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NUMERICAL APPROXIMATION OF THE SMOLUCHOWSKI EQUATION USING RADIAL BASIS FUNCTIONS

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Journal of Computational mathematics 2020年第1期38卷 176-194页

作者： Christiane Helzel Maximilian Schneiders Institut of mathematics Heinrich-Heine-Universitat DusseldorfGermany formerly Institut of mathematics Heinrich-Heine-Universitat DusseldorfGermany

The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle *** numerical method uses radial basis functions(RBF).This is a relatively new approach,which has recently mainly been used for geophysical *** a simplified model problem we compare the RBF approach with a spectral method,*** standard approach used in related physical *** comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.

关键词： Smoluchowski equation Spectral method Radial basis function method

Bounds on partial derivatives of NURBS surfaces

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Applied mathematics(A Journal of Chinese Universities) 2017年第3期32卷 281-293页

作者： WANG Guo-jin XU Hui-xia HU Qian-qian School of Mathematical Sciences Zhejiang University Institute of mathematics Zhejiang Wanli University department of mathematics Zhejiang Gongshang University

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.

关键词： NURBS curve NURBS surface derivative bound Dir function discrete B-spline

Option Pricing by Mean Correcting Method for Non-Gaussian Lvy Processes

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Acta Mathematica Sinica,English Series 2013年第10期29卷 1927-1938页

作者： Luo Gen YAO Gang YANG Xiang Qun YANG School of mathematics and Statistics Hu'nan Business College College of mathematics and Computer Science Hu'nan Normal University

For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivial, this pricing method may lead to arbitrage in some cases. In the latter case, some necessary and sufficient conditions under which option price is arbitrage-free are obtained.

关键词： Non-Gaussian Levy processes mean correcting method option pricing

Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations

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Journal of Systems Science & Complexity 2023年第6期36卷 2703-2724页

作者： XIAO Shuijing ZENG Guangxing department of mathematics Nanchang UniversityNanchang330031China

In this paper,the notion of rational univariate representations with variables is ***,the ideals,created by given rational univariate representations with variables,are *** merit of these created ideals is that some of their algebraic properties can be easily *** the aid of the theory of valuations,some related results are *** on these results,a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.

关键词： Polynomial ideal rational univariate representation(RUR) valuation ring Wu's method

Dynamics of solitons of the generalized(3+1)-dimensional nonlinear Schr(o|¨)dinger equation with distributed coefficients

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Chinese Physics B 2011年第11期20卷 339-345页

作者：刘晓蓓李彪 Nonlinear Science Center and department of mathematics Ningbo University

We present three families of soliton solutions to the generalized （3＋l）-dimensional nonlinear Schrodinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.

关键词： (3+l)-dimensional nonlinear Schodinger Equation optical soliton soliton propagation

Almost sure central limit theorems for random functions

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Science China mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU Jin & XU Jianjun School of mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China department of mathematics, Zhejiang University, Hangzhou 310028, China School of mathematics and Statistics Zhejiang University of Finance and Economics Hangzhou China department of mathematics Zhejiang University Hangzhou China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞ent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| entral limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

Approximate solutions to MHD Falkner-Skan flow over permeable wall

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Applied mathematics and Mechanics(English Edition) 2011年第4期32卷 401-408页

作者：苏晓红郑连存 department of mathematics and Mechanics University of Science and Technology Beijing department of mathematics and Physics North China Electric Power University

The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.

关键词： Falkner-Skan similarity solution magnetohydrodynamic (MHD) boundary layer flow differential transform method (DTM)

On the Well-Posedness for Stochastic Schrodinger Equations with Quadratic Potential

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Chinese Annals of mathematics,Series B 2011年第5期32卷 711-728页

作者： Daoyuan FANG Linzi ZHANG Ting ZHANG department of mathematics Zhejiang University Hangzhou 310027 China Corresponding author. department of mathematics Zhejiang University Hangzhou 310027 China Corresponding author. Department of Mathematics Zhejiang University Hangzhou 310027 China Corresponding author. Department of Mathematics Zhejiang University Hangzhou 310027 China Corresponding author. Department of Mathematics Zhejiang University Hangzhou 310027 China Corresponding author. Department of Mathematics Zhejiang University Hangzhou 310027 China Corresponding author. Department of Mathematics Zhejiang University Hangzhou 310027 China

The authors investigate the influence of a harmonic potential and random perturbations on the nonlinear Schr6dinger equations. The local and global well-posedness are proved with values in the space ∑（R^n）={f E HI（R^n）, ｜·｜f ∈ L^2（R^n）}. When the nonlinearity is focusing and L2-supercritical, the authors give sufficient conditions for the solutions to blow up in finite time for both confining and repulsive potential. Especially for the repulsive case, the solution to the deterministic equation with the initial data satisfying the stochastic blow-up condition will also blow up in finite time. Thus, compared with the deterministic equation for the repulsive case, the blow-up condition is stronger on average, and depends on the regularity of the noise. If φ = 0, our results coincide with the ones for the deterministic equation.

关键词： Stochastic SchrSdinger equation Well-posedness Blow up

A RISK-AVERSE NEWSVENDOR MODEL WITH LIMITED CAPACITY AND OUTSOURCING UNDER THE CVAR CRITERION

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Journal of Systems Science and Systems Engineering 2015年第1期24卷 49-67页

作者： Zhenwei Luo Jinting Wang Wanting Chen department of mathematics School of ScienceBeijing Jiaotong University

For seasonal products, the retailers usually launch various marketing ettorts, llKe aaverusmg tmu promotion, to promote them in a selling season. While facing large demand from the customers, one should take the capacity constraint and outsotlrcing into consideration. Considering the shorten life cycles of most products, in this paper we adopt the traditional newsvendor model to investigate the optimal marketing effort along with optimal order quantity. We address the risk aversion issue and characterize the influence of the sellers＇ risk propensity with CVaR criterion, and we develop an effective algorithm to obtain the optimal strategy. The impact of sellers＇ risk propensity on the performance of the system is illustrated via numerical examples, The innovation of this paper is threefold. First, the optimal joint strategy of the marketing effort and order quantity is investigated and an efficient algorithm to find the optimal strategy is developed. Second, the capacity constraint option and an outsourcing strategy are studied jointly for excess products. Finally, the risk propensity of the seller and its influence are investigated by using the CVaR criterion, through which we obtain some new managerial insights.

关键词： Newsvendor model marketing effort order quantity CVaR capacity constraint,outsourcing