Total dual integrality and b-matchings

Schrijver has shown that any rational polyhedron is the solution set of a unique minimal integer TDI linear system. We characterize this system for the case of b-matchings, one of the few known cases for which such a system is strictly larger than a minimal linear system sufficient to define the polyhedron.     

Dual extremum principles relating to an optimal filter

We obtain here a variational principle characterizing an optimal filter. This variational principle is dual to the one obtained by Berkovitz and Pollard in Ref. 2.The author wishes to thank the referee for his valuable suggestions.     

Partially conserved axial-vector current inS-matrix theory

Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm _π andm _ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ²−mπ²=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.     

On zero-degree stochastic geometric programs

The Mellin transform is used to encode randomness in the constraint and objective function coefficients using the substituted dual function. This enables one to obtain statistical moments and the probability distribution of the optimal objective valueZ*. Advantage is taken of the form of the dual function and the limiting property of the lognormal distribution to prove that the probability distribution ofZ* approximates the lognormal distribution, independent of the distribution of the parameters. This is of importance because those probability distributions are seldom known; even if they are, a derivation of the distribution ofZ* is apt to be elusive. Further, the larger the number of stochastic parameters in the geometric program, the more closely, in general, does the distribution ofZ* approximate the lognormal distribution. Illustrative examples are provided.Credit is due to Keith R. Weiss who developed the examples. The Office of Naval Research supported the work under Contract No. N000-14-75-C-0254.     

A Full Characterization of Multipliers for the Strong ϱ-Integral in the Euclidean Space

We study a generalization of the classical Henstock-Kurzweil integral, known as the strong -integral, introduced by Jarník and Kurzweil. Let be the space of all strongly -integrable functions on a multidimensional compact interval E, equipped with the Alexiewicz norm We show that each element in the dual space of can be represented as a strong -integral. Consequently, we prove that fg is strongly -integrable on E for each strongly -integrable function f if and only if g is almost everywhere equal to a function of bounded variation (in the sense of Hardy-Krause) on E.     

A Wold-type decomposition for commuting isometric pairs

We obtain a Wold-type decomposition theorem for an arbitrary pair of commuting isometries on a Hilbert space. More precisely, can be uniquely decomposed into the orthogonal sum between a bi-unitary, a shift-unitary, a unitary-shift and a weak bi-shift part, that is, a part that can be characterized by the condition that and are shifts. Moreover, contains bi-shift and modified bi-shift maximal parts.

     

Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs

Given two densities on with the same total mass, the Monge transport problem is to find a Borel map rearranging the first distribution of mass onto the second, while minimizing the average distance transported. Here distance is measured by a norm with a uniformly smooth and convex unit ball. This paper gives a complete proof of the existence of optimal maps under the technical hypothesis that the distributions of mass be compactly supported. The maps are not generally unique. The approach developed here is new, and based on a geometrical change-of-variables technique offering considerably more flexibility than existing approaches.

     

A note on the delayed heat equation: Instability with respect to initial data

Working in the context of a simple, one-dimensional, initial-boundary value problem involving homogeneous Dirichlet boundary data, we show that the time delayed heat equation can exhibit a type of instability with respect to the initial condition (IC); specifically, we show that a slight (in the L² sense) change in the IC can change a well-posed problem to an ill-posed one. We also establish that a physically realistic solution is possible only if the IC is of a (very) specific form. The main implication of this study is that the single and dual phase lag models, which have been put forward as possible alternatives to Fourier’s law, are not valid constitutive relations for the thermal flux vector.     

关于半自反空间的一个闭图定理

本文给出了一个关于半自反ｉｎｆｒａ－（ｕ）空间的闭图定理．作为推论,证明了从速完备 Ｍａｚｕｒ空间到半自反ｉｎｆｒａ－（ｕ）空间的闭图线性映照为弱连续、Ｍａｃｋｅｙ连续和强连续的．