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Solutions of three-body problem based on an equivalent system approach 认领 引用 被引量：1
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作者 Jing Tang Xing 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第1期292-309,共18页
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund... Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems. 展开更多
关键词 Three-body problem Equivalent system with solutions Orbit-equation of a conic section Generalised reduced mass Chaotic motions Generalised Kepler’s law N-body problem
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GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES 认领 引用 被引量：1
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作者 唐金芳 张石生 刘敏 《Acta Mathematica Scientia》 SCIE CSCD 2016年第2期602-613,共12页
The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converge... The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results. 展开更多
关键词 General split feasibility problems nonexpansive mappings Hilbert space strong convergence
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ON HILBERT BOUNDARY VALUE PROBLEMS WITH RADICAL 认领 引用 被引量：6
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作者 路见可 《Acta Mathematica Scientia》 SCIE 2005年第4期755-760,共6页
The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t）... The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L. 展开更多
关键词 Hilbert boundary value problem index class h0 Plemelj formula normalized canonical function
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Green’s Functions of a Class of Sturm-Liouville Problems with Eigenparameters in Boundary Conditions 认领 引用
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作者 XIAO Lu MU Dan ZHANG Ruifan 《数学理论与应用》 2025年第1期94-106,共13页
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil... In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem. 展开更多
关键词 Sturm-Liouville problem Eigenparameter-dependent boundary condition Green’s function
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A Class of Quasi-Linear Riemann-Hilbert Problems for General Holomorphic Functions in the Unit Disk 认领 引用 被引量：1
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作者 Xiao-qin Wen Ming-zhong Li 《Advances in Manufacturing》 EI CAS 2000年第4期270-274,共5页
In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this prob... In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this problem was proved by means of Tikhonov's fixed point theorem and corresponding theories for general holomorphic functions. 展开更多
关键词 quasi linear Riemann Hilbert problems fixed point existence theo
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On Solving a System of Generalized Mixed Equilibrium-like Problems in Hilbert Spaces 认领 引用
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作者 LIU Bang-tao LUO Min 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第2期180-189,共10页
A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.
关键词 equilibrium-like problem auxiliary principle iterative algorithm Hilbert space
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(S,T)-WEAK TRACTABILITY OF MULTIVARIATE LINEAR PROBLEMS IN THE AVERAGE CASE SETTING 认领 引用 被引量：2
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作者 Yongping LIU Guiqiao XU 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期1033-1052,共20页
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function... The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem. 展开更多
关键词 (s, t)-weak tractability linear problem linear tensor product problem Hilbert space average case setting
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THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS 认领 引用 被引量：2
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作者 司中伟 杜金元 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期393-403,共11页
Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati... Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated. 展开更多
关键词 Generalized analytic function Hilbert boundary value problem H^u function
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ON THE EXISTENCE OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS OF DUFFING TYPE SYSTEMS 认领 引用 被引量：1
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作者 黄文华 沈祖和 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第8期971-976,共6页
Several existence results of solutions of two-point boundary value problems of Duffing type systems with Dirichlet boundary conditions, Neumann boundary conditions and periodic boundary conditions are presented.
关键词 Hilbert space system of differential equations two-point boundary value problem solution
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HILBERT PROBLEM 15 AND NONSTANDARD ANALYSIS(Ⅰ) 认领 引用 被引量：3
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作者 Banghe LJ 《Acta Mathematica Scientia》 SCIE CSCD 2020年第1期1-15,共15页
Hilbert problem 15 required understanding Schubert's book.In this book,reducing to degenerate cases was one of the main methods for enumeration.We found that nonstandard analysis is a suitable tool for making rigo... Hilbert problem 15 required understanding Schubert's book.In this book,reducing to degenerate cases was one of the main methods for enumeration.We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results,which used degeneration method,but are obviously not rigorous.In this paper,we give a rigorous proof for Example 4 in Schubert's book,Chapter 1.§4 according to his idea.This shows that Schubert's intuitive idea is correct,but to make it rigorous a lot of work should be done. 展开更多
关键词 Hilbert problem 15 nonstandard analysis enumeration geometry
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A RIEMANN-HILBERT APPROACH TO THE INITIAL-BOUNDARY PROBLEM FOR DERIVATIVE NONLINEAR SCHRDINGER EQUATION 认领 引用 被引量：6
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作者 徐建 范恩贵 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期973-994,共22页
We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it ca... We use the Fokas method to analyze the derivative nonlinear Schrodinger （DNLS） equation iqt （x, t） = -qxx （x, t）＋（rq^2）x on the interval [0, L]. Assuming that the solution q（x, t） exists, we show that it can be represented in terms of the solution of a matrix Riemann- Hilbert problem formulated in the plane of the complex spectral parameter ξ. This problem has explicit （x, t） dependence, and it has jumps across {ξ∈C｜Imξ^4 = 0}. The relevant jump matrices are explicitely given in terms of the spectral functions {a（ξ）, b（ξ）}, {A（ξ）, B（ξ）}, and {A（ξ）, B（ξ）}, which in turn are defined in terms of the initial data q0（x） = q（x, 0）, the bound- ary data g0（t）= q（0, t）, g1（t） = qx（0, t）, and another boundary values f0（t） = q（L, t）, f1（t） = qx（L, t）. The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. 展开更多
关键词 Riemann-Hilbert problem DNLS equation, global relation finite interval initial-boundary value problem
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Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients 认领 引用 被引量：1
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作者 Xiaojing LIU Youhe ZHOU Jizeng WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第6期863-882,共20页
The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolati... The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions. 展开更多
关键词 wavelet multiresolution interpolation transcendental nonlinearity localized steep gradient singularly perturbed boundary value problem Troesch’s problem
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Two Kinds of Contact Problems in Dodecagonal Quasicrystals of Point Group 12 mm 认领 引用 被引量：8
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作者 Xuefen Zhao Xing Li Shenghu Ding 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2016年第2期167-177,共11页
In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact pr... In this paper,two kinds of contact problems in 2-D dodecagonal quasicrystals were discussed using the complex variable function method：one is the finite frictional contact problem,the other is the adhesive contact problem.The analytic expressions of contact stresses in the phonon and phason fields were obtained for a flat rigid punch,which showed that：（1） for the finite frictional contact problem,the contact stress exhibited power-type singularities at the edge of the contact zone;（2） for the adhesive contact problem,the contact stress exhibited oscillatory singularities at the edge of the contact zone.The distribution regulation of contact stress under punch was illustrated;and the low friction property of quasicrystals was verified graphically. 展开更多
关键词 2-D dodecagonal quasicrystals contact problem singularity Riemann-Hilbert problem
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Spline Fictitious Boundary Element Alternating Method for Edge Crack Problems with Mixed Boundary Conditions 认领 引用 被引量：1
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作者 Z.Xu M.Chen X.M.Fan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2018年第9期407-431,共25页
The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which... The alternating method based on the fundamental solutions of the infinite domain containing a crack,namely Muskhelishvili’s solutions,divides the complex structure with a crack into a simple model without crack which can be solved by traditional numerical methods and an infinite domain with a crack which can be solved by Muskhelishvili’s solutions.However,this alternating method cannot be directly applied to the edge crack problems since partial crack surface of Muskhelishvili’s solutions is located outside the computational domain.In this paper,an improved alternating method,the spline fictitious boundary element alternating method(SFBEAM),based on infinite domain with the combination of spline fictitious boundary element method(SFBEM)and Muskhelishvili’s solutions is proposed to solve the edge crack problems.Since the SFBEM and Muskhelishvili’s solutions are obtained in the framework of infinite domain,no special treatment is needed for solving the problem of edge cracks.Different mixed boundary conditions edge crack problems with varies of computational parameters are given to certify the high precision,efficiency and applicability of the proposed method compared with other alternating methods and extend finite element method. 展开更多
关键词 Spline fictitious boundary element alternating method mixed boundary conditions edge crack problem Muskhelishvili’s solutions stress intensity factor
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EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS 认领 引用 被引量：1
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作者 Alberto CABADA Nikolay D.DIMITROV 《Acta Mathematica Scientia》 SCIE CSCD 2017年第4期911-926,共16页
This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to t... This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories. 展开更多
关键词 Dirichlet boundary value problem nonlocal perturbations Green＇s function parameter dependence
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NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS 认领 引用 被引量：1
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作者 陈绍春 郑艳君 毛士鹏 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期815-825,共11页
In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the d... In the use of finite element methods to the planar elasticity problems,one diffculty is to overcome locking when elasticity constant λ→∞.In the case of traction boundary condition,another diffculty is to make the discrete Korn＇s second inequality valid.In this paper,a triangular element is presented.We prove that this element is locking-free,the discrete Korn＇s second inequality holds and the convergence order is two. 展开更多
关键词 planar elasticity problems pure displacement and traction boundary conditions nonconforming finite element discrete Korn’s second inequality
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Generalized Strongly Nonlinear Quasi-Complementarity Problems 认领 引用 被引量：2
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作者 李红梅 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第4期307-315,共9页
Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou... Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem. 展开更多
关键词 generalized strongly nonlinear quasi-complementarity problem,Hilbert space cone. H-Lipschitz continuous mapping with re-spect to g ψ-strongly monotone mapping with respect to g
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EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS 认领 引用 被引量：3
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作者 龚循华 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1179-1192,共14页
In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we der... In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set. 展开更多
关键词 Ekeland＇s principle set-valued vector equilibrium problems weakly efficient solution c-approximate solution existence
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RIEMANN BOUNDARY VALUE PROBLEMS WITH GIVEN PRINCIPAL PART 认领 引用 被引量：2
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作者 李卫峰 杜金元 《Acta Mathematica Scientia》 SCIE 2009年第1期25-32,共8页
In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they ... In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable. 展开更多
关键词 Riemann boundary value problems principal part Riemann-Hilbert analysis for orthogonal polynomials
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A Sparse Kernel Approximate Method for Fractional Boundary Value Problems 认领 引用 被引量：1
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作者 Hongfang Bai Ieng Tak Leong 《Communications on Applied Mathematics and Computation》 2023年第4期1406-1421,共16页
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W04[0,1] and W1[... In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W04[0,1] and W1[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs. 展开更多
关键词 Weak pre-orthogonal adaptive Fourier decomposition(W-POAFD) Weak maximal selection principle Fractional boundary value problems(FBVPs) Reproducing kernel Hilbert space(RKHs)
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