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On the growth of transcendental entire solutions of algebraic differential equations 被引量:2
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作者 朱玲妹 杨德贵 王小灵 《Journal of Southeast University(English Edition)》 EI CAS 2003年第1期98-102,共5页
In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where ... In this paper, we investigate the growth of transcendental entire solutionsof the following algebraic differential equation a(z)f'~2 +(b_2(z)f^2 +b_1(z)f +b_0(z))f'=d_3(z)f^3+d_2(z)f^2 +d_1(z)f +d_0(z), where a(z), b_i(z) (0<- i <=2) and d_j (z) (0<=j<= 3) are allpolynomials, and this equation relates closely to the following well-known algebraic differentialequation C(z,w)w'~2 + B(z,w)w' + A(z,w) =0, where G(z,w)not ident to 0, B(z,w) and A(z,w) are threepolynomials in z and w. We give relationships between the growth of entire solutions and the degreesof the above three polynomials in detail. 展开更多
关键词 algebraic differential equation DEGREE entire solutions
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THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS 被引量:19
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期932-938,共7页
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations... We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations. 展开更多
关键词 Growth order algebraic differential equations entire function
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ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS 被引量:6
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作者 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期459-465,共7页
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.
关键词 the growth algebraic differential equations algebroid solutions
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Generalized Higher-Order Algebraic Differential Equations with Admissible Algebroid Solutions 被引量:4
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作者 高凌云 《Northeastern Mathematical Journal》 CSCD 2001年第2期159-168,共10页
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
关键词 algebroid functions admissible solution generalized higher order algebraic differential equations.
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On the Order of the Solutions of Systems of Complex Algebraic Differential Equations 被引量:1
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作者 SU Xian-feng GAO Ling-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期196-199,共4页
This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
关键词 normal family order systems of complex algebraic differential equations
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ON HYPER-ORDER OF MEROMORPHIC SOLUTIONS OF FIRST-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 李叶舟 冯绍继 《Acta Mathematica Scientia》 SCIE CSCD 2001年第3期383-390,共8页
The authors give a precise estimate of the hyper-order of meromorphic solutions of general first-order algebraic differential equations.
关键词 algebraic differential equation meromorphic solution HYPER-ORDER ZERO POLE
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GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 李叶舟 戚建明 袁文俊 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期105-111,共7页
In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give ... In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases. 展开更多
关键词 the normal family theory algebraic differential equations meromorphic solutions GROWTH
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A NEW ALGORITHM FOR SOLVING DIFFERENTIAL/ALGEBRAIC EQUATIONS OF MULTIBODY SYSTEM DYNAMICS
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作者 王艺兵 赵维加 潘振宽 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第9期905-912,共8页
The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding disc... The second order Euler-Lagrange equations are transformed to a set of first order differential/algebraic equations, which are then transformed to state equations by using local parameterization. The corresponding discretization method is presented, and the results can be used to implementation of various numerical integration methods. A numerical example is presented finally. 展开更多
关键词 multibody systems differential/algebraic equations numerical analysis
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A NOTE ON MALMQUIST-YOSIDA TYPE THEOREM OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS
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作者 张建军 廖良文 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期471-478,共8页
In this article, we give a simple proof of Malmquist-Yosida type theorem of higher order algebraic differential equations, which is different from the methods as that of Gackstatter and Laine [2], and Steinmetz [12].
关键词 Malmquist-Yosida type theorem algebraic differential equations meromorphicsolutions
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On the Counting Functions of Meromorphic Solutions of Systems of Higher-order Algebraic Differential Equations
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作者 CHEN Miao-ling GAO Ling-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期7-10,共4页
Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equatio... Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results. 展开更多
关键词 meromorphic solution algebraic differential equations counting function
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ALGEBRAIC DIFFERENTIAL INDEPENDENCE CONCERNING THE EULER Γ-FUNCTION AND DIRICHLET SERIES
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作者 Wei CHEN Qiong WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1035-1044,共10页
This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class... This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1. 展开更多
关键词 Gamma function L-FUNCTIONS algebraic differential independence algebraic differential equations
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On Results the Growth of Meromorphic Solutions of Algebraic Diferential Equations
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作者 Su Xian-feng Li Xiao-meng +1 位作者 He Zhong-wei Ji You-qing 《Communications in Mathematical Research》 CSCD 2013年第4期345-350,共6页
In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the correspon... In this paper, we give an estimate result of Gol'dberg's theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. (Yuan W J, Xiao B, Zhang J J. The general theorem of Gol'dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58:1788 1791). Meanwhile, we also take some examples to show that our estimate is sharp. 展开更多
关键词 meromorphic function algebraic differential equation normal family spherical derivative
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Liouvillian Solutions of Algebraic Ordinary Differential Equations of Order One of Genus Zero
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作者 NGUYEN Tri Dat NGO Lam Xuan Chau 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第2期884-893,共10页
This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C... This paper considers the class of autonomous algebraic ordinary differential equations(AODEs)of order one,and studies their Liouvillian general solutions.In particular,let F(y,w)=0 be a rational algebraic curve over C.The authors give necessary and sufficient conditions for the autonomous first-order AODE F(y,y′)=0 to have a Liouvillian solution over C.Moreover,the authors show that a Liouvillian solutionαof this equation is either an algebraic function over C(x)or an algebraic function over C(exp(ax)).As a byproduct,these results lead to an algorithm for determining a Liouvillian general solution of an autonomous AODE of order one of genus zero.Rational parametrizations of rational algebraic curves play an important role on this method. 展开更多
关键词 algebraic ordinary differential equation autonomous differential equation Liouvillian solution rational algebraic curve rational parametrizations
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Numerical Solution of Constrained Mechanical System Motions Equations and Inverse Problems of Dynamics 被引量:2
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作者 R.G. Muharliamov (Russian Peoples’ Friendship University, 117198, Moscow, Mikluho Maklaya,6,Russia.) 《应用数学》 CSCD 北大核心 2001年第2期103-119,共17页
In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarant... In this paper the method of design of kinematical and dynamical equations of mechanical systems, applied to numerical ealization, is proposed. The corresponding difference equations, which are obtained, give a guarantee of computations with a given precision. The equations of programmed constraints and those of constraint perturbations are defined. The stability of the programmed manifold for numerical solutions of the kinematical and dynamical equations is obtained by corresponding construction of the constraint perturbation equations. The dynamical equations of system with programmed constraints are set up in the form of Lagrange’s equations in generalized coordinates. Certain inverse problems of rigid body dynamics are examined. 展开更多
关键词 Kinematies Dynamical equations CONSTRAINTS Lagrange’s equations Rigid body Numerical solution differential algebraic equations
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ON THE DIFFERENTIAL AND DIFFERENCE INDEPENDENCE OFΓANDζ
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作者 Wei CHEN Qiong WANG 《Acta Mathematica Scientia》 SCIE CSCD 2021年第2期505-516,共12页
In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function... In this paper,we study the algebraic differential and the difference independence between the Riemann zeta function and the Euler gamma function.It is proved that the Riemann zeta function and the Euler gamma function cannot satisfy a class of nontrivial algebraic differential equations and algebraic difference equations. 展开更多
关键词 algebraic differential equations difference equations the Euler gamma function the Riemann zeta function
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Towards a Unified Single Analysis Framework Embedded with Multiple Spatial and Time Discretized Methods for Linear Structural Dynamics
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作者 David Tae Kumar K.Tamma 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第5期843-885,共43页
We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatia... We propose a novel computational framework that is capable of employing different time integration algorithms and different space discretized methods such as the Finite Element Method,particle methods,and other spatial methods on a single body sub-dividedintomultiple subdomains.This is in conjunctionwithimplementing thewell known Generalized Single Step Single Solve(GS4)family of algorithms which encompass the entire scope of Linear Multistep algorithms that have been developed over the past 50 years or so and are second order accurate into the Differential Algebraic Equation framework.In the current state of technology,the coupling of altogether different time integration algorithms has been limited to the same family of algorithms such as theNewmarkmethods and the coupling of different algorithms usually has resulted in reduced accuracy in one or more variables including the Lagrange multiplier.However,the robustness and versatility of the GS4 with its ability to accurately account for the numerical shifts in various time schemes it encompasses,overcomes such barriers and allows a wide variety of arbitrary implicit-implicit,implicit-explicit,and explicit-explicit pairing of the various time schemes while maintaining the second order accuracy in time for not only all primary variables such as displacement,velocity and acceleration but also the Lagrange multipliers used for coupling the subdomains.By selecting an appropriate spatialmethod and time scheme on the area with localized phenomena contrary to utilizing a single process on the entire body,the proposed work has the potential to better capture the physics of a given simulation.The method is validated by solving 2D problems for the linear second order systems with various combination of spatial methods and time schemes with great flexibility.The accuracy and efficacy of the present work have not yet been seen in the current field,and it has shown significant promise in its capabilities and effectiveness for general linear dynamics through numerical examples. 展开更多
关键词 Time integration structural dynamics multiple scale and multiple methods ordinary differential equations differential algebraic equations
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Transcendental Meromorphic Solutions of Second-Order Algebraic Differential Equations 被引量:5
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作者 Hai Chou LI Ling Yun GAO 《Journal of Mathematical Research and Exposition》 CSCD 2011年第3期497-502,共6页
Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some re... Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors. 展开更多
关键词 meromorphic functions transcendental meromorphic solutions second-order algebraic differential equations.
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Rational Solutions of High-Order Algebraic Ordinary Differential Equations
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作者 VO Thieu N. ZHANG Yi 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2020年第3期821-835,共15页
This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational solutions.The authors first prove a sufficient condition for the existence of a bound on the degree of the p... This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational solutions.The authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an AODE.An AODE satisfying this condition is called noncritical.Then the authors prove that some common classes of low-order AODEs are noncritical.For rational solutions,the authors determine a class of AODEs,which are called maximally comparable,such that the possible poles of any rational solutions are recognizable from their coefficients.This generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading coefficient.Finally,the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs,which is applicable to 78.54%of the AODEs in Kamke's collection of standard differential equations. 展开更多
关键词 algebraic ordinary differential equations ALGORITHMS polynomial solutions rational solutions
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Admissible Meromorphic Solutions of a Type of Higher-Order Algebraic Differential Equation 被引量:1
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作者 高凌云 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第3期443-448,共6页
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the form of a type of algebraic differential equation with admissible meromorphic solutions and obtain a Malmquist type theorem.
关键词 meromorphic admissible solutions algebraic differential equations finite accumulations.
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Descent of Ordinary Differential Equations with Rational General Solutions 被引量:1
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作者 FENG Shuang FENG Ruyong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2020年第6期2114-2123,共10页
Let F be an irreducible differential polynomial over k(t)with k being an algebraically closed field of characteristic zero.The authors prove that F=0 has rational general solutions if and only if the differential alge... Let F be an irreducible differential polynomial over k(t)with k being an algebraically closed field of characteristic zero.The authors prove that F=0 has rational general solutions if and only if the differential algebraic function field over k(t)associated to F is generated over k(t)by constants,i.e.,the variety defined by F descends to a variety over k.As a consequence,the authors prove that if F is of first order and has movable singularities then F has only finitely many rational solutions. 展开更多
关键词 algebraic ordinary differential equation differential descent rational general solution
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