准坐标下完整系统的精确不变量与绝热不变量

基于对称性与不变量理论，研究了准坐标下完整系统的精确不变量与绝热不变量。研究了在小扰动作用下准坐标完整系统的对称性摄动。提出了高阶绝热不变量的概念，给出了精确不变量与绝热不变量存在的形式与条件。然后研究了相应的逆问题。     

Collective modes,damping, and the scattering function in classical liquids

An exact representation for the density-density response function is presented. This representation is a generalization of the result obtained in the mean field approximation and amounts to replacing the static, effective potential by one which is both wavenumber- and frequency-dependent. This potential possesses both a real and an imaginary part; the latter describes the collisional damping of collective modes. Analyticity and sum rule arguments are used to describe the basic properties of this complex potential. The formalism allows us to write an exact formula for the scattering functionS(k, ) in which the basic unknown is the collisional damping function. Using a small portion of the recent experimental data on coherent neutron scattering in liquid argon, we are able to calculateS(k, ) and other quantities of interest and to make comparisons with the rest of the data.     

Velocity-space contours of collision integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.     

A SQP Method for Inequality Constrained Optimization

Abstract In this paper, a new SQP method for inequality constrained optimization is proposed and the globalconvergence is obtained under very mild conditions.     

The Connes–Moscovici Approach to Cyclic Cohomology for Compact Quantum Groups

Consider the Hopf algebra (A, ) of regular functions on a compact quantum group. Let (A ^o ,) denote its maximal dual Hopf algebra. We show that the tensor product Hopf algebra (H ₂,₂) of (A ^o ,) and its opposite Hopf algebra is endowed with a modular pair (,) in involution; a notion introduced by A. Connes and J. Moscovici, who associate canonically a cocyclic object to such Hopf algebras. Denote the Hopf cyclic cohomology thus obtained by HC ^* _(,)(H ₂). Next we define an action of H ₂),₂ on A and show that the Haar state of (A, ) is a -invariant -trace on A with respect to this action. This gives us a canonical map from HC ^* _(,)(H ₂) to the ordinary cyclic cohomology of A.     

On Generalized (σ,τ)-Derivations

We generalize the notion of (,)-derivation of Nakajima and Bresar. We define the generalized (,)-derivations, generalized Jordan (,)-derivations, and generalized Lie (,)-derivations, We study interrelations between these classes of derivations as well as their homological properties.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

One and Two Facility Network Design Revisited

The one facility one commodity network design problem (OFOC) with nonnegative flow costs considers the problem of sending d units of flow from a source to a destination where arc capacity is purchased in batches of C units. The two facility problem (TFOC) is similar, but capacity can be purchased either in batches of C units or one unit. Flow costs are zero. These problems are known to be NP-hard. We describe an exact O(n ³3 ⁿ ) algorithm for these problems based on the repeated use of a bipartite matching algorithm. We also present a better lower bound of (n ² k ^*) for an earlier (n ^2k ) algorithm described in the literature where k=d/C and k ^*=mink,(n–2)/2. The matching algorithm is faster than this one for k(n–2)/2. Finally, we provide another reformulation of the problem that is quasi integral. This property could be useful in designing a modified version of the simplex method to solve the problem using a sequence of pivots with integer extreme solutions, referred to as the integral simplex method in the literature.     

Approximate Controllability for the Semilinear Heat Equation Involving Gradient Terms

This paper deals with the approximate controllability of the semilinear heat equation, when the nonlinear term depends on both the state y and its spatial gradient y and the control acts on any nonempty open subset of the domain. Our proof relies on the fact that the nonlinearity is globally Lipschitz with respect to (y, y). The approximate controllability is viewed as the limit of a sequence of optimal control problems. Another key ingredient is a unique continuation property proved by Fabre (Ref. 1) in the context of linear heat equations. Finally, we prove that approximate controllability can be obtained simultaneously with exact controllability over finite-dimensional subspaces.