let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

A dramatic multilayer substrate relaxation is observed for the (square root 19 x square root 19)-13CO adlayer phase on a Pt(111) electrode by surface X-ray scattering. Within the (square root 19 x square root 19) unit cell, a vertical expansion of 0.28 A was determined for the Pt atoms under near-top-site CO molecules, whereas only 0.04 A was found under near-bridge-site CO molecules. The later...

This paper is concerned with weighted least mean square design of two-dimensional (2-D) zero-phase FIR lters with quadrantally symmetric and antisymmetric frequency responses. The optimal solutions are rst characterized by certain integral equations, and the existence, and uniqueness of the weighted least mean square solution for 2-D FIR lter design are then established using contraction mappin...

We study spin models as introduced in [20]. Such a spin model can be defined as a square matrix satisfying certain equations, and can be used to compute an associated link invariant. The link invariant associated with a symmetric spin model depends only trivially on link orientation. This property also holds for quasi-symmetric spin models, which are obtained from symmetric spin models by certa...

Let A be a nonnegative square matrix whose symmetric part has rank one. Tournament matrices are of this type up to a positive shift by 1/2I . When the symmetric part of A is irreducible, the Perron value and the left and right Perron vectors of L(A, α) = (1 − α)A+ αAt are studied and compared as functions of α ∈ [0, 1/2]. In particular, upper bounds are obtained for both the Perron value and it...

Young’s lattice is the lattice of partitions of integers, ordered by inclusion of diagrams. Standard Young tableaux can be represented as paths in Young’s lattice that go up by one square at each step, and more general paths in Young’s lattice correspond to more general kinds of tableaux. Using the theory of symmetric functions, in particular Pieri’s rule for multiplying a Schur function by a c...

The performance of Branch-and-Bound algorithms is severely impaired by the presence of symmetric optima in a given problem. We describe a method for the automatic detection of formulation symmetries in MINLP instances. A software implementation of this method is used to conjecture the group structure of the problem symmetries of packing equal circles in a square. We provide a proof of the conje...

We are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. We will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. We will extend the spectral partitioning method for symmetric m...

In this paper we shall present a parametrization of all symmetric, possibly nonsquare minimal factorizations of a positive semidefinite rational matrix function. It turns out that a pole-pair of such a nonsquare factor is the same as a pole pair for a specific square factor. The location of the zeros is then determined by a solution to a certain algebraic Riccati inequality. We shall also consi...

We study a system of partial differential equations derived from the FitzHugh-Nagumo model. In one dimension solutions are required to satisfy zero Dirichlet boundary conditions on the interval Ω = (−1, 1). Estimates are given to describe bounds on the range of parameters over which solutions exist; numerical computations provide the global bifurcation diagram for families of symmetric and asym...