Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Splitting the Square of a Schur Function into its Symmetric and Antisymmetric Parts

Abstract: We propose a new combinatorial description of the product of two Schur functions. In the particular case of the square of a Schur function SI, it allows to discriminate in a very natural way between the symmetric and antisymmetric parts of the square. In other words, it describes at the same time the expansion on the basis of Schur functions of the plethysms S2(SI) and Λ2(SI). More generally our combinatorial interpretation of the multiplicities c_{IJ}^K \ = \ (S_IS_J, S_K) leads to interesting q-analogues c_{IJ}^K (q) of these multiplicities. The combinatorial objects that we use are domino tableaux, namely tableaux made up of 1 × 2 rectangular boxes filled with integers weakly increasing along the rows and strictly increasing along the columns. Standard domino tableaux have already been considered by many authors l33r, l6r, l34r, l8r, l1r, but, to the best of our knowledge, the expression of the Littlewood-Richardson coefficients in terms of Yamanouchi domino tableaux is new, as well as the bijection described in Section 7, and the notion of the diagonal class of a domino tableau, defined in Section 8. This construction leads to the definition of a new family of symmetric functions (H-functions), whose relevant properties are summarized in Section 9.

Eigenvalue statistics of random real matrices

Abstract: Completing Ginibre's work we determine the joint probability density of eigenvalues in a Gaussian ensemble of real asymmetric matrices, which is invariant under orthogonal transformations. The symmetry parameter r may vary from -1 (antisymmetric ensemble) through 0 (completely asymmetric ensemble) to +1 (symmetric ensemble). The elliptic law for the average density of eigenvalues in the limit of large dimension is recovered. Matrices of the type considered appear in models for neural-network dynamics and dissipative quantum dynamics

Algebraic Flux Correction I. Scalar Conservation Laws

Abstract: An algebraic approach to the design of multidimensional high-resolution schemes is introduced and elucidated in the finite element context. A centered space discretization of unstable convective terms is rendered local extremum diminishing by a conservative elimination of negative off-diagonal coefficients from the discrete transport operator. This modification leads to an upwind-biased low-order scheme which is nonoscillatory but overly diffusive. In order to reduce the incurred error, a limited amount of compensating antidiffusion is added in regions where the solution is sufficiently smooth. Two closely related flux correction strategies are presented. The first one is based on a multidimensional generalization of total variation diminishing (TVD) schemes, whereas the second one represents an extension of the FEM-FCT paradigm to implicit time-stepping. Nonlinear algebraic systems are solved by an iterative defect correction scheme preconditioned by the low-order evolution operator which enjoys the M-matrix property. The dffusive and antidiffusive terms are represented as a sum of antisymmetric internodal fluxes which are constructed edge-by-edge and inserted into the global defect vector. The new methodology is applied to scalar transport equations discretized in space by the Galerkin method. Its performance is illustrated by numerical examples for 2D benchmark problems.