A BRANCH BOUND METHOD FOR SUBSET SUM PROBLEM

ＡＢＲＡＮＣＨＢＯＵＮＤＭＥＴＨＯＤＦＯＲＳＵＢＳＥＴＳＵＭＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，Ｃ...     

MEAN CONVERGENCE OF SOME POSITIVE OPERATORS

ＭＥＡＮＣＯＮＶＥＲＧＥＮＣＥＯＦＳＯＭＥＰＯＳＩＴＩＶＥＯＰＥＲＡＴＯＲＳＳｈｉＹｉｎｇｇｕａｎｇ（史应光）（ＣｏｍｐｕｔｉｎｇＣｅｎｔｅｒ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｐ．Ｏ．Ｂｏｘ２７１９，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈ...     

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

Estimation of the parameters for unstable AR models

ＥＳＴＩＭＡＴＩＯＮＯＦＴＨＥＰＡＲＡＭＥＴＥＲＳＦＯＲＵＮＳＴＡＢＬＥＡＲＭＯＤＥＬＳＡＮＨｏＮＧＺＨＩ（安鸿志）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ,Ｂｅｉｊｉｎｇ１０...     

SOLUTION OF A RESEARCH PROBLEM

ＳＯＬＵＴＩＯＮＯＦＡＲＥＳＥＡＲＣＨＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（巫世权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇｓｈａ４１００７３，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

THE GLOBAL SOLUTIONS FOR A FOURTH ORDER NONLINEAR SCHRaINGER EQUATION

ＴＨＥＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＦＯＲＡＦＯＵＲＴＨＯＲＤＥＲＮＯＮＬＩＮＥＡＲＳＣＨＲǒＩＮＧＥＲＥＱＵＡＴＩＯＮＦｅｎｇＸｕｅｓｈａｎｇ（冯学尚）（ＮｕｍｅｒｉｃａｌＬａｂｏｒａｔｏｒｙｆｏｒＨｅｌｉｏｓｐｈｅｒｉｃｐｈｙｓｉｃｓ，Ｐ．Ｏ．Ｂ...     

ON SOME RESULTS FOR NONLINEAR BEST CHEBYSHEV APPROXIMATION WITH LGH CONDITION

ＯＮＳＯＭＥＲＥＳＵＬＴＳＦＯＲＮＯＮＬＩＮＥＡＲＢＥＳＴＣＨＥＢＹＳＨＥＶＡＰＰＲＯＸＩＭＡＴＩＯＮＷＩＴＨＬＧＨＣＯＮＤＩＴＩＯＮＷｅｉＤａｎ（韦旦）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｗｕｈａｎ...     

Reliability bounds in DFRA class with known mean and variance

ＲＥＬＩＡＢＩＬＩＴＹＢＯＵＮＤＳＩＮＤＦＲＡＣＬＡＳＳＷＩＴＨＫＮＯＷＮＭＥＡＮ　ＡＮＤ　ＶＡＲＩＡＮＣＥＣＨＥＮＧＫＡＮ（程侃）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ,Ｂ...     

Fubini theorem w.r.t. stochastic measure on product measurable space

ＦＵＢＩＮＩＴＨＥＯＲＥＭｗ．ｒ．ｔ．ＳＴＯＣＨＡＳＴＩＣＭＥＡＳＵＲＥＯＮＰＲＯＤＵＣＴＭＥＡＳＵＲＡＢＬＥＳＰＡＣＥＣＨＥＮＰＥＩＤＥ（陈培德）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳ...     

A singularly perturbed second order quasilinear BVP

ＡＳＩＮＧＵＬＡＲＬＹＰＥＲＴＵＲＢＥＤＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩＬＩＮＥＡＲＢＶＰＬＩＮＷＵＺＨＯＮＧ（林武忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｓｈａｎｇｈａｉ２０００６２...     

Nonlinear Stability of General Linear Methods

This paper is devoted to a study of stability of general linear methods for the numerical solution of nonlinear stiff initial value problems in a Hilbert space. New stability concepts are introduced. A criterion of weak algebraic stability is established, which is an improvement and extension of the existing criteria of algebraic stability.     

Non-linear stability of a general class of differential equation methods

For a class of methods sufficiently general as to include linear multistep and Runge-Kutta methods as special cases, a concept known as algebraic stability is defined. This property is based on a non-linear test problem and extends existing results on Runge-Kutta methods and on linear multistep and one-leg methods. The algebraic stability properties of a number of particular methods in these families are studied and a generalization is made which enables estimates of error growth to be provided for certain classes of methods.     

Stability Analysis for Discrete Biological Models Using Algebraic Methods

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems. For finite dynamical systems, methods based on Gr?bner bases and triangular sets are applied to detect steady states. The feasibility of our approach is demonstrated by the analysis of stability and bifurcations of several discrete biological models using implementations of algebraic methods.     

求解延迟微分代数方程的多步Runge-Kutta方法的渐近稳定性

延迟微分代数方程(DDAEs)广泛出现于科学与工程应用领域．本文将多步Runge-Kutta方法应用于求解线性常系数延迟微分代数方程，讨论了该方法的渐近稳定性．数值试验表明该方法对求解DDAEs是有效的．     

一般线性方法的线性与非线性稳定性间的关系

１．引言１９６３年,Ｄａｈｌｑｕｉｓｔ以一类线性问题为模型提出了Ａ－稳定性概念,此后有关如何判断方法是否Ａ－稳定或确定其稳定域的研究十分活跃,袁兆鼎等~［１］中对此有详细的讨论．Ｂｕｒｒａｇｅ与Ｂｕｔｃｈｅｒ［２］以一类非线性问题为模型,就一般线性方法引入了代数稳定性概念．Ｂｕｔｃｈｅｒ［４］探讨了代数稳定性与Ａ－稳定性间的内在联系．为确保代数稳定性蕴涵Ａ－稳定性,Ｂｕｔｃｈｅｒ［５］进一步要求代数稳定性定义中涉及的矩阵Ｇ是正定的。然而这样一来,正如李寿佛［６］中指出的那样,许多ＡＮ稳定且按［４…     

A Generalization of Algebraic Stability for Runge--Kutta Methods

The theory of algebraic stability does not give detailed informationabout the stability properties of explicit methods. This theoryis generalized by considering a monotonic and bounded test problem.The results give additional information about the stabilityproperties of explicit and implicit methods and show how particularexplicit methods may be selected.     

Nonlinear Stability of General Linear Methods

This paper considers the nonlinear stability of general linear methods. The diagonal matrix of an algebraically stable method is shown to be fixed. Readily testable necessary and sufficient conditions are obtained for algebraic stability and, more generally, for nonlinear stability in closed disk regions of the complex plane. It is shown that the latter criteria are satisfied by some explicit methods. It is also shown that certain methods, including some that are L-stable, suffer from nonautonomous instability along the negative real line near zero. A loose classification of methods is given according to nonlinear stability properties.     

Weak Nonlinear Stability of Implicit Runge-Kutta Methods

Two slightly different test problems have been used to examinenonlinear stability behaviour of numerical methods for solvingsystems of ordinary differential equations. These test problems,for BN-stability and for monotonicity, both lead to the conceptof algebraic stability. In this paper, it is shown that thesetwo problems may be combined to yield weaker stability conditions.Nonautonomous systems give a more restrictive stability conditionthan autonomous systems. Irreducible methods with some zeroquadrature weights can be stable in this weak sense.     

B-CONVERGENCE PROPERTIES OF GENERAL LINEAR METHODS

In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.     

Reducible Runge-Kutta methods

Reducible Runge-Kutta methods are characterized by means of special matrices. Previous definitions of reducibility are incorporated. This characterization may be useful in the study of algebraic stability and in studies of existence and uniqueness.