en>Markhurd: Disambiguate Jacobian to Jacobian matrix and determinant using popups

2014-07-02T14:00:24Z

Disambiguate Jacobian to Jacobian matrix and determinant using popups

← Older revision		Revision as of 16:00, 2 July 2014
Line 1:		Line 1:
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	~~In [[relational algebra]], a '''generalized selection'~~'' ~~is a [[unary operation]] written as <math>\sigma_\varphi(R)</math> where <math>\varphi</math> is a [[propositional formula]] that consists of [[atomic formula\|atom]]~~s as ~~allowed in the~~ [~~[selection (relational algebra)\|normal selection]] and the logical operators <math>\and<~~/~~math> ([[logical conjunction\|and]]), <math>\or<~~/~~math> ([[logical disjunction\|or]]) and <math>\lnot<~~/~~math> ([[negation~~]~~]). This selection selects all those~~ [~~[tuple]]s in <math>R<~~/~~math> for which <math>\varphi<~~/~~math> holds~~.

	~~For an example, consider the following tables where the first table gives the relation <math>Person<~~/~~math>~~ and ~~the second the result of <math>\sigma_{Age \ge 30 \ \~~and ~~\ Weight \le 60}(Person)<~~/~~math>~~.

	~~{\| align="center" cellpadding="0" cellspacing="20"~~
	\|-
	~~! <math>Person<~~/~~math>~~
	~~! <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>~~
	\|- ~~style="vertical~~-~~align: top"~~
	\|
	~~{\| align="center" border="0" cellpadding="5" cellspacing="0" style="border~~-~~collapse: collapse; border: 1px solid black"~~
	\|- ~~style="background-color~~: ~~silver; text~~-~~align: left"~~
	~~! style="border: 1px solid black" \| Name~~
	~~! style="border: 1px solid black" \| Age~~
	~~! style="border: 1px solid black" \| Weight~~
	\|-
	~~\| style="border: 1px solid black" \| Harry~~
	~~\| style="border: 1px solid black" \| 34~~
	~~\| style="border: 1px solid black" \| 80~~
	\|-
	~~\| style="border: 1px solid black" \| Sally~~
	~~\| style="border: 1px solid black" \| 28~~
	~~\| style="border: 1px solid black" \| 64~~
	\|-
	~~\| style="border: 1px solid black" \| George~~
	~~\| style="border: 1px solid black" \| 29~~
	~~\| style="border: 1px solid black" \| 70~~
	\|-
	~~\| style="border: 1px solid black" \| Helena~~
	~~\| style="border: 1px solid black" \| 54~~
	~~\| style="border: 1px solid black" \| 54~~
	\|-
	~~\| style="border: 1px solid black" \| Peter~~
	~~\| style="border: 1px solid black" \| 34~~
	~~\| style="border: 1px solid black" \| 80~~
	\|}
	\|
	~~{\| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"~~
	~~\|- style="background-color: silver; text-align: left"~~
	~~! style="border: 1px solid black" \| Name~~
	~~! style="border: 1px solid black" \| Age~~
	~~! style="border: 1px solid black" \| Weight~~
	\|-
	~~\| style="border: 1px solid black" \| Helena~~
	~~\| style="border: 1px solid black" \| 54~~
	~~\| style="border: 1px solid black" \| 54~~
	\|}
	\|}

	~~Formally the semantics of the generalized selection~~ is ~~defined as follows:~~

	: <~~math~~>~~\sigma_\varphi(R) = \{ \ t : t \in R, \ \varphi(t) \ \}~~<~~/math~~>

	~~The result of the selection~~ is ~~only defined if the [[Property (philosophy)\|attribute]] names that it mentions are in the [[~~:~~wikt~~:~~heading\|header]] of the relation that it operates upon.~~

	~~The simulation of a generalized selection that is not a fundamental selection with the fundamental operators is defined by the following rules~~:

	~~: <math>\sigma_{\varphi \and \psi}(R) = \sigma_\varphi(R) \cap \sigma_\psi(R)<~~/~~math>~~
	~~: <math>\sigma_{\varphi \or \psi}(R) = \sigma_\varphi(R) \cup \sigma_\psi(R)<~~/~~math>~~
	~~: <math>\sigma_{\lnot \varphi}(R) = R~~ - ~~\sigma_\varphi(R)<~~/~~math>~~

	~~The generalized selection is expressible with other basic algebraic operations~~.

	~~In [[SQL]], general selections are performed by using <code>[[Where (SQL)\|WHERE]]<~~/~~code> definitions with <code>AND</code>, <code>OR</code>, or <code>NOT</code> operands in <code>[[Select (SQL)\|SELECT]]</code>, <code>[[Update (SQL)\|UPDATE]]<~~/~~code>, and <code>[[Delete (SQL)\|DELETE]]<~~/~~code> statements.~~

	~~==See also==~~
	* [[Selection (relational algebra)]]

	~~[[Category:Relational algebra]~~]

en>Reyk: dab fix: partition function -> partition function (quantum field theory)

2011-10-25T19:52:08Z

dab fix: partition function -> partition function (quantum field theory)

New page

{{unreferenced|date=August 2009}}
In [[relational algebra]], a '''generalized selection''' is a [[unary operation]] written as <math>\sigma_\varphi(R)</math> where <math>\varphi</math> is a [[propositional formula]] that consists of [[atomic formula|atom]]s as allowed in the [[selection (relational algebra)|normal selection]] and the logical operators <math>\and</math> ([[logical conjunction|and]]), <math>\or</math> ([[logical disjunction|or]]) and <math>\lnot</math> ([[negation]]). This selection selects all those [[tuple]]s in <math>R</math> for which <math>\varphi</math> holds.

For an example, consider the following tables where the first table gives the relation <math>Person</math> and the second the result of <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>.

{| align="center" cellpadding="0" cellspacing="20"
|-
! <math>Person</math>
! <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>
|- style="vertical-align: top"
|
{| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"
|- style="background-color: silver; text-align: left"
! style="border: 1px solid black" | Name
! style="border: 1px solid black" | Age
! style="border: 1px solid black" | Weight
|-
| style="border: 1px solid black" | Harry
| style="border: 1px solid black" | 34
| style="border: 1px solid black" | 80
|-
| style="border: 1px solid black" | Sally
| style="border: 1px solid black" | 28
| style="border: 1px solid black" | 64
|-
| style="border: 1px solid black" | George
| style="border: 1px solid black" | 29
| style="border: 1px solid black" | 70
|-
| style="border: 1px solid black" | Helena
| style="border: 1px solid black" | 54
| style="border: 1px solid black" | 54
|-
| style="border: 1px solid black" | Peter
| style="border: 1px solid black" | 34
| style="border: 1px solid black" | 80
|}
|
{| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"
|- style="background-color: silver; text-align: left"
! style="border: 1px solid black" | Name
! style="border: 1px solid black" | Age
! style="border: 1px solid black" | Weight
|-
| style="border: 1px solid black" | Helena
| style="border: 1px solid black" | 54
| style="border: 1px solid black" | 54
|}
|}

Formally the semantics of the generalized selection is defined as follows:

: <math>\sigma_\varphi(R) = \{ \ t : t \in R, \ \varphi(t) \ \}</math>

The result of the selection is only defined if the [[Property (philosophy)|attribute]] names that it mentions are in the [[:wikt:heading|header]] of the relation that it operates upon.

The simulation of a generalized selection that is not a fundamental selection with the fundamental operators is defined by the following rules:

: <math>\sigma_{\varphi \and \psi}(R) = \sigma_\varphi(R) \cap \sigma_\psi(R)</math>
: <math>\sigma_{\varphi \or \psi}(R) = \sigma_\varphi(R) \cup \sigma_\psi(R)</math>
: <math>\sigma_{\lnot \varphi}(R) = R - \sigma_\varphi(R)</math>

The generalized selection is expressible with other basic algebraic operations.

In [[SQL]], general selections are performed by using <code>[[Where (SQL)|WHERE]]</code> definitions with <code>AND</code>, <code>OR</code>, or <code>NOT</code> operands in <code>[[Select (SQL)|SELECT]]</code>, <code>[[Update (SQL)|UPDATE]]</code>, and <code>[[Delete (SQL)|DELETE]]</code> statements.

==See also==
* [[Selection (relational algebra)]]

[[Category:Relational algebra]]

← Older revision		Revision as of 16:00, 2 July 2014
Line 1:		Line 1:
	~~{{unreferenced\|date=August 2009}}~~		Hello. Allow me home std test kit introduce the author. Her name is Emilia Shroyer but it's not the most female title out there. For many at home std test years he's been working as [http://support.kaponline.com/entries/46228144-Endocrine-Illnesses-Canines-Part-1 at home std testing] a meter [http://nxnn.info/user/G8498 at home std test] reader and it's some thing he really enjoy. Her spouse and her live in [http://www.channel4Embarrassingillnesses.com/men-in-white-coats/genital-herpes/symptoms/ Puerto Rico] but she will have to move 1 day or another. The thing she adores most is [http://www.wbli.com/gallery/entertainment/morning-show/celebrities-who-have-admitted-having-stds/gCF9q/ body developing] and now she is attempting to earn money with it.<br><br>Here is my blog post :: [http://tti-ttw.com/index.php?do=/profile-2200/info/ at home std test]
	~~In [[relational algebra]], a '''generalized selection'~~'' ~~is a [[unary operation]] written as <math>\sigma_\varphi(R)</math> where <math>\varphi</math> is a [[propositional formula]] that consists of [[atomic formula\|atom]]~~s as ~~allowed in the~~ [~~[selection (relational algebra)\|normal selection]] and the logical operators <math>\and<~~/~~math> ([[logical conjunction\|and]]), <math>\or<~~/~~math> ([[logical disjunction\|or]]) and <math>\lnot<~~/~~math> ([[negation~~]~~]). This selection selects all those~~ [~~[tuple]]s in <math>R<~~/~~math> for which <math>\varphi<~~/~~math> holds~~.

	~~For an example, consider the following tables where the first table gives the relation <math>Person<~~/~~math>~~ and ~~the second the result of <math>\sigma_{Age \ge 30 \ \~~and ~~\ Weight \le 60}(Person)<~~/~~math>~~.

	~~{\| align="center" cellpadding="0" cellspacing="20"~~
	\|-
	~~! <math>Person<~~/~~math>~~
	~~! <math>\sigma_{Age \ge 30 \ \and \ Weight \le 60}(Person)</math>~~
	\|- ~~style="vertical~~-~~align: top"~~
	\|
	~~{\| align="center" border="0" cellpadding="5" cellspacing="0" style="border~~-~~collapse: collapse; border: 1px solid black"~~
	\|- ~~style="background-color~~: ~~silver; text~~-~~align: left"~~
	~~! style="border: 1px solid black" \| Name~~
	~~! style="border: 1px solid black" \| Age~~
	~~! style="border: 1px solid black" \| Weight~~
	\|-
	~~\| style="border: 1px solid black" \| Harry~~
	~~\| style="border: 1px solid black" \| 34~~
	~~\| style="border: 1px solid black" \| 80~~
	\|-
	~~\| style="border: 1px solid black" \| Sally~~
	~~\| style="border: 1px solid black" \| 28~~
	~~\| style="border: 1px solid black" \| 64~~
	\|-
	~~\| style="border: 1px solid black" \| George~~
	~~\| style="border: 1px solid black" \| 29~~
	~~\| style="border: 1px solid black" \| 70~~
	\|-
	~~\| style="border: 1px solid black" \| Helena~~
	~~\| style="border: 1px solid black" \| 54~~
	~~\| style="border: 1px solid black" \| 54~~
	\|-
	~~\| style="border: 1px solid black" \| Peter~~
	~~\| style="border: 1px solid black" \| 34~~
	~~\| style="border: 1px solid black" \| 80~~
	\|}
	\|
	~~{\| align="center" border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse; border: 1px solid black"~~
	~~\|- style="background-color: silver; text-align: left"~~
	~~! style="border: 1px solid black" \| Name~~
	~~! style="border: 1px solid black" \| Age~~
	~~! style="border: 1px solid black" \| Weight~~
	\|-
	~~\| style="border: 1px solid black" \| Helena~~
	~~\| style="border: 1px solid black" \| 54~~
	~~\| style="border: 1px solid black" \| 54~~
	\|}
	\|}

	~~Formally the semantics of the generalized selection~~ is ~~defined as follows:~~

	: <~~math~~>~~\sigma_\varphi(R) = \{ \ t : t \in R, \ \varphi(t) \ \}~~<~~/math~~>

	~~The result of the selection~~ is ~~only defined if the [[Property (philosophy)\|attribute]] names that it mentions are in the [[~~:~~wikt~~:~~heading\|header]] of the relation that it operates upon.~~

	~~The simulation of a generalized selection that is not a fundamental selection with the fundamental operators is defined by the following rules~~:

	~~: <math>\sigma_{\varphi \and \psi}(R) = \sigma_\varphi(R) \cap \sigma_\psi(R)<~~/~~math>~~
	~~: <math>\sigma_{\varphi \or \psi}(R) = \sigma_\varphi(R) \cup \sigma_\psi(R)<~~/~~math>~~
	~~: <math>\sigma_{\lnot \varphi}(R) = R~~ - ~~\sigma_\varphi(R)<~~/~~math>~~

	~~The generalized selection is expressible with other basic algebraic operations~~.

	~~In [[SQL]], general selections are performed by using <code>[[Where (SQL)\|WHERE]]<~~/~~code> definitions with <code>AND</code>, <code>OR</code>, or <code>NOT</code> operands in <code>[[Select (SQL)\|SELECT]]</code>, <code>[[Update (SQL)\|UPDATE]]<~~/~~code>, and <code>[[Delete (SQL)\|DELETE]]<~~/~~code> statements.~~

	~~==See also==~~
	* [[Selection (relational algebra)]]

	~~[[Category:Relational algebra]~~]

Fujikawa method - Revision history

en>Markhurd: Disambiguate Jacobian to Jacobian matrix and determinant using popups

en>Reyk: dab fix: partition function -> partition function (quantum field theory)