The last twenty years have seen many attempts to calculate formation energies and formation volumes of vacancies and interstitials in facecentred cubic metals. (Johnson [l] has given an authoritative review; for recent developments see refs. [2,3] .) Judged by the effort spent, however, the progress achieved must be considered small. The majority of the model calculations on point-defects in Cu...

The Thesis is devoted to investigating the problem of computing the norm ‖A‖E,F = max x∈E:‖x‖E≤1 ‖Ax‖F of a linear mapping x 7→ Ax acting from a finite-dimensional normed space (E, ‖ · ‖E) to a finite-dimensional normed space (F, ‖ · ‖F ). This problem is important and interesting by its own right and especially due to its role in Robust Optimization. We mainly focus on the case where (E, ‖ · ‖...

We consider some generalizations of the Asymmetric Traveling Salesman Path problem. Suppose we have an asymmetric metric G = (V,A) with two distinguished nodes s, t ∈ V . We are also given a positive integer k. The goal is to find k paths of minimum total cost from s to t whose union spans all nodes. We call this the k-Person Asymmetric Traveling Salesmen Path problem (k-ATSPP). Our main result...

A class of splitting iterative methods are considered for solving fuzzy system of linear equations, which covers Jacobi, Gauss Seidel, SOR, SSOR and their block variance proposed. Theoretical analysis showed that for a regular splitting, the corresponding iterative method converge to the unique fuzzy solution for any initial vector and fuzzy right hand side vector. Finally, we illustrate our ap...

We consider a class of consistently ordered matrices which arise from the discretization of Boundary Value Problems (BVPs) when the finite element collocation method, with Hermite elements, is used. Through a recently derived equivalence relationship for the asymptotic rates of convergence of the Modified Successive Overrelaxation (MSOR) and a certain 2-step iterative method, we determine the o...

Thermochemical relaxation behind a normal shock in Mars and Titan gas mixtures is simulated using a CFD solver, DPLR, for a hemisphere of 1 m radius; the thermochemical relaxation along the stagnation streamline is considered equivalent to the flow behind a normal shock. Flow simulations are performed for a Titan gas mixture (98% N2, 2% CH4 by volume) for shock speeds of 5.7 and 7.6 km/s and pr...

This problem is NP-hard, so there is no known algorithm to determine the solution in polynomial time. Instead we seek to compute an approximate solution in polynomial time. One strategy for accomplishing this, first pioneered by Goemans & Williamson in Ref. [3], is to employ a semidefinite relaxation. This technique consists of three steps: first construct a related problem that is a semidefini...

Linear programming (LP) relaxations are widely used to attempt to identify a most likely configuration of a discrete graphical model. In some cases, the LP relaxation attains an optimum vertex at an integral location and thus guarantees an exact solution to the original optimization problem. When this occurs, we say that the LP relaxation is tight. Here we consider binary pairwise models and de...

Gomory mixed-integer (GMI) cuts are among the most effective cutting planes for general mixed-integer programs (MIP). They are traditionally generated from an optimal basis of a linear programming (LP) relaxation of a MIP. In this paper we propose a heuristic to generate useful GMI cuts from additional bases of the initial LP relaxation. The cuts we generate have rank one, i.e., they do not use...