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Symmetrization information


In mathematics, symmetrization is a process that converts any function in variables to a symmetric function in variables. Similarly, antisymmetrization converts any function in variables into an antisymmetric function.

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Symmetrization

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function and an anti-symmetric function. The symmetrization of a symmetric map is its double, while the symmetrization of an alternating map is zero; similarly...

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Symmetrization methods

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using the Steiner symmetrization method (described below). From this many other isoperimetric problems sprung and other symmetrization algorithms. For example...

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Symmetric function

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general case where f {\displaystyle f} can be recovered if both its symmetrization and antisymmetrization are known is when n = 2 {\displaystyle n=2} and...

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Young symmetrizer

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In mathematics, a Young symmetrizer is an element of the group algebra of the symmetric group, constructed in such a way that, for the homomorphism from...

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Isoperimetric inequality

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In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n {\displaystyle n} -dimensional...

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Voltage symmetrization system

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Voltage Symmetrization System (VSS) was developed especially for electric power networks with great phase voltage unbalance. It is a three-phase system...

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Scotland

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Nagel, Federalism Beyond Federations: Asymmetry and Processes of Re-symmetrization in Europe (Aldershot: Ashgate, 2011), p. 39. R. Quinault, "Scots on...

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Penrose graphical notation

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Contraction of indices is represented by joining the index lines together. Symmetrization of indices is represented by a thick zig-zag or wavy bar crossing the...

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Abstract index notation

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)}\omega _{\sigma (a)\sigma (b)\sigma (c)}} Similarly, we may symmetrize: ω ( a b c ) := 1 3 ! ∑ σ ∈ S 3 ω σ ( a ) σ ( b ) σ ( c ) {\displaystyle...

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Mathematical formulation of quantum mechanics

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using a symmetrized/antisymmetrized wavefunction and that independent treatment of these wavefunctions gives the same result. Hence the symmetrization postulate...

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Quark model

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that the quarks are eight components of a single particle, so the anti-symmetrization applies to all the quarks. A simpler approach is to consider the eight...

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Quantum state

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and can't be described with Schrödinger mechanics). When symmetrization or anti-symmetrization is unnecessary, N-particle spaces of states can be obtained...

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General relativity

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product Hodge star operator Lie derivative Raising and lowering indices Symmetrization Tensor contraction Tensor product Transpose (2nd-order tensors) Related...

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Special relativity

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product Hodge star operator Lie derivative Raising and lowering indices Symmetrization Tensor contraction Tensor product Transpose (2nd-order tensors) Related...

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Kronecker delta

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_{\sigma (1)}}\cdots \delta _{\nu _{p}}^{\mu _{\sigma (p)}}.} Using anti-symmetrization: δ ν 1 … ν p μ 1 … μ p = p ! δ [ ν 1 μ 1 … δ ν p ] μ p = p ! δ ν 1 [...

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Second quantization

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redundant names of the same quantum many-body state. So the symmetrization (or anti-symmetrization) must be introduced to eliminate this redundancy in the...

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Antisymmetric tensor

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U_{ijk\dots }=U_{(ij)k\dots }+U_{[ij]k\dots }.} A shorthand notation for anti-symmetrization is denoted by a pair of square brackets. For example, in arbitrary dimensions...

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Median

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estimator of the population pseudo-median, which is the median of a symmetrized distribution and which is close to the population median. The Hodges–Lehmann...

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Einstein field equations

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semicolon represents a covariant derivative, and the brackets denote anti-symmetrization. The first equation asserts that the 4-divergence of the 2-form F is...

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Helium atom

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{\textstyle s} , this would only be true in the absence of symmetrization postulate. Due to the symmetrization postulate, the choice of s {\textstyle s} will influence...

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Linear map

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product Hodge star operator Lie derivative Raising and lowering indices Symmetrization Tensor contraction Tensor product Transpose (2nd-order tensors) Related...

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Pauli exclusion principle

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Deilamian, K.; et al. (1995). "Search for small violations of the symmetrization postulate in an excited state of Helium". Phys. Rev. Lett. 74 (24):...

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Transpose

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product Hodge star operator Lie derivative Raising and lowering indices Symmetrization Tensor contraction Tensor product Transpose (2nd-order tensors) Related...

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Angular momentum

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product Hodge star operator Lie derivative Raising and lowering indices Symmetrization Tensor contraction Tensor product Transpose (2nd-order tensors) Related...

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