Weyl type theorems for operators satisfying the single-valued extension property

Let T be a bounded linear operator acting on a Banach space X such that T or its adjoint T^∗ has the single-valued extension property. We prove that the spectral mapping theorem holds for the B-Weyl spectrum, and we show that generalized Browder's theorem holds for f(T) for every analytic function f defined on an open neighborhood U of σ(T). Moreover, we give necessary and sufficient conditions for such T to satisfy generalized Weyl's theorem. Some applications are also given.     

Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable.     

A new simplicial cover technique in constrained global optimization

A simplicial branch and bound-outer approximation technique for solving nonseparable, nonlinearly constrained concave minimization problems is proposed which uses a new simplicial cover rather than classical simplicial partitions. Some geometric properties and convergence results are demonstrated. A report on numerical aspects and experiments is given which shows that the most promising variant of the cover technique can be expected to be more efficient than comparable previous simplicial procedures.     

Asymptotic Dual Conditions Characterizing Optimality for Infinite Convex Programs

Characterizations of optimality are presented for infinite-dimensional convex programming problems, where the number of constraints is not restricted to be finite and where no constraint qualification is assumed. The optimality conditions are given in asymptotic forms using subdifferentials and €-subdifferentials. They are obtained by employing a version of the Farkas lemma for systems involving convex functions. An extension of the results to problems with a semiconvex objective function is also given.     

GENERALIZED WEIGHT

In this paper the generalized weight is introduced, and its behaviour is discussed.     

PERTURBATION OF A_0 ~+h

Let Z be a topological space and mapping A2 :Z→B(H) with closed range R(A2 ) be continuous . Some necessary and sufficient conditions of the continuity of M-P inverses A z+ are given in [1], [2]. It is one of them that AZ+ is continuous if ana only if AZ+ is locallybounded. In this paper, we discuss the following problem: if limA n = A0 in B(H) and ||An+||is unbounded (i.e. the above necessary and sufficient condition fails), what h in H will make the equations: limAm+ h = A0+ h or w-limAn+ h= A 0+ h be true. For this purpose three theorems and an error estimation are given in this paper.     

三项记忆梯度法及其投影算法的收敛性分析

对于无约束优化问题,提出了一类新的三项记忆梯度算法．这类算法是在参数满足某些假设的条件下,确定它的取值范围,从而保证三项记忆梯度方向是使目标函数充分下降的方向．在非单调步长搜索下讨论了算法的全局收敛性．为了得到具有更好收敛性质的算法,结合Solodov and Svaiter(2000)中的部分技巧,提出了一种新的记忆梯度投影算法,并证明了该算法在函数伪凸的情况下具有整体收敛性．     

A new positive‐definite regularization of incompressible Navier–Stokes equations discretized with Q1/P0 finite element

A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Nonlinear mappings associated with the generalized linear complementarity problem

We show that the Cottle—Dantzig generalized linear complementarity problem (GLCP) is equivalent to a nonlinear complementarity problem (NLCP), a piecewise linear system of equations (PLS), a multiple objective programming problem (MOP), and a variational inequalities problem (VIP). On the basis of these equivalences, we provide an algorithm for solving problem GLCP.Project partially supported by a grant from Oak Ridge Associated Universities, TN, USA.     

Recurrent dimensions of quasi-periodic solutions for nonlinear evolution equations

In this paper we introduce recurrent dimensions of discrete dynamical systems and we give upper and lower bounds of the recurrent dimensions of the quasi-periodic orbits. We show that these bounds have different values according to the algebraic properties of the frequency and we investigate these dimensions of quasi-periodic trajectories given by solutions of a nonlinear PDE.