A maximum principle is proved for the weak solutions uALNðR TÞ of the telegraph equation in space dimension three utt Dxu þ cut þ lu 1⁄4 f ðt; xÞ; when c40; lAð0; c=4 and fALNðR TÞ (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation u...

Treatments to inhibit browning and decay and prolong shelf life of fresh-cut mangoes were investigated. Combinations of antibrowning agents and modified atmosphere packaging (MAP) resulted in a reduction of browning and deterioration of fresh-cut mangoes stored at 10 degrees C. Combinations of several browning inhibitors were more effective than those applied individually. Among these treatment...

We show that Karger’s randomized contraction method [7] can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient algorithms. For global minimum cuts with a single edge-budget constraint, our extension of the randomized contraction method has running time Õ(n3) in an n-node graph improving upon the best-known randomi...

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a series of specific properties and, in particular, are described in terms of Seiberg-Witten-Whitham theory. The simplest example of ordinary integral is consi...

In this work, we present a theoretical study about NP-hard optimization problems of cuts in graphs and the state of the art in approximation algorithms that use techniques of mathematical programming and of metric spaces. Three problems of cuts in graphs were modeled by integer mathematical programs and they are relaxed to admit solutions with continuous values. The solution of these programs d...

This paper gives a straightforward implementation of simulated annealing for solving maximum cut problems and compare its performance to that of some existing heuristic solvers. The formulation used is classical, dating to a 1989 paper of Johnson, Aragon, McGeoch, and Schevon. This implementation uses no structure peculiar to the maximum cut problem, but its low per-iteration cost allows it to ...

A heuristic algorithm based on VNS is proposed to solve the Max 3-cut and Max 3-section problems. By establishing a neighborhood structure of the Max 3-cut problem, we propose a local search algorithm and a variable neighborhood global search algorithm with two stochastic search steps to obtain the global solution. We give some numerical results and comparisons with the well-known 0.836-approxi...

In this paper, a methodology for testing the accuracy and strength of cut generators for mixed-integer linear programming is presented. The procedure amounts to random diving towards a feasible solution, recording several kinds of failures. This allows for a ranking of the accuracy of the generators. Then, for generators deemed to have similar accuracy, statistical tests are performed to compar...

For a given schedule of a round-robin tournament and a matrix of distances between homes of teams, an optimal home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance. We propose a technique to transform the problem to MIN RES CUT. We apply Goemans and Williamson’s 0.878-approximation algorithm for MAX RES CUT, which is based on a positive semid...

A continuation algorithm for the solution of max-cut problems is proposed in this paper. Unlike the available semi-definite relaxation, a max-cut problem is converted into a continuous nonlinear programming by employing NCP functions, and the resulting nonlinear programming problem is then solved by using the augmented Lagrange penalty function method. The convergence property of the proposed a...