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Stability for basic system of equations of atmospheric rhotion 被引量:2
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作者 施惟慧 徐明 王曰朋 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第2期261-268,共8页
The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate s... The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about "speculating future from past" in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations. 展开更多
关键词 basic system of equations of atmospheric motion STABILITY stratificationtheory transversal stratum
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A CLOSED SYSTEM OF EQUATIONS FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS OF SHEARING STRESS OF DISPERSED PHA’E AT A WALL
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作者 林多敏 蔡树棠 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第8期679-687,共9页
Inthis paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow arc described in Eulerian form. The generalized constitutive relation of... Inthis paper, each of the two phases in dense two-phase flow is considered as continuous medium and the fundamental equations for two-phase flow arc described in Eulerian form. The generalized constitutive relation of the Bingham fluid is applied to the dispersed phase with the analysis oj physical mechanism of dense two-phase flow. The shearing stress of dispersed phase at a wall is used to give a boundary condition. Then a mathematical model for dense two-phase flow is obtained. In addition, the expressions of shearing stress of dispersed phase at a wall is derived according to the fundamental model of the friclional collision between dispersed-plutse particles and the wall. 展开更多
关键词 E AT A WALL A CLOSED system of equations FOR DENSE TWO-PHASE FLOW AND EXPRESSIONS of SHEARING STRESS of DISPERSED PHA
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MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS 被引量:5
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作者 李海绸 高凌云 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期195-206,共12页
Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference... Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj(z)f1(λj1)(z+cj)=R2(z,f2(z)),j=1∑nβj(z)f2(λj2)(z+cj)=R1(z,f1(z)). where λij (j = 1, 2,…, n; i = 1, 2) are finite non-negative integers, and cj (j = 1, 2,… , n) are distinct, nonzero complex numbers, αj(z), βj(z) (j = 1,2,… ,n) are small functions relative to fi(z) (i =1, 2) respectively, Ri(z, f(z)) (i = 1, 2) are rational in fi(z) (i =1, 2) with coefficients which are small functions of fi(z) (i = 1, 2) respectively. 展开更多
关键词 growth order system of equations complex differential equations difference equations Nevanlinna theory value distribution
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SPECTRAL DY-TYPE PROJECTION METHOD FOR NONLINEAR MONOTONE SYSTEM OF EQUATIONS 被引量:2
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作者 Jinkui Liu Shengjie Li 《Journal of Computational Mathematics》 SCIE CSCD 2015年第4期341-355,共15页
In this paper, we propose a spectral DY-type projection method for nonlinear mono- tone system of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the proj... In this paper, we propose a spectral DY-type projection method for nonlinear mono- tone system of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differen- tiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method. 展开更多
关键词 Nonlinear monotone system of equations spectral gradient method DY conjugate gradient method Projection method Global convergence.
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THE NUMERICAL METHODS FOR SOLVING EULER SYSTEM OF EQUATIONS IN REPRODUCING KERNEL SPACE H^2(R) 被引量:2
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作者 Wu, BY Zhang, QL 《Journal of Computational Mathematics》 SCIE EI CSCD 2001年第3期327-336,共10页
Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing ... Provides information on a study which presented a numerical method for solving Euler system of equations in reproducing kernel space. Definition and properties of reproducing kernel space; Construction of reproducing kernel finite difference method; Numerical results of the study. 展开更多
关键词 Euler system of equations reproducing kernel method finite difference method wavelet function
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GLOBAL EXISTENCE AND BLOW-UP PHENOMENA OF CLASSICAL SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGH POROUS MEDIA 被引量:2
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作者 刘法贵 孔德兴 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第6期703-713,共11页
By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result o... By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘small ’ solution. 展开更多
关键词 porous media compressible adiabatic flow system of equations classical solution global existence BLOW-UP
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ON THE EXACT SOLUTIQN TO CERTAIN NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS
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作者 施惟慧 陈达段 唐一鸣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1997年第3期259-265,共7页
This paper, based on the theory of stratifications. gives a brand-new classification of partial differential equations.
关键词 Janet number bad system of equations good system of equations
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EXISTENCE OF NON-TRIVIAL SOLUTION FOR SUPERLINEAR SYSTEM OF INTEGRAL EQUATIONS AND ITS APPLICATIONS 被引量:10
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作者 张志涛 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1999年第2期153-162,共10页
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo... In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations. 展开更多
关键词 CONE topological degree theory completely continuous operators superlinear system of equations non-trivial solution.
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A new smoothing technique for mathematical programs with equilibrium constraints
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作者 朱志斌 罗志军 曾吉文 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第10期1407-1414,共8页
A kind of mathematical programs with equilibrium constraints (MPEC) is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed.... A kind of mathematical programs with equilibrium constraints (MPEC) is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence. 展开更多
关键词 mathematical programs with equilibrium constraints nonlinear complementarity constraints primal-dual stationary point smoothing system of equations global convergence
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PARALLEL NONLINEAR MULTISPLITTING RELAXATION METHODS
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作者 WANG DEREN AND BAI ZHONGZHI(Department of Mathematics, Shanghai University of Science and Technology, Shanghai 201800). 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1995年第3期251-266,共16页
By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxa... By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxation methods such as multisplitting AOR-Newton method, multisplitting AOR-chord method and multisplitting AOR-Steffensen method, etc.. Furthermore,a general convergence theorem for the nonlinear multisplitting AOR-type methods and the local convergence for the multisplitting AOR-Newton method are discussed in detail.A lot of numerical tests show that our new methods are feasible and satisfactory. 展开更多
关键词 Nonlinear system of equations nonlinear multisplitting relaxed method local convergence
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The Existence of Even Cycles with Specific Lengths in Wenger's Graph 被引量:2
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作者 Jia-yu Shao Chang-xiang He Hai-ying Shan 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第2期281-288,共8页
Wenger's graph Hm(q) is a q-regular bipartite graph of order 2qm constructed by using the mdimensional vector space Fq^m over the finite field Fq. The existence of the cycles of certain even length plays an importa... Wenger's graph Hm(q) is a q-regular bipartite graph of order 2qm constructed by using the mdimensional vector space Fq^m over the finite field Fq. The existence of the cycles of certain even length plays an important role in the study of the accurate order of the Turan number ex(n; C2m) in extremal graph theory. In this paper, we use the algebraic methods of linear system of equations over the finite field and the “critical zero-sum sequences” to show that: if m ≥ 3, then for any integer l with l ≠ 5, 4 ≤ l ≤ 2ch(Fq) (where ch(Fq) is the character of the finite field Fq) and any vertex v in the Wenger's graph Hm(q), there is a cycle of length 21 in Hm(q) passing through the vertex v. 展开更多
关键词 GRAPH CYCLE finite field vector space linear system of equations
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A NEW PRECONDITIONING STRATEGY FOR SOLVING A CLASS OF TIME-DEPENDENT PDE-CONSTRAINED OPTIMIZATION PROBLEMS 被引量:2
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作者 Minli Zeng Guofeng Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2014年第3期215-232,共18页
In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distribute... In this paper, by exploiting the special block and sparse structure of the coefficient matrix, we present a new preconditioning strategy for solving large sparse linear systems arising in the time-dependent distributed control problem involving the heat equation with two different functions. First a natural order-reduction is performed, and then the reduced- order linear system of equations is solved by the preconditioned MINRES algorithm with a new preconditioning techniques. The spectral properties of the preconditioned matrix are analyzed. Numerical results demonstrate that the preconditioning strategy for solving the large sparse systems discretized from the time-dependent problems is more effective for a wide range of mesh sizes and the value of the regularization parameter. 展开更多
关键词 PDE-constrained optimization Reduced linear system of equations PRECONDITIONING Saddle point problem Krylov subspace methods.
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BLOCK-TRIANGULAR PRECONDITIONERS FOR SYSTEMS ARISING FROM EDGE-PRESERVING IMAGE RESTORATION 被引量:2
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作者 Zhong-Zhi Bai Yu-Mei Huang Michael K. Ng 《Journal of Computational Mathematics》 SCIE CSCD 2010年第6期848-863,共16页
Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization f... Signal and image restoration problems are often solved by minimizing a cost function consisting of an l2 data-fidelity term and a regularization term. We consider a class of convex and edge-preserving regularization functions. In specific, half-quadratic regularization as a fixed-point iteration method is usually employed to solve this problem. The main aim of this paper is to solve the above-described signal and image restoration problems with the half-quadratic regularization technique by making use of the Newton method. At each iteration of the Newton method, the Newton equation is a structured system of linear equations of a symmetric positive definite coefficient matrix, and may be efficiently solved by the preconditioned conjugate gradient method accelerated with the modified block SSOR preconditioner. Our experimental results show that the modified block-SSOR preconditioned conjugate gradient method is feasible and effective for further improving the numerical performance of the half-quadratic regularization approach. 展开更多
关键词 Block system of equations Matrix preconditioner Edge-preserving Image restoration Half-quadratic regularization.
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ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS
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作者 WANGDEREN BAIZHONGZHI 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1994年第3期335-348,共14页
A class ofparallel nonlinear multisplitting AOR methods is set upby directly ltisplittingthe nonlinear mapping F:D C Rn、R”for solving the nonlinear system of equationsF(x)= 0.The different choices of the relaxati... A class ofparallel nonlinear multisplitting AOR methods is set upby directly ltisplittingthe nonlinear mapping F:D C Rn、R”for solving the nonlinear system of equationsF(x)= 0.The different choices of the relaxation par。ters c。 yield all the kn。n and a lotof new rel8Xatlon methods as well as a M of new relaxatlon parallel nonlinear multisplittingmethods.Thetwrvsided approximation properties and th IMuences on convergence Mmthe relaxatlon parameters about the new methods are shown,and the sufficient conditionsguaranteeing the methods to converge globally are discussed.FlnallL aht ofnumericalresultsshow that the methods are feasible and efficient. 展开更多
关键词 Nonlinear system of equations Nonlinear multlsplltting Monotonlcltys Global convergence.
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Algorithm for simulating ocean circulation on a quantum computer
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作者 Ruimin SHANG Zhimin WANG +3 位作者 Shangshang SHI Jiaxin LI Yanan LI Yongjian GU 《Science China Earth Sciences》 SCIE EI CAS CSCD 2023年第10期2254-2264,共11页
The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential... The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers. 展开更多
关键词 Ocean circulation Primitive equations Linear system of equations Variational quantum linear solver Error mitigation technique
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