Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.     

Exact boundary observability for 1‐D quasilinear wave equations

By means of a direct and constructive method based on the theory of semi‐global C² solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

Orlicz范数下的Hardy-Hilbert不等式

给出了Orlicz范数下的Hardy-Hilbert不等式的一种形式,建立了当N-函数M(u)及其余N-函数N(u)均满足Δ′条件时Orlicz范数下的积分型及双级数型Hardy-Hilbert不等式.     

Persistence of Floquet invariant tori for a class of non-conservative dynamical systems

In this paper we consider a class of non-conservative dynamical system with small perturbation. By the KAM method we prove existence of Floquet invariant tori under the weakest non-resonant conditions.

     

拟线性椭圆变分不等式的障碍最优控制问题

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．     

The Hamiltonian Canonical Form for Euler-Lagrange Equations

Based on the theory of calculus of variation, some suffcient conditions are given for some Euler-Lagrangcequations to be equivalently represented by finite or even infinite many Hamiltonian canonical equations. Meanwhile,some further applications for equations such as the KdV equation, MKdV equation, the general linear Euler Lagrangeequation and the cylindric shell equations are given.     

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.