text:
Real Analysis/Continuity

Now that we've defined the limit of a function, we're in a position to define what it means for a function to be continuous. The notion of Continuity captures the intuitive picture of a function "having no sudden jumps or oscillations". Yet, in this page, we will move away from this elementary definition into something with checklists; something with rigor. This will be important not just in Real Analysis, but in other fields of mathematics as well.

Continuity marks a new classification of functions, especially prominent when the theorems explained later on in this page will be put to use. However, if one is reading this wikibook linearly, then it will be good to note that the wikibook will describe functions with even more properties than continuity. As an example, the functions in elementary mathematics, such as polynomials, trigonometric functions, and the exponential and logarithmic functions, contain many levels more properties than that of a continuous function. We will also see several examples of discontinuous functions as well, to provide some remarks of common functions that do not fit the bill.

Definition
Readers may note the similarity between this definition to the definition of a limit in that unlike the limit, where the function $$f$$ can converge to any value, continuity restricts the returning value to be only the expected value when the function $$f$$ is evaluated. This added restriction provides many new theorems, as some of the more important ones will be shown in the following headings.

Operations
Since limits are preserved under algebraic operations, let's check whether this is also the case with continuity.

Algebraic
We see that if $$f(x)$$ and $$g(x)$$ are both continuous at c, continuity still works out fine for the following situations:

Note that of course, for any division, g(c) must be a valid number i.e. not 0.

This is actually a corollary when you look at the proofs for the preservation of algebraic operation for limits. Simply replace the limit values L and M with ƒ(c) and g(c) respectively.

We can use sequential limits to prove that functions are discontinuous as follows:

 * $$f(x)$$ is discontinuous at $$c$$ if and only if there are two sequences $$(x_n)\rightarrow c$$ and $$(y_n)\rightarrow c$$ such that $$ \lim_{n \rightarrow \infty}(f(x_n)) \not= \lim_{n \rightarrow \infty}(f(y_n))$$.

Composition
Composition is a lot trickier though, as always, but it still works as intuition would suggest; composition of two continuous functions is still a continuous function.

The proof simply works by fulfilling the definition of continuity for the composition function of $$f$$ and $$g$$ using variable substitutions based off fulfilling all requirements for those variables. As such, there is no algebra and no theorems used other than purely definitions.

The Three Continuity Theorems
Think about what an intuitive notion of continuity is. If you can’t the image of a polynomial function always works. The smooth curve as it travels through the domain of the function is a graphical representation of continuity. However, how do we mathematically know that it’s continuous? Well, we’ll start with the Three Continuity Theorems that will verify this notion.

The Intermediate Value Theorem
This is the big theorem on continuity. Essentially it says that continuous functions have no sudden jumps or breaks.

Proof
Let $$S = \{x \in (a,b): f(x) < m\}$$, and let $$c = \sup S$$.

Let $$\epsilon = |f(c) - m|$$. By continuity, $$\exists \delta: |x-c|< \delta \implies |f(x)-f(c)|< \epsilon $$.

If f(c) < m, then $$|f(c+\frac{\delta}{2}) - f(c)| < \epsilon$$, so $$ f(c+\frac{\delta}{2}) < f(c) + \epsilon = m $$. But then $$c + \frac{\delta}{2} \in S$$, which implies that c is not an upper bound for S, a contradiction.

If f(c) > m, then since $$c = \sup S$$, $$\exists x: x \in S, c>x>c-\delta$$. But since $$|x-c|<\delta$$, $$|f(x)-f(c)|<\epsilon$$, so $$f(x)> f(c) - \epsilon$$ = m, which implies that $$x \notin S$$, a contradiction. $$\Box$$

We will now prove the Minimum-Maximum theorem, which is another significant result that is related to continuity. Essentially, it states that any continuous image of a closed interval is bounded, and also that it attains these bounds.

Minimum-Maximum Theorem
This theorem functions as a first part in another bigger theorem. However, on its own, it helps bridge the gap between supremums and infimums in regards to functions.

Proof
Assume if possible that $$f$$ is unbounded.

Let $$x_1=\tfrac{a+b}{2}$$. Then, $$f$$ is unbounded on at least one of the closed intervals $$[a,x_1]$$ and $$[x_1,b]$$ (for otherwise, $$f$$ would be bounded on $$[a,b]$$ contradicting the assumption). Call this interval $$I_1$$.

Similarly, partition $$I_1$$ into two closed intervals and let $$I_2$$ be the one on which $$f$$ is unbounded.

Thus we have a sequence of nested closed intervals $$[a,b]\supseteq I_1\supseteq I_2\supseteq\ldots$$ such that $$f$$ is unbounded on each of them.

We know that the intersection of a sequence of nested closed intervals is nonempty. Hence, let $$x_0\in I_1\cap I_2\cap\ldots$$

As $$f(x)$$ is continuous at $$x=x_0$$, there exists $$\delta >0$$ such that $$x\in V_{\delta}(x_0)\implies f(x)\in (f(x_0)-1,f(x_0)+1)$$ But by definition, there always exists $$k\in\mathbb{N}$$ such that $$I_k\subseteq V_{\delta}(x_0)$$, contradicting the assumption that $$f$$ is unbounded over $$I_k$$. Thus, $$f$$ is bounded over $$[a,b]$$

Extreme Value Theorem
This is the second part of the theorem. It is the more assertive version of the previous theorem, stating that not only is there a supremum and a infimum, it also is reachable by the function ƒ and will be in between the interval you specified.

Proof
Assume if possible, $$M=\sup (f([a,b]))$$ but $$M\notin f([a,b])$$.

Consider the function $$g(x)=\frac{1}{M-f(x)}$$. By algebraic properties of continuity, $$g:[a,b]\to\mathbb{R}$$ is continuous. However, $$M$$ being a cluster point of $$f([a,b])$$, $$g(x)$$ is unbounded over $$[a,b$$, contradicting (i). Hence, $$M\in f([a,b])$$. Similarly, we can show that $$m\in f([a,b])$$.

Appendix
Continuity will come again in other branches in mathematics. You will come across not only different variations of continuity, but you will also come across different definitions of continuity too.

Uniform Continuity
Let $$A\subseteq\mathbb{R}$$

Let $$f:A\to\mathbb{R}$$

We say that $$f$$ is Uniformly Continuous on $$A$$ if and only if for every $$\varepsilon>0$$ there exists $$\delta>0$$ such that if $$x,y\in A$$ and $$|x-y|<\delta$$ then $$|f(x)-f(y)|<\varepsilon$$

Lipschitz continuity
Let $$A\subseteq\mathbb{R}$$

Let $$f:A\to\mathbb{R}$$

We say that $$f$$ is Lipschitz continuous on $$A$$ if and only if there exists a positive real constant $$K$$ such that, for all $$x,y\in A$$, $$|f(x)-f(y)| \le K |x-y| $$.

The smallest such $$K$$ is called the Lipschitz constant of the function $$f$$.

Topological Continuity
As mentioned, the idea of continuous functions is used in several areas of mathematics, most notably in Topology. A different characterization of continuity is useful in such scenarios.

Theorem
Let $$A\subseteq\mathbb{R}$$

Let $$f:A\to\mathbb{R}$$

$$f(x)$$ is continuous at $$x=c$$ if and only if for every open neighbourhood $$V$$ of $$f(x)$$, there exists an open neighbourhood $$U$$ of $$x$$ such that $$U\subseteq f^{-1}(V)$$

It must be mentioned here that the term "Open Set" can be defined in much more general settings than the set of reals or even metric spaces, and hence the utility of this characterization.

title: Real Analysis/Continuity


text:
Talk:Arabic/Basic Phrases

New Ideas
Here are some possible catagories I would like to propose.

 * 1) I don't understand.
 * 2) Important sentences for tourists wanting information. (questions and answers)
 * 3) How are you, Meeting and greeting people.
 * 4) Polite expressions
 * 5) Accepting and giving gifts.
 * 6) Buying somehting (asking for a lower price, etc)
 * 7) Asking for things you want.
 * 8) Food preferences. Refusing food, and giving reasons.
 * 9) Talking about language capabilities.
 * 10) Talking about where you learnt Arabic, etc.
 * 11) Talking about what grade you are in. Or what school you go to. How long you have been there, How long you will stay.
 * 12) Talking about what you are doing (I am visiting, I am on vacation)
 * 13) Talk about occupation, and maritial status, Where one is from, etc.
 * 14) Apologizing
 * 15) Camera, am I allowed to take a picture, can you take this picture for me, etc.
 * 16) Talking on the telephone

I also think, that people who have no knowledge of Arabic, should add phrases to proper catagories. Later on others can translate them, and give information on meaning.

Major addition
Added:
 * some phrases (all are from MSA)
 * word by word transliteration (made it less ambigous)
 * syllable by syllable transliteration

I added some phrases. Including two words understood, but rarely used in the arabic of today (كلا and بلى). All additions are MSA as far as I can see. I improved the method of transliteration. I added curly brackets to distinguish digraphs even-though this method seems clumsy to me. The syllable by syllable transliteration should be very useful for beginners. There are different ways that such phrases could be broken into syllables. I included the most correct way. Perhaps, the other ways will be added later, to improve listening comprehension.

A few questions ought to be answered:
 * 1) What is the exact purpose of the "Arabic Basic Phrases" page?
 * 2) Is it living up to the purpose?
 * 3) Is this page in the right place?
 * 4) Does unilang have editable phrasebook pages, such as this one?

I think there is a need for :
 * Arabic phrase pages for each dialect
 * One phrase repository for phrases that are common to all arabic
 * One that introduces simpler phrases, and then more complex ones.
 * One that has phrases sorted by in what situation they are used.
 * Word by word translation of each word in sequence.

ex.   It should be done like this: الولد      فعل            شيء did         the                <---Top translation line thing                   boy                   <---Bottom translation line Transliteration: al-waladu fa`ala shay'an. (S) Translit.: al-wa-la-du-fa-`a-la-shay-an Translation: The boy did something. Notes:

Notice how "the" lines up with ال because their function is similar. This might require the use of tables. Letters that attach to a word have translations that go on the top translation line, while the main meaning of the word goes on the bottom one.

I'll add some more phrases later.

Changes in appearance
I greatly appreciate your work on Arabic, because Arabic is a language that always thrilled me. I am really happy of being able to help you on it, and I hope you like my changes :-) However, if you think the letters are a bit too big (I wanted them to be easilly readable) just post it here and I'd be happy to change it. Or simply change  to whatever suits best. Please, please continue your work on it, and try to add more information. It's really interesting! :-) Oh, and, by the way, you can use  to change lines --seems you missed it ;-)

We could also move this page to a more appropriate name, such as Arabic:Basic Phrases, so as to maintain some order in this wiki :-)

Oh, and, for anyone interested, I believe [Course on Arabic alphabet] has lots of information on how to read and write, free of charge. --Wizard0 22:36, 19 Feb 2005 (UTC)

Pronunciation
Isn't there a standard way of writing Arabic pronounciation in the latin alphabet? If there is, it might be a good idea to use it instead of doing it phrasebook-style -- Kowey 13:53, 28 Mar 2005 (UTC)

Moved from page: This were some of the basic phrases in arabic, i wrote the pronunciation in normal english to make it comprehensible by any student of any age, sorry the page is a bit messy and misses a lot but i am new to wikibooks, and i am still getting used to the editor...

Age
I don't know how to type in Arabic but there is a mistake - the correct way to ask one's age is not "Cam Umrak?" but "Qadeish Umrak?"
 * Bet you aren't a native speaker, Kam Umrak? is a standard Arabic phrase that is quite understandable anywhere in the Arab World. The other variant you proposed is a one in the local dialect of Bilad Al Shaam (Palestine, Jordan, Lebanon, and Syria). Please keep it as it is.195.229.241.182

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

title: Talk:Arabic/Basic Phrases


text:
Movie Making Manual/Meetings

1st meeting - 10th March 2005

 * 10th March 2005 18:00 GMT
 * http://www.thefleapit.com/

Agenda

 * 1) Promoting the MMM
 * 2) Print (Below The Line? Dazed? DV? Filmmaker? Movie Maker? Showreel Magazine ? Res?
 * 3) Press release
 * 4) Web (SP?, UK screen? ,New Producers Alliance?, Talent Circle?, scriptfactory? Netribution?)
 * 5) Press release
 * 6) Email (BBC newsletters? Film Society news letters? BBC Film Network? BECTU PACT NPA Equity Panaco NFT NFTS LFS)
 * 7) Press release
 * 8) Post card
 * 9) Events (Short film nights, seminars, workshops etc) Use existing events to promote the wiki.
 * 10)  Let people suggest changes to the wiki and make live updates on a big screen.
 * 11) Slides
 * 12) short ads to be shown at screenings animated sequence - call out on SP bulletin
 * 13) Ask the presenter to mention the MMM
 * 14) Training events: master classes, apple events,
 * 15) Get manufacturers to include snapshot sections in products and online (Apple etc)
 * 16) MMM 15 second advert competition not yet
 * 17) Posting forum answers which link to the MMM (e.g. "See this MMM page for info on x")
 * 18) Potential MMM givers - ask for money, ask for employees contribute to experience to MMM
 * 19) Sponsors
 * 20) Training organisations (Raindance, Skillset)
 * 21) Rental Houses (VMI)
 * 22) Equipment manufacturers (Sony, Apple, Adobe, Avid, DreamTech, Digidesign, Panasonic, Canon)
 * 23) Networks (Shooting People, UK screen)
 * 24) Post Production (Pixar, ILM, Framestore)
 * 25) Funding
 * 26) Government (Skillset, CNC)
 * 27) What to do with money?
 * 28) post all accounts on MMM
 * 29) 1/3 of income goes to Wikimedia Foundation
 * 30) Print promotions
 * 31) Google ads
 * 32) Worldwide Party
 * 33) Printing snapshot books
 * 34) MMM structure
 * 35) Icons for text boxes
 * 36) Quotes
 * 37) Tips
 * 38) Examples in films, in scripts etc (eg, tracking shots- with DVD chapter)
 * 39) Icons for section
 * 40) associated wikibooks - create a header to link film related wikibooks
 * 41) directory
 * 42) community
 * 43) film history
 * 44) film theory
 * 45) MMM Front Page
 * 46) Like the CookBook? no
 * 47) A regular updated page like a newsletter (with highlighted articles, summaries, condensed toc etc)? no
 * 48) making MMM international (finding dedicated editors abroad)
 * 49) International promotions - pushing for mass
 * 50) Illustrations, graphics, video and audio yes
 * 51) (slightly off topic: can we edit video in a "wiki" way?  e.g. make access to the original videos free and then upload the most recent EDL... maybe we can have "wiki video tutorials" - tutorials on movie making, shot on video and edited in a wiki fashion)
 * 52) MMM Logo done
 * 1) MMM Logo done

title: Movie Making Manual/Meetings


text:
Talk:Climate Change/FAQs

Hi there,

I think this book is an excellent idea... but I would like to propose that we merge this book with the existing book on Climate change. The Climate Change book plans to include the content which is currently on this EnviroFacts book. Dan AKA Jack 11:33 GMT 18th Feb 2005

title: Talk:Climate Change/FAQs


text:
User:Dan-aka-jack/Business ideas

Have you ever had a great idea for a business but you haven't got the time to get it off the ground? Well, here's a good place for us to collect our ideas so - hopefully - some kind person will make our lives easier (and make loads of money) by taking up the idea.

If you already know of a business which serves one of these ideas then please make a note of this on the relevant page.

=Communications=

Web-based SMS service
We all need to send SMS messages. But it's a real pain doing it from the handset of your phone. So why isn't there a decent web-based SMS messages service? Sure, there are some out there, but they're all crap.

It would be really cool if you could send SMS messages messages from your email client.

I have done a fair amount of research into this idea, but had to shelve it due to other employment commitments and lack of finance. The basic concept is to recive ordinary email which the sender want's relayed to a physical mailing address. The destination address is placed in the subject field of the email so it can be filtered out for printing of envelopes. I called my service "Wemail"

The company acts as a mediating service. The emails are recieved and collated, translated perhaps into postscript and spooled for printing. There are many large companies that allready exist which handle bulk mailing services, and they could be a outsourced to handle large mail runs on the apropriate scale, sending large numbers of mail to different destination addresses.

The only tweaking needed would be to make arangements with mailing service, so that they can handle the printing and collating of letters which have individual contents. I'm sure it can all be done. You set up a website with Information, payment systems, and disclaimers. A customer can register for some credit say 20 virtual stamps, you charge a nominal amount allowing for profit. The customer can then write a letter using their normal email system, and it will be sent to the destination of a normal street address via snail-mail.

=Environment & Wood products= Greenpeace should get into the timber industry, and charge a premium for wood from well managed forest & sell to their environmental buddies.

=Time Management= A combination of a journal and a calendar. This would say the date and time when ever you write in it. It would also show previous entries, so that if you write in it January 2nd, you would see all of your other January 2nd entries. You would open it up and just start typing and it would automatically enter the date and time. It would have 365 pages (one for each day), and it would put entries for each year on the same page.

I think this would be cool because it would help you get a sense of progress, as you compared what you were doing the previous years on the same day.

=Computers=

Battle Field of Ideas--A Wiki based computer game
We should create a system where ideas can compete in a survival of the fittest-tournament.

We could use this website. We would start by letting the popularity of different ideas be used as the strength of an online role-playing-game’s character. Much like [Everquest]'http://en.wikipedia.org/wiki/Everquest'. I would call the game, battle field of ideas? Why would I do this? Because I believe that we should create a system where ideas can compete. This would be a way that people would be interested in the success of an idea.

For example, any of the suggestions on this web site would work. A game player would go looking for the idea that he thought was the best. Then he would try and convince as many people as he could to agree with him, during the duration of the game… Maybe a tournament would last a couple of months.

To accomplish this, first you have a web page where people debate issues. Then you track the popularity of a couple hundred different particular ideas. These popularities will be represented by the percentage of people who agree or disagree with that issue.

You then let these percentages represent different characteristics of a particular character in a role-playing game.

For example, this game would work much like [Everquest] [an online multiplayer computer game -Ed.] However in Ever-quest characters have different pre-programmed strengths. In this game, maybe once a day, your game would download the strengths for your character from our database.

Why would I want to build this game and why would people want to play it?

I would like you to ask me why, and I’ll try to respond, however I’ll explain a little bit more here.

This web site would be ½ discussion board, ½ video game. I’ve been thinking a lot about evolution. Businesses and species evolve because they allow for a system of survival of the fittest. We need to come up with a system where ideas can compete. To do this we should track idea’s popularity over time, much like stocks are tracked. We should also make people want to be involved in the war of ideas. So why not make a video game out of it? However I am bringing up lots of different issues, and we should just do one at a time…

=Electronics=1.0 I would like to discuss the possibility of developing an electronic textbook for our school childern. This single unit would contain all the text books for a set grade and remove a lot of weight from students backpacks. I would also enhance the security of our schools by removing a large bulky space in which something can be hidden. I'll keep an eye out for anyone interested in this discussion.

A CD player that will play the separate parts of songs.
You could control the levels of each track of the different instruments with any given song.

Reason to Agree

Amature Musicians would pay to be able to hear just one part of a song isolated from the whole, so they could learn that part. Record CD's, and build CD players that will maintain the separate tracks from the original recording. Example: Vocals, lead guiter, bass, clap track, etc. Ideas: This should be simple. The technology already exists, however it needs to transition from studio/home recording equipment into a component which fits nice and snug with the DVD player, reciever, etc. Why: This would be of special benefit to those who are interested in trying to play an instrument. Principal: Empower future musicians. Let them take control of the music that they listen prefer to learn from and allow them isolate the tracks for ease of learning. It would follow that the source CD compnent could export out the individual tracks for editing and remixing.

=Transport=

GPS map wiki
GPS map wiki for satellite navigation - Most of the GPS maps used for car sat nav systems get out of date very quickly. So why not apply the wiki concept to GPS maps?

GPS maps used in car sat nav systems get out of date very quickly as the roads develop. So what better way to update the maps than with a wiki system? If you, as a driver, find an error in the map then you can submit a change using a very simple interface on the map system. This wiki idea could also be applied to the mapping of speed cameras, restaurants etc.

A wiki on building new maps and online maps already exists, but I wish it were easier for individuals to make small corrections to maps. Other wiki would benefit a lot from wiki-like map updates.

Giving Bus location info by SMS.
The most frustrating thing about catching the bus is not knowing how long it will be until the next one comes. Sometimes it might be quicker walking, or catching a bus other than the one you usually wait for. The bus LED Bus schedule screens in the UK are expensive (prohibitively so I suspect), often out of order and have proven prone to vandalism. This could be easily solved by putting a GPS tracker in all the buses and linking them up to a cental database.

The person waiting for the bus would then SMS the code of the bus stop they are waiting at followed by the number of the bus they are waiting for and receive a SMS reply with an estimated time until arrival. The transport authority could charge a small fee for the SMS and tehreby recoup the cost of the system.

Note: In Swindon, UK, this system is already in place. Each bus stop has an alphacode on it, which can be texted to a 5-digit number for a list of the next buses, and their estimated times of arrival. Thamesdown Transport Ltd charges a fee of 25p (I think) on top of your normal text rate.

See also

 * http://www.st-andrews.ac.uk/estates/txt2traveline%20leaflet1.pdf
 * http://www.camcnty.gov.uk/sub/eandt/highways/bustimes/sms/full_list_19_19a.pdf
 * http://www.travelwm.co.uk/events/ptv/bconnections.asp
 * http://thamesdowntransport2.sequence.co.uk/text_go/text_go.htm
 * http://www.devon.gov.uk/index/transport/public_transport/buses/services-4/text_messaging_service.htm
 * Malcolm may be able to tell you a little more about the little history behind the Text Code 84268.
 * He might say, 'Imagine a wheel on your phone keypad, and for UK, the service number starts with Eight, anti-clockwise'

Reason to amend this idea: Each Stop should have a smart card or RF tag in it which trasmit a standarized signal within a foot raduis of the bus stop. PDA, phone, notebooks should develop an interface that recieved and display the bus schedule.

 * This idea is also in use in Dublin, Ireland by Dublin Bus, you can text them a code, and you get a list of the next bus and expected arrival for that route. CGorman 20:50, 13 Mar 2005 (UTC)

An e-bay style hitchhiking network.
E-bay lets you rate a seller after you buy something from them. This concept could be used in many more areas letting peers-to-peer networks replace current institutions. For instance, instead of having the government or a single business provide a city's transportation needs, people could organize rides on the web. All you would need to do is let people pick where they are and where they need to go, and up would pop a list of people who are going the same way and are looking to car pool, charge a small fee, or who are just looking for company.

After each ride people would evaluate the other person Of course people could choose to only ride with people of the same sex, and luckily for us we live in an age of very little online privacy. Maybe you could have links to sites that do criminal checks or other things. In a perfect society this would be the way to go. It might also work in small towns, where everyone already knows each other, but they might not know the travel plans of their friends.

This might not work among the larger population, but if you were able to enter in people that you already know it may just work. For instance, I know about 30 people at work, and about 30 people at church, and about 30 people from school that I could catch rides to places with. If I wanted to go into town on any given Saturday, there is a chance I could catch a ride with one of them.

This is already in use in Germany and it works not only in small towns also in EU. Here is a website from Germany: www.mitfahrzentrale.de

Use GPS To Find Lost Items
Inventory Control tags for personal use. They could be placed on cell phones, iPods, wallets, you name it. Anything that you have tagged could them be located by your GPS device when misplaced or lost. --137.53.180.128 22:52, 27 Feb 2005 (UTC)

But then you would have to have a GPS attachted to each of these items and some means of broadcasting that information to the wider world which whilst may help you find your MP3 player but it would also help criminals because your stuff will be advertising its location to the world through Radio waves. Also, a gps would not fit inside a wallet or cell phone. And finally! GPS units can be rendered completely disabled by placing an empty packed of crisps above the reciever. So provided your GPS's are small enough to fit in whatever you want whilst having enough battery life for you to be able to find it, if it is underneath something it wont know where it is.

A simpler idea is just for a little radio broadcast unit inside the personal item just to broadcast beeps and without the complication of GPS but using the same priniciples you can triangulate the location of your item with 3 or more recievers.

Better yet might be a small label with a phone number and dollar number you are offering for return safely.

title: User:Dan-aka-jack/Business ideas


text:
Cookbook:Chile

| Pepper

Chile, chili, and chilli are ambiguous terms that refer to similar but distinct ingredients. To avoid confusion, this cookbook—like several other sources  —uses "chile" with an "e" to refer to the pure chile pepper (either fresh or processed), and "chili" with an "i" to refer to the stew and its associates such as the spice blend chili powder. However, do know that the spellings can be ambiguous in other sources, and make sure to use the correct ingredient called for in a given recipe.

 * Chile peppers, fruits known for their "heat"
 * Chile flakes, made from dried and crushed chiles
 * Chili powder, a spice blend of ground chiles and other spices like cumin
 * Chili (see below), a dish made with chili peppers and/or chili powder, usually containing meat and often tomatoes or beans
 * Chile, the South American country

title: Cookbook:Chile


text:
Robotics/Communication Sensors

Data transmission channels
Being able to send data to and from your robot can be a very handy addition. There are 2 commonly used methods for wireless data transmission: IR (InfraRed) and RF (Radio Frequency). Both methods have their own advantages and disadvantages. Which to use depends on several factors.

IR
IR data transmission best known example is the TVs remote control. Using IR on a robot is quite easy and very cheap. The disadvantage of IR is that it's limited to line-of-sight transmission.Line-of-sight or the distance of operating can be increased by use of microwaves (transmission-receiver) systems

RF
RF are well known in radio controlled cars. RF is more expensive than IR, but doesn't have the line-of-sight limitation. These days there are complete RF "modems" available which can be connected to a robot without much (or even any) extra components. Although possible building your own RF communication modules isn't advisable. There are strict laws about which frequencies you can use and with how much power you can transmit.

Using IR
IR is not much more than modulated lightflashes. Since IR falls outside of the visual spectrum humans can't see these flashes without e.g. a digital camera (the CMOS image chip can see IR, on the screen those IR flashes appear bright white).

Remote Control
The great thing about IR remote controls is that you can use many of these directly to control your robot. Although there are several (very) differend IR remote control standards, there is one standard that is used by multiple manufacturers. This standard, called RC5, is very easy to use as many programming languages for microcontrollers have build in RC5 support. The hardware is limited to an integrated receiver module (e.g. TSOP1736), a capacitor and a resistor.

title: Robotics/Communication Sensors


text:
Phoenix/Helper

The Helper (AKA: Wingman) is an extra ship that stays to your side. It fires using a weapon which is 4 times as powerful as Weapon 1 and fires approximately 4 shots per second. You can only have one Helper at a time. Purchasing a Helper while you already have one will result in healing the helper.

title: Phoenix/Helper


text:
SPM/Batch

Batch Scripts
See this Powerpoint presentation for an overview.

See the relevant chapter in the SPM manual.

For general comments on scripting with MATLAB and SPM see the programming intro.

Batch Script for SPM12
Any batch script should follow the template:

spm('defaults','fmri'); spm_jobman('initcfg'); matlabbatch{1}.spm... = ...; spm_jobman('run',matlabbatch);

Batch Script for SPM8
SPM12's advices also apply to SPM8.

The Batch Scripts for SPM5 below can also be used in SPM8.

Batch Script for SPM5
Examples of script (for SPM5 and compatible with SPM8) are provided with the SPM Data Sets, for example:
 * First Level block fMRI data analysis
 * First Level event-related fMRI data analysis
 * Second Level fMRI data analysis
 * DCM/PPI
 * Multi-Subject PET data analysis

See also:
 * http://www.icn.ucl.ac.uk/courses/MATLAB-Tutorials/Sessions2008_09/sessions2008_09.htm#S13 for a generic multi-subject preprocessing script.
 * http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal/analysis.html
 * http://imaging.mrc-cbu.cam.ac.uk/imaging/SpmBatch5

Batch Script for SPM2
There is an example batch script written by Rik Henson, for a single subject fMRI data set (preprocessing and statistics).

title: SPM/Batch


text:
Talk:Electronics/Vacuum Tubes

You probably don't want to refer to vacuum tubes as "Vacuum Tube transistors". The word transistor wasn't coined until well after world war II. Take a look at the transistor page on Wikipedia, it has a great history section.

 * vacuum-tube based transistors??? (wtf, mate.) - Omegatron 18:48, 19 Feb 2005 (UTC)
 * I give you the vacuum tube transistor Pete (discuss • contribs) 19:33, 24 May 2017 (UTC)

Updated..
Updated, added some material

TerryKing

title: Talk:Electronics/Vacuum Tubes


text:
Talk:C Sharp Programming

Attributes are missing
I couldn't find the topic of attributes in C#. Where should this subchapter added? And: I propose that other important missing subjects should also be included in the table of contents so that it is easier find missing information. Sae1962 (discuss • contribs) 09:43, 17 August 2011 (UTC)

General info missing
On a few pages the phrase "assembly" or "assemblies" is used. This is quite a common term used in C# documents. There is, however, no mention in the book what this actually means.

The "using" directive isn't really explained as far as I can tell. What's it for? How does one include code (compiled or not) by others like libraries.

The same goes for indexes, it is mentioned ones but never really explained, nor are the basic data types.

It would also be good to elaborate a bit more on the subject of actually creating an application instead of only focussing on the language itself. Compiling is mentioned briefly, but what is next? What would be a general structure to set up an application? What is an .pa file, how and when should it be used? --Prodoc (discuss • contribs) 20:09, 24 August 2011 (UTC)

Inheritance as an advanced topic
Does the Inheritance chapter deserve to be under advanced topics? It seems to me that inheritance is an integral part of understanding classes/objects and some new readers may avoid it altogether (I know I try to stick to what are considered the "basics" of a language for a time before moving on to more advanced ideas when learning) to their detriment when trying to understand basic OOP concepts. I'm new here and just figured I'd throw it out there. HumanThePequenino (discuss • contribs) 09:03, 25 January 2013 (UTC)

adding async as an advanced topic
With the introduction of async await, asynchronous programming is becoming increasingly easier and more heavily used. I think it deserves one of it's own topic. Peter Zhong (discuss • contribs) 04:31, 11 July 2016 (UTC)
 * Thank you for C Sharp Programming/Asynchronous Programming. JackPotte (discuss • contribs) 21:15, 14 August 2016 (UTC)

Disconnect between book organization on main page and sub-pages
The main topic links on the cover page differ from those on the navigational sub-pages (i.e., Intro, Basics, Advanced, etc.). Recommend one of two approaches: KenoSarawa (discuss • contribs) 14:17, 9 September 2019 (UTC)
 * 1) SIMPLE SOLUTION: Change the navigation template so that it takes the reader to the headings on the cover page, then change the navigational sub-pages to redirects to sections on the cover page.
 * 2) WIKI SOLUTION: Change the cover page so that it includes template-ready versions of the navigational sub-pages so that any edits to the sub-pages will show up on the cover page.

Adding C-Sharp Tutorial
Hello,

I have seen your wikipedia page about c-sharp programming. Please visit my [https://c-sharptutorial.com/ c-sharptutorial. com] web site and look my web site content if looks appropriate please add the following link on your external links section

C-Sharp Tutorial | C# Tutorial

Thanks 39.41.67.126 (discuss) 04:56, 3 March 2024 (UTC)

title: Talk:C Sharp Programming


text:
Fortran/Fortran procedures and functions

Functions and Subroutines
In most programs, a block of code is often re-used at several places. In order to minimize duplicating code and facilitate maintaining the code, such blocks of code should be placed within a function or subroutine. A Fortran  is similar to a mathematical function, which takes one or many parameters as inputs and returns a single output value. A Fortran  is a block of code that performs some operation on the input variables, and as a result of calling the subroutine, the input variables are modified.

An expression containing a function call:

A call to a subroutine:

Many programming languages do not distinguish between functions and subroutines (e.g. C/C++, Python, Java). Pure functional programming languages (e.g. Haskell) only allow functions, because subroutines can, in some case, modify input variables as side-effects, which can complicate the code.

Functions are simpler than subroutines. A function must return a single value, and can be invoked from within expressions, like a  statement, inside an if declaration , etc. A subroutine does not return a value, but can return many values via its arguments and can only be used as a stand-alone command (using the keyword  ).

Function
In Fortran, one can use a  to return a value or an array of values. The following program calls a function to compute the sum of the square and the cube of an integer. The  attribute of argument   means that   cannot be changed inside the function and in contrast, the return value   has automatic. Note that the return type of  needs to be declared. If this is omitted, some compilers will not compile. Open64 will compile the resulting code with warning, but the behavior is ill-defined.

An alternative formulation (F77 compatible) is The return type of the  still needs to be declared, as above. The only difference is how the return type of  is referenced within. In this case, the return variable has the same name as the function itself.

Recursion
Recursive functions can be declared, in a way such as the one shown below, in order for the code to compile.

Subroutine
A  can be used to return several values through its arguments. It is invoked with a  statement. Here is an example.

Intent
When declaring variables inside functions and subroutines that need to be passed in or out, intent may be added to the declaration. The default is no intent checking - which can allow erroneous coding to be undetected by the compiler.

- the value of the dummy argument may be used, but not modified, within the procedure.

- the dummy argument may be set and then modified within the procedure, and the values returned to the caller.

- initial values of the dummy argument may be both used and modified within the procedure, and then returned to the caller.

Different function result definitions
Functions can define the data type of their result in different forms: either as a separate variable or by the function name.

See the examples below

External
Procedures must be included by module  or by specifying them as   procedures. supplies only an implicit interface which is inferior as the compiler doesn't know the number of arguments and neither their data types. Thus, it cannot yield warnings at compile time (in contrast to an explicit interface given from a module, c.f. Fortran/OOP in Fortran).

Pure procedures
Both functions and subroutines can modify their input variables. By necessity, subroutines modify input variables, since they do not return any output value. Functions do not have to, but are allowed, by default, to modify input variables. A function can be turned into a pure function, which does not have any side-effects through the use of the  attribute on all input variables, and further enforced through the keyword. The  keyword imposes additional restrictions, which essentially prevents the function from having any side-effects.

An example of a  function.

Keyword arguments
One can use any order of the input arguments if one specifies them by their dummy name. That is possible as long as the calling procedure has an interface block of the intended procedure (which is automatically created if one includes the function by  usage uses modules).

There is also a hybrid method where one specifies some parameters by position and the rest by their dummy name.

An example is given

Optional arguments
Arguments can be set. The intrinsic function  can be used to check if a specific parameter is set.

An example is given below.

Interface block
If a procedure has another procedure as dummy argument then one has to specify its type, just as the type of other parameters. An  block is used for this case. It consists of the procedure statement with the definitions of its arguments.

Note, that each interface block has its own scope. Thus, if one needs to access outside values one needs to explicitly load them. This can be achieved by the, or   statements.

An example is given below.

Save attribute
The value of a variable can be saved in-between procedure calls by explicitly giving the  attribute.

An example is given below.

Generic
It is possible to create generic functions with the same name for different input arguments, similar to the  function which works for integer, real, and complex data types.

The following example illustrates how to create a function  which adds either two integers or character strings.

Deferred
One can set type-bound procedures of an abstract type as  such that it needs to be reimplemented in derived types. For more information see the section on abstract types.

Elemental
One can create procedures that operate parameters of arbitrary dimension. The keyword  is used where one defines the operation on a single object (e.g. integer) and the general case is automatically handled.

An example for the addition of arbitrary long integer dimension is given.


text:
German/Grammar/Adjectives and Adverbs

Adjectives
Adjectives are words that describe nouns. Most adjectives are stand-alone words; however, present and past participles can also be used as adjectives. Numbers are also adjectives, though they do not decline.

Adjectives can have three functions in a sentence:

 * Attributive
 * Predicative
 * Adverbial

An adjective is only declined when it is attributive. The predicative and adverbial functions are not declined. You can determine what function an adjective plays in a sentence by looking at what the adjective modifies.

Attributive Adjectives
An attributive adjective precedes the noun it describes; it directly modifies the noun. Example of an attributive adjective:

Der große Mann ist lustig.

The tall man is funny. Attributive adjectives are always declined.

Predicative Adjectives
A predicative adjective follows a copulative verb (for example, sein, bleiben, werden) in a sentence. A copulative verb links the subject of a sentence with an adjective or a noun. Example of a predicative adjective:

Der große Mann ist lustig.

The tall man is funny. In the example above, the copulative verb is sein (to be). This verb links the subject (Der große Mann) with the adjective (lustig). Another example of a predicative adjective using the adjective groß:

Der Mann ist groß.

The man is tall. Predicative adjectives are not declined.

Adverbial Adjectives
An adverbial adjective is an adjective that performs the function of an adverb in a sentence. That is, the adverbial adjective modifies a verb or an adjective. In German, any adjective can be used as an adverb. Example of an adverbial adjective:

Der große Mann läuft gut.

The tall man runs well. In the example above, the adjective modifies the verb laufen (läuft is the third person singular conjugation of the verb) and accordingly, it acts like an adverb.

Adverbial adjectives, like adverbs, are not declined.

Declension of Attributive Adjectives
Learning the adjective endings for attributive adjectives is an important aspect of the study of German. Declension of adjectives is frequently cited as one of the hardest topics for new students to learn. It is best to commit the declension tables to memory, while attempting to speak independently. Proper use of adjective endings, especially in speaking, will come with repeated use.

This section makes use of the Oklahoma mnemonic, which denotes the fields of nominative masculine; nominative neuter; accusative neuter; nominative feminine; and accusative feminine, which resemble the state of Oklahoma in the tables used below.

Forms of Declension
There are three forms of declension that you must learn for attributive adjectives. The manner in which adjectives are declined depends on what precedes them:

 * Strong declension (no article preceding the adjective).
 * Weak declension (a definite article or der-word precedes the adjective).
 * Mixed declension (an indefinite article or ein-word precedes the adjective).

The guiding principle for adjective endings is that a noun, whenever possible, should have a primary case ending. Definite articles and der-words always provide a primary case ending. Indefinite articles and ein-words provide primary case endings outside of Oklahoma. Sometimes nouns have no article, in which case adjectives provide the primary case ending.

Strong Declension
Strong declension describes the declension of adjectives that are not preceded by either a definite or indefinite article (e.g. der, die, das, ein, or eine). The table below sets out the endings for adjectives in this situation.

The strong adjective endings are nearly the same as the der-word endings, with the exception of masculine and neuter adjectives in the genitive case (both marked in bold).

Weak Declension
Weak declension describes the declension of adjectives that are preceded by a definite article or der-word, e.g. der, die, das, jeder, alle, etc.

If an attributive adjective has weak declension, you simply add an -e or an -en to the end of the adjective depending on the case of the noun that the adjective modifies. The table below sets out the endings for adjectives in this situation.

Make note of the Oklahoma shaped region in the table below for the nominative and accusative cases.

Mixed Declension
Mixed declension describes the declension of adjectives that are preceded by an indefinite article or ein-word, e.g. ein, eine, mein, meine, kein, keine, etc). The table below sets out the endings for adjectives in this situation.

Forms in Context of Articles
This terminology - strong and weak endings - is confusing for many students. As the student develops, they will develop an ear for case endings and will recognize when a noun has and has not received a case ending. Nonetheless, it is worth providing the three declension tables that result from this principle.

Adjectives following a definite article or der-word always have a weak ending. Within Oklahoma, that is "-e", and outside of Oklahoma, that is "-en". Also dies.., jed.., manch.., welch.., solch.. and all.. get the same ending as in the table above.

Note how, within Oklahoma, adjectives take strong endings, and outside Oklahoma, they take weak endings. This is because indefinite articles provide primary endings only outside of Oklahoma. Also mein.., dein.., sein.., ihr.., unser.., euer.. and Ihr.. get the same ending as in the table above.

Forms of nouns without articles are rare compared to those with definite and indefinite articles; however, one must still know the strong declension. Note that the strong adjective declension is almost the same as the der-word endings, with the exceptions of masculine and neuter in the genitive case (in bold).

Adverbs
Adverbs based on adjectives are one of the simplest parts of German grammar. Any adjective can be used as an adverb simply by placing its uninflected form within the sentence, usually towards the end.

Das Ehepaar ging gestern fröhlich spazieren. (The married couple went for a walk joyfully yesterday.)

Other adverbs have no adjectival equivalent. Many of these express time.

Damals (at that time) Ich bin gestern dort gewesen. (I was there yesterday.) Morgens bin ich normalerweise im Büro. (I am normally in the office in the morning.)

Adverbs can also be based on participles (past and present). These are less common.

Er betrachtete mich bedrohlich. (He looked at me threateningly.)

Some adverbs are formed by adding -weise to adjectives and nouns in the plural form, and mean "regarding", "with respect to", or "-wise" in English. Construction of new adverbs of this sort is usually frowned upon.

Adverbs based on prepositions
Much of the material in this section will be explained in greater detail in the chapter on prepositions.

German has a complex system of adverbs based on prepositions, which are used to indicate direction of motion, location, time, and other concepts. English also possesses such a system, though it is used less. Consider the following sentences in English:

1) Could you take the garbage out? 2) Come over this evening if you get the chance. 3) You should just give up. 4) I will look you up in the phone book. 5) The contract, and the conditions contained therein, is hereby declared null and    void. (Legalese)

In both English and German, prepositions and particles derived from prepositions are treated as adverbs. In many cases, these prepositional adverbs are associated with specific verbs.

In the first two examples, the italicized prepositions are used as adverbs of motion; in the first example, the word "out" indicates the direction "out of the apartment"; in the second case, "over" not only means means the direction "towards", but also implies visitation of a residence.

The third and fourth examples correspond to separable-prefix verbs in German. The word "up" is integral to the verb, which would have a different meaning without the adverb. "To give up", whose infinitive in German would be "to up-give", means "to quit", in sharp contrast to "to give". In the fourth example, it is not even possible to "look someone", whereas it is possible to "look someone up," or "look a candidate's resume over". (English even has inseparable prepositional prefix verbs; compare "to look s.o. over" to "to overlook s.o." Many of these verbs have been replaced by verbs based on Latin and Greek.)

The adverbs in the fifth example correspond to da-, wo-, hin- and her- compounds in German. Such compounds are often used in legal texts in English. In such compounds, the object of the preposition is replaced with the words "there" or "here", compounded with the preposition. "Therein" simply means "in it".

The German system of adverbs based on prepositions is considerably more rigorous, and forms the basis of a large part of the language's morphology. "To catch on" means "to begin" in English; In German, the primary word for "to begin" is literally "to catch on" (anfangen), from which the equivalent noun, der Anfang (the beginning) is derived. A remnant of this in English can be found when describing a child's upbringing.

As in English, prepositional adverbs in German to varying degrees alter the meaning of their associated verb.

Separable-prefix verbs. This topic is better explored in the chapter on verbs. Separable prefixes are themselves adverbs. As in English, many of them are integral to the meaning of the verb. Fangen means "to catch," whereas anfangen means "to begin".

Most prepositional adverbs are treated as part of the root word in the infinitive, and are used as such in the construction of participles. However, not all possible separable-prefix verbs are lexical; "vorbeikommen" (to come over), "vorbeibringen" (to bring over), and so on, may not all be listed in a dictionary. It is better to learn "vorbei" as an adverb implying visitation.

The German prefix in is of note. It has two adverbial forms. As in it describes location; when describing movement, it becomes ein. Thus, for example, darin means "in there", whereas darein means "in(to) there". Another example is the word, einleiten, to introduce.

Hin- and her-. Prepositional adverbs of motion are usually based on hin-, implying motion or direction away from the speaker, and her-, implying motion or direction towards the speaker. Hin and her are themselves stand-alone adverbs meaning the same thing, and describe less-specific motion or direction. (One example in which hin is an integral separable prefix is the verb hinrichten, which means "to execute.) Not all verbs formed from hin- and her- compounds are lexical.  Some examples of hin- and her- compounds are:

herab (down, down from) hinein (in, inside) hinaus (out, out of, onto) darüber hinaus (furthermore, above all) dahin (in the direction/towards of known location)

Mastery of hin- and her- requires considerable effort from the student.

Da- compounds are also adverbs, corresponding to "there-" compounds in English. They replace specific prepositional objects. Although are used principally in legal texts and therefore sound formal in English, they are often employed in written and spoken German and are convenient replacements for long and complicated prepositional phrases. Their comprehension and active use are essential in German. Da- compounds are formed by adding da- before the preposition, with an "r" inserted before prepositions starting with a vowel. There are exceptions to this, and da- compounds are given a fuller treatment in the chapter on prepositions.

Hier- and dort- compounds also exist in German, though they are used less frequently. As in English, they are considered formal, and are used primarily in academic and legal texts. They are best memorized as vocabulary.

hierhin und dorthin - hither and thither

Tedesco/Declinazione dell'aggettivo Alemão/Gramática/Adjetivos e advérbios

title: German/Grammar/Adjectives and Adverbs


text:
User talk:Information Ecologist

Mesopotamian Marshlands
Note that the Mesopotamian Marshlands book is under a Vote for Deletion right now. You should answer that at least. The book appears to be abandoned.

It is generally a good idea to finish a book before you start on a new one. If you have abandoned a book, you should place it on the Vote for Deletion page yourself, so that people aren't left to wonder if it will ever be finished.

AlbertCahalan 03:39, 19 Feb 2005 (UTC)

database wikibook
"DataPerfect" may have been a nice piece of software at one time. But I suspect it is no longer available. Perhaps it would be better to make a wiki book discussing a more easily available database. Doesn't http://OpenOffice.org/ have a simple database ? Or perhaps one of the other databases listed at http://osdb.sourceforge.net/. --DavidCary 05:44, 19 Feb 2005 (UTC)

 * DataPerfect is freely available and is alive and well - as is its author, Lew Bastian, the Data Oefect Users Discussion Group, and a dedicated group of DataPerfect practitioners who gathered in the 2004 DataPerfect Developers Conference in September 2005 in Huntignton Beach California. A video of the conference is available - in a set of seven DVDs of almost the entire proceedings.

 * Lew's latest modifications to the database include the ability to run - and manage web sites - from directly on a web server and to translate accented ASCII chanacters, line field, bold, underline, italic, special characters, etc. into their html equivalents.

 * DataPerfect is being used in many creative ways for such diverse purposes including managing domain registration, an online store and a community web site as well as increasingly to generate web sites based on extensive sets of pages - in conjunction with a design based on elementary html with tables, cells and cascading style sheets. DataPerfect remains, imho, unsurpassed as a relational database in its elegance, power, robustness and integrity. Information Ecologist 23:51, 28 Feb 2005 (UTC)

VfD
I moved some text down from speedy deletion to the regular area, where you may have missed an ongoing discussion about your books. I hope you will soon explain how your books fit in here. It appears that you expect to update them in large chunks, likely replacing text from other contributers. Wiki books are normally hand-edited by the whole community. This is not a place to dump data with the expectation that nobody else will touch it. This is a place for non-fiction works, generally being educational and factual in nature. AlbertCahalan 23:45, 20 Feb 2005 (UTC)

 * I hope by now you will have read my several responses to the Vfd discussion, including my response to your comment about this issue there. Since writing that, I have realized that it might make sense also to make use of forms that contributors can use to edit and add to the Wikibook - essentially an experimentl hybrid - so that they can participate without having to learn the ins and outs of wiki codes. I am also planning to devote what will effectively be a common Appendix with guidance on how to work in a Wiki platform; this section would build on the framework I had been developing under User:Information Habitat in wikipedia.

VfD Again
Sorry to push this up, but I'd like to know what happened to the Wikibook Information Ecology? It is currently up on a vote for deletion (or at least the remaining pages of it). I'd really like you to try to defend your work here, and what the purpose of this Wikibook can serve. Seriously, I'd like to see you continue to contribute to Wikibooks, but inactivity on some of these Wikibooks may lead to their removal. It is more about the fact that we don't really understand the content, and would like you to try and explain what it is all about. --Rob Horning 05:02, 7 August 2005 (UTC)

Image:Apex-l-409x480-r1.png
You cannot upload noncommercial images to Wikibooks. --Derbeth talk 09:23, 15 September 2006 (UTC)

Missing license information
Please fill license information of the following images: Image:T-square-cube-0-474x747.png, Image:Light-cube-0-0579x0830.png, Image:Apex-r-409x480.png, Image:Apex-l-409x480.png. --Derbeth talk 09:26, 15 September 2006 (UTC)

title: User talk:Information Ecologist


text:
Talk:Spanish/Lesson 3

Untitled
Hacer needs to be shown that it is not just "to do", and that the "do" in the question (for example) "Do you want a car?" would be translated "Quiere usted un carro?" instead of "Hace querrer un carro?"; the "to do" in these cases is understood.--Naryathegreat 04:01, 19 Feb 2005 (UTC)

Just Hacer?
I think that salir and poner should also be introduced alongside hacer, because they share the same difference with the first person.

Fiesta.jpg
Could someone please restore the image? Gracias.

title: Talk:Spanish/Lesson 3


text:
Talk:Discrete Mathematics/Finite fields

Who is the designer of this page because you have a multiplication error.

If you go down the page to the section:

then to the line:

"So then(a+bx)(c+dx)=ac+bdx2+ad+bc "

This line should read: ... + (ad+bc)x

m(x) has several roots
Hi!

You say <=F(α) where α is "the root of" m(x) - we define α to be the root of m(x).>>

I think we are talking about a finite field F (although, I believe, this fact isn't stated in the page and I think it would be good if it were). Nevertheless, the polynomial m(x) has several roots, so a commentary stating the isomorphism of F(α) for every root α of m(x) may be useful. In fact, if F isn't finite, then the F(α) can be distinct! (We can take for example x^3-2 over Q). I would add my last comment as well, for completeness!

Regards, Jose Brox -

title: Talk:Discrete Mathematics/Finite fields


text:
Cookbook:Parboiling

Parboiling is the act of partly cooking an ingredient by boiling for less than the full time needed to cook it. For example, potatoes and other vegetables may be parboiled before being roasted (as in roast potatoes), or green beans may be parboiled (and immediately chilled in cold water) as a preparation for freezing.

This technique is also used as a method to quickly cook pork ribs before grilling, although I would never, ever, in my life, do this. You get pork broth if you boil ribs!

title: Cookbook:Parboiling


text:
Wikibooks:Engineering bookshelf

This bookshelf contains a number of wikibooks in various stages of completion. All books on this shelf deal with the topic of Engineering, broken down into a number of subdisciplines. For more information about the different disciplines in engineering, or about engineering in general, go here to find out more.

To suggest a new book, go to the requested books page. Do not put red links on this bookshelf, they will be removed.

General Engineering

 * Control Systems
 * Engineering Analysis
 * Engineering Tables
 * Probability for Engineers
 * Statics
 * System Troubleshooting

Aeronautical Engineering

 * Jet Propulsion

Astronautical Engineering

 * Astrodynamics
 * Space Transport and Engineering Methods
 * Space Transport and Engineering Methods

Automotive Engineering

 * Automotive Systems
 * Electric vehicle conversion

Chemical Engineering

 * Introduction to Chemical Engineering Processes

Civil Engineering
This section will contain books on the subjects of Civil Engineering, Architectural Engineering, Structural Engineering, and Environmental Engineering.

 * House Construction
 * Materials Science
 * Soil mechanics
 * Structural Engineering
 * Vibrations of Structures
 * Fundamentals of Transportation
 * Advanced Structural Analysis

Electrical Engineering
This section contains books on the subjects Electrical Engineering, Electronic Engineering, and Computer Engineering.

 * Analog and Digital Conversion
 * Basic Electrical Generation and Distribution
 * Biography of Nikola Tesla
 * Circuit Idea
 * Circuit Theory
 * Communication Networks
 * Communication Systems
 * Computer Systems Engineering
 * Data Coding Theory
 * Digital Circuits
 * Digital Signal Processing
 * Electric Circuits
 * Electronics
 * Embedded Control Systems Design
 * Embedded Systems
 * Microprocessor Design
 * Power Systems Analysis, Design, and Control
 * Practical Electronics
 * Robotics
 * Semiconductor Electronics
 * Semiconductors
 * Signals and Systems
 * Television Manufacture and Repair

Geospatial Engineering

 * Geographic Information Systems

Mechanical Engineering

 * Engineering Acoustics
 * Engineering Mechanics
 * Engineering Thermodynamics
 * Fluid Mechanics
 * Heat Transfer
 * Pro_Engineer:Contents
 * Robotics
 * Solid Mechanics

Micro and Nanotechnology

 * Microtechnology
 * Nanotechnology

Petroleum Engineering
cy:Silff lyfrau:Peirianneg

title: Wikibooks:Engineering bookshelf


text:
Korean/Dates and times

In Korean, time is expressed like "Now is...". So one would say "지금은 여섯시 입니다" to express "It is six o'clock." The "지금은" means "now is," the "여섯시" means "six o'clock," and the "입니다" means roughly "it is/be."

Dialogue

 * 지금 몇 시에요? (jigeum myeot sieyo?)
 * What is the time now?

 * 지금 7시에요. (jigeum 7sieyo.)
 * It's 7 o'clock right now.

 * 지금 2시 30분입니다. (jigeum 2si 30bunimnida.)
 * It's 2:30 right now.

 * 지금 4시 반입니다. (jigeum 4si banimnida.)
 * It's 4:30 right now.

Vocabulary

 * 지금 (只今), 현재 (現在): now, at present
 * 몇: how many
 * 시 (時): hour
 * 분 (分): minute
 * 반 (半): half [an hour]

title: Korean/Dates and times


text:
User:WoWo

I like the Wikipedia concept, but Wikiversity is even more fascinating.

This concept should neither die nor be developed to a second class university copy.

Think fresh - think Orange!

title: User:WoWo


text:
User:Rohan~enwikibooks

Hi, I am Rohan Vishwasrao from Mumbai. Visit me at My Web Page

title: User:Rohan~enwikibooks


text:
Ecology/Contributors

Contributors
While Wikibooks offers somewhat clearer opportunities for "authorship" than Wikipedia, there remains the fact that anything put here is really just a contribution, and everyone who furthers the effort is a contributor. In this respect there are no "authors". If you are interested in developing a particular subject within ecology as part of this textbook, please start the module and link it here. We will work out the chapter arrangement after you get started. Of course, you can also just expand on an existing chapter.

 * Eric Guinther is a biologist and environmental consultant living in Kane'ohe, Hawai'i. He first envisioned and applied the approach of creating a textbook around articles found in Wikipedia with the Wikibooks Botany textbook. By working to expand and improve those articles at Wikipedia referred to as "assignments", the quality and quantity of the Study Guide to Basic Ecology was gradually enhanced. These efforts were done with the steady help of numerous talented contributors at Wikipedia who, collectively, would have no interest in working on a textbook project per-se.  Ultimately, the user of the guide benefits from the textbook's approach: 1) by having more control over the depth into any subtopic pursued and 2) being limited in that pursuit only by that considerable information available at Wikipedia and other linked websites.
 * Others (add your name and thoughts here if you are a serious contributor)
 * Other anonymous Wikibook contributors (see individual page histories).
 * Numerous other Wikipedia contributors.

title: Ecology/Contributors


text:
US History/W Bush

2000 Election
As Clinton's presidency came to a close, Democratic voters chose Al Gore, Clinton's vice president, as their nominee. Republicans chose George W. Bush, the governor of Texas and son of former President George H.W. Bush.

With 25 electoral votes, Florida emerged as an important battleground state. Florida had traditionally been a Democratic-leaning state, but explosive population growth in the late nineties had brought many social and economic conservative Cubans to southern Florida. The growth had left Florida very evenly split among the parties.

On election night, the news media outlets first called Florida for Gore; this appeared to substantially diminish Bush's prospects for victory. This call was retracted, however, when the actual returns did not line up with the exit polls. Florida was eventually called for Bush, but this too was retracted when the vote tightened. Florida law provided for an automatic recount when votes differ by such a small margin, and when Florida decided that Bush had won, Gore sued to force further recounts in several Florida counties. Bush counter-sued, and the case went to the Supreme Court of the United States. In a 5-4 decision, the Court decided that the state of Florida must recount all the ballots in all the Florida counties and not just those for which Gore had sued, in accordance with the Equal Protection Clause of the U.S. Constitution. As Florida was required by the Florida Constitution to certify its election within days of the Court's decision, there was not enough time to recount the entire state. Thus, the final state count stood, with Bush winning Florida by 537 votes. The electoral vote was thus 271-267 in favor of Bush, who thus won the presidency despite losing the national popular vote.

9/11 and its Aftermath
Less than a year later, on September 11, 2001, terrorists hijacked four airline jets. At 8:46 a.m., the first plane crashed into the 110-story North Tower of the World Trade Center, and seventeen minutes later the South Tower was hit by a second plane, resulting in a huge explosion and a fire. In just two hours, both of the buildings collapsed, killing thousands, including hundreds of firefighters and police officers responding to the catastrophe. At 9:37, a third plane was flown into the Pentagon, the U.S. military headquarters in Arlington, Virginia, which sustained a huge hole in its west side. A fourth hijacked airliner crashed in Pennsylvania, perhaps as a result of resistance by the passengers. It appeared to have been heading in the direction of Washington, D.C., and its intended target is believed to have been either the U.S. Capitol building or the White House. Approximately 3000 people died in what came to be known as "9/11", making it the deadliest ever attack on the country by a foreign enemy.

Responsibility for the attacks was soon attached to Osama Bin Laden, the leader of al-Qaeda, an Islamic terrorist network with training camps in Afghanistan. Bin Laden's exact grievances have been debated, but include US military presence in major Islamic nations and US support of Israel. There had been many smaller terrorist attacks aimed towards Americans by al-Qaeda before 2001, including the bombing of US embassies in Kenya and Tanzania in 1998.

The attacks, while devastating and deadly, abruptly ended the period of sharp division after the 2000 election. Many world leaders and countries expressed solidarity with the American people following the attacks. Soon after the attacks, U.S. President George W. Bush declared a “war on terrorism,” warning countries that harbored terrorists would face the full power of the U.S. military. The United States charged Al Qaeda with responsibility and demanded that the Taliban turn over bin Laden and the Al Qaeda leadership, and dismantle terrorist training camps in Afghanistan. In October, the United States and Great Britain launched an attack on the Taliban and terrorists within Afghanistan. The Taliban government quickly collapsed and many Al Qaeda leaders were captured or killed, though Bin Laden would remain at large for nearly ten years. Bin Laden’s role in enabling the attacks appeared to be confirmed by videotapes in which he said that the September 11th attacks had been even more destructive than he had hoped they would be. In the weeks following September 11, a series of letter containing anthrax spores went through the mail in the United States, ultimately killing five people. No evidence was found to link the anthrax to Al Qaeda, but the anthrax scares contributed to an atmosphere of uncertainty and even panic. In response to the September 11th attacks, security has been considerably tightened on airplanes, in buildings, and in public areas. U.S. authorities detained hundreds of people whose actions or immigration status made them appear questionable, and Bush created special military tribunals that could try foreign nationals accused of terrorism.

The attacks also shook the worldwide economy. Stocks tumbled when the New York Stock Exchange reopened the week following the attacks. The travel industry also declined because fewer Americans wanted to fly (due to the nature of the 9/11 attacks). In the immediate aftermath of the September 11 attacks, the United States and other countries around the world were placed on a high state of alert against potential follow-up attacks. Civilian air travel across the U.S. and Canada was — for the first time ever — almost completely suspended for three days with numerous locations and events affected by closures, postponements, cancellations, and evacuations. Other countries imposed similar security restrictions. In the United Kingdom, for instance, civilian aircraft were forbidden to fly over London for several days after the attack. Many airlines went bankrupt. A recession, following the economic boom during Bill Clinton's second term, was exacerbated by the attacks.

The World Trade Centers were occupied by a lot of firms conducting key economic activities (e.g., stock trading). As a result of the attacks the stock market began to decline. This had an impact on employment and decreased the amount of available jobs for Americans.

The War on Terror
Directly following the September 11th attacks, Congress drafted and overwhelmingly passed the USA PATRIOT Act, which was signed into law on October 26, 2001. The law, while forcing citizens to forfeit some rights, strengthened the government's ability to gather information and convict suspected terrorists. Hundreds of accused terrorists have been charged and approximately half have been convicted. There have, however, been reports of abuse of the law, which went under reexamination by Congress in 2005.

In response to the attacks, the United States declared a symbolic war on terrorism. The first target in the war was Afghanistan, where the Taliban government was believed to be hiding Bin Laden and al-Qaeda. After the Taliban refused to turn Bin Laden over, American and British forces began bombing strategic Taliban centers on October 7. The invasion was swift, and major fighting had ended by the middle of 2002. The Taliban government was eliminated, and the Afghanis soon participated in their first democratic processes in many years.

In his 2002 State of the Union address, Bush named Iraq, Iran, and North Korea as a part of the "Axis of Evil," a phrase he partially coined from the World War II Axis Powers. President Bush specifically named these three countries because they were all described as rogue states, either fostering terrorists or trying to obtain nuclear weapons.

The successful invasion of Afghanistan was the first time that the newly adopted Bush Doctrine had been carried out. The Bush Doctrine stated that there was no difference between a terrorist and one who fosters a terrorist, and that the U.S. would practice pre-emptive strikes against perceived threats to American security (acting alone if needed), as it was the United States' duty to spread freedom and democracy to the rest of the world.

War in Iraq
In the middle of 2002, the United Nations began focusing its attention on Iraq, as American and international intelligence agencies had intelligence indicating that Iraq possessed a number of Weapons of Mass Destruction (WMD), as well as the ongoing capacity to produce them. The United Nations Security Council passed Resolution 1441, requiring Iraq to open up to U.N. weapons inspectors or else face "serious consequences." Two of the veto-wielding members (France and Russia) of the Security Council did not wish to use military force against Iraq, and promised to veto any resolution ordering such force.

As a result to a perceived security threat verified by intelligence (which has now been found to have been unreliable), President Bush and a number of allies, deemed by the President as the "coalition of the willing," began the invasion without U.N. sanction. On the night of March 17, 2003, President Bush gave Hussein and his two sons, Uday and Qusay, an ultimatum to leave Iraq in 48 hours or face an invasion. They refused. After the expiration of the deadline given by the President, the invasion of Iraq began. The invasion lasted only a short time, and the Iraqi government and military collapsed within three weeks.

Uday and Qusay Hussein were killed in a firefight with U.S. forces in July. Saddam Hussein was found in a spider-hole and captured on December 13. Weapons of Mass Destruction were never located in Iraq. Continued suicide bombings and the ongoing American casualties led to a steady decline in American popular support for the war.

The invasion of Iraq is considered by many to mark the end of the political unity following the September 11th attacks. Although both the public and Congress favored going to war by overwhelming majorities, a substantial minority expressed reservations about invading. Many feared that the administration lacked a plan for rebuilding once the war was over. Still others worried that an invasion would alienate U.S. allies. On February 15, just one month before the invasion commenced, millions protested worldwide, including hundreds of thousands in 150 U.S. cities.

Gay Marriage
Another key issue of the 2004 election was same-sex marriage. On November 18, 2003, the Massachusetts Supreme Court ruled that the banning of gay marriage is unconstitutional, thereby allowing gay marriage in that state. Following the Massachusetts ruling, California, Vermont, Maine, Hawaii, New Jersey, the District of Columbia, and Connecticut allowed for same-sex civil unions, reciprocal benefits, or domestic partnerships. In February 2004, President Bush called for a constitutional amendment defining marriage as between a man and a woman. The Senate looked into the issue, but only a minority supported the provision, while a two thirds majority is needed to pass an amendment in Congress. "The union of a man and a woman is the most enduring human institution, honored and encouraged in all cultures and by every religious faith," President Bush said. "Marriage cannot be severed from its cultural, religious and natural roots without weakening the good influence of society."

The gay rights movement took a major hit on Election Day, when seven states (Georgia, Arkansas, Michigan, North Dakota, Kentucky, Oklahoma, and Utah) made it unconstitutional for marriage, civil unions, or domestic partnerships between same-sex couples. Three more (Oregon, Mississippi, and Montana) made it illegal only for homosexuals to marry, and one more (Ohio) passed an amendment illegalizing any benefits whatsoever for homosexual couples.

2004 Election
As the incumbent, Bush was unopposed for the 2004 Republican nomination. On the Democratic side, presumed favorites Hillary Clinton and Al Gore both declined to run. With the field wide open, ten Democrats sought their party's nomination. Former Vermont governor Howard Dean emerged as the front-runner, and received Gore's endorsement. However, Massachusetts senator John F. Kerry managed to win the Iowa Caucus, and rode the momentum from there.

Kerry chose North Carolina Senator John Edwards, ostensibly the Democratic candidate who received second place in terms of delegates, as his running mate. Kerry was recognized as a liberal Senator - he openly supported gay rights and same sex civil unions, was pro-choice and supported embryonic stem cell research, and opposed drilling in Alaska for oil. The Bush campaign targeted Kerry as a "flip-flopper," a term coined by the campaign to indicate that the Senator from Massachusetts changed his position constantly. The flip-flopping label was directed particularly toward Kerry's positions on the war in Iraq. In regard to a bill that passed the United States Senate providing $87 billion in funding to the war, Senator Kerry made the remark that "I actually voted for the eighty-seven billion - before I voted against it." The Bush campaign took advantage of this remark and used it as the epicenter of their flip-flopping campaign against the Senator. With Bush and Kerry running close in the polls, it appeared that the election might come down to Florida or Ohio. Bush won both, widening his margin of victory in Florida this time around. As there appeared to be no doubt about the outcome, Kerry conceded on the following day. The final electoral vote total was 286 for Bush and 251 for Kerry (with one Minnesota elector casting a ballot for John Edwards for both President and Vice President). Additionally, Republicans strengthened their hold in both houses of Congress, particularly increasing their majority in the Senate to 55-44. The strengthening of the control of the Senate would be important to the Republicans in the following year.

Social Security
Created in 1935, Social Security OASDI is a government program that provides most seniors with a steady income based on the real value of their prior earnings, funded by a 6.2% tax on each workers' pay and and on each employers' payrolls. Surpluses are held in Treasury securities in special Trust Funds which are credited with interest. The surplus is projected by government actuaries to peak around 2018 or 2019 and then to decline until the Trust Funds are exhausted in sometime between 2042 and 2052.

In the latter part of his first term and in his 2004 campaign, Bush focused on the issue of Social Security, and how to prevent its bankruptcy. He proposed a plan to have young workers set up stock funds which might turn out to produce better retirement benefits than OASDI but would not solve the system deficits. Many experts expect that the only long-term solution is a tax increase of about 2 percent of payroll, or a government subsidy of the same size.

Cabinet Replacements
At the start of his second term, Bush's cabinet saw significant changes. Colin Powell departed as Secretary of State, replaced by National Security Advisor Condoleeza Rice, the first African American female to hold the position. Alberto Gonzales replaced John Ashcroft as attorney general the first Mexican American to hold this post. Tom Ridge, former Governor and Vietnam War hero, also resigned from the post of Secretary of Homeland Security. Michael Chertoff, a Justice Department official, took his place.

The Double Vacancy on the Supreme Court
In October, 2004, William H. Rehnquist was diagnosed with thyroid cancer. In July, 2005, he informed the press that he would remain on the Court as long as his health permitted.

Despite all expectations, Sandra Day O'Connor ended up being the first member of the Court to retire. Prior to O'Connor's retirement, the Court had consisted of three conservatives, five liberals, while O'Connor was the Court's swing vote. In many cases relating to restrictions on abortion, affirmative action, and detention of unlawful combatants, O'Connor had been the deciding vote. Liberals feared the replacement of O'Connor with a conservative, while conservatives realized that the replacement of O'Connor would leave them only one vote away from a majority on the Court.

John Roberts
On July 19, President Bush nominated John Roberts, a judge serving on the US Circuit Court of Appeals for the District of Columbia, to fill the vacancy created by O'Connor. Liberals were for the most part against the Roberts nomination, claiming that he would be far to the right of O'Connor. Conservatives had mixed reactions, based on quotes he had made concerning Roe v. Wade.

On September 3, 2005, Chief Justice William H. Rehnquist died of complications from thyroid cancer, creating a double vacancy. On September 6, President Bush withdrew the nomination of Roberts to the office of Associate Justice and instead nominated him to be Chief Justice. The Senate Judiciary Committee began holding hearings for John Roberts on September 12. On September 22, the Committee voted 13-5 to approve the Roberts nomination. On September 29, the Senate confirmed the nomination of John Roberts to the Supreme Court by a vote of 78-22. Hours later, Associate Justice John Paul Stevens swore him in as the seventeenth Chief Justice of the United States.

Samuel Alito
Having successfully nominated John Roberts to the Supreme Court, Bush now turned his attention back to filling O'Connor's vacancy. On October 3, 2005, he chose the White House Counsel, Harriet Miers. Miers withdrew her nomination on October 27, 2005, after weeks of criticism. On the morning of October 31, 2005, President Bush announced the nomination of a Circuit Court judge named Samuel Alito.

Conservatives were quick to applaud President Bush for nominating Alito to the Court, and liberals were quick to oppose the new nomination. Conservatives saw in him a competent judge who would develop a truly conservative reputation on the Court and oppose Roe v. Wade. Unlike with the Miers nomination, Bush's conservative base was mostly in support of the Alito nomination.

On January 24, 2006, the nomination of Samuel Alito was approved by the Committee, and the Senate debates began the next day. On January 31, 2006, Samuel Alito was confirmed by the Senate by a vote of 58-42. Thereafter, Sandra Day O'Connor officially retired. Samuel Alito was sworn in as the 110th Associate Justice hours later. The next day, he was ceremonially sworn in.

Souring Public Mood
A confluence of events, beginning at the end of 2005, began to turn public opinion against the Bush Administration and the Republican-controlled congress, and, as many argue, toward the opposition Democrats in the 2006 election year.

Hurricane Katrina
The summer of 2005 saw a very active hurricane season, with a total of five hurricanes striking the Gulf Coast. Of these, on August 29, Hurricane Katrina, struck New Orleans as a strong, 'category three' hurricane, breached the levees on Lake Pontchartrain, flooding the city, devastated the surrounding coasts of Alabama, Mississippi, and to a lesser extent, the already struck Florida panhandle (it also struck South Florida, but the effects were far less than those seen in the Gulf). The catastrophic flooding and subsequent responses from all levels of the government highlighted many far reaching deficiencies in the government's ability to protect the country in times of disaster. Mistakes at the state and local levels were made primarily before the storm. The most glaring mistake made by the state of Louisiana was its issuance of evacuation orders, but no provision of transportation for the estimated 120,000 poor, elderly, and sick unable to leave the inner city. After the storm struck, governor Kathleen Blanco's (of Louisiana) alleged refusal to give control of the state's National guard troops to the President caused the rampant looting crisis in the city to be firmly her responsibility. She did not commit herself to fighting the looting in the city until September 2, nearly five days after landfall.

But by far, most criticism was directed towards the federal response and the Bush Administration. The American people, aided by angry criticism from the news media, perceived the response as proof that America was woefully unprepared for another disaster, even after the governmental reforms following 9/11. President Bush did not survey the disaster area until August 31, and was criticized by the media for treating the disaster too casually. President Bush is famously quoted as saying "Brownie, you're doing one heck of a job." This was the same day that Michael Brown, head of the Federal Emergency Management Agency (FEMA) and the man he was referring to, told reporters that he and the federal government were unaware of the horrific conditions in the Louisiana Superdome (the primary shelter for those unable to evacuate), even though the news media had been reporting on them for days.

The result of the storm was a realization by the American people that disaster relief agencies were unprepared for what they were created to do. President Bush's approval dropped to its lowest point during his entire presidency, and he was accused of cronyism for hiring unqualified officials to the Department of Homeland Security. Congressional hearings to investigate the matter were to commence in the coming months.

Growing Scandal
In addition to complaints of cronyism, a multitude of scandals were brewing in Washington. The CIA Leak scandal ("Plamegate") involved pre-Iraq War intelligence. Joseph C. Wilson, a former diplomat to African countries in previous decades, was recommended by his wife, CIA agent Valerie Plame, to investigate claims that Iraq was buying uranium from Niger. He alleges that he found no connection between the two countries, but President Bush said in his January 2003 State of the Union Address that "The British government has learned that Saddam Hussein recently sought significant quantities of uranium from Africa." That summer, Wilson wrote a column in the New York Times that was highly critical of this remark, and told reporters in several anonymous interviews that the Bush administration was misrepresenting intelligence. A few days after Wilson's column was published, the Washington Post published a column in its paper revealing the identity of the undercover Valerie Plame, thus ruining her career as an agent. Wilson claimed that high officials, namely Karl Rove, the President's chief of staff and a top Republican strategist, leaked her identity to the paper for "retribution" for Wilson's dissent. Eventually, an investigation into the matter was opened up. It is illegal for high officials, elected or not, to leak classified information without going through a declassification process. A special prosecutor, Patrick Fitzgerald of Illinois, was appointed to head the investigation. In 2005, he indicted Lewis "Scooter" Libby, Vice President Cheney's chief of staff, for perjury and obstruction of justice in the investigation. Later, Libby testified that he was authorized by White House "superiors" to leak classified info regarding prewar intelligence. The investigation remained ongoing, and many speculated that Fitzgerald was aiming to indict a higher official for the actual investigated offense, leaking Plame's identity, rather than lying to investigators.

Meanwhile, investigations regarding lobbying and political corruption in Congress were ongoing. Jack Abramoff, a top Republican lobbyist, pleaded guilty in early 2006 to three felony charges related to his defrauding of his Native American tribe lobbying clients and tax evasion. He consented to enter a plea bargain in which he agreed to testify in related Congressional corruption investigations in return for a lesser sentence.

Late in 2005, the House Republican leader, Tom Delay, was indicted for conspiracy to violate election law, money laundering, and conspiracy to engage in money laundering. Because of the indictments, Republican house rules forced Delay to temporarily step down as majority leader. A judge threw out the election law violations, but upheld the other charges, causing the rest of Delay's caucus to successfully pressure him to permanently step down as majority leader. Eventually, Delay's heavy association with a litany of scandals forced him to resign from the House in order for his party to retain his congressional seat.

2006 Midterm Elections
The Democrats won back the House and the Senate. This mid-term election is notable for the fact that no incumbent Democrat vying for a national congressional position was voted from office. The Democratic party gained control of six Senate seats by defeating Republican senators in the states of Montana, Pennsylvania, Missouri, Rhode Island, Ohio, and Virginia. The Democrats gained a 51–49 majority in the Senate House by caucusing with independent senators. The Democratic party gained thirty House seats from the Republican party. This was the first time since the midterm elections of 1994, the Democratic Party gained control of both houses of the United States Congress.

Falling Dollar
The U.S. economy and its currency as an instrument of world trade has suffered a series of major setbacks in recent months. Some analysts say that the Federal Reserve's September 18th dramatic rate cut to 4.75% from 5.25% may be a case of "too little, too late", or that it was excessive and dooms the dollar.

On September 20, 2007, Saudi officials declined to cut interest rates in lockstep with the US Federal Reserve for the first time in decades. According to Ambrose Evans-Pritchard, International Business Editor for The Daily Telegraph, "it's a signal that the oil-rich Gulf kingdom is preparing to break the dollar currency peg in a move that risks setting off a stampede out of the dollar across the Middle East."

Hans Redeker, the Currency Chief at BNP Paribas, stated that Saudi Arabia's move to not adjust their own interest rates in sync with the Fed's cuts is a very dangerous situation for the US dollar. Redeker points out that "Saudi Arabia has $800bn (£400bn) in their future generation fund, and the entire region has $3,500bn under management. They face an inflationary threat and do not want to import an interest rate policy set for the recessionary conditions in the United States.

American consumers, meanwhile, stood to be hurt. A drooping dollar means that foreign imports should cost more, from Murano glassware to French candles, to the Middle Eastern oil that powers the boats that bring all this stuff to America.

Advancing Technology
Technology in this era saw large refinements, following trends from previous years.

The 2001 antitrust case United States v. Microsoft Corp. was a significant antitrust action, before it was settled.

By the mid 2000's flat screen televisions and monitors became readily available, as had digital video recorders and other advancements in entertainment. Cell phones continued to advance, with many phones adding cameras and additional features during this time. 2007 saw the launch of the iPhone, one of the first smartphones with a minimalist slate deign that found wide market success.

In April of 2003 the Human Genome Project was declared complete, creating a map of the human genome.

NASA's Mars Exploration rovers landed in January 2004, with Spirit working till 2010, and Opportunity continuing to work diligently till 2018, both well past their expected service lives.

The 2004 DARPA Grand Challenge was one of the first major competitions meant to spur the development of autonomous vehicles. Though no vehicles successfully completed the 2004 course, the 2005 course did have winners.

title: US History/W Bush


text:
Talk:Climate Change/Causes/Scientific Consensus

Oh, and this page is cagegorized on the top level Climate_change page as "Evidence that we're not to blame". Thus, it's not even supposed to present a balanced viewpoint in isolation. It's part of a larger work. Changing this page to hold the opposite viewpoint is downright offensive.

This page should be moved into the Climate Change hierarchy or pseudo namespace to avoid this confusion. Rebuttals should be considered par for the course, though. Kellen T 23:57, 11 August 2005 (UTC)


text:
Cookbook:Bacon Cheese Omelet

| Breakfast Recipes | Omelet Recipes

Ingredients

 * 3 eggs
 * 2 medium (10 oz) slices of cooked bacon
 * 2 slices of American cheese
 * 1 Tablespoon of butter

Equipment

 * 10-inch non-stick skillet
 * Non-stick spatula
 * Fork or whisk

Procedure

 * 1) Cut or break bacon into 1-inch pieces.
 * 2) Cut or break slices of cheese into 1-inch wide strips.
 * 3) Melt the butter in a pan over a high heat. Make sure the pan is evenly covered in butter.
 * 4) When half the butter is melted, turn the heat to medium.
 * 5) Beat or whisk eggs until evenly colored.
 * 6) Pour in the eggs, and rotate the pan so that the egg covers the entire surface of the pan.
 * 7) Continue rotating until the edges become thick, then use a spatula to lift side of the now cooked egg, allowing the remaining liquid egg from the centre to flow underneath on to the pan and start cooking. Continue to rotate the pan and move the spatula to adjacent areas until most of the liquid egg is cooked.
 * 8) Lay the cheese down one side of the centre of the omelette.
 * 9) Place the bacon on top of the cheese.
 * 10) Carefully, flip the side with no ingredients over the top of the bacon and cheese side, so you now have a semi-circle omelette.
 * 11) Turn to low heat until cheese has melted. Makes two servings; great with vegetables or salad.

Nutritional Information
Energy: 650 kCal

Fat: 45g

Carbohydrate: 3g

Glycemic Load: 0

title: Cookbook:Bacon Cheese Omelet