弱耦合一维扩展赫伯特模型的基态相图

我们利用玻色化和重整化群分析的方法研究了半满填空且排斥势小于跃迁动能时的一维扩展赫伯特模型的基态相图,发现基态相图是由自旋密度波,电荷密度波和键荷密度波组成.这些结果揭示了扩展赫伯特模型和赫伯特模型基态相图的差异.     

Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions

In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the pe...     

A self-adaptive trust region method for the extended linear complementarity problems

By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under strict complementarity conditions. This work is supported by National Natural Science Foundation of China (No. 10671126) and Shanghai Leading Academic Discipline Project (S30501).     

Travelling wave solutions for a class of generalized KdV equation

In this work, the K^∗(l,p) equation is investigated. The sine-cosine method, the tanh method and the extended tanh method are efficiently used for analytic study of this equation. New solitary patterns solutions and compactons solutions are formally derived. The proposed schemes are reliable and manageable.     

Stochastic functional differential equations modelling materials with selective recall

We study a problem in stochastic functional differential equations which, in addition to a standard one-one-parameter noise term involves a random perturbation of the memory. This problem can also be regarded as a first order hyperbolic system of stochastic partial differential equations with given initial data and nonlocal boundary data. Existence and uniqueness of a solution is established and the generator of the associated Markov process is analyzed. Thereafter, for two model problems arising from first- and second-order integro-differential equations suggested by physical applications we establish asymptotic stability in probability of the associated stochastic processes.     

ON SINGLE LAWS FOR VARIETIES OF QUASIGROUPS ASSOCIATED WITH EXTENDED CYCLE SYSTEMS

It has been previously shown by Lindner and Rodger that quasigroups associated with 2-perfect extended m-cycle systems can be equationally defined if and only if m ∈ {3, 5, 7}. In this paper we present a single identity for each such m which is equivalent to the identities given for these varieties.

     

Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method＊

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.     

On a Family of Covering Extended Building Sets

Recently Davis and Jedwab introduced the notion of covering extended building sets to construct abelian difference sets. In this paper we consider a family of covering extended building sets similar to the ones corresponding to Hadamard difference sets and Spence difference sets and derive some numerical restrictions on the parameters.     

Assessment of conservative weighting scheme in simulating chemical vapour deposition with trace species

Low‐pressure or ultra‐high vacuum chemical vapour deposition often involves important trace species in both gas‐phase and surface reactions. The conservative weighting scheme (J. Thermophys. Heat Transfer 1996; 10 (4) : 579) has been used to deal with the trace species often involved in some non‐reactive physical processes, which is otherwise considered computationally impossible using the conventional DSMC method. This conservative weighting scheme (CWS) improves greatly the statistical uncertainties by decreasing the weighting factors of trace‐species particles and ensures the conservation of both momentum and energy between two colliding particles with large difference of weighting factors. This CWS is further extended to treat reactive processes for gas‐phase and surface reactions with trace species, which is called extended conservative weighting scheme (ECWS). A single‐cell equilibrium simulation is performed for verifying both the CWS and ECWS in treating trace species. The results of using CWS show that it is most efficient and accurate for weight ratio (trace to non‐trace) equal to or less than 0.01 for flows with two and three species. The results of a single‐cell simulation using ECWS for gas‐phase reaction and surface reactions show that only ECWS can produce acceptable results with reasonable computational time. Copyright © 2003 John Wiley & Sons, Ltd.