On the Linear Complexity Profile of Nonlinear Congruential Pseudorandom Number Generators with Dickson Polynomials

Linear complexity and linear complexity profile are important characteristics of a sequence for applications in cryptography and Monte-Carlo methods. The nonlinear congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. Recently, a weak lower bound on the linear complexity profile of a general nonlinear congruential pseudorandom number generator was proven by Gutierrez, Shparlinski and the first author. For most nonlinear generators a much stronger lower bound is expected. Here, we obtain a much stronger lower bound on the linear complexity profile of nonlinear congruential pseudorandom number generators with Dickson polynomials.     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Some results on quasipolyhedral convexity

The objective of this paper is to analyze under what well-known operations the class of quasipolyhedral convex functions, which can be regarded as an extension of that of polyhedral convex functions, is closed. The operations that will be considered are those that preserve polyhedral convexity, such that the image and the inverse image under linear transformations, right scalar multiplication (including the case where λ=0⁺) and pointwise addition.      

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Viscosity solutions of fully nonlinear parabolic systems

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128.     

Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field

The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues.     

Eigenvalue and stability of singular differential delay systems

The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability.     

一类非线性椭圆问题的schwarz算法

其中考虑下述泛函最小问题:求u∈W01,α(Ω),使F(u)=     

一类催化反应中的非线性奇摄动边值问题的渐近解

本文研究了催化反应非线性奇摄动边值问题．利用微分不等式理论和方法，得到了问题的解的任意次近似渐近估计．