求解全局最优问题的多重点样本水平值估计的相对熵算法

研究有界闭箱约束下的全局最优化问题,利用相对熵及广义方差函数方程的最大根与全局最小值之间的等价关系,设计求解全局最优值的积分型水平值估计算法.对采用重点样本采样技巧产生的函数值按一定规则进行聚类,从而在各聚类中产生的若干新重点样本,结合相对熵算法,构造出多重点样本进行全局搜索的新算法.该算法的优点在于每次迭代选用当前较好的函数值信息,以达到随机搜索到更好的函数值信息.同时多重点样本可有利挖掘出更好的全局信息.一系列的数值实验表明该算法是非常有效的.     

Collective Excitations in Spin-2 Bose-Einstein Condensates

The Green＇s functions and the correlation functions in spin-2 Bose-Einstein condensates at finite temperature are defined and the generalized Dyson-Beliaev equations are introduced. We discuss the spin conservation in z direction and decouple the Green＇s functions and the generalized Dyson-Beliaev equations according to different spin conservations in z direction. The anomalous vertex functions are introduced and the self-energies are separated into the proper self-energies and the improper self-energies. The generalized Dyson-Beliaev equations are decoupled according to separation of the self-energies. We calculate the Green＇s functions step by step in the Bogoliubov approximation and discuss the collective excitations in spin-2 Bose-Einstein condensates in the polar, ferromagnetic, and cyclic cases, respectively.     

离散的五次非线性薛定谔方程的精确孤子解

利用推广的双曲函数法，我们研究了离散的五次非线性薛定谔方程。当方程的系数满足某种约束关系时，我们得到了新的局域解。这些解包括亮孤子解，暗孤子解，相位交替变化的亮孤子解和相位交替变化的暗孤子解。     

非线性离散微分方程的双曲函数法求解

本文推广了双曲函数方法用于求解非线性离散系统。求解离散的(2+1)维Toda系统和离散的mKdV系统，成功地得到了离散钟型孤立子、离散冲击波型孤立子及一些新的精确行波解。     

Equivalence Relation between Initial Values and Solutions for Evolution p-Laplacian Equation in Unbounded Space

In this paper,an equivalence relation between the ω-limit set of initial values and the ω-limit set of solutions is established for the Cauchy problem of evolution p-Laplacian equation in the unbounded space Yσ(RN).To overcome the difficulties caused by the nonlinearity of the equation and the unbounded solutions,we establish the propagation estimate and the growth estimate for the solutions.It will be demonstrated that the equivalence relation can be used to study the asymptotic behavior of solutions.     

关于“评测指标权重确定的结构熵权法”的注记

本文基于文献[1]所提出的观点,根据熵理论和德尔斐专家调查法,对文献[1]所提出的方法进行了改进,得到了改进的结构熵权法,并运用此方法对环保项目指标进行权重确定,同时与经典的德尔斐专家调查法确定的权重进行比较,并对二者的差异作出了合理解释。     

Computation of direct intensity and medium intensity by using the discrete ordinates method

On the basis of the discrete ordinate scheme with (an) infinitely small weight(s), an easy-to-use and comprehensive method, named multi-rays method, is developed to calculate total, direct and medium intensities in arbitrarily specified directions. In doing this, for each of the specified directions, three identical discrete directions with infinitely small weights are employed to represent the three intensities. The new method is verified with two standard test problems, and is used to compute the intensities in two anisotropically scattering problems.     

Note on Fractional Green's Function

In this paper, we modify some errors on the definition of fractional Green''s function in monograph [5], and give the solution of the inhomogenous equation which satisfies the given inhomogenous initial conditions by fractional Green''s function.     

Hierarchy of the Selberg Zeta Functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15     

Extended structures and new infinite-dimensional hidden symmetries for the Einstein–Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for . An Ernst-like matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective.