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An explicit solution for a Series and Parallel Queue with Retrial,Losses,and Bernoulli Schedule

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Journal of the Operations Research Society of China 2016年第1期4卷 121-129页

作者： Shi-Zhong Zhou Li-Wei Liu Jian-Jun Li Department of Statistics and Financial Mathematics School of ScienceNanjing University of Science and TechnologyNanjing 210094China

This paper deals with the series and parallel queueing system in which there are two servers whose service time follow two exponential *** arriving customer either enters into the tandem service with probability or joins the service of the single server with complementary *** assume that the customers of arriving at the first server who find the first server is busy join an orbit and retry to enter the server after some time and of arriving at the second server who find the second server is busy are *** this model,we obtain the explicit expressions of the joint stationary distribution between the number of customers in the orbit and the states of the servers.

关键词： Series and parallel queue Retrial Bernoulli schedule explicit solution Hypergeometric function

THE explicit solution OF HOMOGENEOUS LINEAR ORDINARY DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

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Applied Mathematics and Mechanics(English Edition) 1992年第12期13卷 1115-1120页

作者：黄永念 Department of Mechanics Peking University Beijing

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients. In fact, we give the general formula for calculating the elements of the matrix exp[At] . We also give the results when the characteristic equation has the repeated roots. The present method is simpler and better than the other methods.

关键词： tensor differential equation characteristic tensor explicit solution

The explicit solution to Equation AX ＋ X B = C in Matrices

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Chinese Quarterly Journal of Mathematics 2009年第4期24卷 516-524页

作者： YOU Xing-hua MA Sheng-rong YAN Shi-jian Department of Basic Courses Nanjing Institute of Technology Nanjing 211167 China Department of Mathematics Nanjing Xiaozhuang College Nanjing 210017 China College of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China

Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical ex... 详细信息

关键词： matrix equation g-inverse explicit solution formulae Jordan canonical form 2000 MR Subject Classification: 15A24, 65F10

The Baicklund Transformation and explicit solution of Volterra Lattice Equation

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Chinese Quarterly Journal of Mathematics 2010年第1期25卷 81-85页

作者： WU Yong-qi College of Mathematics and Computer Science Zhanjiang Normal University Zhanjiang 524048China

The Backlund transformation and the generalized Miura transformation for the Volterra lattice equation are constructed by using point symmetry method. As an application, the explicit solution to the lattice equation i... 详细信息

关键词： Backlund transformation Miura transformation Volterra lattice equation explicit solution

Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations

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Communications in Theoretical Physics 2024年第5期76卷 1-15页

作者： Alemu Yilma Tefera Shangshuai Li Da-jun Zhang Department of Mathematics Shanghai UniversityShanghai 200444China Newtouch Center for Mathematics of Shanghai University Shanghai 200444China Department of Applied Mathematics Faculty of Science and EngineeringWaseda UniversityTokyo 169-8555Japan

This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable *** the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated *** this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit *** equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral *** solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex *** solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

关键词： Cauchy matrix approach Sylvester equation nonlinear Schrödinger equation non-isospectral integrable system explicit solution

explicit solutions to some nonlinear physical models by a two-step ansatz

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Chinese Physics B 2008年第8期17卷 2774-2782页

作者：胡建兰 College of Applied Science Beijing University of Technology

explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.

关键词： explicit solution nonlinear physical model two-step ansatz method

explicit solutions for a New (2+1)-Dimensional Coupled mKdV Equation

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Communications in Theoretical Physics 2008年第2期49卷 396-400页

作者： WANG Zheng-Yan ZHANG Jin-Shun Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Mathematics Huaqiao University Quanzhou 362021 China

An integrable （2＋1）-dimensional coupled mKdV equation is decomposed into two （1 ＋1）-dimensional soliton systems, which is produced from the compatible condition of three spectral problems. With the help of decomposition and the Darboux transformation of two （1＋1）-dimensional soliton systems, some interesting explicit solutions of these soliton equations are obtained.

关键词： soliton Darboux transformation explicit solution

explicit solutions for a (2+1)-Dimensional Toda Lattice with Two Discrete Variables

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Communications in Theoretical Physics 2007年第10期48卷 667-670页

作者： WANG Zheng-Yan YANG Xiao Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China Department of Mathematics Zhengzhou University Zhengzhou 450052 China

An integrable(2+1)-dimensional Toda lattice with two discrete variables is investigated again,which isproduced from a compatible condition of the Lax *** Darboux transformation for its spectral problems is *** an appl... 详细信息

关键词： Toda lattice two discrete variables Darboux transformation explicit solution

explicit solutions for a class of nonlinear BSDEs and their nodal sets

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Probability, Uncertainty and Quantitative Risk 2022年第4期7卷 283-300页

作者： Zengjing Chen Shuhui Liu Zhongmin Qian Xingcheng Xu School of Mathematics Shandong UniversityJinan 250100China Mathematical Institute University of OxfordOxford OX26GGUnited Kingdom School of Mathematical Sciences Peking UniversityBeijing 100871China Shanghai AI Laboratory Shanghai 200032China

In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding ***,we are able to obtain explicit solutions to an interesting class of nonlinear BSDEs,including the k-ignorance BSDE arising from the modeling of ambiguity of asset ***,we show its applications in PDEs and contingent pricing in an incomplete market.

关键词： explicit solution Feynman-Kac formula Girsanov’s formula Nodal set Nonlinear BSDE Parabolic equation Tanaka’s formula.