PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

On ℤ<Subscript>2</Subscript>-graded identities of the super tensor product of <Emphasis Type="Italic">UT</Emphasis><Subscript>2</Subscript>(<Emphasis Type="Italic">F</Emphasis>) by the Grassmann algebra

Let F be a field of characteristic zero and E be the unitary Grassmann algebra generated over an infinite-dimensional F-vector space L. Denote by \(\mathcal{E} = \mathcal{E}^{(0)} \oplus \mathcal{E}^{(1)}\) an arbitrary ?₂-grading of E such that the subspace L is homogeneous. Given a superalgebra A = A ⁽⁰⁾ ⊕ A ⁽¹⁾, define the superalgebra \(A\hat \otimes \mathcal{E}\) by \(A\hat \otimes \mathcal{E} = (A^{(0)} \otimes \mathcal{E}^{(0)} ) \oplus (A^{(1)} \otimes \mathcal{E}^{(1)} )\). Note that when E is the canonical grading of E then \(A\hat \otimes \mathcal{E}\) is the Grassmann envelope of A. In this work we find bases of ?₂-graded identities and we describe the ?₂-graded codimension and cocharacter sequences for the superalgebras \(UT_2 (F)\hat \otimes \mathcal{E}\), when the algebra UT ₂(F) of 2 ×2 upper triangular matrices over F is endowed with its canonical grading.     

Restart strategies for GRASP with path-relinking heuristics

GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i ₁, i ₂, …} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem.     

Adaptive memory in multistart heuristics for multicommodity network design

This paper focuses on the use of different memory strategies to improve multistart methods. A network design problem in which the costs are given by discrete stepwise increasing cost functions of the capacities installed in the edges is used to illustrate the contributions of adaptive memory and vocabulary building strategies. Heuristics based on shortest path and maximum flow algorithms are combined with adaptive memory in order to obtain an approximate solution to the problem in the framework of a multistart algorithm. Furthermore, a vocabulary building intensification mechanism supported by the resolution of a linear program is also explored. Numerical experiments have shown that the proposed algorithm obtained the best known solutions for some instances in the literature. These results show the contribution of each memory component and the effectiveness of their combination.     

Rank Properties in Finite Semigroups II: The Small Rank and the Large Rank

This paper is concerned with the application of two possible definitions of rank to certain well-known semigroups.AMS Subject Classification (2000), 20M10     

Erratum to: Some Applications of the Hodge-de Rham Decomposition to Ricci solitons

The aim of this note is to clarify a minor mistake in the article: Some Applications of the Hodge-de Rham Decomposition to Ricci solitons.     

A spatial scan statistic for case event data based on connected components

We propose a new spatial scan statistic based on graph theory as a method for detecting irregularly-shaped clusters of events over space. A graph-based method is proposed for identifying potential clusters in spatial point processes. It relies on linking the events closest than a given distance and thus defining a graph associated to the point process. The set of possible clusters is then restricted to windows including the connected components of the graph. The concentration in each of these possible clusters is measured through classical concentration indices based on likelihood ratio and also through a new concentration index which does not depend on any alternative hypothesis. These graph-based spatial scan tests seem to be very powerful against any arbitrarily-shaped cluster alternative, whatever the dimension of the data. These results have applications in various fields, such as the epidemiological study of rare diseases or the analysis of astrophysical data.     

A Hybrid Improvement Heuristic for the One-Dimensional Bin Packing Problem

We propose in this work a hybrid improvement procedure for the bin packing problem. This heuristic has several features: the use of lower bounding strategies; the generation of initial solutions by reference to the dual min-max problem; the use of load redistribution based on dominance, differencing, and unbalancing; and the inclusion of an improvement process utilizing tabu search. Encouraging results have been obtained for a very wide range of benchmark instances, illustrating the robustness of the algorithm. The hybrid improvement procedure compares favourably with all other heuristics in the literature. It improved the best known solutions for many of the benchmark instances and found the largest number of optimal solutions with respect to the other available approximate algorithms.     

Switching preconditioners using a hybrid approach for linear systems arising from interior point methods for linear programming

Numerical Algorithms - In general, interior point methods are successful in solving large-scale linear programming problems. Their effectiveness is determined by how fast they calculate each...