The complete and elementary symmetric functions are specializations of Schur functions. In this paper, we use this fact to give two identities for the complete and elementary symmetric functions. This result can be used to proving and discovering some algebraic identities involving rWhitney and other special numbers.

A branch and bound algorithm for finding the minimal cost symmetric assignment is discussed. The matching problem in graph theory and the Chinese postman puzzle are all special cases of the symmetric assignment problem, and hence this algorithm can be applied to solve them.

We prove that Welch Costas arrays are in general not symmetric and that there exist two special families of symmetric Golomb Costas arrays: one is the well-known Lempel family, while the other, although less well known, leads actually to the construction of dense Golomb rulers. © 2008 Elsevier B.V. All rights reserved.

-equilibrium allows for worse actions to be played with higher probability than better actions. I introduce a refinement that addresses this shortcoming: an -equilibrium is monotonic if each player assigns (weakly) higher probabilities to better actions. This concept is logically independent of strong -equilibrium. I study these refinements of -equilibrium in games with countably many players a...

An analytic approach for the generation of non-periodic and periodic complementary sequences is advanced for lengths that are powers of two. The periodic complementary sequences can be obtained using symmetric or anti-symmetric extensions. The properties of their autocorrelation functions are studied. The non-periodic complementary sequences are the intersection between anti-symmetric and symme...

We review the correspondence between symmetric affine theories and the nonlinear Einstein-Proca system that was found by Einstein and Schrödinger. With the use of this correspondence, we investigate static spherically symmetric solutions in symmetric affine theory with no matter fields. Use of the correspondence leads to a significant simplification of the calculation. A special instance of “no...

In additional to the parity ($\mathcal{P}$) symmetric, time reversal ($\mathcal{T}$) and $\mathcal{PT}$ symmetric nonlocal integrable systems, some other types of Klein-Gordon models with space-time exchange nonlocality moving nolocality are proposed. The Lax pairs established nonlinear equations explicitly given. A special soliton solution, composed $\mathcal{PT}$-symmetric part $\mathcal{PT}$...

Self–scaled barrier functions are fundamental objects in the theory of interior–point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self–scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with...

We study the matrix equation X+A>X−1A = Q, where A is a complex square matrix and Q is complex symmetric. Special cases of this equation appear in Green’s function calculation in nano research and also in the vibration analysis of fast trains. In those applications, the existence of a unique complex symmetric stabilizing solution has been proved using advanced results on linear operators. The s...