基于神经网络改进WENO-Z重构方法

本文通过使用深度神经网络对WENO-Z格式的非线性权重进行改进,提出了一种新的WENO-Z-NN格式．新格式首先用神经网络去随机扰动有限体积系数集,然后用代表偏微分方程解的波形生成的数据,采用L2正则化来学习扰动的最优函数,最后引入测试函数并结合最小总变差和最小总偏差作为评估依据进行后处理,从而得到新的权重．一维波动方程和一维Euler方程的数值结果表明,无论是在粗网格还是在细网格,本文所提出的WENO-Z-NN格式的激波捕捉能力明显优于传统的WENO-Z和WENO-JS-NN格式．     

Aggregating preferences rankings with variable weights

One of the most important issues for aggregating preferences rankings is the determination of the weights associated with the different ranking places. To avoid the subjectivity in determining the weights, Cook and Kress (1990) [5] suggested evaluating each candidate with the most favorable scoring vector for him/her. With this purpose, various models based on Data Envelopment Analysis have appeared in the literature. Although these methods do not require predetermine the weights subjectively, some of them have a serious drawback: the relative order between two candidates may be altered when the number of first, second, …, kth ranks obtained by other candidates changes, although there is not any variation in the number of first, second, …, kth ranks obtained by both candidates. In this paper we propose a model that allows each candidate to be evaluated with the most favorable weighting vector for him/her and avoids the previous drawback. Moreover, in some cases, we give a closed expression for the score assigned with our model to each candidate.     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

The Two-Dimensional,Linear Orthotropic Plate

We First define a continuous extension of the Laquerre polynomials and give some properties of this continuous extension. Then we define a continuous Laguerre transform for square integrable functions, give some properties of this transform and give a sampling theorem that is similar to the well known Shannon-Whittaker Sampling Theorem for Fourier transform. The inverse of this transform is also given.     

Solutions of a system of forced burgers equation in terms of generalized laguerre polynomials

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|ⁿ⁻¹eβ|x|²/2,${\left|x\right|}^{n-1}{e}^{\beta {\left|x\right|}^2}/2,$, β≥0, x ∈?n$\beta \ge 0,\hspace{0.17em}x\hspace{0.17em}\in {?}^n$. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Simple Conformal Superalgebras of Finite Growth

In this paper, we construct six families of infinite simple conformal superalgebras of finite growth based on our earlier work on constructing vertex operator superalgebras from graded assocaitive algebras. Three subfamilies of these conformal superalgebras are generated by simple Jordan algebras of types A, B, and C in a certain sense.Research supported by Hong Kong RGC Competitive Earmarked Research Grant HKUST709/96P.2000 Mathematics Subject Classification: primary 17A30, 17A60; secondary 17B20, 81Q60     

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.