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recursion formulae for Obtaining Surfaces with Constant MeanCurvature inR^2,1

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Communications in Theoretical Physics 2007年第2期47卷 203-208页

作者： TIAN Yong-Bo NAN Zhi-Jie TIAN Chou Department of Mathematics University of Science and Technology. of China Hefei 230026China

Though the Bǎcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Bǎcklund transformation is used, For sake of this, in this article, some special work is done to reform the Bǎcklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.

关键词： Bǎcklund transformation time-like surfaces with mean curvature Lax pairs recursion formula

Construction of recursion formulas for Lax Pairs of (2+1)-Dimensional Equation: Modified Generalized Dispersive Long Wave Equation

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Communications in Theoretical Physics 2004年第6期41卷 807-812页

作者： TIANYong-Bo CHENGYi SHAONan DepartmentofMathematics UniversityofScienceandTechnologyofChinaHefei230026China DepartmentofChemistry UniversityofScienceandTechnologyofChinaHefei230026China

In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.

关键词： Lax pairs modified generalized dispersive long wave equation recursion formula solutions

DOUBLE-MARKOV RISK MODEL

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Acta Mathematica Scientia 2013年第2期33卷 333-340页

作者：莫晓云周杰明欧辉杨向群 College of Mathematics and Computer Science Hunan Normal University Hunan University of Finance and Economics College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Education Ministry of China)Hunan Normal University

Given a new Double-Markov risk model DM = （μ, Q, v, H; Y, Z） and Double-Markov risk process U = {U（t）, t 〉 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.

关键词： Q process Markov chain Double-Markov risk characterization survival prob-ability recursion formula

A Unified Model of All Generalizations from the Jones Polynomial

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Communications in Theoretical Physics 2001年第4期35卷 431-434页

作者： QIANShang－Wu GUZhi－Yu 等 DepartmentofPhysics PekingUniversityBeijing100871China DepartmentofPhysics CapitalNormalUniversityBeijing100037China

From the basic properties of skein systems, we build a generalized tangle algebra (GTA). The elements of GTA are four basic tangles. There are three operations, which are connection, splicing and scalar multiplication. From GTA we derive two generalized recursion formulae (GRF) and prove the existence of a generalized skein relation which satisfies GRF. The obtained generalized skein relation epitomizes all generalizations from the Jones polynomial and thus forms a unified model. Two important topological parameters, twisting measure and loop values, appear explicitly in the expressions of the unified model, and this fact greatly simplifies the operations.

关键词： Jones polynomial skein relation tangle algebra recursion formula

formulas to Solve the （2＋1）—Dimensional System：The （2＋1）—Extension of Classical Boussinesq System

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Communications in Theoretical Physics 2001年第5期35卷 519-522页

作者： TIANYong－Bo CHENGYi 等 DepartmentofMathematics UniversityofScienceandTechnologyofChinaHefei230026China

We deal with the (2 + 1)-extension of classical Boussinesq system,which can reduce to several meaningful(1 + 1)-dimensional *** studying its Lax pair,we put forward invariances of Lax pair at first,then a recursionformula depending on an arbitrary function is *** last,some solutions of the (2 + 1)-extension of classicalBoussinesq system are digged out by using the formula.

关键词： 2+1-extension system Lax pair recursion formula

Some formulas Involving Hypergeometric Functions in Four Variables

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维普期刊数据库

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Computer Modeling in Engineering & Sciences 2022年第2期130卷 887-902页

作者： Hassen Aydi Ashish Verma Jihad Younis Jung Rye Lee Universit´e de Sousse Institut Sup´erieur D’Informatique etDes Techniques de CommunicationH.Sousse4000Tunisia Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences UniversityGa-RankuwaSouth Africa ChinaMedical University Hospital ChinaMedical UniversityTaichung40402Taiwan Department of Mathematics V.B.S.Purvanchal UniversityJaunpur222003India Department of Mathematics Aden UniversityKhormaksarP.o.Box 6014Yemen Department of Data Science Daejin UniversityKyunggi11159Korea

Several(generalized)hypergeometric functions and a variety of their extensions have been presented and investigated in the literature by many *** the present paper,we investigate four new hypergeometric functions in four variables and then establish several recursion formulas for these new ***,some interesting particular cases and consequences of our results are discussed.

关键词： recursion formula quadruple hypergeometric functions pascal identity

Generalizations of Euler Numbers and Euler Numbers of Higher Order

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Chinese Quarterly Journal of Mathematics 2005年第1期20卷 54-58页

作者： LUOQiu-ming QIFeng DepartmentofMathematics JiaozuoUniversityJiaozuo454003China DepartmentofAppliedMathematicsandInformationScience HenanPolytechnicUniversityJiaozuo454001China

The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler... 详细信息

关键词： Euler numbers higher order Euler numbers generalized Euler numbers generalized higher order Euler numbers recursion formula

HURWITZ-HODGE INTEGRAL IDENTITIES FROM THE ORBIFOLD MARIO-VAFA formula

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Acta Mathematica Scientia 2016年第1期36卷 139-156页

作者：赵晨 School of Mathematical Sciences Center of Mathematical Sciences Zhejiang UniversityHangzhou 310027 China

In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion f... 详细信息

关键词： Hurwitz-Hodge integral orbifold Marifio-Vafa formula polynomial identities recursion formula

Generalized Series of Bernoulli Type

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Advances in Pure Mathematics 2023年第9期13卷 537-542页

作者： Thomas Beatty Nicholas Bianco Nicole Legge Department of Mathematics Florida Gulf Coast University Fort Myers FL USA

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

关键词： Bernoulli Series Convergence Sum recursion formula Zeta-Function Sine Maclaurin Series Infinite Product