lab - [[Image:Leafgreen40.jpg]]

 * 7. Sugar Crystal Lab - [[Image:Leafgreen40.jpg]]

 * 8. Lipids Lab -

Teachers Laboratory Guide

 * 1. Cells and the Microscope  -  [[Image:Leafgreen40.jpg]]

 * 2. Red Onion Osmosis Lab-  [[Image:Leafgreen40.jpg]]

 * 3. Organic Chemistry Lab- [[Image:Leafgreen40.jpg]]

 * 4. Fermentation Lab- [[Image:Leafgreen40.jpg]]  [[Image:Leaforange40.jpg]]

 * 5. Mitosis and Meiosis Lab- [[Image:Leafgreen40.jpg]]

 * 6 DNA lab - [[Image:Leafgreen40.jpg]]

 * 7. Sugar Crystal Lab - [[Image:Leafgreen40.jpg]]

Index

 * Topic Index
 * Question Index

Key
Some topics have pages with more than one difficulty level. The Leaf Icons show what levels are available for each topic.

Easy - These topics can be easily understood by a young or casual reader.

Intermediate - More advanced topic may require more outside knowledge.

Advanced - Covers material at level of College Biology Majors

Audio version available.


text:
Biology, Answering the Big Questions of Life/Foreword

Foreword
What attracts people to Biology and Science? I think it's curiosity. As a child we question the world around us constantly. We ask adults about it. We test and experiment. In fact children are the first scientists. But as we age, we learn not to question, and some of the big questions of our childhood may never be answered.

I think the best way to teach science is to rekindle the spirit that asks those big questions, and to endeavor to awaken the heart that wants to explore the universe and discover what rules govern it.

This material is based on lectures that I presented to students in introductory college Biology courses presented at Navarro Community College. That doesn't mean that you have to be taking a college course to understand this work. I have tried to make this book easily readable and browseable by anyone interested. This is a work in progress. Hopefully I will be able to update the book as I find which parts of it work and which parts do not.

I would like to say first that I make mistakes, and sometimes I say things that are completely wrong. I write this book as an open book partially in the hope that others will find my mistakes and correct them.

I hope that this work will be useful and help to awaken an interest in Science and a love of Biology.

About the Author
Rosalyn Hunter received her Bachelors Degree from the University of Texas and her Masters Degree from the University of Arizona. She has helped manage a research lab, taught high school science, and has taught Biology at the college level at both Navarro Community College, and Hill College where she is currently a professor. She embraces open source, and was excited to start this collaborative textbook.

 Previous < Up > Next : Index


text:
Biology, Answering the Big Questions of Life/Osmosis

--Red Onion Osmosis Lab -- Make a wet mount of the onion leaf. Use a small piece of paper towel to pull a salt solution through the mount by placing a drop of salt water on one side of the coverglass, and the paper towel on the other.

Using red onion really helps in this lab because the cells are already dyed. The problem is that you cannot use the thin membrane between the onion layers to perform this experiment. You must peel the top layer off of the onion off to do this lab. For this reason, It may be prudent for the instructor to use a razor blade and prepare the samples in advance.

Smaller samples will make better pictures. Closing the diaphram on the condensor will prevent the sample from appearing washed out under the microscope.

Students should focus on only the colored layer of cells. For best results focus on the cells on the edge of the sample as the salt will affect them first.

We prepared a 20% by weight salt solution and observed results within 5 minutes.

Alternatives
This laboratory can be done with other plant cells, but cells with many chloroplasts, such as Elodea are the best.

Onion skin slides can be made and dyed with iodine which makes the cells slightly yellow. (Note) Iodine fixes (kills) the cells. To make onion skin slides, peel a piece of onion. The skin is a thin area on the bottom of an onion leaf that can be peeled off and laid between a slide and a coverglass in a wet mount.

A demonstration can be done with blood cells, but remember that in this era fear of AIDS means that all blood samples must be treated with extreme caution. See your administrator before doing any laboratory using blood.


text:
Biology, Answering the Big Questions of Life/Organic chem

Laboratory Setup
In this laboratory it is important to rinse all glassware well before use. Trace amounts of detergent on the glassware will affect the results.

The experiment requires about: 15 minutes of student prep, 5 minutes to perform, and 15 - 20 minutes clean up.

The dyes
Sudan IV is a strongly hydrophobic dye and will give good results, but it does have some health hazards, so you may want the students to wear gloves.

Read the stains file entry on Sudan IV here.

http://stainsfile.info/StainsFile/dyes/26105.htm

Methylene blue is pretty safe. It may be an irritant. It is hydrophilic, but if there is detergent in the glass blue dots will also be suspended in the emulsion making results unclear.

The detergent will form an emulsion. Have the students compare the tubes to the control if they have difficulty determining which dyes are hydrophobic.

If Methelene blue is unavailable, most store-bought food colorings will do. For inexpensive hydrophobic dyes, you might try a deep colored oil. Although I have not had a chance to test it, some brands of hot pepper oil found in the Asian sections of grocery stores are dyed with red dye that may work in this experiment. Test out different substances before hand to see which work best.

relevance
This process of extracting chemicals by seeing which fraction (oil or water) they will dissolve in is a basic technique in organic chemistry.


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WebObjects/EOF/Modeling/Attributes

An attribute is, abstractly speaking, a piece of information about an entity. For example, an EOEntity may represent a person. The first name of the person is an attribute. The zip code of the person's address may be an attribute. An attribute is represented in EOF as a com.webobjects.eoaccess.EOAttribute instance. If an entity's information comes strictly from a table, then an attribute will be the object representation of a column. A relationship in an entity may also be an attribute of the entity.

A "class" EOAttribute" is distinguished from a non-class EOAttribute by whether or not the attribute is supposed to be an attribute of the class which models it. For example, if you have the first name of a person, that would be a class attribute. If you have an attribute you use in the entity to act as a key for a join, that attribute itself is not part of the class as such. It is part of the machinery used by the class. That key, itself, would not be something that one would want a user to know about. If that attribute is used in a join, and that join defines a relationship, then one would want to expose the relationship to a user. The relationship would be a class EOAttribute and the key in the join would be a non-class EOAttribute.

title: WebObjects/EOF/Modeling/Attributes


text:
Biology, Answering the Big Questions of Life/Organic Chemistry

Lab 3 - Organic Chemistry Lab
Organic molecules are chemicals which contain carbon. The structure of a molecule and its charge determine whether or not it will dissolve in water.

Chemicals which can dissolve in water are said to be 'hydrophilic'(water loving) while those which do not dissolve in water are said to be 'hydrophobic' (water fearing).

In the cell, hydrophilic molecules are found in the cytoplasm, while hydrophobic molecules are found in the phospholipid membranes.

Some molecules have both hydrophilic and hydrophobic parts. These molecules are said to be 'amphipathic'.

Phospholipids, the molecules which make up the plasma membrane are amphipathic, they have a charged phosphate group which is hydrophilic as well as a hydrocarbon chain which is hydrophobic. This allows cells to remain dissolved in water.

Amphipathic chemicals will form 'emulsions'. Solutions where oil droplets stay suspended in the water. Hydrophobic molecules will separate into the oil layer, while hydrophilic molecules will dissolve in the water fraction of the cell.

In this lab we will determine if molecules are hydrophilic, hydrophobic or amphipathic.

Instructions:
1. Place four test tubes with lids in a test tube rack. Fill each tube to about 1/4 full with corn oil, then Add water until tube is about 2/3 full.

2. Add the following to each tube.

 * Tube 1 - Control (do not add anything to this tube)
 * Tube 2 - Sudan IV dye ( about 10 to 12 drops)
 * Tube 3 - Methylene blue (about 5 drops)
 * Tube 4 - Dishwashing detergent (about 1/2 dropper)

3. Seal each test tube and mix it well.

4. Let the tubes sit for several minutes in the test tube rack as the solutions separate out.

5. Sketch each tube showing whether the substance dissolved in the oil or water fraction. If the tube does not separate out after several minutes, and the control has separated, list the chemical as amphipathic.

6. Fill the table.


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Talk:Muggles' Guide to Harry Potter/Places/Hogwarts School of Witchcraft and Wizardry

Teachers' Hours
The paragraph starting Other fan sites have noted that there are not enough teachers for the stated school population... amounts to having a problem with teachers teaching up to 28 sessions a week, and making an assumption that there are other teachers for the same subjects. While I'm sure there would be unnamed members of staff at Hogwarts, assuming a lesson at Hogwarts is approximately an hour in length, that amounts to 28 hours a week of teaching time, far shorter than the 48 hours maximum limit for UK staff. Even with all the extra work teachers have to do, and the residential status of Hogwarts staff, this doesn't really seem to be a problem! —Preceding unsigned comment added by Pookiyama (discuss • contribs) 14:08, 4 November 2017 (UTC)
 * The calculation is based on the assertion that it is impossible for Hermione to take 12 subjects without recourse to a time-turner to increase the length of her day. It is only by dropping two, leaving her 10 subjects, that she is able to continue without a Time-Turner. If it is impossible to take 12 subjects, the assumption is that it is equally impossible to teach 12 subjects, let alone 28 (7 years in each of four houses).
 * Your calculation of 28 hours a week is suspect also, in that it implicitly assumes only one one-hour instructional section per week for each class. If we instead guess that there are six classes in a day, thirty a week, for students, that would mean that Hermione's full schedule contains three classes per week in each subject. Three instructional hours per week, times seven grades, times four houses, is 84 contact hours a week, almost three times as many hours as classes are in session. Chazz (talk) 16:12, 4 November 2017 (UTC)
 * Revision: There is mention that classes are one and a half hours. A full schedule of 10 courses would then be either 20 classes, as 4 classes per 6-hour school day, five days a week, or 25 classes, as 5 classes per seven-and-a-half hour school day. In either event, we are still looking at either three contact hours (as two classes) in the first case per course per week, or an average of three and three quarters contact hours per week (assuming 2 classes in week A, three in week B, alternating, so five classes, seven and a half contact hours, per two weeks). In either case, we're still looking at significantly more contact time than there are hours in the working week: in the first case, the same 84 hours per week to be fit into 30 instructional hours, in the latter case, an average of 105 hours per week to be fit into 37.5 hours. Chazz (talk) 19:56, 4 November 2017 (UTC)

Characters Missing from Infobox
Is there a reason that many characters are missing from the infobox as permanant residents (eg: Dumblebore, multiple professors etc.)? I will add these soon if there is no response of why they arn't included at the moment. --DanielBC 10:58, 9 June 2006 (UTC)
 * Go for it. The page just hasn't been filled in yet. We need a lot of that around here since the content base is so large. -Matt 14:25, 9 June 2006 (UTC)
 * The staff, as you see in HBP does not live at the school, only during the school year. However, the grey lady is not mentioned in the permenant residence, she's the Ravenclaw ghost.
 * Isn't that the idea of a Wiki? You see a mistake, you're always free to fix it. In any event, I have made that change... Chazz 16:33, 9 November 2006 (UTC)

Map
Were all the countries on the map in existence in 1991-1998? Therequiembellishere 21:25, 9 May 2007 (UTC)
 * Does it matter? If we wanted to pick nits, we would actually have to go back to a medieval map, because it is, after all, supposed to reflect the wizarding world; and the names of the national Quidditch teams seem to reflect the world map from ca. 1600. Transylvania? As it is, we show the areas where the schools possibly are and where they draw from, and you can superimpose the national boundaries that you yourself prefer. Chazz (talk) 07:25, 10 May 2007 (UTC)

Map of the locations of the know wizarding schools in Europe
Is this image worth putting in this book, and is it valuable for this particular page? Image:HP Wizarding Schools possible locations.PNG

 * Here are my assumptions for the coloured areas:
 * First assumption: the school is located in a place where the language of the school is a mother tongue of the surrounding population.
 * Second assumption: It is very difficult for an 11 year old student to follow the lessons in a language that is not the students's mother tongue, therefore the school is recruiting primarily in countries where the school teaching language is mother tongue.
 * Third assumptions: The school may also recruit, but less frequently, in places where the language is close enough from the school language so that the students do not have to learn a language that is too different from the school language.

 * Locations
 * Hogwarts location: Rowling says it is in Scotland in an Interview. I have assumed that it is not in the populated areas (Edimbourough and Glasgow) since GoF says the nearest muggle town is several miles away (that does not exist around Edinburgh and Glasgow). I have also excluded the Scottish Islands, since you can go to Hogwarts by train from London.
 * Beauxbatons location: French speaking area. Hot weather (school uniform is very light), bouillabaisse is part of the food.
 * Durmstrang location: Slavic country (Victor Krum is from Bulgaria, all other known students/teachers have a slavic name, all have a slavic accent when they speak). Latitude needs to be higher than Scotland (Dumbledore says that they are "from the North" while he is ins Scotland), and Krum says that the winter days are very short, and summer days particularly long, compared to Hogwarts. Also her says that there are lakes and mountains around it. I have chosen those spots that match all 3 pieces of information (Slavic language, latitude higher than Scotland, lake + mountain areas).

 * Recruitment ground
 * Hogwarts recruitment ground: Britain, but maybe Republic of Ireland (no language barrier to prevent it).
 * Beauxbatons recruitment ground: All french speaking countries in Europe + maybe other latin speaking countries (the languages are close enough to French to make the linguistic jump?) and north African countries where French is taught in primary school.
 * Durmstrang recruitment ground: once we have established that Durmstrang can only be in northern Russia, we can assume that Russian speaking countries are the primary recruitment ground. Bulgaria and other slavic speaking countries qualify as secondary recruitment ground because the other slavic languages could be close enough to Russian for the students to learn it.

I am happy to discuss the level of speculation that is acceptable for this book, and provide a new version of the image with less speculation if the muggle's guide main authors feel it is better so.

I can't wait for your feedback! --Lgriot 12:38, 2 August 2007 (UTC)

 * That is certainly a well-thought-out argument. It would be great if you could integrate this into the image's discussion on the actual article page. I haven't criticized this technically since I'm a bit busy but users Chazz and Jokes Free4Me will most likely want to discuss this a bit. -within focus 14:02, 2 August 2007 (UTC)

 * I actually was subconsciously making the same assumptions when I originally saw the map. I have to agree with all of them, and say that your comments are better reasoned than I had ever managed to come up with. My only concern is that I'm not 100% sure of how we define "original research"... but to my mind, this is much less speculative than many other things that we have speculated on in the process of writing these articles. To my mind, this is a useful image, and I would like to see it re-instated on the page. Chazz (talk) 04:29, 3 August 2007 (UTC)

 * Thanks both for your support. Unless Jokes Free4Me (I have contacted him) opposes it by tomorrow, I will add the map this week-end to the "location" section of the page with a written explanation that uses the above and hopefully fits with the style of the page. --Lgriot 12:06, 3 August 2007 (UTC)

 * Fwiw, my own (probably biased) opinion would have been that the images are quite valuable... They are in the spirit of the textbook: they are "commenting" on (or, they represent views based on) existing information about the discussed subject. They only present it better. :-D -- Jokes Free4Me 13:46, 3 August 2007 (UTC)
 * Sorry for the delay, everyone, the map is finnaly back. --Lgriot 19:38, 18 August 2007 (UTC)

"The Black Lake"
A number of times, editors have called the lake on the Hogwarts grounds The Black Lake. I have just realized where that comes from. During the run-up to the Second Task in the movie Harry Potter and the Goblet of Fire, which I watched last night, it is referred to as the Black Lake repeatedly. Thus I think that it is purely an artifact of the films, as I certainly don't recall it being referred to by that name in the books. Chazz (talk) 00:20, 16 December 2008 (UTC)

Class Sizes
One of the biggest problems in this series is the population of the school.

The author has pleaded an inability to work with numbers, saying that she had not been able to work out the size of the Wizarding classes, but that she had intended the student body at Hogwarts to number between 600 and 1000. The closest we have to a true number is that in chapter 12 of Harry Potter and the Order of the Phoenix, where we are told that the normal class size is 30. While we only ever see Harry's dorm mates, Ron, Neville, Dean, and Seamus, and two of Hermione's, Lavender and Parvati, it is possible that there are additional dorms, possibly totaling three 5-person dorm rooms per year. The author has said that she limned characters for five male and five female individuals per house per year, and didn't carry things beyond that.

Given 30 students per House per year, then, each year group has a population of 120, for a total school student body of 840. This seems to tally with the mention of "hundreds" of students in the Great Hall at Harry's arrival, and the "hundreds" of people in the Slytherin stands at Quidditch — Slytherin house, with 30 people in each of 7 years, would have 210 students.

This number does seem unworkable on a number of fronts; in particular, it seems "double Potions with the Slytherins" or "double Herbology with the Hufflepuffs" would put sixty adolescent students in one dungeon or greenhouse under the supervision of a single teacher. Further, it would seem that with 28 sections (divided by house and year), a teacher of one of the six core subjects would somehow have to multiply themselves in order to teach more than once a week, as there are either 20 or 30 class periods in a week. Yet, the only subject with more than one teacher is Divination, which is jointly taught by Trelawney and Firenze after Harry's fifth year, despite Divination only being available to third-years and higher, and thus presumably needing fewer total contact hours.

The description of the first flying lesson in the first year mentions that there were 20 broomsticks waiting, and each student in the lesson (combined Gryffindor and Slytherin) gets a broomstick.

???
Why are the Questions and the Greater Picture' sections entirely blank? --Whoop whoop pull up (talk) 00:49, 7 November 2010 (UTC)

 * Because nobody has yet come up with anything to put in either of those sections? For characters, if they don't appear in a book, we can eliminate the section for that book in the character write-up, but that is a sub-section, where Questions and Greater Picture are main sections. Chazz (talk) 18:21, 2 January 2011 (UTC)

More countries green
Shouldn't the Netherlands, Norway, Sweden, Iceland, Denmark, Germany, Austria, the German-speaking portion of Switzerland, and the Swedish-speaking portion of Finland be colored light green in the map, as they all speak Germanic languages like English? --Whoop whoop pull up Bitching Betty 18:49, 12 March 2011 (UTC)
 * I'd argue against. Scandinavian countries, while they do teach English in school, don't generally have school-age students who are fluent in English; and we don't see any Scandinavian natives in Hogwarts during the seven years there. And likewise, English in the German areas you discuss is pretty thin on the ground. Chazz (talk) 20:35, 13 March 2011 (UTC)

Fewer countries green
Shouldn't only the English-speaking parts of Ireland be colored green (because Gaelic is not related in any way to English), and shouldn't they be colored medium green, like most of Great Britain (because they speak the same language as said country)? --Whoop whoop pull up Bitching Betty 23:46, 27 March 2011 (UTC)
 * Is there any Irishman who does not have a working knowledge of English? For that is the criterion here, not what they name as their native tongue when asked.--2001:A61:260C:C01:F8FA:881C:C75F:F533 (discuss) 20:37, 1 August 2018 (UTC)

More fewer countries orange
Shouldn't Romania and Moldova be colored light orange in the map, as they both speak Romance languages, such as Romanian? --Whoop whoop pull up Bitching Betty 18:49, 12 March 2011 (UTC)
 * I don't think so. As with the green areas mentioned above, the language being in the same family does not imply an ability to speak that language. I think Romanians would have a great deal of trouble learning magic and French at the same time... in fact, I have some trouble with Spain and Italy being colored light orange, having been fluent in Spanish and knowing the difference between that and French. I could see Spain and Italy sharing a magic school, however... Chazz (talk) 20:35, 13 March 2011 (UTC)
 * In that case, don't you think Italy, Spain, and the Italian-speaking parts of Switzerland be recolored from light orange to gray, because of the language difference? --Whoop whoop pull up Bitching Betty 23:48, 27 March 2011 (UTC)

New boundaries
Should we redo the map so that medieval boundaries are shown in dotted red lines in addition to the modern boundaries in solid white lines, since the characters and localities mentioned seem to have strong ties (Transylvania etc.) to medieval countries and locations? --Whoop whoop pull up Bitching Betty 23:54, 27 March 2011 (UTC)
 * Would it really help? In my not-so-humble opinion, it would add confusion for not much actual gain. Chazz (talk) 16:53, 4 August 2011 (UTC)

Fewer countries pink?
Just exactly how close are the other Slavic languages actually to Russian (especially the South Slavic languages, such as Bulgarian and Croatian)? --Whoop whoop pull up Bitching Betty 23:58, 27 March 2011 (UTC)

More magical schools?
I don't know whether someone updates this book, but computer game in 2014 stated that Russia has it's own magical school. So Durmshtrang is Scandinavian most likely. --185.13.35.122 (discuss) 16:03, 16 June 2017 (UTC)
 * We've determined that the computer games, not having much input from Jo, are in fact not canon and so aren't considered for this book. Chazz (talk) 16:14, 16 June 2017 (UTC)


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Talk:Statistics/Numerical Methods/Random Number Generation

Does anyone know how to create a 2D random number such that the variables in both dimensions have some sort of correlation ?

Organization
In my opinion, the Chi-Squared Goodness-of-Fit Tests, The Kolmogorov-Smirnov Test and Linear Dependence Test should not be on this page. It would be better to include them in chapter 9 Testing Statistical Hypothesis. PAC2 (talk) 15:00, 23 May 2010 (UTC)


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Parallel Computing and Computer Clusters

Parallel computing and computer clusters are two separate subjects. However, there is a very large cross over between the two which would make for large quantities of duplicated material should they be described separately.

The aim of this book is to provide a solid foundation for understanding all aspects of both parallel computing and computing clusters. It will begin by providing an overview of both of the terms used in the book's title and then breaking down existing hardware and software practices to see how they fit into the overall picture. The text will continue on to describe common features of parallel computing & computer clusters in their basic forms - sometimes they are features not readily associated with the field such as the task scheduling in everyday operating systems. To conclude the book aims to cover common uses for the technologies and provide some examples.

Table of Contents

 * /Overview/
 * /Micro Processor Units/
 * /Memory/
 * /Software/
 * Theory
 * /Feature Set/
 * /The End Result/
 * /Example Technologies/

Contributors

 * Barthax


text:
Parallel Computing and Computer Clusters/Overview

Overview of the subject matter
As mentioned in the Introduction, both parallel computing and computing clusters have a heavy overlap in their subject matter.

Parallel Computing
Parallel computing is an ambiguous term covering two distinct areas of computing: designing single machines with many processors (hardware parallel computing) and designing software to split complex scenarios into manageable chunks (software parallel computing).

Parallel Computer
A parallel computer is one which has been designed and houses multiple MPUs each of which can work independently of its peers. Many modern PCs are capable of housing two CPUs and an individual CPU can house multiple cores each of which can work independently of the others - both are examples of a computer which can perform multiple tasks in parallel. Note that a single-CPU, single-core machine running a multi-tasking operating system (such as MS Windows or one of the various flavours of Unix/Linux) is not running in parallel but is instead running many small chunks of tasks serially: the software is parallelised but the hardware is not.

Parallel Software
When designing software to work on a large data set it is often possible to split the data set into multiple smaller subsets without affecting the goal of the work as a whole. For example, to retrieve all of the static web pages on an individual server, it is possible to retrieve each one individually without affecting the end result and the chunks of the data set can therefore be performed in parallel. Once the data has been successfully determined to be split then the software can be designed in a way to allow individual CPUs to work on the smaller chunks & thus many CPUs can work in parallel on many different chunks.

Computer Clusters
Computer clusters are a network made up of multiple individual machines to work towards or provide a common theme or aim. For example, a simple search engine could be comprised of a pair of machines: one machine to retrieve and index the data and one machine to provide a front end for people to access the indexes. In this manner, the cluster is formed of multiple different tasks, but are seen to be a single entity by those utilising the cluster.

Many clusters are set up to work towards the same common goal, working on similar data sets in similar manners. In this form of scenario the cluster is computing in parallel and thus the divide between Parallel Computing and Computer Clusters becomes unclear.


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Biology, Answering the Big Questions of Life/Plants

The world around us is full of plants. Trees, flowers, and grass surround us all of our lives, but what are plants? What makes a plant a plant and an animal an animal? Why don't plants move?  This chapter talks about plants and why they are something that humans can't live without.


text:
Talk:Developing A Universal Religion/Why Bother?

On speaking about a universal religion one should seriously consider the 'collective subconscious' as a real and immaterial existing entity which is something that engulfs the entire globe, like an egg shell. This 'thing' exists within our solar system and has over the life of the planet collected all experiences by every oxygen breathing being. We all add to it. No life experience is in vain and we also collect from it (as in dreams) continuously (sort of like a biological internet. The question to be raised is whether this 'thing' is of and simultaneously separate from the planet and does the planet leave it's experiences behind if it should exit this realm of 'collective subconscious' for another planets inhabitants to inherit?

 * What evidence is there to think this, please? David Hockey 19:26, 9 June 2006 (UTC)

Based on the evolution of life on earth, a collective organism where we are just a part could be the next logical step. As one cell united to other cells as complex ogranism developed like us, the same process may happening now. It is not immaterial though, but it is not easy to see, because we are just a part. As for a cell in your body, for the cell it is not obvious its purpose, or the meaning why it's there. There is no evidence, just analogy. We are getting more and more dependent on each other and on a system. If you look into a cell, it's small, but still very complex. A singe cell organism was able to survive on its own, but not the cell in your body, it became specialized and dependent. We as human being are getting more and more specialized and dependent. Ervinn 00:57, 19 July 2006 (UTC)

Yes, I agree. Life could evolve so that separate entities become closely interdependent and thus form one composite structure.

However, a mutation can modify a cell to form one that may assist their host’s survival; this cell may survive and be replicated. This is how new cells originate. Organelles (for example, the bacterial endosymbiont that may have evolved into mitochondria, possibly) may be absorbed by a life-form and eventually become an integral part of the absorbing life-form.

Cells in our body obtain their energy from our body and, in return, contribute to our body’s maintenance or survival. This is why they are there. And you are right—a cell doesn’t live outside its supporting body for long.

What you suggest may happen, but it is likely to take a long time. Between then and now, I think that we have to evolve a better social-survival structure than the hit-and-miss one that organisations like the United Nations use now. David Hockey 15:55, 19 July 2006 (UTC)

Based on your suggestion, that is to aim to create oB (omnipotent being), a 'conscious civilisation'(collective consciousness) came to my mind. For us, the 'conscious civilisation' would look like as an omnipotent being. We would be the "genes" of these "beings". Actually we would be the keeper of "memes" coined in 1976 by famous evolutionary biologist Richard Dawkins, refers to a unit of cultural information transferable from one mind to another. We exsist so our genes can survive. Civilisation exsist so we can survive. Genes have the information how to build our body. We have the information how to build a civilisation.

By undertanding how consciousness works, and some other things, we would keep the information how a "good" conscious civilisation should function. Those information would be copied when a new civilisation is created. The newly created civilisation would live in isolation with the other so it can change and improve or die, using the force of natural selection. Then it will be just metter of time when a civilisation will be able to leave our solar system, before the sun burns out. Ervinn 03:28, 16 November 2006 (UTC)

 * If only what you write could happen!
 * But, I think that religious beliefs prevent humans from contributing to the formation of an oB entity.
 * Most religions teach us that this life is just a precursor to an after-life, and that behaving to achieve that is more important than behaving to ensure civilisation’s future.
 * However, many groups see the need to plan and act for our future. For instance, many of us know that we should reduce our pollutants, lower our population (so that the bio-system could support it), etc. But this knowledge achieves nothing—because these groups do not unite. They do not formulate a single, unifying purpose. If such a thing existed, then a critical mass of people might form and they might formulate the kind of goals that are needed for our civilisation to survive.
 * Perhaps another civilisation, maybe in a few million years on Earth, more likely upon other planet (since humans are exhausting this planet’s resources), might help form some kind of oB.
 * But I don’t think our descendants will contribute. David Hockey 17:45, 17 November 2006 (UTC)


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Parallel Computing and Computer Clusters/Memory

In the early stages of single CPU machines the CPU would typically sit on a dedicated system bus between itself and the memory. Each memory access would pass along the bus and be returned from RAM directly. As the speed of CPUs increased the speed of the RAM and the bus speed also increased. Due to the electronics involved the cycle of memory access and RAM response became a bottleneck forcing the CPU to lose precious computing cycles waiting for the response to be returned (termed latency).

To overcome this latency some designs involved placing a memory controller on the system bus which took the requests from the CPU and returned the results - the memory controller would keep a copy (a cache) of recently accessed memory portions locally to itself and therefore being able to more rapidly respond to many requests involving sequential (such as program code) or locally scattered requests (such as variables regularly accessed by the program code).

As CPUs became even faster, the latency involved in retrieving RAM even from memory controller-cached areas became significantly costly. The next stage of development would see the memory controller being positioned inside the die cast of the CPU itself (in many cases leaving memory controller on the bus as a duplicate) and thus the CPU cache was born. As the CPU cache was on the CPU die cast, the bus between the CPU core and the CPU memory controller was far less in length and the memory controller could respond more rapidly, leaving less latency for the CPU until a non-cached element was required.

Still later and further engineering improvements meant the speed of the CPU cache began to mirror the speed of the CPU itself allowing each instruction cycle to go without wait states from it's cache. Unfortunately the cost of such designs were significant and so a second layer or level of cache was placed onto the die cast and made from the cheaper (older) designs: CPUs now had Level 1 and Level 2 caches. As the level 2 cache was cheaper it could be die cast in larger quantities than the level 1 cache and retain both reasonable production costs and savings over ordinary RAM access speeds as well as significant savings in populating the limited level 1 cache from the level 2 cache by comparison to RAM access speeds.

RAM and multiple MPUs
With the simplest of multiple MPU designs each MPU has no cache and sits directly on the bus which allows for RAM accesses (direct RAM access or through a memory controller). Extending from the single-CPU design, a multi-MPU design which only ever reads information can be simply designed: each MPU sends it's request on the bus but needs a way to identify from where the request came. To this end the request must be extended in some fashion to label the request & the most obvious identification is the slot in which the MPU sits (as indicated by the BIOS during the CPU's boot up process). Responses coming back to the MPU without it's ID in the response can be safely ignored. The identification process is often performed by a controller which is not a part of the multi-MPU make-up but instead a separate, specialist, MPU on the bus referred to as the Programmable Interrupt Controller (PIC).

Unfortunately, a system unable to write any data will be very limited in it's flexibility and must therefore be capable of writing the data back to the RAM. The mechanism for writing back to the RAM becomes, again, a simple extension on that of the single-CPU system: write back the RAM indicating the MPU slot the request came from and any acknowledgement responses can be correctly identified in the same way allowing for any individual MPU to know their write request succeeded.

Alas, there's one significant flaw: what happens if two (or more) MPUs work on the same piece of data at the same time? Each MPU reads the data from RAM, processes the data based on the program code the individual MPU is working on and writes back the result to RAM. The issue resides in which MPU performed the write request last as it is that MPU's result which will reside in RAM and not the first. To illustrate the issue more clearly, consider the following where the activity references the same memory location (a number).

If this were an SMP system, both MPUs would be processing at the same speed and both would reach each phase of the pipeline at the same time. As a result, each would attempt to write their interpretation of the data back to RAM location 0002 at the same time. What would be the value of RAM location 0002 afterwards? Unfortunately, there's no guarantee unless some other method is put in place first to force this race condition not to occur.

Non-caching MPUs
In non-caching MPUs the MPU would request on the bus that a set range of memory be locked to prevent other processors from updating the memory region until the locking MPU has completed its own task. This approach is inefficient as the locking prevents a second (or subsequent) MPU from accessing the memory region.

Introducing caching
With the introduction of caches into the processors, the problem at first becomes more prevalent. Going back to a single-processor architecture with a cache to better illustrate the issue, the cache presents fast-access to a region of memory that has already been accessed. The MPU begins with a cache which is entirely marked as invalid and from there any request for a byte of RAM will automate a page of RAM to be loaded into the cache (filling only a portion of the cache). When the processor accesses a different section of non-cached RAM, that page of RAM is also loaded along-side the already cached page(s). The process continues until the cache is full of valid pages.

Once the cache is full and the processor requires access to a page of RAM not yet cached, it must make a decision as to where in it's cache it will write this new page: wherever the page is written to it will overwrite existing cached RAM. So, how does the processor decide? Two basic methods are used: most recent kept and random. In the first method the MPU's memory controller keeps track of the order in which the cached pages have been most recently accessed and chooses the eldest of the cached pages as the one to overwrite.

In particularly complex algorithms the eldest-accessed cached page may not be the most convenient to be removed: the code may jump around the RAM pages accessing very little from numerous different pages while rarely accessing the data set (by comparison to all program code) or vice versa. As a result of the jumping around in RAM the cache looses the data set (the most regularly-accessed single page of RAM) from it's cache. In this scenario, the processor would be better loosing any one of the infrequently accessed program code pages than the data set itself (note that there is a very big argument to state any program behaving in this manner is either poorly programmed or badly compiled).

In addition to the caching of data being read from RAM, the writing of data back to RAM can be similarly cached by the processor and then written as an entire page when the page is flushed. With a single-MPU system the caching of writes has no effect on other components in the system and can therefore take its time in writing back any modified cached pages (note that the RAM remains unchanged until the CPU writes the modified data back to RAM). This method is termed lazy write.

Simple cached writing
Back to a multiple-MPU system and the issue of using caches becomes far more obvious: when any processor writes to a portion of RAM the data is placed into its cache and not back into RAM. If another MPU attempts to read that same section of RAM the data it receives will be out of date. It is necessary to have the content of each of the MPU caches to be in tune with each other (or coherent, hence the term cache coherency). Various methods have been devised to ensure the caches remain as coherent as they can. The simplest of these methods involves ensuring any write operations push the data immediately back to the RAM via the bus with all MPUs in the architecture monitoring the bus for write operations: when a write operation is seen on the bus the MPU checks it's own cache for that same page of RAM and if it is cached the page is immediately re-loaded from RAM. This is a very expensive method for large parallel systems using common sub-sets of data: when a single MPU writes the data section each other MPU with the data cached must re-request the data. The method is vastly improved by the other MPUs reading the data off the bus as it is written back to RAM (termed snooping) thereby negating the need for a potential n - 1 requests for reading the same RAM location. In more advanced improvements, snooping is applied to all bus packets such that any single read operation can potentially become cached into all MPUs in the architecture.

Directory-based writing
Whether a cache is in use or not, a directory-based writing technique involves all RAM being controlled by a centrally located memory manager. The MPUs involved respect only the information given to them by the memory manager and requests for writes can come from the memory manager to an individual MPU requesting for the data to be written back immediately.

MOESI & predecesors
More advanced techniques exist for cache coherency and these begin with a similar set of abilities. Almost universally, each of these methods mark all pages of RAM as one of Modified, Shared or Invalid. More complex methods introduce the markings of Exclusive and/or Owner. The names of the methods are most commonly referred to by the initials of the methods implemented: MSI, MESI, MOSI and MOESI.

Avoiding the race condition
No matter which of the memory management techniques are used (and many more variations and techniques exist than described above), there remain possibilities to generate invalid data in the caching. However, these possibilities are due to the nature of poor or misunderstood programming techniques and/or poor compilation. This is covered in depth under the software chapter.

Unified Memory Access
As the name suggests, Unified Memory Access (UMA) describes a method by which all accesses to memory are performed in a unified, equal, manner. In a UMA design the RAM is typically pooled together and often a memory controller is available to assist the CPU(s) in accessing the RAM. UMA is by far the most common method of implementing RAM access in a SMP.

Non-Unified Memory Access
Very popular in massively parallel processing architectures and clusters alike. The Non-Unified Memory Access (NUMA) architecture is a system (single machine or cluster) which houses a single RAM block which is distributed throughout the system. For example, a four-processor architecture could be made up of two pairs of processors, each pair having direct access to 2GB of RAM. In this scenario each pair is attached to a local bus and it's shared 2GB. Access to the other pair's 2GB is performed through an inter-bus link (typically a memory controller).

A more extreme example of a NUMA system is often employed in clusters which attempt to present a single-system image: each node in the cluster houses a portion of the system RAM with the cluster software being a localised memory controller. A process existing on one node of the cluster must access a memory portion housed on another node. By comparison to the first node accessing its own real RAM (through the localised cluster memory controller thereof), attempting to access the RAM portion on the alternate node involves a much more complex scenario: the first node must make the request of the second node to send the RAM across the network; the second node must check whether the portion is already being modified to another (third) node; if being modified, the second node must request the third node relinquishes the RAM access; the third node writes the modifications back to the second node and finally the second node releases the RAM portion to the requesting node. Should two nodes require frequent modification access to the same RAM portion, the results can impact severely on the cluster's ability to process data in a worthy fashion. Thankfully, software techniques exist (much the same as those described here) to lessen the impact of such a scenario.


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Parallel Computing and Computer Clusters/Software

Software
Under old-fashioned designs programs are often cited as being akin to a document format: they begin with a header section; they then go into a loop perform the same task or series of tasks over and over until some condition is met and finally they perform some form of exit cleanup. During the loop condition, the program performs a single task to completion prior to performing any subsequent condition and thus each task is performed in serial to its prior and subsequent tasks.

Sometimes in a serial design the individual tasks have no bearing on each other and as such could be executed in any order. Under these circumstances each task is ripe for being parallelised. Many programs, however, are staged - tasks are interdependent and the amount of dependency determines how simply a set of serial tasks may be redesigned to work in parallel.

Designing parallel tasks
Before work can begin in earnest on the implementation of parallelising a suite of tasks, it is necessary to identify the inter-dependencies of the tasks. To illustrate the principal problems faced by parallelising processes some fairly basic mathematical problems can be used as examples.

The sum of all numbers
The well-known problem faced by Carl Friedrich Gauss and his fellow class mates: add up all the integers between 1 and 100. Supposing there was no mathematical formula [(1 + N)*(N/2)] to calculate this particular problem and that the individual numbers really did have to be added up individually to each other:

The mathematical properties of adding any group of integers together allows the additional to take place in any order. For example, 1 + 2 + 3 + 4 and 4 + 3 + 2 + 1 result in the same summation of 10. By the same token (1 + 2) + (3 + 4) results in the equivalent calculation of 3 + 7 and in the end the same summation of 10. The problem of adding just four numbers can be described in alternative ways also:1 + (2 + 3) + 4 or (1 + (2 + (3 + 4))). In order to provide efficient parallelisation, it is important to design how best to split the problem at hand. These latter two examples show more dependency on previous calculations than that of dividing the problem down the middle:

This approach for dividing down the middle works for any series of numbers where the count of numbers is a factor of two: 8, 16, 32. However, taking this initial approach to a longer series which utilises an even count of numbers provides another problem in the quest for parallelisation: 1 + 2 + 3 + 4 + 5 + 6. This calculation can no longer be simply divided down the middle: 1 + (2 + 3) + (4 + 5) + 6. It is already known that the calculation of 1 + 6 could be done, yet in this approach it is left out. To combat this deficiency it is therefore necessary to alter the approach to work for all even counts of numbers: pairing. Using pairing it is possible to reduce the calculations: (1 + 2) + (3 + 4) + (5 + 6). The parallelisation has now reduced the original problem to that of 3 + 7 + 11. The problem now enters a new phase entirely...

The problem still has not been solved for all counts of numbers - so far only even counts have been solved. Due to mathematical properties it is not possible to break down the summation of 3 + 7 + 11 into the separate parts of 3 + 7 and 7 + 11 and thus knowing your subject matter becomes an ever-increasingly important aspect of the parallisation: ensuring that individual parts to do repeat the whole or part of another part. For the problem at hand, then, it is a logical assumption that the tasks at hand can be partitioned into pairs and pairs of pairs until the problem as a whole is consumed with the possible exception of a single number to be added as the last step. Thus, 1 + 2 + 3 + 4 + 5 + 6 can be reduced into the parallelised form of ((1 + 2) + (3 + 4)) + (5 + 6) as it's most efficient.

The final step
The final step in the quest for the design of the parallelised problem may come as a surprising reversal: can the individual tasks be better implemented as a serial process? Knowing the architecture the problem is to be implemented on becomes an additional design principal. In the case of adding a small quantity of any numbers (not necessarily sequential as above), the majority of MPUs are very capable of performing on-die calculations in the form ((a + b) + c) + d faster and more efficiently than of the form (a + b) + (c + d) due to the need to load and store the data into registers. A command sequence for both tasks might appear as follows:

Specific Theories
...?

Compilers
...?


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Biology, Answering the Big Questions of Life/Atoms and Molecules

 Previous < Up > Next : Index

What is the world made of?
The ancient Greek philosophers studied the nature of all things.

They wanted to know what things were made of. They knew that the things in the world had substance. They take up space. You can touch them and push against them. They called this substance that all things are made of matter.

Matter is defined as any substance in the universe that has mass and occupies space.

Mass is a measure of how much matter there is in an object. On earth we measure mass by weighing an object. Weight, however can change. A person who weighs 180 pounds on the Earth would only weigh about 30 pounds on the moon even though their mass would stay the same.

But these philosophers wanted to know what the fundamental things were that the universe was built of. If you take an object and cut it in half, and then cut that object in half, eventually you should get to some thing that you can't cut. Something that is the building block that all things are made of. They called this the 'atom', which comes from the Greek prefix a which means not and the root tom which means to cut.

In the fifth century B.C. two philosophers, Democritus and Leucippus presented the first theory of atoms, however it took humans almost two an a half millennia to find out the structure of the atom.

What is an Atom?

An atom is the smallest component of an element that still has the properties of that element.

Atoms are made of three particles. protons, neutrons, and electrons. The protons and neutrons reside in the center of the atom, called the nucleus, while the electrons circle around them.

The protons have a positive charge and the neutrons have no charge. They make up the bulk of the weight of the atom. Around the nucleus, small charged particles called electrons move in complicated patterns called orbitals.

The discovery of the structure of the atom changed how we looked at the world. For one, it explained chemistry. Chemical reactions are interactions between the electrons on the surface of atoms. The properties of atoms are directly related to the number of protons found in their nucleus, which determines the number of electrons.(In normal matter you have one electron for every proton). The variation between different types of atoms such as hydrogen, which is very reactive, and helium, which is not, is directly related to the fact that hydrogen has one proton in its nucleus and helium has two.

Read more about it

 * Atom
 * Molecule
 * Organic compound


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User:TakuyaMurata/Differential forms

In particular, the chapter covers subharmonic functions.

Implicit function theorem
4 Theorem A linear operator $$T$$ from a finite-diemnsional vector space $$\mathcal{X}$$ into itself is injective if and only if it is surjective.

Proof: Let $$e_1, ... e_n$$ be a basis for $$\mathcal{X}$$. The following are equivalent: (i) $$T$$ has zero kernel. (ii) $$0 = T(\sum_{j=1}^n a_j e_j) = \sum_{j=1}^n a_j T(e_j)$$ implies that all the $$a_j$$ are zero. (iii) $$T(e_1), ... T(e_n)$$ is a basis for $$\mathcal{X}$$. Since the range of T is the span of the set $$\{ T(e_1), ... T(e_n) \}$$, the theorem now follows. $$\square$$

4 Theorem ''Let $$\Omega$$ be a neighborhood of a point $$(a, b) \in \mathbb{R}^n \times \mathbb{R}^m$$. If $$f_j(a, b) = 0$$ and $$f_j \in \mathcal{C}^1 (\Omega)$$ for $$j = 1 ... n$$, and if the matrix
 * $$\begin{bmatrix} {\partial f_1 \over \partial x_1} & \cdots & {\partial f_1 \over \partial x_n} \\ \vdots &

\ddots & \vdots \\ {\partial f_n \over \partial x_1} & \cdots & {\partial f_n \over \partial x_n}\end{bmatrix}$$ is invertible at $$(a, b)$$, then the equations $$f_j(x, y) = 0, j = 1 ... n$$, has a unique solution $$x$$ such that $$x(b) = a$$ and $$x$$ is $$\mathcal{C}^1$$ in some neighborhood of $$b$$.

Proof (from ):

We need

4 Lemma ''If a linear operator $$T$$ is injective in $$\Omega$$, then $$T^{-1}$$ is defined and continuously differentiable in $$T(\Omega)$$.

Let $$F(x, y) = (f(x, y), y)$$ for $$(x, y) \in \Omega$$.

Connected spaces
A set $$E$$ is connected if there exists no open cover of $$E$$ consisting of two disjoint open sets.

A connected component of a set $$E$$ in $$G$$ is the "maximal" connected subsets containing $$E$$; that is, the component = $$\bigcup$$ connected set $$\subset G$$ containing $$E$$. Every topological space, in other words, consists of components, which are necessarily disjoint and closed. That a topological space consists of exactly one component is equivalent to that the space is connected.

To give an example, induce to an arbitrary set $$G$$ a topology as a collection of any subsets of $$G$$ (i.e., the finest topology). The topological space $$G$$ has no closed sets since every open set in $$G$$ is also closed. The components of $$G$$ are the same as all the subsets of $$G$$ since.

4.3 Theorem ''The following are equivalent. Given a topological space $$G$$, '' Proof: Suppose $$G = A \cup B$$ for some sets $$A$$ and $$B$$. If $$\overline{A}$$ and $$B$$ are disjoint, so are $$A$$ and $$B$$ since $$A \subset \overline{A}$$. This is to say that (1) is false, which also follows if $$A$$ and $$\overline{B}$$ are disjoint for the same reasoning. This shows that (1) implies (2). Now suppose $$E$$ is nonempty, open, closed subset of $$G$$ that is not $$G$$. Then so is $$G \backslash E$$. Thus, $$G = E \cup (G \backslash E)$$, the disjoint union of an open set and a closed set. This contradicts (2). Hence, (2) implies (3. Finally, suppose (1) is false; that is, there are at least two components of $$G$$, either of which has empty boundary but is not $$G$$. $$\square$$
 * 1) $$G$$ is connected.
 * 2) If $$G = A \cup B$$, then both $$\overline{A} \cap B$$ and $$A \cap \overline{B}$$ are nonempty.
 * 3) Only $$\varnothing$$ and $$G$$ have empty boundary.

A path is a continuous function from [0, 1] to some space; e.g., a straight-line represented by $$f(t)$$ = A path is a loop if f(0) = f(1). e.g., a unit circle represented by $$f(t) = e^{t 2 \pi i}$$.

Two points $$a$$ and $$b$$ are said to be jointed by a path $$f$$ if f(0) = a and f(1) = b. We say the space is path-connected, the importance of which notion is the following.

5.1 Theorem A set $$E$$ is path-connected set if and only if it is connected.

Two paths are said to be homotopic if FIXME.

We say a space is simply connected if every path in the space is homotopic to a point. For example, in the plane $$\mathbb{R}^2$$, every circle centered at the origin is homotopic to the origin. But in $$\mathbb{R}^2 / {0}$$ the circle fails to be homotopic to the origin. Hence, the former is simply connected while the latter is not. We also see, in light of theorem 3.1, that every simply-connected space is connected.

5.1 Theorem ''Let $$E$$ be a set. The following are equivalent.''
 * (i) $$df = 0$$ implies that $$f$$ is constant for any $$f \in \mathcal{C}^1(E)$$
 * (ii) $$E$$ is connected.

Partition of unities
4 Lemma (Urysohn) ''A topological space $$X$$ is normal if and only if for any disjoint closed sets $$A$$ and $$B$$ there exists a continuous function $$f$$ such that $$0 \le f \ge 1$$, $$f = 0$$ on $$A$$ and $$f = 1$$ on $$B$$. Proof (from Urysohn's lemma):

4 Corollary A topological space $$X$$ is completely regular if and only if there exists a continuous injection from $$X$$ to a compact Hausdorff space with continuous inverse.

4 Theorem A Hausdorff space is paracompact if and only if it admits a partition of unity.

to be merged
In this chapter, we shall prove (after some works are done) Cauchy's integral formula, first by the Stoke's theorem then again by the notion of the winding number.

6.1 Theorem There exists a partition of unity $$\phi_i$$ subordinate to the cover $$\{G_j\}$$; that is: Proof: Let $$G$$ = the union of all $$G_j$$. Choose $$g_j$$ in $$C^{\infty}(G)$$ so that {all $$\mbox{supp }g_j$$} covers $$G$$ and $$ 0 \le g_j \ge 1$$. (See the lemma for why this is possible.)
 * (a) $$\phi_i$$ is infinitely differentiable in every $$G_j$$.
 * (b) $$\mbox{supp }\phi_j$$ is in $$G_j$$.
 * (c) If $$x$$ is in $$G_j$$, then $$\sum_1^N \phi_j = 1$$ for some $$N$$. (locally finite)

Let $$\phi_1 = g_1$$, $$\phi_2 = (1 - g_1)g_2$$, $$\phi_3 = (1 - g_1)(1 - g_2)g_3$$ and so forth. If $$\sum_1^m \phi_j = 1 - \prod_1^m g_j$$ for some $$m$$, then the computation gives: $$\sum_1^{m + 1} \phi_j = 1 - \prod_1^{m + 1} g_j$$. Since $$\phi_1 = 1 - (1 - g_1)$$, by induction,
 * $$\sum_1^{\infty} \phi_j = 1 - \prod_1^{\infty} g_j$$, which is locally finite.

For $$x$$ in $$G_j$$, some $$g_j(x) = 1$$. Thus, (c) holds and the others (a) and (b) are also true by construction. $$\square$$

We define the integral of a form $$\theta$$ over $$E$$ by for a partition of unity $$\phi_j$$ subordinate to the locally finite cover $$\{E_j\}$$ of $$E$$,
 * $$\int_E \theta = \sum \int_{E_j} \phi_j \theta$$.

6.1 Theorem If $$u$$ is analytic in $$\Omega$$, then:
 * $$ f(z) = \frac{1}{2 \pi i} \int_{\partial \Omega} \frac{f(\zeta) d\zeta}{\zeta-z} \ \ \ \forall z \in \Omega $$.

(See also: Calculus:Complex_analysis)

We say a function f satisfies the mean value property when:

 * $$f(z) = {1 \over 2 \pi} \int (z + \epsilon e^{i \theta}) d\theta$$.

An analytic function is an archetypical example, for the property is the immediate consequence of Caucy's integral formula. If f has the mean value property, then, for one, $$f$$ is harmonic, and for another, the maximal principle become applicable to it.

6.1 Theorem

If $$u$$ is analytic in $$\Omega$$, then the following are equivalent: and if any of the above is true, then Proof: Let $$E = \{ f : f \mid_\omega \}$$. If $$u$$ is in $$E$$, then its derivative:
 * (a) $$u^{(k)}$$ (z) = 0 for all $$k$$.
 * (b) $$u \mid_\omega$$ = 0 for some $$\omega \subset \Omega$$ open.
 * (c) $$u$$ has a non-isolated zero.
 * (d) $$u \mid_\Omega$$ = 0.
 * $$\dot u = \lim_{h \rightarrow 0} h^{-1} (f(x + h) - f(x))$$

is 0 in $$\Omega$$ since $$\omega$$ consists of interior points, and so we may suppose $$x + h$$ is $$\omega$$. Thus, from (b), (a) follows. That (b) implies (c) is obvious since an interior point is non-isolated. To show (d), let Z be $$\{ z \subset \Omega : f(z) = 0 \}$$. Then $$Z$$ is closed since the inverse of $$f$$, which is continuous by the inverse theorem, maps a closed set {0} back to $$Z$$ in $$\Omega$$. $$Z$$ is also open, which we can know by considering a power series expansion. Since $$Z$$ is nonempty by assumption, (d) follows after (a). $$\square$$ (FIXME: this is still a partial proof)

6 Theorem (Runge) ''Let $$K \subset \mathbb{C}$$ be compact, and $$\omega$$ be an arbitrary open subset of $$\mathbb{C}$$ containing $$K$$. Then the following are equivalent:''
 * (a) For any $$f \in \mathcal{A}(K)$$ and an integer $$j$$, we can find a $$u \in \mathcal{A}(\omega)$$ so that:
 * $$\sup_K | f - u | < 2^{-j}$$
 * (b) K is holomorphically convex.

Proof: The theorem is a consequence of the Hahn-Banach theorem.

A compact subset K of a complex plane is said to have the Runge property if $$K$$ satisfies any of the statements in the theorem.

6.2 Theorem (Weierstrass) ''Let $$\Omega \subset \mathbb{C}$$ be open. Let the sequence $$z_j \subset \Omega$$ be discrete, and $$n_j$$ be a sequence of arbitrary integers. Then there exists a nonzero $$f \in \mathcal{A}(\Omega \backslash \{ z_1, z_2, ... \})$$ such that for each $$j$$ $$(z - z_j)^(-n_j) f$$ is nonzero and analytic in some open set containing $$z_j$$.

Proof: Let $$K_j$$ be an exhaustion by compact sets of $$\Omega$$ with the Runge property. By the Runge property, for each $$j$$, we find a $$u_j \in \mathcal{A}(\Omega)$$ so that:
 * $$\sup_{K_j} | (z - z_j)^{n_j} + u_j | < 2^{-j}$$

where since the sequence $$z_j$$ is discrete, we may suppose $$z_k \not \in K_j$$ for any $$k \le j$$. Let
 * $$g = \sum_1^\infty (z - z_j)^{n_j} + u_j$$, and $$f(z) = e^{\int_0^z g(s)ds}$$.

Then $$f$$ is analytic in $$\Omega$$ except for all $$z_j$$. Also, let $$j$$ be fixed and $$\omega$$ be an open set containing $$z_j$$ and no other terms in the sequence. Then $${\dot f \over f} = g$$ in $$\omega$$. Thus, by Cauchy's integral formula,
 * $$2 \pi i n_j = \int_{\omega} g(s)ds = \int_{\omega} { \dot f(s) \over f (s) }ds$$

It now follows that the argument principle says $$f$$ has a zero of order $$n_j$$ (if the order is negative, then it is actually a pole). $$\square$$

This formulation is probably more illustrative, if it states more weakly.

6.2 Corollary Every discrete subset of $$\Omega \subset \mathbb{C}$$ is the zero and pole set of some analytic function.

Proof: Every discrete set is countable.

6 Theorem ''Let $$\Omega \subset \mathbb{R}^n$$ be open and connected and $$\eta$$ be one-form. Then the following are equivalent:
 * (1) $$\eta$$ is exact on $$\Omega$$.
 * (2) $$\int_{\gamma} = 0$$ if $$\gamma$$ is a closed path.
 * (3) $$\int_a^b \eta$$ is independent of path.

Proof: On $$\Omega$$, if $$\eta$$ is exact, then $$\eta = df$$ for some zero-form $$f$$. It thus follow:
 * $$\int_a^b \eta = \int_{\gamma} df = f(\gamma(1)) - f(\gamma(0))$$.

If $$\gamma$$ is a closed path, then $$\gamma(1) = \gamma(0)$$ by definition, and hence, (2) is true. Let $$\gamma_1$$ and $$\gamma_2$$ be arbitrary paths from $$a$$ to $$b$$. Then
 * $$\int_{\gamma_1 - \gamma_2} \eta = 0$$ if (2) is true.

Thus, (2) implies (3). Finally, show (3) implies (1). Let $$f(x) = \int_0^x \eta$$. Then $$df = \sum_1^n {\partial f \over \partial x_i} dx_i$$. For each $$i$$, if \int_x^{x + h_i} \eta = g(x + h_i) - g(x), then since $$\int_0^{x + h_i} - \int_0^x = $$,

Here the derivative of $$f$$ does exist since the integral is independent of path. We conclude that $$ df = \sum_1^n {\partial f \over \partial x_i} dx_i = \eta$$.
 * $${\partial f \over \partial x_i} (x)$$
 * $$= lim_{h_i \to \infty} {1 \over h_i} (\int_x^{x + h_i}\eta$$
 * $$= lim_{h_i \to \infty} {1 \over h_i} (g(x + h_i) - g(x))$$
 * $$= {\partial g \over \partial x_i}(x)$$
 * }
 * $$= lim_{h_i \to \infty} {1 \over h_i} (g(x + h_i) - g(x))$$
 * $$= {\partial g \over \partial x_i}(x)$$
 * }
 * }

Stokes formula
4 Theorem (Stokes) If $$\omega \subset \mathbb{C}$$ has boundary which consists of finitely many Jordan curves, then:
 * $$\int_{\partial \omega} \eta = \int_\omega d\eta$$

Proof: (FIXME: To be written)

4 Corollary (Green) If $$\omega \subset \mathbb{C}$$ has boundary which consists of finitely many Jordan curves, then we have:
 * ''$$\int_\omega (f\Delta g - g\Delta f) dx \wedge dy = \int_{\partial \omega} \left( f{\partial \over \partial x} g - g{\partial \over \partial x} f \right)dy - \left(f{\partial \over \partial y} g - g{\partial \over \partial y} f \right)dx$$.

Proof: $$d \left( f{\partial \over \partial x} g - {g \over \partial x} f \right) \wedge dy = \left( f {\partial^2 \over \partial x^2}g - g {\partial^2 \over \partial x^2}f \right) dx \wedge dy$$. $$\square$$

Harmonicity
Let $$\Omega \subset \mathbb{R}^n$$. A function $$u \in \mathcal{C}^2(\Omega)$$ is said to be harmonic if
 * $$\sum_1^n {\partial^2 u \over \partial x_j^2} = 0$$ (the Laplace equation)

We also define the poisson kernel
 * $$P(x / R, y) = {C_n}^{-1} (1 - | x / R |^2) | y - x / R |^{-n}$$

where $$C_n$$ is the volume of a unit ball in $$\mathbb{R}^n$$.

4. Theorem ''Let $$\Omega = \mbox{Ball}_R$$. Then $$u$$ is harmonic on and continuous on $$\overline{\Omega}$$ if and only if
 * $$u(x) = \int P(x / R, y) u(Ry) d\omega(y)$$.

Proof: Suppose $$u$$ is harmonic on $$\Omega$$. Then using the Green's function
 * $$u(x) = \int P(x / r, y) u(ry) d\omega(y)$$ for $$|x| < r < R$$.

Letting $$r \to R$$ gives the direct part. Conversely, if $$x \in \Omega$$, then the second derivative of $$u$$ = 0 since $$P$$ is harmonic on $$\Omega$$. $$\square$$

4. Corollary (mean value property) ''Let $$\Omega = \mbox{Ball}_R$$ and $$u$$ be harmonic on and continuous on $$\overline{\Omega}$$. Then''
 * $$u(0) = \int u(Ry) {d\omega(y) \over C_n}$$.

Proof: Let $$x = 0$$ in the theorem. Then $$P(0, y) = {C_n}^{-1}$$.

4. Corollary (maximum principle) If $$\Omega \subset \mathbb{R}$$ and $$u:\Omega \to \mathbb{R}$$ is harmonic on $$\Omega$$ and continuous on $$\overline{\Omega}$$, then for $$x \in \Omega$$,
 * $$\min_{\mbox{b}\Omega}u \le u(x) \le \max_{\mbox{b}\Omega}u$$

where if the equality holds at some $$x \in \Omega$$, then $$f$$ is constant in the component of $$x$$. Proof: (i) Suppose $$\Omega = \mbox{Ball}_R$$. Then for $$x \in \Omega$$

since
 * $$u(x)$$
 * $$= \int_{|y| = 1} P(x / R, y) u(Ry) d \omega(y)$$
 * $$\le \sup_{\mbox{b}\Omega} u \int_{|y| = 1} P(x / R, y) d\omega(y)$$
 * $$= \sup_{\mbox{b}\Omega} u$$
 * }
 * $$\le \sup_{\mbox{b}\Omega} u \int_{|y| = 1} P(x / R, y) d\omega(y)$$
 * $$= \sup_{\mbox{b}\Omega} u$$
 * }
 * $$= \sup_{\mbox{b}\Omega} u$$
 * }
 * $$\int_{|y| = 1} P(x / R) d\omega(y) \sup_{\mbox{b}\Omega} = 1$$ when $$|x| \le |R|$$.

Likewise, $$-u(x) \le \sup_{\mbox{b}\Omega} -u$$. Thus,
 * $$\inf_{\mbox{b}\Omega}u \le u(x) \le \sup_{\mbox{b}\Omega}u$$

where $$\inf$$ and $$\sup$$ are actually $$\min$$ and $$\max$$, respectively since the continuity of $$u$$ and the compactness of a closed ball. (ii) Suppose $$\Omega$$ is arbitrary. Let $$x \in \Omega$$. From (i) it follows that $$u$$ is constant on every open ball containing $$x$$. Since $$\Omega$$ is open, every component of $$\Omega$$ is open. Since an open set is the union of non-disjoint open balls, $$u$$ is constant on the component of $$x$$. $$\square$$

4. Theorem ''Let $$u$$ be continuous on $$\Omega \subset \mathbb{R}^n$$. Then the following are equivalent:'' Proof: The mean value property says:
 * (i) $$u$$ is harmonic.
 * ''(ii) If $$\delta \le 0$$ is given,
 * $$\int u(x + ry) {d\omega(y) \over C_n} \wedge d\mu(r) = u(x) \int d\mu(r)$$
 * where $$d(x, \mbox{b}\Omega) \le \delta$$ and $$\mbox{supp} (d\mu) \subset [0, \delta]$$.
 * (iii) If $$\delta > 0$$ is given, then (ii) holds.
 * $$u(x) = \int u(x + ry) {d\omega(y) \over C_n}$$

By integrating both sides we get:
 * $$u(x) \int d\mu(r) = \int u(x + ry) {d\omega(y) \over C_n} \wedge d\mu(r)$$

Hence, (i) implies (ii). Clearly, (ii) implies (iii). Suppose (iii), and let $$B$$ be an open ball with $$\overline{B} \subset \omega$$. Let $$h$$ be harmonic on $$B$$ and continuous on $$\overline{B}$$ such that $$u = h$$ on $$\mbox{b}B$$. If $$\mbox{Ball}_{\delta, x} \subset \Omega$$, then using (iii)
 * $$\int (h - u)(x + ry) {d\omega(y) \over C_n} \wedge d\mu(r) = (h - u)(x) \int d\mu(r)$$

where $$h - u = 0$$ on the boundary of $$B$$. Since $$d\mu(r)$$ has non-zero measure, $$u = h$$ on $$B$$. Thus, (iii) implies (i). $$\square$$

Cauchy's integral formula
4 Thorem ''Let $$G$$ be a bounded open subset of $$\mathbb{C}$$ whose boundary is smooth enough that Stokes' formula is applicable. If $$u \in \mathcal{C}^1(\overline{G})$$, we have:
 * $$u(w) = {1 \over 2 \pi i} \int_{\partial G} {u(w) \over z - w} dz - {1 \over \pi} \int_G {\partial u \over \partial \bar z} (z) {1 \over z - w} dx \wedge dy$$ for $$w \in G$$

4 Theorem ''Let $$\mu$$ be a complex-valued measure with compact support in $$\mathbb{C}$$ and define
 * $$u(w) = \int {1 \over z - w} d\mu$$

Schwarz lemma
4 Lemma (Schwarz) ''If $$f$$ is analytic and $$|f(z)| \le 1$$ for all $$|z| < 1$$ and $$f(0) = 0$$, then we have:
 * $$|f(z)| \le |z|$$ for all $$|z| \le 1$$

Moreover, if the equality in the above holds at some point $$w \ne 0$$, then $$f$$ is proportional to $$z$$

Proof: The hypothesis means that we can write $$f(z) = zg(z)$$. Furthermore, if $$0 < r < 1$$, the maximum principle says
 * $$\sup_{|z| \le r} |g(z)| = \sup_{|z| = r} |g(z)| \le {1 \over r}$$.

and $$g$$ is constant if $$g = 1$$ at some point on the circle $$|z|=r$$. Letting $$r \to 1$$ completes the proof. $$\square$$

Addendum
A Lie algebra is an algebra whose multiplication, denoted by $$[,]$$, satisfies for all $$x, y, z$$. Under the assumption (ii) we see (i) is equivalent to
 * (i) $$[x, x] = 0$$, and
 * (ii) $$[[x, y], z] + [[y, z], x] + [[z, x], y] = 0$$
 * $$0 = [x + y, x + y] = [x, y] + [y, x]$$.

When given an algebra is associative; i.e., $$(xy)z = x(yz)$$ we can turn the algebra into a Lie algebra by defining $$[x, y] = xy - yx$$, called a commutator. Indeed, it is clear that $$[x, y]$$ distributes over scalars and addition and the condition (i) holds. It then follows $$x,y],z] = [x,[y,z - [y,[x,z]]$$.

Also, $$ \int e^x = f(u^n) $$

title: User:TakuyaMurata/Differential forms


text:
Parallel Computing and Computer Clusters/Feature Set

Redundancy and failover
High availability

Redundant tasks
How do you know the task worked correctly?

Task failover
How to determine whether a task has failed


text:
Parallel Computing and Computer Clusters/The End Result

The end result
What reason is the set up required?

What future aims should be encompassed?


text:
Parallel Computing and Computer Clusters/Example Technologies

Clustered MySQL
... and many more...


text:
Talk:Ancient History/Human Evolution/Neolithic Age

This page needs either editing, or breaking down into multiple modules which should then be extended. I'm too close to the text right now to deal with that; maybe in a few weeks after I've got some distance from the text. Andrew Watt 15:17, 9 June 2006 (UTC)

 * Note that that's only a guideline. The browser problem no longer applies, and the 30KB limit guideline is now used to make encyclopedia articles on Wikipedia succinct and digestible, which would not apply to textbooks. Some featured articles on Wikipedia are even as long as 100KB without any complaints. --hagindaz 23:18, 9 June 2006 (UTC)

I dispute the dates and probably some facts stated in the page
In a fallow up necessary to verify the correctness of an edit in regards to the domestication of cats I've come to note that most if not all of the dates (List of domesticated animals) where incorrect. As such I have serious doubt that the problem is continued in the rest of the book, I haven't checked outside of this section that I have now attempted to correct. If you verify the facts and dates please comment here and remove the tag. --Panic (discuss • contribs) 03:07, 16 October 2011 (UTC)