The symmetric traveling salesman problem (STSP) is a special case of ATSP in which the cost function is symmetric (i.e. c(u, v) = c(v, u)). Christofides in 1976 [6] discovered a 3/2approximation algorithm for STSP. No better approximation algorithm has since been found for the general symmetric metric case. However, polynomial-time approximation schemes have been found when the distances are sh...

A pair of Mond-Weir type second order mixed symmetric duals is presented for a class of non-differentiable multi-objective nonlinear programming problems with multiple arguments. We establish duality theorems for the new pair of dual models under second order generalized convexity assumptions. This mixed second order dual formulation unifies the two existing second order symmetric dual formulat...

The symmetric traveling salesman problem (STSP) is a special case of ATSP in which the cost function is symmetric (i.e. c(u, v) = c(v, u)). Christofides in 1976 [6] discovered a 3/2approximation algorithm for STSP. No better approximation algorithm has since been found for the general symmetric metric case. However, polynomial-time approximation schemes have been found when the distances are sh...

Editorial comments. The Schur functions sλ are a special basis for the algebra of symmetric functions Λ. They are also intimately connected with representations of the symmetric and general linear groups. In what follows we will give two alternative definitions of these functions, show how they are related to other symmetric function bases, explicitly describe their connection with representati...

The Jacobian Conjecture has been reduced to the symmetric homogeneous case. In this paper we give an inversion formula for the symmetric case and relate it to a combinatoric structure called the Grossman-Larson Algebra. We use these tools to prove the symmetric Jacobian Conjecture for the case F = X−H with H homogeneous and JH = 0. Other special results are also derived. We pose a combinatorial...

We quantify the informational content of special regressors in heteroskedastic binary regressions with median-independent or conditionally symmetric errors. We measure informational content by two criteria: the set of regressor values that help point identify coe¢ cients in latent payo¤s as in (Manski 1988); and the Fisher information of coe¢ cients as in (Chamberlain 1986). We …nd for median-i...

Two mixed symmetric dual models for a class of non-differentiable multiobjective nonlinear programming problems with multiple arguments are introduced in this paper. These two mixed symmetric dual models unify the four existing multiobjective symmetric dual models in the literature. Weak and strong duality theorems are established for these models under some mild assumptions of generalized conv...

Given an undamped gyroscopic system GðλÞ 1⁄4 Mλ þ CλþK with M , K symmetric and C skew-symmetric, this paper presents a real-valued spectral decomposition of GðλÞ by a real standard pair ðX;TÞ and a skew-symmetric parameter matrix S . When T is assumed to be a block diagonal matrix, the parameter matrix S has a special structure. This spectral decomposition is applied to solve the quadratic inv...

Gabor system plays an important role in signal processing, image processing and other applications because of their redundancy properties. In this paper, symmetric or antisymmetric Gabor frames in two dimensions about any symmetric points are constructed from Gabor frames given. In special, symmetric or antisymmetric Parseval Gabor frames with better properties are obtained. Some thoughts of ex...

We review the method of differential renormalization, paying special attention to a new constrained version for symmetric theories.