Color histogram - Revision history

en>Ymshang: /* Characteristics of a color histogram */

2015-01-07T01:38:45Z

Characteristics of a color histogram

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	~~The name of the author~~ is ~~generally Gabrielle Lattimer. For years she~~'s ~~been working whereas~~ a ~~library assistant~~. ~~For a while she's yet~~ been ~~in Massachusetts. As~~ a ~~woman what your girl really likes is mah jongg but she has~~ not ~~made a dime utilizing it~~. ~~She~~ is ~~actually running and maintaining any kind of blog~~ here: http://~~circuspartypanama~~.~~com~~<br><br>~~Here is~~ my web~~-site~~ [http://~~circuspartypanama~~.~~com~~ clash of clans ~~hack ipad download~~]		Eusebio Stanfill is what's produced on my birth marriage certificate although it is not the name on a good birth certificate. Vermont has become where my home can. Software developing has been my afternoon job for a not to mention. To bake is the only past time my wife doesn't agree to. You can acquire my website here: http://prometeu.net<br><br>Stop by my web page; [http://prometeu.net hack clash of clans gems]

en>FrescoBot: Bot: link syntax

2014-02-07T12:42:45Z

Bot: link syntax

← Older revision		Revision as of 14:42, 7 February 2014
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	~~{{Unreferenced\|date=December 2009}}~~		The name of the author is generally Gabrielle Lattimer. For years she's been working whereas a library assistant. For a while she's yet been in Massachusetts. As a woman what your girl really likes is mah jongg but she has not made a dime utilizing it. She is actually running and maintaining any kind of blog here: http://circuspartypanama.com<br><br>Here is my web-site [http://circuspartypanama.com clash of clans hack ipad download]
	In [[physics]], a '''pseudoscalar''' is a quantity that behaves like a [[scalar (physics)\|scalar]], except that it changes sign under a [[Parity (physics)\|parity inversion]] such as [[improper rotation]]s while a true scalar does not.

	The ~~prototypical example~~ of ~~a pseudoscalar is~~ the [[scalar triple product]]. A pseudoscalar, when multiplied by an ordinary [[vector space\|vector]], becomes a [[pseudovector\|pseudovector (axial vector)]]; a similar construction creates the [[pseudotensor]].

	~~Mathematically, a pseudoscalar~~ is ~~an element of the top [[exterior power]] of a [[vector space]], or the top power of a [[Clifford algebra]]; see [[pseudoscalar (Clifford algebra)]]. More~~ generally~~, it is an element of the [[canonical bundle]] of a [[differentiable manifold]]~~.

	~~==Pseudoscalars in physics==~~
	~~In [[physics]], a pseudoscalar denotes a [[physical quantity]] analogous to~~ a ~~[[scalar (physics)\|scalar]]~~. ~~Both are [[physical quantity\|physical quantities]] which assume~~ a ~~single value which is invariant under [[proper rotation]]s. However, under the [[parity transformation]], pseudoscalars flip their signs~~ while ~~scalars do not. As [[Reflection (mathematics)\|reflection]]~~s ~~through a plane are the combination of a rotation with the parity transformation, pseudoscalars also change signs under reflections.~~

	~~One of the most powerful ideas~~ in ~~physics is that physical laws do not change when one changes the coordinate system used to describe these laws~~. ~~The fact that~~ a ~~pseudoscalar reverses its sign when the coordinate axes are inverted suggests that it~~ is not ~~the best object to describe a physical quantity. In 3-space, quantities which are described by~~ a pseudovector are in fact anti-symmetric tensors of rank 3, which are invariant under inversion. The pseudovector is a much simpler representation of that quantity, but suffers from the change of sign under inversion. Specifically, in 3-space, the [[Hodge dual]] of a scalar is equal to a constant times the 3-dimensional [[Levi-Civita symbol\|Levi-Civita pseudotensor]] (or "permutation" pseudotensor); whereas the Hodge dual of a pseudoscalar is in fact a anti-symmetric (pure) tensor of rank three. The Levi-Civita pseudotensor is a completely [[anti-symmetric]] pseudotensor of rank 3. Since the dual of the pseudoscalar is the product of two "pseudo-quantities" it can be seen that the resulting tensor is a true tensor, and does not change sign upon an inversion of axes. The situation is similar to the situation for pseudovectors and anti-symmetric tensors of rank 2. ~~The dual of a pseudovector~~ is ~~a anti-symmetric tensors of rank 2 (~~and ~~vice versa). It is the tensor and not the pseudovector which is the representation of the physical quantity which is invariant to a coordinate inversion, while the pseudovector is not invariant.~~

	~~The situation can be extended to~~ any ~~dimension. Generally in an ''N''-dimensional space the Hodge dual~~ of a rank ''n'' tensor (where ''n'' is less than or equal to ''N''/2) will be a anti-symmetric pseudotensor of rank ''N''-''n'' and vice versa. In particular, in the four-dimensional spacetime of special relativity, a pseudoscalar is the dual of a fourth-rank tensor which is proportional to the four-dimensional [[Levi-Civita symbol\|Levi-Civita pseudotensor]].

	~~===Examples===~~
	* the [[magnetic charge]] (as it is mathematically defined, regardless of whether it exists physically),
	* the [[magnetic flux]] - it is result of a [[dot product]] between a vector (the [[surface normal]]) and pseudovector (the [[magnetic field]]),
	* the [[Helicity (particle physics)\|helicity]] is the projection (dot product) of a [[spin (physics)\|spin]] pseudovector onto the direction of [[momentum]] (a true vector).

	~~==Pseudoscalars in geometric algebra==~~
	~~{{See also\|Pseudoscalar (Clifford algebra)}}~~

	A pseudoscalar in a [[geometric algebra]] is a highest-[[graded vector space\|grade]] element of the algebra. For example, in two dimensions there are two orthogonal basis vectors, <math>e_1</math>, <math>e_2</math> and the associated highest-grade basis element is

	:~~<math>e_1 e_2 = e_{12}.<~~/~~math>~~

	~~So a pseudoscalar is a multiple of ''e''<sub>12<~~/~~sub>~~. ~~The element ''e''~~<~~sub~~>12<~~/sub~~> ~~squares to −1 and commutes with all even elements – behaving therefore like the imaginary scalar ''i'' in the [[complex numbers]]. It~~ is ~~these scalar~~-~~like properties which give rise to its name.~~

	~~In this setting, a pseudoscalar changes sign under a parity inversion, since if~~

	:~~(''e''<sub>1<~~/~~sub>, ''e''<sub>2<~~/~~sub>) → (''u''<sub>1</sub>, ''u''<sub>2</sub>)~~

	~~is a change of basis representing an orthogonal transformation, then~~

	~~:''e''<sub>1</sub>''e''<sub>2</sub> → ''u''<sub>1</sub>''u''<sub>2</sub> = ±''e''<sub>1</sub>''e''<sub>2</sub>,~~

	~~where the sign depends on the determinant~~ of ~~the rotation. Pseudoscalars in geometric algebra thus correspond to the pseudoscalars in physics.~~

	~~[[Category:Geometric algebra]]~~
	~~[[Category:Clifford algebras]]~~
	~~[[Category:Linear algebra]~~]

124.123.187.42: /* Drawbacks and other approaches */

2014-01-09T19:45:49Z

Drawbacks and other approaches

← Older revision		Revision as of 21:45, 9 January 2014
Line 1:		Line 1:
	~~Andera~~ is ~~what you~~ can ~~call her but she never really favored~~ that ~~name~~. The ~~favorite hobby~~ for ~~him~~ and ~~his children~~ is to ~~perform lacross and he~~'ll be ~~beginning some thing else alongside with~~ it. ~~I am currently~~ a ~~journey agent~~. ~~Her family life~~ in ~~Ohio but her spouse wants them to move.~~<br><br>~~My web page: telephone psychic~~ - ~~[http~~://~~www~~.~~imrealestates~~.~~com~~/~~forum~~/~~easy-ideas-follow-boost-your-gardening-skills http~~://~~www~~.~~imrealestates~~.~~com/forum/easy-ideas-follow-boost-your-gardening-skills~~],		{{Unreferenced\|date=December 2009}}
			In [[physics]], a '''pseudoscalar''' is a quantity that behaves like a [[scalar (physics)\|scalar]], except that it changes sign under a [[Parity (physics)\|parity inversion]] such as [[improper rotation]]s while a true scalar does not.

			The prototypical example of a pseudoscalar is the [[scalar triple product]]. A pseudoscalar, when multiplied by an ordinary [[vector space\|vector]], becomes a [[pseudovector\|pseudovector (axial vector)]]; a similar construction creates the [[pseudotensor]].

			Mathematically, a pseudoscalar is an element of the top [[exterior power]] of a [[vector space]], or the top power of a [[Clifford algebra]]; see [[pseudoscalar (Clifford algebra)]]. More generally, it is an element of the [[canonical bundle]] of a [[differentiable manifold]].

			==Pseudoscalars in physics==
			In [[physics]], a pseudoscalar denotes a [[physical quantity]] analogous to a [[scalar (physics)\|scalar]]. Both are [[physical quantity\|physical quantities]] which assume a single value which is invariant under [[proper rotation]]s. However, under the [[parity transformation]], pseudoscalars flip their signs while scalars do not. As [[Reflection (mathematics)\|reflection]]s through a plane are the combination of a rotation with the parity transformation, pseudoscalars also change signs under reflections.

			One of the most powerful ideas in physics is that physical laws do not change when one changes the coordinate system used to describe these laws. The fact that a pseudoscalar reverses its sign when the coordinate axes are inverted suggests that it is not the best object to describe a physical quantity. In 3-space, quantities which are described by a pseudovector are in fact anti-symmetric tensors of rank 3, which are invariant under inversion. The pseudovector is a much simpler representation of that quantity, but suffers from the change of sign under inversion. Specifically, in 3-space, the [[Hodge dual]] of a scalar is equal to a constant times the 3-dimensional [[Levi-Civita symbol\|Levi-Civita pseudotensor]] (or "permutation" pseudotensor); whereas the Hodge dual of a pseudoscalar is in fact a anti-symmetric (pure) tensor of rank three. The Levi-Civita pseudotensor is a completely [[anti-symmetric]] pseudotensor of rank 3. Since the dual of the pseudoscalar is the product of two "pseudo-quantities" it can be seen that the resulting tensor is a true tensor, and does not change sign upon an inversion of axes. The situation is similar to the situation for pseudovectors and anti-symmetric tensors of rank 2. The dual of a pseudovector is a anti-symmetric tensors of rank 2 (and vice versa). It is the tensor and not the pseudovector which is the representation of the physical quantity which is invariant to a coordinate inversion, while the pseudovector is not invariant.

			The situation can be extended to any dimension. Generally in an ''N''-dimensional space the Hodge dual of a rank ''n'' tensor (where ''n'' is less than or equal to ''N''/2) will be a anti-symmetric pseudotensor of rank ''N''-''n'' and vice versa. In particular, in the four-dimensional spacetime of special relativity, a pseudoscalar is the dual of a fourth-rank tensor which is proportional to the four-dimensional [[Levi-Civita symbol\|Levi-Civita pseudotensor]].

			===Examples===
			* the [[magnetic charge]] (as it is mathematically defined, regardless of whether it exists physically),
			* the [[magnetic flux]] - it is result of a [[dot product]] between a vector (the [[surface normal]]) and pseudovector (the [[magnetic field]]),
			* the [[Helicity (particle physics)\|helicity]] is the projection (dot product) of a [[spin (physics)\|spin]] pseudovector onto the direction of [[momentum]] (a true vector).

			==Pseudoscalars in geometric algebra==
			{{See also\|Pseudoscalar (Clifford algebra)}}

			A pseudoscalar in a [[geometric algebra]] is a highest-[[graded vector space\|grade]] element of the algebra. For example, in two dimensions there are two orthogonal basis vectors, <math>e_1</math>, <math>e_2</math> and the associated highest-grade basis element is

			:<math>e_1 e_2 = e_{12}.</math>

			So a pseudoscalar is a multiple of ''e''<sub>12</sub>. The element ''e''<sub>12</sub> squares to −1 and commutes with all even elements – behaving therefore like the imaginary scalar ''i'' in the [[complex numbers]]. It is these scalar-like properties which give rise to its name.

			In this setting, a pseudoscalar changes sign under a parity inversion, since if

			:(''e''<sub>1</sub>, ''e''<sub>2</sub>) → (''u''<sub>1</sub>, ''u''<sub>2</sub>)

			is a change of basis representing an orthogonal transformation, then

			:''e''<sub>1</sub>''e''<sub>2</sub> → ''u''<sub>1</sub>''u''<sub>2</sub> = ±''e''<sub>1</sub>''e''<sub>2</sub>,

			where the sign depends on the determinant of the rotation. Pseudoscalars in geometric algebra thus correspond to the pseudoscalars in physics.

			[[Category:Geometric algebra]]
			[[Category:Clifford algebras]]
			[[Category:Linear algebra]]

en>StanfordProgrammer: /* Overview */ grammatical

2012-06-22T17:09:51Z

Overview: grammatical

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