An adiabatic quantum optimization for exact cover 3 problem

A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.     

New exact solutions of a （3＋1）-dimensional Jimbo-Miwa system

By using the (G'/G)-expansion method and the variable separation method, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is obtained. Based on the derived solitary wave solutions, we obtain some special localized excitations and study the interactions between two solitary waves of the system.     

Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types

Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.     

Fundamental frequency of a doubly connected membrane: a modified perturbation method

The fundamental frequency of a membrane is the square root ofthe lowest eigenvalue of the negative Laplace operator withDirichlet boundary conditions. A doubly connected membrane withthe inner region of vanishing maximal dimension 2c is consideredin this paper. A modified perturbation method is developed toprovide an asymptotic expansion (c 0) for the fundamental frequencyof the membrane. The first three order terms of the asymptoticexpansion for the fundamental frequency of a doubly connectedmembrane with the circular inner region are derived explicitly.The results are compared with the exact solutions and the approximationsdetermined by other investigators. The error of the perturbationcalculations compared with the exact values is less than 1%as c is less than or equal to 0·25 and is less than 4%as c is less than or equal to 0·35.     

The Gravitational Field of a Radiating and Contracting Spherically-Symmetric Body with Heat Flow

A model of a highly idealized spherically symmetric object radiating away its mass with constant luminosity is presented. The body starts at t = – with both infinite mass and radius and contracts to a point at t = 0 without forming an event horizon. Its material particles are moving non-geodesically and shearfree while transporting heat to the surface. Unlike in some radiating star models of a similar type, all physically required conditions are satisfied in this model.     

变厚度圆柱壳的轴对称弯曲问题

本文详细地研究了厚度h=h_0ξ~的圆柱壳的轴对称弯曲问题.文中通过引入一个位移函数H(ξ),将该问题的方程组化成一个关于H(ξ)的6阶常微分方程,用广义超几何函数给出问题的精确解.     

Newman-Penrose Formalism and Gravitational Impulsive and Shock Waves

Vacuum spacetimes endowed with two commuting spacelike Killing vector fields are considered. Subject to the hypothesis that there exists a shearfree null geodesic congruence orthogonal to the two-surface generated by the two commuting spacelike Killing vector fields,it is shown that, with a specific choice of null tetrad, the Newman-Penrose equations are reduced to an ordinary differential equation of Riccati type. fiom the consideration of this differential equation, exact solutions of the vacuum Einstein field equations with distribution valued Weyl curvature describing the propagation of gravitational impulsive and shock wave of variable polarization are then constructed.     

An application of hypervirial perturbation theory to calculate energy eigenvalues of the Morse potential for various diatomic molecules

The Schrödinger equation with the potentialV(r)=D[exp(?2β(r?r _e))?2exp(?β(r?r _e))] is treated in the framework of the hypervirial-renormalization parameter scheme. The energy eigenvalues of various eigenstates for different molecules are calculated.     

Exact Fixed-node Quantum Monte Carlo： Self-optimizing Procedure

In this paper, a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self-optimizing and self-improving procedure. In contrast to the previous EFN-QMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not be-fore beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent tech-nique is used, in which the step size is automatically adjustable.The procedure is quasi-Newton type and converges super linear-ly. The present method also uses a novel trial function, which has correct electron-electron and electron-nucleus cusp condi-tious. The novel EFNQMC algorithm and the novel trial func-tion are employed to calculate the energies of 1 ^1A1 state of CH2, ^1Ag state of Cs and the ground-states of H2, LiH, Li2 and H2O.