antisymmetric

• 反対称性の、反対称な

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antisymmetrically、antisymmetricity

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/01/22 12:43:14」(JST)

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The word antisymmetric refers to a change to an opposite quantity when another quantity is symmetrically changed. This concept is related to that of Symmetry and Asymmetry. The difference between these three concepts can be simply illustrated with Latin letters. The character "A" is symmetric about the vertical axis while the character "B" is not. The character "S" is antisymmetric about the vertical axis since the left side is flipped relative to the right. A character such as "H" fits the definition of both symmetric and antisymmetric. In this case the correct term is symmetric.

Other uses of the term:

• Antisymmetry in linguistics.
• Antisymmetric relation in mathematics (also see below).
• Skew-symmetric matrix in matrix properties.
• Antisymmetric tensor in matricies and index subsets.

Mathematics

In set theory, the adjective antisymmetric usually refers to an antisymmetric relation.

The term "antisymmetric function" is sometimes used for odd function, although some meanings of antisymmetric are essentiality f(−y, −x) = −f(x, y). In operator notation the latter is called anticommutativity.

In linear algebra and theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (usually the exchange of two indices, which becomes the transposition of the matrix) is performed. See:

• antisymmetric matrix (a matrix A for which A^T = −A)
• antisymmetric tensor

See also

• Symmetry in mathematics

References

English Journal

• Phononic crystal surface mode coupling and its use in acoustic Doppler velocimetry.

• Cicek A1, Salman A2, Kaya OA3, Ulug B4.
• Ultrasonics.Ultrasonics.2016 Feb;65:78-86. doi: 10.1016/j.ultras.2015.10.017. Epub 2015 Oct 23.
• It is numerically shown that surface modes of two-dimensional phononic crystals, which are Bloch modes bound to the interface between the phononic crystal and the surrounding host, can couple back and forth between the surfaces in a length scale determined by the separation of two surfaces and frequ
• PMID 26565078

• Shear horizontal feature guided ultrasonic waves in plate structures with 90° transverse bends.

• Yu X1, Manogharan P2, Fan Z3, Rajagopal P4.
• Ultrasonics.Ultrasonics.2016 Feb;65:370-9. doi: 10.1016/j.ultras.2015.08.012. Epub 2015 Sep 11.
• Antisymmetric and symmetric Lamb-type feature guided waves (FGW) have recently been shown to exist in small angle plate bends. This paper reports Semi-Analytical Finite Element (SAFE) method simulations revealing the existence of a new family of Shear Horizontal (SHB) type of FGW mode in 90° bends
• PMID 26409768

• Impact of the electron-phonon coupling symmetry on the polaron stability and mobility in organic molecular semiconductors.

• Ribeiro LA1, Stafström S.
• Physical chemistry chemical physics : PCCP.Phys Chem Chem Phys.2016 Jan 21;18(3):1386-91. doi: 10.1039/c5cp06577a. Epub 2015 Dec 16.
• The influence of the interplay between symmetric and antisymmetric inter-molecular electron-phonon (e-ph) coupling mechanisms on the polaron stability and mobility in organic semiconductors has been theoretically investigated at a molecular level. A semi-empirical Holstein-Peierls model is used whic
• PMID 26674995

Japanese Journal

• Pomeranchuk Instability of Spin-Antisymmetric Channel in SrRuO

• YOSHIOKA Yu,MIYAKE Kazumasa
• Journal of the Physical Society of Japan 81(2), 023707-1-4, 2012-02
• NAID 40019151103

• 長方形容器における液体スロッシングの粘性ポテンシャル流解析: 連成振動

• 舟田 敏雄
• 沼津工業高等専門学校研究報告 46, 237-242, 2012-01-31
• … A linear model shows typical effects of the viscosity in damping disturbances ofsymmtric and antisymmetric modes and nonlinear models are solved numerically to reveal th mode- mode coupling. …
• NAID 110009424275

Related Links

• antisymmetric | planetmath.org

Antisymmetric is not the same thing as “not symmetric”, as it is possible to have both at the same time. However, a relation ℛ ℛ \mathcal{R} that is both antisymmetric and symmetric has the condition that x ℛ y ⇒ x = y x ...

• Antisymmetric - Definition and More from the Free Merriam ...

an·ti·sym·met·ric adjective \ ˌ an-tē-sə-ˈ me-trik, ˌ an-ˌ tī-\ Definition of ANTISYMMETRIC: relating to or being a relation (as “ is a subset of ”) that implies equality of any two quantities for which it holds in both directions <the relation R is ...

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「反対称」

　　[★]

英

antisymmetric、antisymmetrically

関

反対称性

「反対称性」

　　[★]

英

antisymmetricity、antisymmetric

関

反対称

「antisymmetrically」

　　[★]

• 反対称に

関

antisymmetric

「antisymmetricity」

　　[★]

• 反対称性

関

antisymmetric