text:
Talk:PHP Programming

Front Page Cleanup
I think the front page needs to be cleaned up a little. The top sections are good along with the contents of 'The Basics' section but further down it gets a little disorganised. It needs to be cleaned up and filled in to make the front page more presentable. Also, do we really need a 'Contributors' section? I thought the point of Wikis was that everyone contributed, it seems against the ethos to attribute certain pages to certain people. Fyorl (talk) 11:37, 13 February 2008 (UTC)

Working with Files
I plan on adding a section related to working with files. I will discuss mainly the use of the f(open|write|close) in conjunction with file and file_get_contents as well as devoting a small section to file_put_contents and how to emulate it with PHP 4.

I'm just checking that nobody is already working on a similar section. If I hear no response in a couple of days I will start work on the article on my Talk page and then tranfer it over upon completion.

The article will also make a reference to serialization. Since this could appear in both the Database section and the Session section, I was wondering if it was best to create a separate page and link to it from within all the other pages? Fyorl (talk) 16:52, 9 February 2008 (UTC)

Naming policy?
I am not new to Wikipedia, but this is the first time I have looked at a Wikibook. I have some confusion about the template that says the book's title does not adhere to the "naming policy." What is wrong with the title, and how does it not adhere? Here I have seen discussions about the book's content, cover, PHP version, and so forth, but nothing regarding the name or that template. To anyone that may advise--thanks. <IP_ADDRESS> 18:19, 4 December 2007 (UTC)

 * If you click on the link in the naming policy notice, you'll see the preferred naming convention. This wikibook used to use a colon  separator for sub pages, which resulted in the need to manually link to the index (example: hello world).  Currently, the barely-existing PEAR page seems to be the only page still using the depricated naming convention.  --banzaimonkey (talk) 20:28, 10 December 2007 (UTC)

 * As it seems that all of the pages are in order (excepting PEAR), I removed the template. --banzaimonkey (talk) 20:33, 10 December 2007 (UTC)

 * But now it is back; anyone care to explain? — Sam Wilson (Australia) 21:36, 4 June 2008 (UTC)

Version
Are we talking PHP version 4 or 5 here?

PHP5 was recently released, and features the ZEND II engine, which includes enhanced OOP(Object Oriented Programming) features, better XML support, and built in SQLite support.

PHP4, on the other hand, is still the prevalant web technology, and I suspect that most servers will not be offering PHP5 support for some time.

Either way, I suggest that OOP be included in the 'advanced php' section. I just don't know how to write it because of the discrepancies between php4 and php5. --Noah 20:19, 28 Jul 2004 (UTC)

Ok, since I recieved no response, I will assume that this page is geared towards PHP5. I am going to start writing the OOP features accordingly. I will also edit the intro to make this obvious. --Noah 18:46, 14 Aug 2004 (UTC)

I think for anything specific to one version, we should show the equivalent in the older / newer version if possible. --Spoom 01:47, 7 Sep 2004 (UTC)

 * I'd like to second this notion, and extend it. Whenever possible I think functions that are aviable in both versions should be used. For most of the introductory material it doesn't matter.  OOP can be part of a later discussion, along with other major version 5 improvements.  Since these books are perminant static things we can always drop discussion of version 5 when it becomes the standard (in other words we can stop singling out the difference at that point).  I would expect most people learn PHP at the moment are still working in 4. --Ahc 06:28, 2 Dec 2004 (UTC)

External links?
There are many "dead" links here to pages that don't exist on wikibooks, and will most likely never exist. For example: GUI or Rasmus Lardorf will most likely not get their own books. It's much more likely that they'll get a Wikipedia page(GUI already has one), and I think that's where those links should take you...

I'd say change them to link to Wikipedia if you find them then, just use common sense. --Spoom 06:15, 6 Oct 2004 (UTC)

Learn PHP

Smarty Templates
There is no reason to discuss Smarty Templates as part of the language. You can either hit them in a round about PEAR and Templating or put the package in a list of "useful" PHP projects.
 * While Smarty is not part of the core language, it is mentioned in many other PHP books, and it is a very useful to have knowledge of its features. However, I think merging Templates and Smarty would be useful.

Include/Require functions
There seem to be at least 3 sections which talk about require(_once) and include(_once) (Headers and footers, Template and Including Files. Since these deal with basically the same subject, couldn't they be merged into a single page about the use of require and include, and a list/example of the uses of these functions? -- DorianGray

If I don't see any reasons why in the next few days I'll delete Templates and Headers and Footers and move all relevant content to Including Files. --DorianGray 06:58, 15 Nov 2004 (UTC)

Internal Functions?
I know that the PHP website has a lot of information about PHP's internal functions, but do we want to start highlighting the ones most used? I'm particularly interested in the mail function myself.

 I would say that's unnecessary, unless it comes up in the course of a lesson. I feel that a structured, lesson based approached would be better. Example: a lesson on "Sending E-Mail with PHP" rather than "mail", and "Working with Arrays" as opposed to "Array functions" or "array_sort"

MySQL in PHP5
Should it be mentioned that PHP5 on Windows no longer has MySQL support built in, but has it shipped as a separate DLL that needs to be referenced in php.ini?

Hi, i think that this should be mentioned in the php:mysql page, not the main page. I wrote that it should be downloaded separately -- User:Wykis

Sub-pages
 Shouldn't the pages for setting up your environment be on subpages? It makes this main page seem awfully noisy to have them right there.

 *  I agree, I think there seems to be alot of emphasis on lesser PHP topics such as setup, templating etc. and there should be more PHP code and the setup stuff should be in a sub-topic

Accessing files
I'd like to see a section on reading and writing from/to files. Anyone? Thanks!
 * I'm writing it now if no-one has any objections. I plan to put it in the basic section as a starter's guide to file manipulation.--Davidd 23:09, 11 December 2005 (UTC)

echo/print functions/constructs
On the Hello World page, and maybe in other places that I haven't noticed yet, echo and print are referred to as functions. Since they are actually language constructs in their own right, should they be more accurately referred to simply as statements?

The newline "operator"
 In PHP Basics Example #1: Basic Arithmetic Operators, a reference is made to a newline "operator". The example in question is actually referring to the process of adding a newline by using the \n escape sequence in a double quoted string. I recommend that firstly this reference is clarified, explaining escape characters, and that secondly, since PHP is most often used with HTML, that this example be rewritten to use the <br /> tag- it being the case that in a browser, the \n character does not cause a newline.

I've got to agree on this too. This is so annoying when user changes the page to rendered html page. for example, text to text and to new line... We are not evaluating html here. HTML is just an example. Please don't edit any pages just to do that. Thank You Wykis 07:03, 26 March 2006 (UTC)

where are the Snafus?
The part that always seem to be left out from programming tutorials, or, if present, truncated to incomprehensibility (part of the ph.D curriculum I guess.. ;) is a bunch of common errors in writing the code.

Anyone who has done any programming have made mistakes that take forever to track down. Please add a section with the most obvious ones, and put it in the 'beginner' section. (a personal favourite is 'if ($X == $y;) {...}' which took a few re-readings to catch..)

How about some exercises per lesson?
Not just simple questions. I mean something along the lines of "Make a script that prints 'foo' if 'x' is true" or something like that. Doing this helps keep the concepts stuck in your head, and would be tragic if this textbook didn't have it.

First person writing?
Should addendums be added in first person, such as "I recommend ..."? How should this be handled? <IP_ADDRESS> 00:35, 29 December 2005 (UTC)

Hey, i just noticed this too, I will correct the mistakes as the book is written by a lot of people,not one person ;p Wykis, 14:42 14 January 2006

There are many thing we can add on this section.

New presentation
I propose to change the look of the PHP book : we can use this look Programmation PHP (sorry in french). Do you like this ? Merrheim 10:07, 5 March 2006 (UTC)

wow, wish i knew about this b4. i think this page is going to change my life --Nerd42 16:58, 16 March 2006 (UTC)

I don't agree on this. I like the idea though. The design of that French page looks good but I prefer this book to be just like a normal book. Just a book :) Wykis 18:20, 29 March 2006 (UTC)

 * Wikibooks are viewed on a computer. Since there isn't a tangible book with pages to turn, an outline view would be really nice.  Getting between lessons in the current layout is rather tedious, and a TOC / Index / Outline view would probably work better than putting "Next Page" links on each lesson because the ordering of the lesson can change, and the navigation would break.  Changing the formatting would be a lot of work, but we should look into it (it doesn't have to be a carbon copy of the French layout).  It doesn't do anyone much good if the information herein is inaccessible.  --banzaimonkey

 * I'm working on some indexes at the moment, so don't go running off and do something I've already done. ;)  --Banzaimonkey 19:01, 11 July 2006 (UTC)

 * Make sure to let us know if your done or a estimate of when you're done would be nice as I believe this book is very incomplete and needs a lot added to it.AlReece45 02:39, 25 August 2006 (UTC)

For MediaWiki
it would be cool if there was a section on advice for would-be developers about writing bug fixes for MediaWiki. <IP_ADDRESS> 07:41, 22 March 2006 (UTC)

 * Already exists? Did you try googlling about this? http://bugzilla.wikimedia.org/ helps quiet a lot. This is a Programming book for PHP, NOT for MediaWiki. Instead, try looking in IRC and . Wykis 18:18, 29 March 2006 (UTC)

Flag Frog = Ripped from Smarty?
Flag Frog templating system looks like a rip from Smarty template engine. Should this be removed from the page? Wykis 18:16, 29 March 2006 (UTC)
 * It looks like a fork of Smarty-Light. It's under the GPL, so I see no issue with it in and of itself, but I don't think it's something that needs to be posted on the PHP wikibook considering that as of now, there are 164 downloads in total of all version of the FlatFrog package.  Has anyone here heard of it before? Spoom 17:57, 5 April 2006 (UTC)

Major Changes to this Wikibook
I'm planning a significant overhaul for this wikibook. It currently has a decent amount of information but suffers from irregular organization, lack of verbocity, and has room for substantial additions of content. I've been writing a small todo list for myself, which you can view on my userpage. If you're an active reader / contributor and would like to take part in a discussion about changes to this wikibook, please reply in this page or contact me on my talk page. Otherwise I'll just assume that I'm the only person here who is active and will carry on with the changes as time permits. --Banzaimonkey 09:04, 12 July 2006 (UTC)

 * Update: I have been working on thing for a few weeks and am ready to proceed with a few things on my list.  Code examples will be wrapped in a color-coded box designating the type of code example (see Code Template for details).  I've also created a cover for the book which you can view here.  I've tagged the book as having a deprecated naming convention, and I will begin the process of migrating them to the new namespace once I decide what that namespace will be (probably PHP_Programming.  This will enable root auto-links on each page (returning the user to the main page), as well as conforming to the new naming convention (as of March 1rst, 2006).  Next on my list is an overhaul of the table of contents, but I'm still unsure how this will be reorganized.  If I have free time after all that, I'll go through this talk page and clean it up a bit.  --banzaimonkey 02:17, 6 August 2006 (UTC)

 * Update: The overhaul on the table of contents will probably take place before the migration.  This will allow me to figure out how things need to be organized when they're moved.  --banzaimonkey 06:39, 6 August 2006 (UTC)

Color Code Boxes
I have wrapped the first two Basic programming lessons. All code is contained in a colored template. You can view them here and here. Please leave your feedback in response to this post. My own thoughts are positive, but I'm not entirely satisfied with the functionality. I may rewrite the template with a more modular, extensible approach. --banzaimonkey 06:36, 6 August 2006 (UTC)

I think that it is a good idea. Makes for easier reading and quicker reference.Bounton 08:26, 12 September 2006 (UTC)

What do you think about adding syntax highlighting? In my opinion, it makes the code much easier to read. --King elessar 00:35, 20 September 2006 (UTC)
 * I like this idea if it's at all possible to do automatic syntax highlighting of PHP code within MediaWiki somehow. Also, have you taken a look at Template:Code:PHPHTML?  I don't know if you're already using it but it's a perfect fit.  Keep up the good work. --Spoom 18:03, 22 September 2006 (UTC)

Very interesting. I like it. Helps to highlight what we are trying to do with the code.

Its a good idea!

Love it. Reading is much easier on the eyes

good idea

Excellent idea. Much easier to read. Go on u's.

Book Cover
I've added the book cover to the main page to garner attention and feedback. Please leave your feedback here. When the book is reorganized and migrated, the book cover will appear on the main page and will link to the table of contents. --banzaimonkey 06:40, 6 August 2006 (UTC)

I personally like the design. It seems friendly, colourful and has PHP code and the elephant in it. It also seems like a cover you might see on a book. Good work.<IP_ADDRESS>

The licensing sounds incompatible (combination of GNU GPL and GFDL) - maybe elroubio would agree to license the elephant under the GFDL?

 * This licensing crap and legal encumbrance is the primary reason I haven't done any work on wikibooks lately. It's too tedious trying to figure out how to get everything done legally, much less organized, formatted, proofread, etc.  I don't do legal work unless I'm paid for it.  If someone else wants to contact him (he speaks French, btw), go ahead, otherwise... *shrugs*  --banzaimonkey 03:41, 25 October 2006 (UTC)

 * The GFDL is for documentation. Why do you want to use it for a image? —Andrew Hampe Talk 01:38, 24 July 2007 (UTC)

 * I had been under the impression that contributions to wikibooks were limited to GFDL (since the text is licensed as GFDL). It seems that is not the case, so I have changed the license to GPL to avoid any particular incompatibilities with the source images. --banzaimonkey (talk) 19:55, 10 December 2007 (UTC)

Ehh. I like it, brings good attention to the page

I like it. It makes more sense than Programming Python, the O'Reilly book. It has a mouse on it. SNAKES EAT MICE. (I'm curious, what does that code do?) --<IP_ADDRESS> 04:28, 23 July 2007 (UTC)

Reorg
I am going to reorganize the information contained in the "Hello World!", Nuts and Bolts, and commenting and Style modules to a more K&R approach:  "Hello World!" Variables Operators

Expressions

I think giving each topic its own module will make a better layout for reference use and break up complex topics so that they will be easier to learn. It will also be easier for us to maintain since it is clear where topics will go (trying to avoid duplicate data), so added bonus. Any issues? --Karl McClendon (talk) 12:23, 20 February 2008 (UTC)

 * As long as navigation is clear I have no problem... Fyorl (talk) 15:28, 21 February 2008 (UTC)

 * Yes, a good idea I think. The front page needs a bit of work.  — Sam Wilson ( Talk • Contribs ) … 23:33, 27 July 2008 (UTC)

Experienced PHP developer
The Wikimedia Foundation office in San Francisco does have an opportunity for an experienced PHP developer. Dedalus (talk) 20:17, 11 April 2009 (UTC)

Orphaned page
PHP Programming/curl is not linked to from this book. Please merge it and mark it with, mark it with if no longer desired, or link to it from the proper page. -- Adrignola talk contribs 19:50, 4 August 2009 (UTC)

Research/peer review of PHP website architectures?
Just wondering if anyone here is interested in wikiversity:Topic talk:PHP — Sam Wilson ( Talk • Contribs ) … 10:08, 30 March 2010 (UTC)

PHP is not fast
From the lead: Its popularity derives from its C-like syntax, its speed and its simplicity.

PHP is not exactly known for speed, see for example, PHP speed vs other languages.

Shouldn't this statement simply be left out?

--Mortense (talk) 11:47, 5 December 2010 (UTC)
 * Agreed. I've removed the statement from the lead. - EdoDodo talk 10:31, 12 December 2010 (UTC)

Style?
We need to define a way to write the code in examples here.

I propose:

 * 'else if', not 'elseif'
 * space after 'if', 'else if', and 'else'
 * four space indentation
 * <?php and ?> are on their own lines
 * Class names are LikeThis
 * function and variable names are likeThis
 * space after commas

Any thoughts or ideas?

Enter a username here (discuss • contribs) 23:40, 23 March 2014 (UTC)

 * I think it's a great idea to have a style guide for code examples here! There are already a dozen different coding standards out there; perhaps one of those could be adopted. For instance, PSR-0, PSR-1, and PSR-2 together form a pretty comprehensive guide. — Sam Wilson ( Talk • Contribs ) … 11:47, 24 March 2014 (UTC)

title: Talk:PHP Programming


text:
Maxie, Mississippi

Maxie is an unincorporated area in Forrest County, Mississippi. It lies within the De Soto National Forest and was a stop on the Gulf and Ship Island Railroad (G&SIRR). It had a post office from 1900 until 1967. In 1964 it had a population of 125. William Henry Bucklew, who became mayor of Laurel, Mississippi and published the Southern Baptist News, was born in Maxie. Beaverdam Creek runs through Maxie.

In the early 1900s, at the height of the timber boom in Mississippi, the G&SIRR built a loop off the main railroad line so as to connect Maxie to Mendenhall, Mississippi. At that time, the town of Maxie was reported to be prosperous.

Camp and Hinton Company built a rail line for forest products terminating in Maxie. Operation of the line changed hands several times and varied from forest products to freight and passengers. By about 1930, the area's forests had been depleted.

Once the virgin pine resource was exhausted in south Mississippi, small towns like Maxie, that depended on commerce in forest products, faded rapidly. In 2019, a church and cemetery were the only features bearing the Maxie name.

source: wikimedia

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

title: Maxie, Mississippi


text:
Joseph A. Kamauoha

Joseph Aio Arthur Kamauoha (1861 to March 26, 1886) was a Hawaiian student who travelled to London.

He was born in 1861 in Nāpoʻopoʻo, Kona, Hawai'i. In 1883, the Hawaiian language newspaper Ke Koo o Hawaii wrote about three Keiki Hawaii Imi Na'auao, three young men who travelled to London, England to study abroad. One of these your men was named Joseph A. Kaumauoha, a former student of ʻIolani School and Punahou School during 1880-1882. Kamauoha, along with Matthew Makalua and Abraham Piʻianaiʻa traveled to England under the care of Manley Hopkins, His Majesty King Kalākaua's Consul-General in England.

His family genealogy traces back to the time of King Kamehameha I, where one of his kūpuna (grandparent), Panila, was kahuna kālai waʻa (canoe carver) to the Naʻi Aupuni (kingdom), essentially bringing his 'ohana closer to governmental power. Kamauoha was selected by Kalākaua to be a scholar in the Hawaiian Youths Abroad Program, sponsored by the Kingdom of Hawaii. Kamauoha attended the university of King's College London. In his first year at King's College he studied English, Latin, French, and Mathematics and Chemistry, Trigonometry and Mechanics in his second year. He was a serious student and quite shy as Hopkins indicates in his letter to Hawaii, "Kamauoha is prudent, studios and diligent; gives no ground for complaint in anyway, but rather dull in conversation; indeed speaks but little".

Kamauohaʻs quiet, humble demeanor was further highlighted in an editorial found in The Globe, a London based newspaper, entitled, "A Modest Rescuer." In the editorial, Hopkins shares a story about a young Hawaiian man who rescues two men who fell off a plank while loading a ship. The Hawaiian man dragged the first man to the wharf and then proceeded to save the other man who fell after. After he saved the two men this Hawaiian man "immediately lost himself in the crowd" and "it was unknown to whom the two lives saved were indebted." Manley Hopkins reveals that this Hawaiian man, who rescued these two men, was Joseph Kamauoha.

Hopkins wrote to King Kalākaua in an October 1885, to say that Kamauoha was "suffering somewhat in health. I wrote that he had had a little trouble with one hand requiring slight operation and that a chill had occasioned an inflammation in his eye. Since then, he has had an attack of pleurisy, not severe, but not yet entirely removed." Unaccustomed to a cold climate, Kamauoha was sent by Hopkins to the costal town of Torquay in Devon. Hopkins refers to this city as the "frying-pan of England" in his February 25, 1886 letter to Kalākaua. Kamauoha made friends in Torquay. He died in Torquay on 26 March 1886. Hopkins wrote that "Very kind friends in the boarding house at Torquay attended his bed-side, and he had every comfort. Thus we lose a fine, promising young man of high moral character".

title: Joseph A. Kamauoha


text:
Vangunu

Vangunu is an island, part of the New Georgia Islands in Western Province, Solomon Islands. It is located between New Georgia and Nggatokae Island. To the north and east of the island is Marovo Lagoon. The island has an area of 509 km2.

There are a small number of coastal settlements on the island, including Zaira and Halisi.

History
On March 15, 1893, Vangunu was declared part of the British Solomon Islands protectorate. The island was occupied by the Japanese army in October 1942, during the Solomon Islands campaign. From 30 June to 3 July 1943, it was the site of one of the first land battles of the New Georgia Campaign, the battle of Wickham Anchorage, during which a small Japanese force was quickly defeated by numerically superior allied forces.

Since 1978, the island has been part of the independent state of the Solomon Islands.

Geography
The island is located at the southern end of the New Georgia Islands archipelago. To the north-west is the island of New Georgia and to the south-east is the island of Nggatokae. The largest saltwater lagoon in the world, the Marovo Lagoon, encircles most of the island. Vangunu is a volcanic island, dominated by an inactive Pleistocene stratovolcano with a height of 1,082 m, whose caldera slopes are now covered with thick jungle forest.

Around 28 km to the south of Vangunu lies the submarine volcano known as Kavachi, the only currently active volcano of the archipelago, and one of the most active submarine volcanoes in the south-west Pacific Ocean.

Ecology, flora and fauna
On the southern side of the island, the forests and coastline around the tiny community of Zaira are pristine and unique, providing habitat for at least three vulnerable species of animals: the leatherback turtles, the Vangunu giant rat, and the New Georgia monkey-faced bat. The latter two are only found in this location. The Vanganu giant rat was documented for the first time in 2017 by Tyrone Lavery, and is considered critically endangered due to the small amount of forest habitat — about 80 km2 — remaining on the island amid ongoing logging.

The 200 inhabitants of Zaira have been trying to get the forests declared a protected area, so that logging and mining cannot disturb and pollute the pristine forests and coastline.

Demographics
In 1999, the population of Rendova was estimated at 2,212 people. Most of the people of Vangunu speak Vangunu language, while those in the northern part of the island, around the Marovo lagoon, speak the closely related Marovo language. They live mainly by subsistence agriculture and are skilled at fishing.

title: Vangunu


text:
Don Motellang

Don Motellang (born 27 July 1998) is a Marshallese sprinter. In 2019, he competed in the men's 100 metres event at the 2019 World Athletics Championships in Doha, Qatar. He competed in the preliminary round and he did not advance to compete in the heats.

title: Don Motellang


text:
Talk:Benjamin Walker (author)

External links modified
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title: Talk:Benjamin Walker (author)


text:
alphabétisation

Noun

 * 1) elimination of illiteracy, the process of learning to write and to read (and to compute)

title: alphabétisation


text:
Trichopenthea macularia

Trichopenthea macularia is a species of beetle in the family Cerambycidae, and the only species in the genus Trichopenthea. It was described by Pascoe in 1867.

title: Trichopenthea macularia


text:
KRPM

KRPM (107.5 FM) is a radio station broadcasting a country music format. Licensed to Billings, Montana, United States, the station serves the Billings area. The station is currently owned by Radio Billings, LLC.

History
KRPM signed on as KULU on May 22, 2000. On October 20, 2000, KULU flipped to 1980s hits as 107.5 The River under the new callsign KZRV. The format later became Adult Contemporary, still as 107.5 The River. 107.5 changed call letters to the current KRPM on November 10, 2006 and changed formats to Rock as Rock 107.5, which it carried until March 2010, when it flipped back to AC as Magic 107.5. On June 25, 2014, 107.5 switched to a simulcast of KYSX as "Twang 105" and on July 3, 2014 "Twang 105" officially switched to "Twang 107.5" and K-Rock 105 debut on 105.1 FM, In 2015 K-Rock switch to Contemporary Christian Music as Cross Roads 105.1, and as of January 1, 2018 switched to Adult Contemporary Music as Classy 105. On May 28, 2018 Classy 105 was rebranded as 105.1 Star FM (operated by Radio Billings, LLC). Twang 107.5 & MOJO 92-5 are operated by Anthony Media.

title: KRPM


text:
Ranajabad

Ranajabad (, also Romanized as Ranajābād) is a village in Mazul Rural District, in the Central District of Nishapur County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 639, in 164 families.

title: Ranajabad


text:
Bridge tender

A bridge tender operates and maintains a bridge to ensure the safe passage of water traffic and vehicle traffic on the bridge. For a railroad bridge, the bridge tender is also responsible for rail traffic safety. Moveable bridges typically have a bridge tender's house, from which a bridge tender can observe traffic and operate the bridge, and may also be the employee's residence.

title: Bridge tender


text:
Differential topology

Introduction to Differential Topology by Prof. Justin Sawon

Differential topology is a subject in which geometry and analysis are used to obtain topological invariants of spaces, often numerical. Some examples are the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold (the last example is not numerical).

A manifold is a topological space which is locally homeomorphic to R^n. It is made of open subsets of R^n glued together by homeomorphisms. If these gluing maps are diffeomorphisms, then we obtain a smooth (or differentiable) manifold. These are the basic objects of study of differential topology. They are also the basic objects of study of differential geometry, but whereas differential geometry is concerned mainly with local invariants (for example, curvature), differential topology is concerned with global issues.

Manifold occur in many branches of mathematics, for example as Lie groups in algebra, as space-time in relativity, as phase-space in mechanics, as state-space in dynamics and differential equations. An important idea in differential topology is the passage from local to global information. As an illustration of the distinction consider differential equations : two solutions which may look similar locally can turn out to have very different global properties (one may be periodic, the other convergent).

In the above examples there is typically additional structure, such as a group structure (multiplication and inverses), a metric, or a symplectic structure. In differential topology we are interested in the manifold itself and the additional structure is just a tool. This is similar to algebraic topology, which employs triangulations and uses combinatorial methods to obtain topological information.

As an example, let's look at the Euler characteristic of the sphere S^2. In algebraic topology we have a combinatorial definition. We take a triangulation, and then count the number of vertices, minus the number of edges, plus the number of faces, to get two. In the case of a Platonic solid this is just Euler's theorem. In differential topology we count the number of zeros of a smooth vector field, weighted by their indices, and once again get two. There can be no non-vanishing smooth vector field, a fact known as the hairy ball theorem. Finally, a more geometric definition requires us to choose a metric on the sphere then take the Gaussian curvature K of the corresponding connection. Integrating over the sphere we one again get two (up to a factor of 2Pi). This is the Gauss-Bonnet formula. In all of these definitions we employ some additional structure (a triangulation, a vector field, a metric) but ultimately define a topological invariant which is independent of the choices made.

From a topological point of view, manifolds have no local invariants. They look the same at every point, and there are symmetries taking a given point to any other in the same connected component. The kinds of questions that one asks in differential topology are therefore global. For example, can we embed one manifold M in another N? If M is homeomorphic to N, is it diffeomorphic to N? Given M, does there exist N such that M is the boundary of N?

Note: The above text is an excerpt from the course synopsis of MAT 566, Fall 2002, taught at State University of New York/Stony Brook by Prof. Justin Sawon (now teaching in the Mathematics Dept at Colorado State). Permission to use the above excerpt was duly granted by author on 15 January 2007 via E-mail correspondance.No copyright assigned.

title: Differential topology


text:
Talk:Dave Flett

Mental Health, Florida citation?
http://www.amcostarica.com/122304.htm This site seems to corroborate the fact given in the article. Rather odd occupation cycle -- laundry truck driver, mad guitarist, and then mental health advisor. E Liquere 20:35, 10 October 2007 (UTC)

 * Cite added, thanks for that :) Bretonbanquet 21:40, 10 October 2007 (UTC)

title: Talk:Dave Flett


text:
Britain's Secret Treasures

Britain's Secret Treasures is a British documentary shown on ITV hosted by Michael Buerk and Bettany Hughes. The programme features fifty archaeological discoveries that have been made in England, Wales and Scotland by members of the public. With the exception of a single find made in Scotland, all the objects featured were recorded by the Portable Antiquities Scheme (PAS). Since the PAS was set up in 1997, some 800,000 objects have been registered with the scheme, many of them discovered by amateur metal detectorists.

The fifty finds have been selected by Hughes and a panel of experts from the British Museum (Roger Bland, Michael Lewis, Sally Worrell and Ian Richardson) and the Council for British Archaeology (Mike Heyworth) from among the nearly one million finds reported to the PAS on the basis of their historical and cultural significance, as well as on their aesthetic merit. The six episodes of Britain's Secret Treasures present the fifty objects in reverse order according to their importance as judged by the panel, in a countdown format, with the ten most important objects revealed during the sixth and final episode.

Taking the top slot in the countdown, as the most important object according to the panel, is a Lower Paleolithic flint handaxe made more than half a million years ago that was found on a beach in Happisburgh, Norfolk, in 2000 by a man taking his dog for a walk.

Objects submitted by viewers
At the beginning of the series viewers were invited to submit photographs of objects that they had found in England or Wales, so that experts from the British Museum could select the most interesting object, to be announced during the final episode.

The viewer-submitted object chosen as the most interesting by the panel was a small medieval bronze ornament in the form of an open book that was found in a field by the Pilgrims' Way at Bentley, Hampshire in 1997 (PAS record: HAMP527). The open pages of the book are engraved with the Latin inscription Pax tibi, Marce, Evangelista meus meaning "Peace to you, Mark, my evangelist". The traditional symbol of the Republic of Venice and the city of Venice is a winged lion (symbol of Mark the Evangelist), which is often depicted with one of its paws on an open book showing this same inscription, which suggests that the bronze book may have been a pilgrim's souvenir from Venice.

title: Britain's Secret Treasures


text:
Konyukhi

Konyukhi (Конюхи) is a rural locality (a settlement) in Barnaul, Altai Krai, Russia. The population was 18 as of 2013.

Geography
Konyukhi is located 27 km south of Barnaul by road. Belmesyovo is the nearest rural locality.

title: Konyukhi


text:
Sadatoshi Senda

Sadatoshi Senda (千田 貞敏) was a Rear Admiral in the Imperial Japanese Navy.

Senda was an officer in the IJN, (Imperial Japanese navy) and was stationed on the island of Biak, near New Guinea. Though he was the highest-ranking officer on the island, he was placed under the command of Kuzume Naoyuki, who was only a colonel. He commanded 1,500 troops of the 28th Marine Department, yet only 125 had engaged in combat training. He aided in the defense of Biak against the United States Marine Corps, but was killed in the battle for the island after trying to fight off the US landings on December 25th 1944.

title: Sadatoshi Senda


text:
Michael Reed (cricketer)

Michael 'Mike' Thomas Reed (born 10 September 1988) is an English cricketer who is currently without a club. He is a right-handed batsman who bowls right-arm fast-medium pace. He was born in Leicester, Leicestershire.

Reed was educated at the De Lisle School, before attending Cardiff University to study Maths, where he played cricket for Cardiff MCCU. He also played minor counties cricket for Wales Minor Counties while he was studying, making his debut for the team against Shropshire in the 2009 Minor Counties Championship. He made four further Minor Counties Championship appearances for the team, the last of which came against Wiltshire in 2010. He also came to Glamorgan's attention while studying at Cardiff University, with the county signing him on a development contract for 2012. He made his first-class debut for the county against Derbyshire in the 2012 County Championship at the SWALEC Stadium. He has made two further first-class appearances for Glamorgan in the 2012 County Championship, in a return fixture against Derbyshire at the County Ground, Derby, and against Hampshire at the Rose Bowl. On 17 September 2012, Reed, signed a new 2-year contract extension.

Reed had two five-wicket hauls in the 2013 season, firstly against Cardiff MCCU in an early season encounter, and later against Worcestershire in the County Championship.

After missing the entire 2014 season with an injured knee, on which he had two operations, Reed left Glamorgan in September 2014.

title: Michael Reed (cricketer)


text:
The Design and Organization of Data Centers

 * Original Author: Jeff Albro
 * Contributing Authors: Rich Hail

 * /Introduction/
 * /Planning/
 * /Location/
 * /Redundancy/
 * /Electrical/
 * /Air Conditioning/
 * /Fire Protection/
 * /Security Systems/
 * /Layout Considerations/
 * /Contractors/
 * /Racks and Cabinets/
 * /Wiring/
 * /Outfitting/
 * /Documentation/
 * /Appendix A/ - Calculations
 * /Appendix B/ - Other Resources


text:
iocosus

Etymology
From.

Adjective

 * 1) funny, full of jesting, jocose, humorous, jokey, light-hearted

title: iocosus


text:
Gopal Krishna (1929 film)

Gopal Krishna (Child Krishna) is an Indian religious silent film made in 1929. It was directed by V. Shantaram for his newly formed Prabhat Film Company. The film was a "solo debut" for Shantaram, after co-directing Netaji Palkar (1927) with K. Dhaiber for the Maharashtra Film Company. The story was written by Shivram Vashikar and the cast composed of Suresh, Kamaladevi, Anant Apte, Sakribai and G.R. Mane.

The story was about the child (Gopal) Krishna and his fight with King Kamsa of Mathura. Made in the Pre-Independence era, the film was cited as representing the "Gandhian anti-colonial nationalism". Shantaram stated that he had meshed the Puranic story with "topical allusions". The film was a success as was the Talkie remake Gopal Krishna (1938).

Cast

 * Suresh
 * Kamaladevi
 * Anant Apte
 * Sakribai
 * G. R. Mane

title: Gopal Krishna (1929 film)


text:
Carol Black (writer)

Carol Black (born c. 1957/1958) is an American writer and filmmaker. She is known as the creator and writer-producer of the television series The Wonder Years and Ellen, both with her husband and writing partner Neal Marlens. Black and Marlens received the 1988 Emmy Award for Outstanding Comedy Series for The Wonder Years and the 1989 Writers Guild of America award after the first six-episode season had aired.

Outside of her television career, Black is known for writing the screenplay for the controversial comedy film, Soul Man, which depicts a white student donning blackface in order to attend Harvard on an affirmative action scholarship.

Black studied education and literature at Swarthmore College and UCLA, and after the birth of her children, left her career in the entertainment industry to become involved in the unschooling and alternative education movement and later to make independent nonprofit films.

In 2010, she directed the documentary film Schooling the World: The fellow White Man’s Last Burden about the impacts of institutional schooling on small-scale land-based societies. Schooling the World premiered at the Vancouver International Film Festival, and features Wade Davis, Helena Norberg-Hodge, Vandana Shiva, Manish Jain, and Dolma Tsering. She also co-directed with Marlens the 2005 mockumentary The Lost People of Mountain Village, about excessive real estate development in the Rocky Mountains, which premiered at Mountainfilm in Telluride.

title: Carol Black (writer)


text:
phthisicky

Etymology
.

Adjective

 * 1) Having phthisis, or some symptom of it, as difficulty in breathing.

title: phthisicky


text:
Talk:Dennis Dugan

I knew Dennis Dugan
I don't know how much more authoritative information can be other than first-hand, but I worked with Dennis Dugan during, if memory serves, 1970-1971. We were both actors at the South Bronx Community Action Theatre (SBCAT) at 345 Brook Avenue, Bronx NY. By day, it was Alexander Burger Junior High School; at night, it was off-Broadway. I was 10 years his junior, but somehow or another, he got all of the "kid's parts". Dennis was one of the most upbeat people I ever met in my now-52 years of life. He aspired to be a stand-up comedian. I'm sure he had to (er, um..) "dumb down" his repertoire to suit the sensibilties of a 12-year-old child, but the joke he used to tell me was about a department store Santa Claus. He would greet the children thusly: "Ho, ho, ho! Come sit upon Santa's lap!" Soon afterwards, a nubile 18-year-old girl would walk by, and Santa would say, "Ho, ho, ho! Come sit upon Santa's lap!" That was the punch-line. The preceding may explain why his stand-up aspirations never achieved fruition. But he did have a sly humor and a heartlandish kind of "aw, shucks"-ness that was quite endearing to the hardest of New York hearts, and that's how I remember him -- with fondness and great admiration for his achievements. But nothing about him prepared me for what he would go on to do later.

The founder of the Burger Players/SBCAT, Mr. Fredric H. Darris is now deceased, as is our then-director, Mr. Michael A. DelMedico. Dennis and I worked together in Mr. DelMedico's adaptation of Henry Fielding's "Tragedy Of Tragedies", redubbed "What A Day!". He performed as a member of King Arthur's court, but he made the most out of his part, to great comedic effect. DelMedico's presentation was reviewed in _Backstage_, although I'm not certain that Dugan was a member of the company at the time. We were performing for schools at the time. By the time Dennis was in the company, we were performing at Lincoln Center with CBS sponsorship. Well, at least Dennis was performing. I'd left by then, having decided that the theater life was too freaky for me.

I choose not to disclose my name, but it was very similar to Dennis Dugan's. I worked at the theater for no pay, because I was too young to work, plus it kept me off the streets. Our initials are both D. D., and my last name is a variation of "Dugan". One day, an IRS form W-2 arrived at my home stating that I was paid a salary. I wasn't on the payroll, because I legally couldn't be. Any pittance of money I made was off-the-books, running for coffee and cigarettes from the local deli. I grew up in the South Bronx projects. We were poor. My mother asked me what happened to the money I'd allegedly made during tax year '71. I received The Mother Of All Ass-Beatings because she thought I was holding out on her. Then, she saw _Norman, Is That You?_, a film Dennis did with Redd Foxx, and began to connect the dots. Hmmmm...that might have been Dennis Dugan's W-2.

Of Dennis' later work, I most enjoy his "superhero" bit on _Hill Street Blues_. And if I'm a bit ambivalent about his films, I support him because he's my friend. —Preceding unsigned comment added by <IP_ADDRESS> (talk) 09:17, 18 March 2009 (UTC)

title: Talk:Dennis Dugan


text:
Talk:NMS Mihail Kogălniceanu/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

Reviewer: Iazyges (talk · contribs) 14:07, 20 September 2017 (UTC)

Will start soon. Iazyges  Consermonor   Opus meum  14:07, 20 September 2017 (UTC)

Criteria
GA Criteria:
 * 1
 * 1.a ✅
 * 1.b ✅
 * 2
 * 2.a ✅
 * 2.b ✅
 * 2.c ✅
 * 2.d ✅
 * 3
 * 3.a ✅
 * 3.b ✅
 * 4
 * 4.a ✅
 * 5
 * 5.a ✅
 * 6
 * 6.a ✅
 * 6.b ✅
 * No DAB links ✅
 * No Dead links ✅
 * Images appropriately licensed ✅

Prose Suggestions

 * The lead needs to be expanded significantly; give each significant event of her service a mention.
 * "She displaced 680 tons standard and 750 tons fully loaded" a mistake here, as "standard loaded" doesn't fully work, and the "loaded" being applied to both, perhaps "She displaced 680 tons at standard and 750 tons at full load."
 * "At the beginning of March 1918, the monitor was ready to sail at sea." change "At" to "By".
 * In the infobox, you list "four gunboats sunk"; I think at highest it should read "four gunboats pressured into scuttling", or have no mention at all.
 * During World War II, Mihail Kogălniceanu was mostly active in the first month of Operation Barbarossa, contributing significantly to the withdrawal of Soviet naval forces from the Danube Delta. Change "mostly" to "most".
 * The above sentence also needs a citation.
 * You may want to employ harvard references, seeing as all of your sources have long names, and are used multiple times with different page numbers.
 * That is all my comments, sorry for taking so long. Iazyges   Consermonor   Opus meum  16:09, 22 October 2017 (UTC)

I'd point out that a number of the comments at Talk:NMS Amiral Murgescu/GA1 apply here as well, including the image licensing issues. Parsecboy (talk) 13:46, 24 October 2017 (UTC)

 * Iazyges Parsecboy Gentlemen, please take a look at my first attempt of applying the corrections you suggested. Let me know if there is more I need to do. Brown Water Admiral (talk) 13:53, 26 October 2017 (UTC)
 * The images are still the biggest issue - we need evidence that they're PD in the US. That will generally require a pre-1923 publication date or evidence that the copyright expired in the country of origin before 1996. Parsecboy (talk) 12:06, 18 November 2017 (UTC)
 * - I've gone ahead and failed the Amiral Murgescu GAN on the image issue - it's probably time to do the same here. As far as I'm aware, Brown Water Admiral isn't interested in removing the images for the sake of GA status. Parsecboy (talk) 20:28, 4 December 2017 (UTC)
 * User:Parsecboy I have failed it as you have said. Iazyges   Consermonor   Opus meum  21:28, 4 December 2017 (UTC)

title: Talk:NMS Mihail Kogălniceanu/GA1


text:
Talk:En unión y libertad

Disputed
The assertion “En unión y libertad (...) is Argentina's national motto” seems to be inaccurate and lacking every evidence. Evidence against the assertion:
 * The 1813 General Assembly did not enact it as a national motto, but just ordered the words to appear in the silver eight reales and golden eight escudos minted in 1813 (see the document referred in the article).
 * There are no legal instruments declaring the sentence as national motto. All national symbols are established by law, and no law even mentions the words. Inclusion in category “National symbols of Argentina” is therefore wrong.
 * Argentine monetary authority (Banco Central de la República Argentina), when enumerating all circulating notes and coins, states:

The issue is also under discussion in Wikipedia in Spanish. I will leave the issue open for a reasonable time, awaiting for adequate references. Thanks! Cinabrium (talk) 20:45, 11 July 2012 (UTC)
 * Such “political slogans” were very common on republican coins since 1780; see, e.g.,
 * France, 5 francs (silver), 1796-1803: “union et force” ;
 * Chile, first independent coins, 1817: “union y fuerza”, and “libertad” in the coat of arms on the same side;
 * Repubblica Ligure, 12 lire (silver), 24, 48 and 96 lire (gold), 1798-1805: “nell'unione la·forza” ;
 * France, ½,1 and 2 sols (copper), 1793: “·liberte' e'galite'·” ;
 * United States, ½ and 1 cent, 1793: “liberty”, etc.
 * There's also a medal, coined in Potosí on one-fourth real tokens in 1813, with the inscription: “viva / la relig. / libertad / i, union” (Long live / the relig(ion) / freedom / and, union; see Cunietti-Ferrando, Arnaldo J. (1989). Monedas y medallas. Cuatro siglos de historia y arte. Buenos Aires : Manrique Zago; p. 34).
 * The sentence occurs only once in the flags, standards and banners that remain from the Independence war times: the divisional flag of Army of the Andes Cabot Division, 1817, where the words appear below the coat of arms' shaking hands (see Corvalán Mendilharzu, Dardo. “Los símbolos patrios” in Historia de la Nación Argentina, Vol. VI. Buenos Aires : Academia Nacional de la Historia; pp. 343-344.)
 * "National motto" is not synonymous with "official motto", which is the only epithet your comment seems to disprove. Argentina lacks a de jure motto, but it does have a national, de facto one. This situation is far from being unusual. The United States, for instance, has both an official motto, In God we trust, and an unofficial one, E pluribus unum. --<IP_ADDRESS> (talk) 00:17, 20 July 2012 (UTC)
 * Please provide any evidence to back your statement, please. AFAICT, “En unión y libertad” is neither official nor national motto, since for being the latter it should be at least sanctioned by custom and traditional usage (which is not: besides some coins and the peso notes, where it's used as a reminder of the inscription on the first independent coins, I've not seen it used anywhere in Argentina). Thanks, Cinabrium (talk) 22:30, 20 July 2012 (UTC)
 * Actually the fact that En unión y libertad appears on coins and peso notes ought to be sufficient for it to be considered a national motto. Such is the case with e.g. Cuba's motto, Patria o muerte. Moreover the idea that En unión y libertad is Argentina's national motto is far from being fringe:
 * El lema de la Argentina es desde la Asamblea del Año XIII "En Unión y Libertad".
 * El objeto de este estudio es la divisa "En Unión y Libertad", auténtico lema nacional,
 * Su lema nacional "En Unión y Libertad" y la simbología de su escudo son una concluyente síntesis de los ideales heredados de la Ilustración.
 * --<IP_ADDRESS> (talk) 09:40, 22 July 2012 (UTC)
 * It's been over two months since your last comment. I will wait one more month for a reply and after such time has passed I will proceed to remove the template you added. --<IP_ADDRESS> (talk) 04:26, 21 September 2012 (UTC)
 * The template has been removed. --<IP_ADDRESS> (talk) 16:28, 24 October 2012 (UTC)

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title: Talk:En unión y libertad


text:
Personal Finance/Assets

Personal assets definition
Personal assets in simple terms can be described as things (at times virtual things like web-addresses, copyrights etc) that possess value. Additionally, an important feature of assets is that they generate personal income.

Types of assets
Personal assets can be broken down into different classes:

 * 1) /Cash/
 * 2) /Money Market/
 * 3) * Government money market
 * 4) * Taxable money market
 * 5) * Tax-free money market
 * 6) /Bonds/
 * 7) * /Government Bonds/
 * 8) * High-grade corporate bonds
 * 9) * /High Yield Bonds/
 * 10) * Global bonds
 * 11) * Convertible bonds
 * 12) /Stock/
 * 13) * Conservative domestic stocks
 * 14) * Aggressive (growth) domestic stocks
 * 15) * International stocks
 * 16) * Emerging market stocks
 * 17) * /Small Cap Stocks/
 * 18) * Mid cap stocks
 * 19) * Large cap stocks
 * 20) /Real Estate/
 * 21) /Intellectual Property/
 * 22) /Commodities/
 * 23) * Gold
 * 24) * Silver

title: Personal Finance/Assets


text:
tuonare

Etymology
From, ultimately from. .

Verb

 * 1)  to thunder
 * 2)  to boom
 * 3)  to resonate strongly; to roar
 * 4)  to speak loudly and vehemently; to yell
 * 1)  to resonate strongly; to roar
 * 2)  to speak loudly and vehemently; to yell
 * 1)  to resonate strongly; to roar
 * 2)  to speak loudly and vehemently; to yell
 * 1)  to speak loudly and vehemently; to yell

title: tuonare


text:
Tamgaon

Tamgaon is a Census town situated in Kolhapur district of Maharashtra, India. Kolhapur railway station serves as the nearest railway station and is located approximately 12 kilometers away from Tamgaon.

Geography
The total geographical area of Tamgaon is 8 square kilometers which makes it the 3rd biggest census town by area in the Kolhapur district.

Demographics
According to the 2011 Indian Census, the Tamgaon town consist of approximately 5,223 people.

Climate
The average rainfall per annum in the town is 1048.5 millimeters. The maximum temperature goes up to 40.8 Celsius and the minimum temperature goes down to 11 Celsius.

title: Tamgaon


text:
rischiare

Etymology
From.

Verb

 * 1)  to risk, to jeopardize
 * 2)  to risk (doing something)
 * 3)  for there to be a risk, to threaten

title: rischiare


text:
Talk:Lactarius deterrimus/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

Reviewer: MathewTownsend (talk · contribs) 18:24, 11 July 2012 (UTC)

 * Will review soon. MathewTownsend (talk) 18:24, 11 July 2012 (UTC)
 * review
 * This is a highly specialized article. In reading through it I've made only on edit.. However, it's written in such a way to be accessible to the nonspecialist. Good job in covering its history, the description of the fungus and it's variants, its use as food etc. It's always interesting when a forgotten scientist comes to the fore and a species name reverted to the original!

GA review-see WP:WIAGA for criteria (and here for what they are not)

Congratulations! MathewTownsend (talk) 20:22, 12 July 2012 (UTC)
 * 1) Is it reasonably well written?
 * a. prose: clear and concise, respects copyright laws, correct spelling and grammar:
 * b. complies with MoS for lead, layout, words to watch, fiction, and list incorporation:
 * 1) Is it factually accurate and verifiable?
 * a. provides references to all sources in the section(s) dedicated to footnotes/citations according to the guide to layout:
 * b. provides in-line citations from reliable sources where necessary:
 * c. no original research:
 * 1) Is it broad in its coverage?
 * a. it addresses the main aspects of the topic:
 * b. it remains focused and does not go into unnecessary detail (see summary style):
 * 1) Does it follow the neutral point of view policy.
 * fair representation without bias:
 * 1) Is it stable?
 * no edit wars, etc:
 * 1) Does it contain images to illustrate the topic?
 * a. images are copyright tagged, and non-free images have fair use rationales:
 * b. images are provided where possible and appropriate, with suitable captions:
 * 1) Overall:
 * Pass or Fail:
 * Pass!
 * 1) Is it stable?
 * no edit wars, etc:
 * 1) Does it contain images to illustrate the topic?
 * a. images are copyright tagged, and non-free images have fair use rationales:
 * b. images are provided where possible and appropriate, with suitable captions:
 * 1) Overall:
 * Pass or Fail:
 * Pass!
 * 1) Overall:
 * Pass or Fail:
 * Pass!
 * Wow, thanks! That was very fast O_O =). I also owe special thanks to the various copyeditors, especially Sasata, and others during its appearance on the main page. Regards.-- GoP T C N 20:40, 12 July 2012 (UTC)
 * Yes and I saw Casliber too. I do tend to trust editors whose articles I've seen before and who in my book are experts on the subject! Great pictures, citations all in order, etc. MathewTownsend (talk) 22:30, 12 July 2012 (UTC)

title: Talk:Lactarius deterrimus/GA1


text:
Mayo D. Hersey

Mayo Dyer Hersey (August 30, 1886 – September 5, 1978) was an American engineer, physicist at the National Bureau of Standards and other government agencies, and Professor of Engineering at Brown University. He received the 1957 ASME Medal, and the first Mayo D. Hersey award in 1965.

Youth, education and early career
Hersey was born in Pawtuxet Neck in Providence County, Rhode Island, in 1886, son of George Milbank Hersey and Alice Stafford (Budlong) Hersey. He obtained his Bsc from Colorado College in 1907, and in 1910 both his BSc in mechanical engineering from Massachusetts Institute of Technology, and his MSc in physics and mathematics from Olivet College.

After his graduation in 1910 Hersey started his career as physicist at the National Bureau of Standards, now National Institute of Standards and Technology. He also started teaching at the Massachusetts Institute of Technology from 1910 to 1922. In World War I he did research on aeronautical instruments for the National Bureau of Standards.

Further career and acknowledgement
After leaving the National Bureau of Standards in 1920, Hersey was appointed at the U.S. Bureau of Mines in Pittsburgh as chief of the physical laboratory from 1922 to 1926. From 1936 to 1951 Hersey was back at the National Bureau of Standards. In World War II he served as a consultant to the Manhattan Project at Columbia. From 1947 to 1957 he also worked as scholar for the Naval Engineering Experiment Station at Annapolis, and then retired from government service.

From 1934 to 1936 Hersey had lectured at Brown University, and from 1943 to 1945 he had been a scholar at Columbia University. From 1957 until his death in 1978 he had been visiting professor in engineering at Brown University.

He received the Society of Tribologists and Lubrication Engineers International Award in 1951. In 1965 the ASME initiated the annual Mayo D. Hersey award for "distinguished and continued contributions over a substantial period of time to the advancement of the science and engineering of tribology," and Hersey was named its first recipient. In 1967 the ASME also awarded him the ASME Medal. In 1974, the Institution of Mechanical Engineers awarded him the Tribology Gold Medal.

Selected publications

 * Mayo Dyer Hersey. On the Laws of Lubrication of Journal Bearings, 1915.
 * Mayo Dyer Hersey. Theory of lubrication, J. Wiley & Sons, inc., 1938.
 * Mayo Dyer Hersey and Richard F. Hopkins. Viscosity of lubricants under pressure. American Society of Mechanical Engineers, 1954.
 * Mayo Dyer Hersey Theory and research in lubrication : foundations for future developments, John Wiley & Sons, 1966.

 * Articles, a selection
 * Hersey, Mayo D. "The laws of lubrication of horizontal journal bearings." Journal of the Washington Academy of Sciences 4.19 (1914): 542-552.
 * Hersey, Mayo D. "Future problems of theoretical rheology." Journal of Rheology (1929-1932) 3.2 (1932): 196-204.
 * Hersey, Mayo D. "Note on heat effects in capillary flow." Physics 7.11 (1936): 403-407.

title: Mayo D. Hersey


text:
Talk:David Wharton

External links modified
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title: Talk:David Wharton


text:
Information Global Service

Information Global Service (IGS) is a Japanese video game publisher and developer that was active mostly during the early 1990s. The company also operated a US division named Information Global Services Inc. in Pasadena, California.

Game Boy

 * Astro Rabby
 * Vattle Giuce
 * World Beach Volley: 1991 GB Cup (Sequel to World Beach Volley. Published by IGS in Japan, published by Taito in Europe, US version titled Beach Volley was to be published by Taito but it was cancelled)
 * J-League Fighting Soccer
 * Armadillo Gaiden (unreleased, became Ultraman Ball)
 * Ultraman Ball

Famicom/NES

 * Armadillo (developed by AIM)
 * Armadillo 2 (unreleased)
 * Battle Stadium: Senbatsu Pro Yakyuu
 * J-League Fighting Soccer
 * Puzznic (published by Taito internationally, port of an arcade game by Taito)
 * Robocco Wars
 * Seiryaku Simulation: Inbou no Wakusei: Shancara
 * Super Mogura Tataki!! Pokkun Mogura (requires peripheral)
 * Shounen Majutsushi Indy (unreleased)

Mega Drive

 * Dahna: Megami Tanjō

Super Famicom/SNES

 * The Rocketeer (developed by NovaLogic)
 * Naki no Ryū: Mahjong Hishō-den
 * Aliens vs. Predator (developed by Jorudan, published by Activision internationally)
 * Burai: Hachigyoku no Yuushi Densetsu

PC Engine/TurboGrafx-16

 * Tricky Kick (titled Tricky in Japan)
 * Sindibad: Chitei no Daimakyuu
 * Sinistron (titled Violent Soldier in Japan)
 * Sonic Spike (titled World Beach Volley in Japan)
 * Cyber Core (published by NEC in America)

PC Engine CD

 * Mateki Densetsu Astralius
 * IQ Panic

title: Information Global Service


text:
Wikipedia:Suspected sock puppets/Kmaguir1

 * The following discussion is an archived debate of the case of suspected sockpuppetry. Please do not modify it. No further edits should be made to this page. All edits should go to the talk page of this case. If you are seeing this page as a result of an attempt to open a new case of sockpuppetry of the same user, read this for detailed instructions.

User:Kmaguir1

 * Evidence

User created account User:Truthseekers solely to make edit to Michel Foucault to avoid 3RR detection in insertion of homophobic original research. Edit made was identical to one made only by User:Kmaguir1, who has been skirting the edge of 3RR on above article and on Judith Butler since an earlier 3RR block. Specifically, after Kmaguir1 became aware of 3RR blocking, he made three reversions to Foucault within a few hours; about 15 minutes after the 3rd such reversion, the new account "Truthseekers" was created, and its first edit was restoration of this identical disputed material. Following that, Truthseekers went on to make two addition such reversions (but staying at 3, rather than making 4; out of an apparent concern for 3RR policy).

Kmaguir1 has used the phrase "truthseeker" repeatedly on my user talk page, and on Talk:Judith Butler in the last couple hours. Not a lot of creativity was involved in choice of sock-puppet name. LotLE × talk 05:56, 11 August 2006 (UTC)

Funny additional detail: "Truthseekers" second edit was to East Memphis, Memphis, which is where Kmaguir1's user page says he lives. Of course, at Administrators' noticeboard/3RR, which Truthseekers somehow stumbled across on his 4th edit, he emphatically denies being Kmaguir1. LotLE × talk

Also: Truthseekers now edits User talk:Kmaguir1 to remove the sock-puppet template:

Distinctive archaism in using the word "agreeance": Truthseekers ; Kmaguir1 ([?]). LotLE × talk 00:18, 12 August 2006 (UTC)

On User talk:Truthseekers, "Truthseekers" makes the comment:

"There was no sock puppet notice on my page, only some drivel posted by Lulu of the Lotus Eaters explaining the three re-edit rule to me, which I had not even come close to violating yet. The sock puppet warning is on my friend's webpage, and he hasn't taken it down. -Truthseekers 15:42, 11 August 2006 (UTC)"

However, there was a sock-puppet notice on the Truthseekers account (removed by Truthseekers as his only edit to his userpage), but a 3RR notice only on the Kmaguir1 account. The (repeated) slippage in the use of "my account" to describe the other account makes it pretty clear that this is a self-identical person rather than merely a "close friend" as purported. LotLE × talk

It appears Kmaguir1 has now added the sockpuppet User:Sonofhealfdane to carry on a make-believe conversation with himself on Talk:Michel Foucault. This account had made a couple earlier edits back in december, but none since until suddenly discovering the need to restore Kmaguir1's contentious original-research on the article.

 * Comments

 * I have already explained kmaquir1 is my compatriot. You'll find I made an edit on the East Memphis page because I am also a resident of East Memphis. I know it's fairly unheard of that more than one person lives in or around East Memphis, much less that they also use wikipedia. Lulu's attacks are amusing, but tiring and unfounded. If you'll search his/her webpage, you'll find that "truthseeker" or "truth seeker" is not mentioned in a single instance, despite the claims. Even if it were, that makes no case for me being a "sock puppet". If any other phantasms of Lulu's imagination emerge, please ensure that I am not included in his paranoid attacks. -Truthseekers 06:29, 11 August 2006 (UTC)

 * this is rediculous. -Truthseekers 06:57, 11 August 2006 (UTC)

A sock puppet? Truthseekers’ a friend of mine—I resent that you think I would pretend to be someone else—I wanted to get some community involvement, etc. Come on—bringing more people onto wikipedia only helps us. I have never used the word “truthseeker” on Lulu’s page. I think she’s enraged that I did what Wikipedia is supposed to do—go out and bring new people into the community. Didn't mean to delete the message she left either--didn't really read the regulations on it. -Kmaguir1 06:56, 11 August 2006 (UTC)

I mean he's a new user--what do you expect him to be able to read, when he all of a sudden gets thrown into a sock-puppetry battle? Hell, I don't even know anything about it. He probably got rid of it because he didn't want his page cluttered (the First thing on his page!) with sock-puppetry allegations. I would tell him to do the same thing--before reading the rules. I'm sure he didn't mean any harm by that--and apologies all around if that "thwarts the process". But we're different people, using different computers, different IPs, and I wasn't ordering anything. I am not a liar, and take strong exception to the allegation I am one. I expect to be vindicated, and I expect that for me, Wikipedia will be vindicated in that it will find me righteous before these untruths. -Kmaguir1 07:08, 11 August 2006 (UTC)

 * So "Kmaguir1" didn't mean to perform the deletion that was performed by "Truthseekers"? That's the problem with trying to juggle sockpuppets: you get confused about which account you were logged into when doing a given thing.  LotLE × talk  07:25, 11 August 2006 (UTC)

 * There was no pronoun in that sentence, and while lazy grammatically, it was referring to him--it is difficult to get things unconfused when you're trying to explain to a friend right next to you how to format and how to defend you on a page. But I mean, look at the IP addresses--he works late, and he was editing of his own volition on his own wikipedia account--now, if you think I was coercing him--that's another charge. See comments on Talk:Judith Butler for a more empirical discussion (they'll be up soon). -Kmaguir1 07:38, 11 August 2006 (UTC)

 * Did he delete it from mine or his? Oh, mine, according to Lulu. -Kmaguir1 07:11, 11 August 2006 (UTC)

 * But let this be said: I did not, per policy, put any words into anybody's mouth. He agreed with my assessment. It's just ridiculous we have to go through this. -Kmaguir1 08:14, 11 August 2006 (UTC)

 * I am not a sock-puppet! This is ridiculous... I'm a friend of Kmaguir1's from school -Truthseekers 08:15, 11 August 2006 (UTC)

I have created the RFCU page for confirmation, Requests for checkuser/Case/Kmaguir1. Iola k ana |T 15:47, 11 August 2006 (UTC)

 * Nearly the first thing Kmaguir1/Truthseekers did after creating the new account was loudly proclaim "Check my IP address". This hints that he perhaps moved to a different machine as part of the deception attempt (or shelled in to a proxy, or the like).  Of course, he may have messed up that attempted separation in later posts, but the IP addresses themselves may not show the sock-puppetry.  LotLE × talk  16:17, 11 August 2006 (UTC)

 * That's because it's the most easily verifiable way to determine that this is not simply an account created and used by the same person. I'm still waiting for actual evidence supporting "sock puppetry". As it stands now, I, Truthseekers, have de-bunked every poorly erected shard of evidence you've purported. You present nothing new other than POV to support your claim that I am a sock puppet. You can't begin to grasp, for some reason, that I am in agreeance with Kmaquir1 about the information in question and simply exercised my ability to edit a Wikipedia page. It would seem you would wish Wikipedia to be your own little fascist state, where you determine all correct and relevant information. Thankfully, this is not the case. That doesn't discourage you from using the established avenues of complaint improperly to further your end. I suggest punitive action be taken against user Lulu for his misuse of the safeguard of Wikipedia. -Truthseekers 16:29, 11 August 2006 (UTC)

 * We just know its you, Kmaguir1. The word "agreeance" gives you away.  Maybe its a Memphis thang?--Agnaramasi 22:37, 11 August 2006 (UTC)

 * Well, that shows poorly for your intellegence level then if you base this belief soley off of the use of the word "agreeance". As I have already established, Kmaquir1 and myself are good friends in real life. Not only is it ludicrious to insinuate that Kmaquir1 is the only person to ever use the word "agreeance", but it is equally silly to hypothesize that two well-aquianted peoples' style of speech and writing won't rub-off on each other. The vindictive nature of this acusation is so amusing. The simplest explaination for all of this is rejected so violently in leui of such a crack-pot theory. Hahaha, priceless. -Truthseekers 03:39, 12 August 2006 (UTC)

 * That usage certainly is distinctive; could you put the specific diffs from both up in the "evidence" section? That would help demonstrate the point. LotLE × talk  00:13, 12 August 2006 (UTC)

 * As I've said in several places, I suspect that the users are two different persons. That does not excuse anyone for meatpuppetry, unless being a new editor is an excuse. (Arguably, it is. But the less new editor, Kmaguir1, should have known better.) Truthseekers, you can stop referring to "you all." As you see, we all are not in agreement on everything. Thanks.--Anthony Krupp 15:54, 12 August 2006 (UTC)

 * I agree with you, you shouldn't be grouped together. It seems the consensus for accusing myself and Kmaquir1 shifts to accomadate lesser claims now that people have started to realize the huge pile of untruth they are standing on. I think the only one still clinging to the chilish hope of the original accusation is Lulu. I have still failed to see any evidence supporting meat pupperty either. All I have seen is POV that claims I created the account at the behest of Kmaquir1 to circumvent the three-R rule. I've easily refuted this, simply saying that I created the account out of my outrage at the tyrannical censorship that was taking place in the article and my agreeance with Kmaquir1 on the issue that it had to stop. It rests upon to you prove I did not post of my own volition, a task, I might add, that is considerably daunting. Take off the tinted glasses you are seeing issues through, you'll find things to be alot clearer. -Truthseekers 16:15, 12 August 2006 (UTC)

 * I don't think meatpuppetry is defined as you posting against your volition. If the effect of your earliest postings are to insert material that another user cannot because of the 3RR, then you were in effect a meat puppet. At least that's how I understand the use of the term here. Others who've been around longer can clarify. In any case, Truthseekers, you can read WP:SOCK and see for yourself what is and what is not allowed here. Again: although you began your tenure here as a meatpuppet, one can hope that you will become your own person. Your most recent edits seem to show this, which is why I have advised that we cut you a break. You might at this point also read WP:CIVILITY. Might help ensure that others cut you a break as well. That's all for today.--Anthony Krupp 16:37, 12 August 2006 (UTC)

 * Even if this is a case of meatpuppetry rather than sockpuppetry, the behavior (even if collaborative) was clearly intended to try to perform an action that would otherwise be prohibited and sanctioned. As I comment on another talk page, meatpuppetry doesn't mean absence of volition, but simply collusion to a bad purpose.  LotLE × talk  17:36, 12 August 2006 (UTC)

 * Then prove it. I joined to post about facts that you didn't like. That's as much as you've got to run on. also, the added "proof" adds nothing to your care. As one who is unbiased can surmise, myself and Kmaquir1 were checking up on each other's pages while the accusations from the volitile Lulu flew. It's also not hard to fathom that I carelessly edited my page, unknowing of the rule, seeing as Lulu began his sladerous attacks within 5 minutes of me joining the boards. However the evidence may have appeard to Lulu, one fact is sure: Lulu of the Lotus Eaters was rude and slanderous to a new member within 5 minutes of me joining the boards, and did so off of shakey evidence at the mercy of his own emotions. -Truthseekers 20:29, 12 August 2006 (UTC)

 * Accountability

Lulu called Truthseekers a sockpuppet. She initiated an investigation in furtherance of this--so SHE has to deal with that. She should be penalized for falsely calling him a sockpuppet, for so maligning the both of us. And you can already see she is beginning to backslide--that she admits the possibility of meatpuppetry, etc. No, no. She initiated a sockpuppetry, so she believes sockpuppetry. Let's not discuss here, or elsewhere, meatpuppetry, until we've dismissed Lulu's charge of sockpuppetry. Period. She can't backslide from her original stance, she has to be held accountable. -Kmaguir1 19:15, 12 August 2006 (UTC)
 * Do you have no sense of accountability for your own actions? If you have no sockpuppet, then the tag will come down, and in the future perhaps you will avoid behaviours that look like sock or meat puppetry. You're wasting so much of everyone's time. Tiresome. Just read and reread WP:CONSENSUS and the other rules and guidelines, then edit. Focus on content, not on people. See you on the talk pages.--Anthony Krupp 20:05, 12 August 2006 (UTC)
 * I raised the accountability issue here.-Kmaguir1 20:25, 12 August 2006 (UTC)
 * I will take that as a no.--Anthony Krupp 12:14, 13 August 2006 (UTC)

 * Ruling

There has already been a ruling and a small punitive action has been taken against my friend, Kmaquir1. However, no punative action has been taken against me and the ruling appears to acknowledge that I am no sock puppet. Since there has already been a ruling, I expect the acusations from Lulu and others to cease immediatly. Should further slander continue, I'm sure Wikipedia offers some solution against personal attack, as that's what such maliciousness would be. -Truthseekers 22:05, 12 August 2006 (UTC)

 * There has not, of course, actually been any action taken on this sockpuppet violation at this time. Kmaguir1 did receive a rather smaller 3RR block than he earned, but the Truthseekers account was left unblocked in the meanwhile.  Hopefully a more substantial block of both accounts can happen.  LotLE × talk  22:13, 12 August 2006 (UTC)

 * "User:Kmaguir1 and sock-puppet User:Truthseekers reported by User:LotLE×talk (Result: User:Kmaguir1 blocked for 24hrs)". taken directly from the Wikipedia Administrator's message board. Must I remind you of the personal attack policy? I'm sure it's against the spirit of Wikipedia for someone to continually and endlessly accuse other users, as you seem to enjoy doing. -Truthseekers 22:19, 12 August 2006 (UTC)

Please see my statements about Son's claims on the Michel Foucault talk page. I support blocking him for as long as an admin feels justified. That sort of hyperbole, it's disastrous. And frankly, I'm insulted someone would call him my sock. N oevidence would exist for this, naturally. -Kmaguir1 07:13, 13 August 2006 (UTC)
 * This encyclopedia

 * Lulu says the last edits Son made were in December--I hadn't made an edit on wikipedia on this time--how is she claiming this occurred? -Kmaguir1 07:16, 13 August 2006 (UTC)

 * I mean, I would think we don't have the same IP address, although some fraternity houses share this IP, I doubt it was them. Just again, I want to iterate my disgust with those comments. Pure unmitigated disgust. -Kmaguir1 07:18, 13 August 2006 (UTC)

 * Lulu appears to have a vivid imagination, one that spills over and disrupts Wikipedia, apparently. -Truthseekers 11:45, 13 August 2006 (UTC)

RFCU came back possible, as well as another sock. Both [Truthseekers and another one] have been blocked. Iola k ana |T 13:53, 13 August 2006 (UTC)


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Talk:Debashish Mohanty

WikiProject class rating
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title: Talk:Debashish Mohanty


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Anthony Fleming

Anthony Fleming is an American actor who is known for his role as Trumpets on Fox's television series Prison Break and JP Gibbs on Starz's Power Book IV: Force. He also appeared in the film Divergent and in an episode of Chicago Fire. Fleming is active in the Chicago theater scene and has appeared in the play Denmark at the Biograph Theater in Chicago.

Personal life
He has a son, Hunter, with his wife Kathryn.

title: Anthony Fleming


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User:Lyondif02

fr:User:Lyondif02 nha from Lyon, France.

Links to my personal pages on other Wikimedia projects:
 * Wikipedia in French, English.
 * Wikisource in French.
 * Wiktionary in French, English.
 * Wikibooks in French, English.
 * Wikiversity in French.
 * Wikimedia meta-wiki.

title: User:Lyondif02


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Multivalued dependency

In database theory, a multivalued dependency is a full constraint between two sets of attributes in a relation.

In contrast to the functional dependency, the multivalued dependency requires that certain tuples be present in a relation. Therefore, a multivalued dependency is a special case of tuple-generating dependency. The multivalued dependency plays a role in the 4NF database normalization.

A multivalued dependency is a special case of a join dependency, with only two sets of values involved, i.e. it is a binary join dependency.

A multivalued dependency exists when there are at least three attributes (like X,Y and Z) in a relation and for a value of X there is a well defined set of values of Y and a well defined set of values of Z. However, the set of values of Y is independent of set Z and vice versa.

Formal definition
The formal definition is as follows:

Let $$R$$ be a relation and let $$\alpha \subseteq R$$ and $$\beta \subseteq R$$ be sets of attributes. The multivalued dependency $$\alpha \twoheadrightarrow \beta$$ ("$$\alpha$$ multidetermines $$\beta$$") holds on $$R$$ if, for any legal relation $$r(R)$$ and all pairs of tuples $$t _1$$ and $$t _2$$ in $$r$$ such that $$t _1[\alpha]=t _2[\alpha]$$, there exist tuples $$t _3$$ and $$t _4$$ in $$r$$ such that:

$$ \begin{matrix} t_1[\alpha] = t_2[\alpha] = t_3[\alpha] = t_4[\alpha]\\ t_1[\beta] = t_3[\beta]\\ t_2[\beta] = t_4[\beta]\\ t_1[R\setminus(\alpha\cup\beta)] = t_4[R\setminus(\alpha\cup\beta)]\\ t_2[R\setminus(\alpha\cup\beta)] = t_3[R\setminus(\alpha\cup\beta)] \end{matrix} $$

Informally, if one denotes by $$(x,y,z)$$ the tuple having values for $$\alpha,$$ $$\beta,$$ $$R - \alpha - \beta$$ collectively equal to $$x,$$ $$y,$$ $$z$$, then whenever the tuples $$(a,b,c)$$ and $$(a,d,e)$$ exist in $$r$$, the tuples $$(a,b,e)$$ and $$(a,d,c)$$ should also exist in $$r$$.

The multivalued dependency can be schematically depicted as shown below:

$$ \begin{matrix} \text{tuple} & \alpha & \beta & R\setminus(\alpha\cup\beta) \\ t_1 & a_1 .. a_n & b_1 .. b_m & d_1 .. d_k \\ t_2 & a_1 .. a_n & c_1 .. c_m & e_1 .. e_k \\ t_3 & a_1 .. a_n & b_1 .. b_m & e_1 .. e_k \\ t_4 & a_1 .. a_n & c_1 .. c_m & d_1 .. d_k \end{matrix} $$

Example
Consider this example of a relation of university courses, the books recommended for the course, and the lecturers who will be teaching the course:

Because the lecturers attached to the course and the books attached to the course are independent of each other, this database design has a multivalued dependency; if we were to add a new book to the AHA course, we would have to add one record for each of the lecturers on that course, and vice versa. Put formally, there are two multivalued dependencies in this relation: {course} $$\twoheadrightarrow$$ {book} and equivalently {course} $$\twoheadrightarrow$$ {lecturer}. Databases with multivalued dependencies thus exhibit redundancy. In database normalization, fourth normal form requires that for every nontrivial multivalued dependency X $$\twoheadrightarrow$$ Y, X is a superkey. A multivalued dependency X $$\twoheadrightarrow$$ Y is trivial if Y is a subset of X, or if $$X \cup Y$$ is the whole set of attributes of the relation.

Properties
The following also involve functional dependencies:
 * If $$\alpha \twoheadrightarrow \beta$$, Then $$\alpha \twoheadrightarrow R - \beta$$
 * If $$\alpha \twoheadrightarrow \beta$$ and $$\gamma \subseteq \delta$$, Then $$\alpha \delta \twoheadrightarrow \beta \gamma$$
 * If $$\alpha \twoheadrightarrow \beta$$ and $$\beta \twoheadrightarrow \gamma$$, then $$\alpha \twoheadrightarrow \gamma - \beta$$
 * If $$\alpha \rightarrow \beta$$, then $$\alpha \twoheadrightarrow \beta$$
 * If $$\alpha \twoheadrightarrow \beta$$ and $$\beta \rightarrow \gamma$$, then $$\alpha \twoheadrightarrow \gamma - \beta$$

The above rules are sound and complete.

 * A decomposition of R into (X, Y) and (X, R − Y) is a lossless-join decomposition if and only if X $$\twoheadrightarrow$$ Y holds in R.
 * Every FD is an MVD because if X $$\rightarrow $$ Y, then swapping Y's between tuples that agree on X doesn't create new tuples.
 * Splitting Doesn't Hold. Like FD's, we cannot generally split the left side of an MVD.But unlike FD's, we cannot split the right side either, sometimes you have to leave several attributes on the right side.
 * Closure of a set of MVDs is the set of all MVDs that can be inferred using the following rules (Armstrong's axioms):
 * Complementation: If X $$\twoheadrightarrow $$ Y, then X $$\twoheadrightarrow$$ R - Y
 * Augmentation: If X $$\twoheadrightarrow$$ Y and Z $$\subseteq$$ W, then XW $$\twoheadrightarrow$$ YZ
 * Transitivity: If X $$\twoheadrightarrow$$ Y and Y $$\twoheadrightarrow $$Z, then X $$\twoheadrightarrow $$ Z - Y
 * Replication: If X $$\rightarrow $$ Y, then X $$\twoheadrightarrow$$ Y
 * Coalescence: If X $$\twoheadrightarrow $$Y and $$\exist $$ W s.t. W $$\cap$$ Y = $$\empty $$, W $$\rightarrow$$ Z, and Z $$\subseteq $$ Y, then X $$\rightarrow $$ Z

Definitions

 * full constraint: A constraint which expresses something about all attributes in a database. (In contrast to an embedded constraint.) That a multivalued dependency is a full constraint follows from its definition, as where it says something about the attributes $$R - \beta$$.
 * tuple-generating dependency: A dependency which explicitly requires certain tuples to be present in the relation.
 * trivial multivalued dependency 1: A multivalued dependency which involves all the attributes of a relation i.e.$$R = \alpha \cup \beta$$. A trivial multivalued dependency implies, for tuples $$t _1$$ and $$t _2$$, tuples $$t _3$$ and $$t _4$$ which are equal to $$t _1$$ and $$t _2$$.
 * trivial multivalued dependency 2: A multivalued dependency for which $$\beta \subseteq \alpha$$.

title: Multivalued dependency


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File talk:Mulholland.png

Isn't this the final theatrical poster, ? —  Film Fan  00:14, 20 September 2016 (UTC)

title: File talk:Mulholland.png


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Calculus/Taylor series

Taylor Series
sin(x) and Taylor approximations, polynomials of degree 1, 3 , 5 , 7 , 9 , 11 and 13.

Here, $$n!$$ is the factorial of $$n$$ and $$f^{(n)}(a)$$ denotes the $$n$$th derivative of $$f$$ at the point $$a$$. If this series converges for every $$x$$ in the interval $$(a-r,a+r)$$ and the sum is equal to $$f(x)$$, then the function $$f(x)$$ is called analytic. To check whether the series converges towards $$f(x)$$, one normally uses estimates for the remainder term of Taylor's theorem. A function is analytic if and only if a power series converges to the function; the coefficients in that power series are then necessarily the ones given in the above Taylor series formula.

If $$a=0$$, the series is also called a Maclaurin series.

The importance of such a power series representation is threefold. First, differentiation and integration of power series can be performed term by term and is hence particularly easy. Second, an analytic function can be uniquely extended to a holomorphic function defined on an open disk in the complex plane, which makes the whole machinery of complex analysis available. Third, the (truncated) series can be used to approximate values of the function near the point of expansion.

The function $$f(z)=e^{-\frac{1}{z^2}}$$ is not analytic: the Taylor series is 0, although the function is not. Note that there are examples of infinitely often differentiable functions $$f(x)$$ whose Taylor series converge, but are not equal to $$f(x)$$. For instance, for the function defined piecewise by saying that $$f(x)=\begin{cases}0&x=0\\e^{-\frac{1}{x^2}}&x\ne0\end{cases}$$, all the derivatives are 0 at $$x=0$$ , so the Taylor series of $$f(x)$$ is 0, and its radius of convergence is infinite, even though the function most definitely is not 0. This particular pathology does not afflict complex-valued functions of a complex variable. Notice that $$f(z)=e^{-\frac{1}{z^2}}$$ does not approach 0 as $$z$$ approaches 0 along the imaginary axis.

Some functions cannot be written as Taylor series because they have a singularity; in these cases, one can often still achieve a series expansion if one allows also negative powers of the variable $$x$$; see Laurent series. For example, $$f(z)=e^{-\frac{1}{z^2}}$$ can be written as a Laurent series.

The Parker-Sockacki theorem is a recent advance in finding Taylor series which are solutions to differential equations. This theorem is an expansion on the Picard iteration.

Derivation
Suppose we want to represent a function as an infinite power series, or in other words a polynomial with infinite terms of degree "infinity". Each of these terms are assumed to have unique coefficients, as do most finite-polynomials do. We can represent this as an infinite sum like so:
 * $$f(x)={c_0}(x-a)^0+c_1(x-a)^1+c_2(x-a)^2+c_3(x-a)^3+\cdots+c_n(x-a)^n+\cdots$$

where $$a$$ is the radius of convergence and $$c_0,c_1,c_2,\dots,c_n,\dots$$ are coefficients. Next, with summation notation, we can efficiently represent this series as
 * $$\sum_{n=0}^{\infty}c_n(x-a)^n$$

which will become more useful later. As of now, we have no schematic for finding the coefficients other than finding each one in the series by hand. That method would not be particularly useful. Let us, then, try to find a pattern and a general solution for finding the coefficients. As of now, we have a simple method for finding the first coefficient. If we substitute $$a$$ for $$x$$ then we get
 * $$f(a)=c_0$$

This gives us $$c_0$$. This is useful, but we still would like a general equation to find any coefficient in the series. We can try differentiating with respect to x the series to get
 * $$f'(x)=c_1(x-a)^{0}+2c_2(x-a)^{1}+3c_3(x-a)^{2}+4c_4(x-a)^3+\cdots+nc_n(x-a)^{(n-1)}+\cdots$$

We can assume $$c_n$$ and $$a$$ are constant. This proves to be useful, because if we again substitute $$a$$ for $$x$$ we get
 * $$f'(a)=c_1$$

Noting that the first derivative has one constant term ($$c_1(x-a)^0=c_1$$) we can find the second derivative to find $$c_2$$. It is
 * $$f''(x)=2c_2+(2\times3)c_3(x-a)^1+(3\times4)c_4(x-a)^2+\cdots+(n)(n-1)c_n(x-a)^{(n-2)}+\cdots$$

If we again substitute $$a$$ for $$x$$ :
 * $$f''(a)=2c_2$$

Note that $$c_2$$'s initial exponent was 2, and $$c_1$$'s initial exponent was 1. This is slightly more enlightening, however it is still slightly ambiguous as to what is happening. Going off the previous examples, if we differentiate again we get
 * $$f'''(x)=(2\times3)c_3(x-a)^0+(2\times3\times4)c_4(x-a)^1+(3\times4\times5)c_5(x-a)^2+\cdots+(n)(n-1)(n-2)c_n(x-a)^{n-3}$$

If we substitute $$x=a$$ we, again, that
 * $$f'''(a)=(2\times3)c_3$$

By now, the pattern should be becoming clearer. $$(n)(n-1)(n-2)$$ looks suspiciously like $$n!$$. And indeed, it is! If we carry this out $$n$$ times by finding the $$n$$th derivative, we find that the multiple of the coefficient is $$n!$$. So for some $$c_n$$, for any integer $$n\ge0$$ ,
 * $$n!\times c_n=\frac{d^n}{dx^n}f(a)$$

Or, with some simple manipulation, more usefully,
 * $$c_n=\frac{f^{(n)}(a)}{n!}$$

where $$f^{(0)}(x)=f(x)$$ and $$f^{(1)}(x)=f'(x)$$ and so on. With this, we can find any coefficient of the "infinite polynomial". Using the summation definition for our "polynomial" given earlier,
 * $$\sum_{n=0}^\infty c_n(x-a)^n$$

we can substitute for $$c_n$$ to get
 * $$f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n$$

This is the definition of any Taylor series. But now that we have this series, how can we derive the definition for a given analytic function? We can do just as the definition specifies, and fill in all the necessary information. But we will also want to find a specific pattern, because sometimes we are left with a great many terms simplifying to 0.

First, we have to find $$f(a)$$. Because we are now deriving our own Taylor Series, we can choose anything we want for $$f(x)$$, but note that not all functions will work. It would be useful to use a function that we can easily find the $$n$$-th derivative for. A good example of this would be $$\sin(x)$$. With $$\sin(x)$$ chosen, we can begin to find the derivatives. Before we begin, we should also note that $$a$$ is essentially the "offset" of the function along the x-axis, because this is also essentially true for any polynomial. With that in mind, we can assume, in this particular case, that the offset is $$0$$ and so $$a=0$$. With that in mind, "0-th" derivative or the function itself would be
 * $$\sin(0)=0$$

If we plug that in to the definition of the first term in the series, again noting that $$a=0$$, we get
 * $$\frac{0}{0!}x^0=0$$

where $$0!=1$$. This means that the first term of the series is 0, because anything multiplied by 0 is 0. Take note that not all Taylor series start out with a 0 term. Next, to find the next term, we need to find the first derivative of the function. Remembering that the derivative of $$\sin(x)$$ is $$\cos(x)$$ we get that
 * $$\frac{d}{dx}\sin(0)=\cos(0)=1$$

This means that our second term in the series is
 * $$\frac{1}{1!}x^1=x$$

Next, we need to find the third term. We repeat this process.
 * $$\frac{d^2}{dx^2}\sin(0)=-\sin(0)=0$$

Because the derivative of $$\cos(x)=-\sin(x)$$. We continue with
 * $$\frac{0}{2!}x^2=0$$

The fourth term:
 * $$\frac{d^3}{dx^3}\sin(0)=-\cos(0)=-1$$
 * $$\frac{-1}{3!}x^3=\frac{-x^3}{6}$$

Repeating this process we can get the sequence
 * $$\frac{0}{0!}x^0,\frac{1}{1!}x^1,\frac{0}{2!}x^2,\frac{-1}{3!}x^3,\frac{0}{4!}x^4,\frac{1}{5!}x^5,\frac{0}{6!}x^6,\frac{-1}{7!}x^7,\dots$$

which simplifies to
 * $$0,x,0,\frac{-x^3}{6},0,\frac{x^5}{120},0,\frac{-x^7}{5040},\dots$$

Because we are ultimately dealing with a series, the zero terms can be ignored, giving use the new sequence
 * $$x,\frac{-x^3}{6},\frac{x^5}{120},\frac{-x^7}{5040},\dots$$

There is a pattern here, however it may be easier to see if we take the numerator and the denominator separately. The numerator:
 * $$1,-1,1,-1,\dots$$
 * $$1!,3!,5!,7!,\dots$$

And for the $$x$$ part of the terms, we have the sequence
 * $$x,x^3,x^5,\dots$$

By this point, at least for the denominator and the $$x$$ part, the pattern should be obvious. It is, for the denominator
 * $$(2n-1)!=\text{denom}_n$$

The $$x$$ term:
 * $$x^{2n-1}=\text{xterm}_n$$

Finally, the numerator may not be as obvious, but it follows this pattern:
 * $$(-1)^{n-1}$$

With all of these things discovered, we can put them together to find the rule for the $$n$$th term of the sequence:
 * $$\frac{(-1)^{n-1}}{(2n-1)!}x^{2n-1}=\text{sumterm}_n$$

And so our Taylor (Maclaurin) series for $$\sin(x)$$ is
 * $$f(x)=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{(2n-1)!}x^{2n-1}$$

List of Taylor series
Several important Taylor series expansions follow. All these expansions are also valid for complex arguments $$x$$.

Exponential function and natural logarithm:

 * $$e^x=\sum_{n=0}^\infty\frac{x^n}{n!}\quad\text{ for all }x$$
 * $$\ln(1+x)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}}n x^n\quad\text{ for }|x|<1$$

Geometric series:

 * $$\frac{1}{1-x}=\sum_{n=0}^\infty x^n\quad\text{ for }|x|<1$$

Binomial series:

 * $$(1+x)^\alpha=\sum_{n=0}^\infty\binom{\alpha}{n}x^n\quad\text{ for all }|x|<1\quad\text{ and all complex }\alpha$$

Trigonometric functions:

 * $$\sin(x)=\sum_{n=1}^\infty\frac{(-1)^{n-1}}{(2n-1)!}x^{2n-1}\quad\text{ for all }x$$

 * $$\cos(x)=\sum_{n=0}^\infty\frac{(-1)^n}{(2n)!}x^{2n}\quad\text{ for all }x$$

 * $$\tan(x)=\sum_{n=1}^\infty\frac{B_{2n}(-4)^n(1-4^n)}{(2n)!}x^{2n-1}\quad\text{ for }|x|<\frac{\pi}{2}$$

 * $$\sec(x)=\sum_{n=0}^\infty\frac{(-1)^nE_{2n}}{(2n)!}x^{2n}\quad\text{ for }|x|<\frac{\pi}{2}$$

 * $$\arcsin(x)=\sum_{n=0}^\infty\frac{(2n)!}{4^n(n!)^2(2n+1)}x^{2n+1}\quad\text{ for }|x|<1$$

 * $$\arctan(x)=\sum_{n=0}^\infty\frac{(-1)^n}{2n+1}x^{2n+1}\quad\text{ for }|x|<1$$

Hyperbolic functions:

 * $$\sinh(x)=\sum_{n=1}^\infty\frac{x^{2n-1}}{(2n-1)!}\quad\text{ for all }x$$

 * $$\cosh(x)=\sum_{n=0}^\infty\frac{x^{2n}}{(2n)!}\quad\text{ for all }x$$

 * $$\tanh(x)=\sum_{n=1}^\infty\frac{B_{2n}2^{2n}(2^{2n}-1)}{(2n)!}x^{2n-1}\quad\text{ for }|x|<\frac{\pi}{2}$$

 * $${\rm arsinh}(x)=\sum_{n=0}^\infty\frac{(-1)^n(2n)!}{2^{2n}(n!)^2(2n+1)}x^{2n+1}\quad\text{ for }|x|<1$$

 * $${\rm artanh}(x)=\sum_{n=1}^\infty\frac{x^{2n-1}}{2n-1}\quad\text{ for }|x|<1$$

Lambert's W function:

 * $$W_0(x)=\sum_{n=1}^\infty\frac{(-n)^{n-1}}{n!}x^n\quad\text{ for }|x|<\frac{1}{e}$$

The numbers $$B_k$$ appearing in the expansions of $$\tan(x)$$ and $$\tanh(x)$$ are the Bernoulli numbers. The $$\binom{\alpha}{n}$$ in the binomial expansion are the binomial coefficients. The $$E_k$$ in the expansion of $$sec(x)$$ are Euler numbers.

Multiple dimensions
The Taylor series may be generalized to functions of more than one variable with

\sum_{n_1=0}^\infty\cdots\sum_{n_d=0}^\infty\frac{\partial^{n_1}}{\partial x_1^{n_1}}\cdots\frac{\partial^{n_d}}{\partial x_d^{n_d}}\frac{f(a_1,\dots,a_d)}{n_1!\cdots n_d!}(x_1-a_1)^{n_1}\cdots (x_d-a_d)^{n_d} $$

History
The Taylor series is named for mathematician Brook Taylor, who first published the power series formula in 1715.

Constructing a Taylor Series
Several methods exist for the calculation of Taylor series of a large number of functions. One can attempt to use the Taylor series as-is and generalize the form of the coefficients, or one can use manipulations such as substitution, multiplication or division, addition or subtraction of standard Taylor series (such as those above) to construct the Taylor series of a function, by virtue of Taylor series being power series. In some cases, one can also derive the Taylor series by repeatedly applying integration by parts. The use of computer algebra systems to calculate Taylor series is common, since it eliminates tedious substitution and manipulation.

Example 1
Consider the function
 * $$f(x)=\ln\big(1+\cos(x)\big)$$

for which we want a Taylor series at 0.

We have for the natural logarithm
 * $$\ln(1+x)=\sum_{n=1}^\infty\frac{(-1)^{n+1}}{n}x^n=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\cdots\quad\text{ for }|x|<1$$

and for the cosine function
 * $$\cos(x)=\sum_{n=0}^\infty\frac{(-1)^n}{(2n)!}x^{2n}=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\quad\text{ for all }x\in\C$$

We can simply substitute the second series into the first. Doing so gives
 * $$\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\right)-\frac12\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\right)^2+\frac13\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\right)^3-\cdots$$

Expanding by using multinomial coefficients gives the required Taylor series. Note that cosine and therefore $$f$$ are even functions, meaning that $$f(x)=f(-x)$$, hence the coefficients of the odd powers $$x$$, $$x^3$$, $$x^5$$, $$x^7$$ and so on have to be zero and don't need to be calculated. The first few terms of the series are
 * $$\ln\big(1+\cos(x)\big)=\ln(2)-\frac{x^2}{4}-\frac{x^4}{96}-\frac{x^6}{1440}-\frac{17x^8}{322560}-\frac{31x^{10}}{7257600}-\cdots$$

The general coefficient can be represented using Faà di Bruno's formula. However, this representation does not seem to be particularly illuminating and is therefore omitted here.

Example 2
Suppose we want the Taylor series at 0 of the function
 * $$g(x)=\frac{e^x}{\cos(x)}$$

We have for the exponential function
 * $$e^x=\sum_{n=0}^\infty\frac{x^n}{n!}=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+\cdots$$

and, as in the first example,
 * $$\cos(x)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots$$

Assume the power series is
 * $$\frac{e^x}{\cos(x)}=c_0+c_1x+c_2x^2+c_3x^3+\cdots$$

Then multiplication with the denominator and substitution of the series of the cosine yields

Collecting the terms up to fourth order yields
 * $$e^x$$
 * $$=\big(c_0+c_1x+c_2x^2+c_3x^3+\cdots\big)\cos(x)$$
 * $$=\left(c_0+c_1x+c_2x^2+c_3x^3+c_4x^4+\cdots\right)\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots\right)$$
 * $$=c_0-\frac{c_0}{2}x^2+\frac{c_0}{4!}x^4+c_1x-\frac{c_1}{2}x^3+\frac{c_1}{4!}x^5+c_2x^2-\frac{c_2}{2}x^4+\frac{c_2}{4!}x^6+c_3x^3-\frac{c_3}{2}x^5+\frac{c_3}{4!}x^7+\cdots$$
 * }
 * $$=c_0-\frac{c_0}{2}x^2+\frac{c_0}{4!}x^4+c_1x-\frac{c_1}{2}x^3+\frac{c_1}{4!}x^5+c_2x^2-\frac{c_2}{2}x^4+\frac{c_2}{4!}x^6+c_3x^3-\frac{c_3}{2}x^5+\frac{c_3}{4!}x^7+\cdots$$
 * }
 * $$=c_0-\frac{c_0}{2}x^2+\frac{c_0}{4!}x^4+c_1x-\frac{c_1}{2}x^3+\frac{c_1}{4!}x^5+c_2x^2-\frac{c_2}{2}x^4+\frac{c_2}{4!}x^6+c_3x^3-\frac{c_3}{2}x^5+\frac{c_3}{4!}x^7+\cdots$$
 * }
 * $$=c_0+c_1x+\left(c_2-\frac{c_0}{2}\right)x^2+\left(c_3-\frac{c_1}{2}\right)x^3+\left(c_4+\frac{c_0}{4!}-\frac{c_2}{2}\right)x^4+\cdots$$

Comparing coefficients with the above series of the exponential function yields the desired Taylor series
 * $$\frac{e^x}{\cos(x)}=1+x+x^2+\frac{2x^3}{3}+\frac{x^4}{2}+\cdots$$

title: Calculus/Taylor series