An Investigation of a Pair of Integral Equations for the Biharmonic Problem

The paper contains an elementary investigation of the questionof uniqueness of a pair of integral equations connected withthe plane biharmonic problem. It is shown that for two particularexceptional geometries of the boundary curve the pair of integralequations does not have a unique solution. This defect can beremoved by adding two supplementary integral conditions whichthe solution of the integral equations must satisfy. As an illustrationthe integral equations are solved numerically with and withoutthese extra conditions.     

Numerical Solutions for Two-dimensional Annular Electrochemical Machining Problems

Present address: Department of Applied Mathematics, University of Western Ontario, London, Ontario, Canada. Numerical solutions are obtained for a quasi-steady model ofthe electrochemcial machining process for two-dimensional problemswith the electrodes being represented by closed curves, oneinside the other. The accuracy of the procedure is checked bythe solutions obtained by it for a particular case with a perturbationsolution. The two solutions agree well. The applicability ofthe numerical procedure is indicated by presenting results whichshow the making of a notch in a circular cylinder.     

A CC2 dielectric continuum model and a CC2 molecular mechanics model

In this paper we present theory and applications for the second-order approximate singles and doubles coupled cluster (CC2) electronic structure method coupled to either a dielectric continuum (the CC2/DC model) or a molecular mechanical intermolecular force field (the CC2/MM model). Calculations of the interaction energy, solvation energy, electric dipole moment and electric quadrupole moment of liquid water are presented using the correlated CC2 approach. The results are compared to the corresponding results using the uncorrelated Hartree-Fock (HF) and the correlated coupled cluster singles and doubles (CCSD) methods. Also, a hierarchy in the coupling between the quantum mechanical (QM) and the molecular mechanical (MM) part of the system is investigated in the QM/MM model for the three different electronic structure methods.     

The QM/MM approach for wavefunctions,energies and response functions within self-consistent field and coupled cluster theories

This paper presents the coupled cluster/molecular mechanics (CC/MM) and self-consistent field/molecular mechanics (SCF/MM) approaches for wavefunctions, energies and response properties. Two physically different theories are derived, the mean-field and the direct-field interaction approaches, together with expressions for the optimization condition of both variational and non-variational wavefunctions and energies. Also derived are the linear response functions at the CC/MM and SCF/MM levels of theory, and the expressions are compared with the vacuum response functions.     

不可微不可逆映象中的V型阵发

一个既不可微(或不连续)又不可逆的一维映象可以展示一种新型的阵发。它的机制是稳定不动点与映象不可微或不连续点碰撞而消失。这种阵发可以在该不动点附近的线性化映象本征值绝对值在阵发前为小于1的任何值的情况发生,因而可能突然出现在倍周期分岔序列中途任一部分,使序列中断进入混沌。在稳定不动点消失后映象产生的阵发时间序列中,层流相长度呈现与外控参数距临界值距离的对数依赖关系。这种新型标度规律不依赖于映象的细节。作者认为这种阵发应广泛存在于许多实际系统之中。 关键词：     

A Perturbation Solution for a Two-dimensional Annular Electrochemical Machining Problem

Present address: Deparment of Applied Mathematics, University of Western Ontario, London, Canada. A two-dimensional electrochemical machining problem which consistsof an almost circular anode placed inside a circular cathodeis solved using a perturbation procedure. The smoothing of roughmetal parts is studied by solving the resulting perturbationequations numerically.     

Integral Equations without a Unique Solution can be made Useful for Solving some Plane Harmonic Problems

Using Green's third identity an integral equation for a twodimensional harmonic problem is derived. For a particular exceptionalgeometry the integral equation does not have a unique solutionbut by applying Green's third identify a supplementary integralcondition is derived. When the integral equation and the integralcondition are solved simultaneously we obtain always a uniquesolution. The procedure is demonstrated by some numerical examples.