Papers by Keyword: Saddle Point

Abstract: Elastic fields, generating by defects of the structure, influence the diffusion processes. It leads to the alteration of the phase transformation kinetic. One of the chief aims of our work is to obtain general equations for the diffusion fluxes under strain that give the possibility for using these equations at low temperatures, as in this case the strain influence on the diffusion fluxes is manifested in maximal degree. Our approach takes into consideration, that the strains can alter the surrounding atom configuration near the jumping one and consequently the local magnitude of the activation barrier and a rate of atom jump. The rates of atom jumps in different directions define the flux density of the vacancies. Now we take into account, that strain values are different in the saddle point and in the rest atom position, in differ from our consideration that was done by us earlier. As a result in the development of our approach the general equations for the vacancy fluxes are obtained for fcc and bcc metals. In our paper we discuss the main features of the theory of diffusion under stress and its applications. In particular we examine how elastic stress, arising from nanovoids, influence the diffusion vacancy fluxes and the growth rate of voids in metals.

Abstract: In this paper, a matching theorem for weakly transfer compactly open valued mappings is established in GFC-spaces. As applications, a fixed point theorem, a minimax inequality and a saddle point theorem are obtained in GFC-spaces. Our results unify, improve and generalize some known results in recent reference.

Abstract: This paper discusses two-person zero-sum stochastic differential games for discrete-time systems. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weighting matrices in payoff/cost functional are not assumed to be definite. A generalized difference Riccati equation is introduced and the relationship between solvability of the equation and the existence of the saddle point has been given. Furthermore, making use of upper and lower solutions to Riccati equation, we obtained some other results.

Abstract: The existence of maximum point, oddity point and saddle point often leads to computation failure. The optimization idea is based on the reality that the optimum towards the local minimum related the initial point. After getting several optimal results with different initial point, the best result is taken as the final optimal result. The arithmetic improvement of multi-dimension Newton method is improved. The improvement is important for the optimization method with grads convergence rule or searching direction constructed by grads. A computational example with a saddle point, maximum point and oddity point is studied by multi-dimension Newton method, damped Newton method and Newton direction method. The importance of the idea of blind walking repeatedly is testified. Owing to the parallel arithmetic of modernistic optimization method, it does not need to study optimization problem with seriate feasible domain by modernistic optimization method.