差分系统平衡点的判别

平衡点在研究差分系统的零解的稳定性时具有极其重要的作用.本文首先给出了线性差分系统平衡点存在的充要条件,然后给出非线性差分系统平衡点存在的充分条件,最后给出了高阶差分系统平衡点存在的充分条件.     

Necessary and sufficient conditions in constrained optimization

Additional conditions are attached to the Kuhn-Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications. Necessary and sufficient conditions are also given for optimality of the dual problem. Duality and converse duality are treated accordingly.     

两邻接B样条曲面的G1连续条件

本文得到了非均匀重内节点邻接B样条曲面间G1连续的充要条件 ,给出了一类G1连续的充分条件 ;基于对B样条曲线参数连续性的分析 ,本文着重给出了这类充分条件成立的内在约束 ,即对公共边界控制顶点的约束条件 .     

G~1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N > 2) patch B-spline surfaces meeting at a common corner are given at the end.     

The Coercivity of Functional Differential Equations

New sufficient conditions for the Gårding inequality for variable-coefficient functional differential equations with expanded and contracted arguments of higher derivatives of the unknown function are found. These sufficient conditions generalize earlier known sufficient conditions.     

Linearizability of planar polynomial Hamiltonian systems

Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system. Using computer algebra systems we provide necessary and sufficient conditions for linearizability of Hamiltonian systems with homogeneous non-linearities of degrees 5, 6 and 7. We also present some sufficient conditions for systems with nonhomogeneous nonlinearities of degrees two, three and five.     

Leakage delays in BAM

A well known bidirectional associative memory (BAM) model is generalized with the introduction of discrete time delays in the leakage (or forgetting) terms. By using a model transformation, the system is converted to one of a neutral delay system. Two sets of delay dependent sufficient conditions are derived for the existence of a unique equilibrium as well as its asymptotic and exponential stability. The methods of degenerate Lyapunov-Kravsovskii functionals and inequalities together with some properties of M-matrices are used in the derivation of sufficient conditions. In the absence of leakage delays, the sufficient conditions lead to some known sufficient conditions.     

First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems

First-order and second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The necessary conditions are immediate generalizations of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as illustrated by a counterexample. Here, to go from finite to infinite dimensions, causes an essential change in the proof-techniques and the results. We present modified sufficient conditions of first-order and of second-order which are based on a strengthening of the usual assumptions on the derivative of the objective function and on the second derivative of the Lagrangian.     

On the Itô excursion process

Summary Necessary and sufficient conditions are given, for a process to be the excursion process of some strong Markov process. These are modifications of necessary conditions of Itô, which are here shown by example not to be sufficient.     

Slant and pseudo-slant submanifolds in LCS-manifolds

We show new results on when a pseudo-slant submanifold is a LCS-manifold. Necessary and sufficient conditions for a submanifold to be pseudo-slant are given. We obtain necessary and sufficient conditions for the integrability of distributions which are involved in the definition of the pseudo-slant submanifold. We characterize the pseudoslant product and give necessary and sufficient conditions for a pseudo-slant submanifold to be the pseudo-slant product. Also we give an example of a slant submanifold in an LCS-manifold to illustrate the subject.     

Integrability and linearizability of the Lotka-Volterra systems

Integrability and linearizability of the Lotka-Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka-Volterra systems. Sufficient conditions for integrable Lotka-Volterra systems with 3:−q resonance are given. In the particular cases of 3:−5 and 3:−4 resonances, necessary and sufficient conditions for integrable systems are given.     

On stability of three-dimensional periodic motions in hydrodynamics : PMM vol. 37, n6, 1973, pp. 1044–1048

We obtain exact conditions for the stability of periodic motions. We show that the conditions found in [1] are necessary and sufficient, but they are only applicable to motions not dependent on time. The conditions given in [2] are applicable in the general case but are only sufficient (necessary) conditions of instability (stability). We consider the dependence of stationary motions on parameters.     

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown.     

Optimization of higher order differential inclusions with initial value problem

This paper concerns the sufficient conditions of optimality for initial value problem with higher order differential inclusions (HODIs) and free endpoint constraints. Formulation of the transversality conditions plays a substantial role in the next investigations without which hardly any necessary or sufficient conditions would be obtained. In terms of Euler–Lagrange and Hamiltonian forms the sufficient conditions of optimality both for convex and “non-convex” HODIs are based on the apparatus of locally adjoint mappings. Moreover, by applying the main result to a Bolza problem described by a polynomial differential operator with constant coefficients in terms of the adjoint differential operator the sufficient condition of optimality is obtained.     

AOR方法的收敛性定理

获得了著名的AOR方法收敛的实用条件和H矩阵的实用判别条件。所得AOR方法的收敛条件便于实际计算应用,适用范围不要求方程组系数矩阵对角占优,适用于数学物理问题中广泛的矩阵类。给出的数值例子表明了所得结果的实用性。     

Nondominated decisions and cone convexity in dynamic multicriteria decision problems

The concepts of domination structures and non-dominated decisions are extended to dynamic decision problems. Previously derived results are utilized in conjunction with optimal control theory to deduce necessary as well as sufficient conditions for nondominated controls. Cone convexity for dynamic problems is discussed, and sufficient conditions are given for a class of linear systems.     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．     

Ergodic properties of stationary stable processes

We derive spectral necessary and sufficient conditions for stationary symmetric stable processes to be metrically transitive and mixing. We then consider some important classes of stationary stable processes: Sub-Gaussian stationary processes and stationary stable processes with a harmonic spectral representation are never metrically transitive, the latter in sharp contrast with the Gaussian case. Stable processes with a harmonic spectral representation satisfy a strong law of large numbers even though they are not generally stationary. For doubly stationary stable processes, sufficient conditions are derived for metric transitivity and mixing, and necessary and sufficient conditions for a strong law of large numbers.     

Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions

Second-order necessary conditions and sufficient conditions with the envelope-like effect for optimality in nonsmooth vector optimization are established. We use approximations as generalized derivatives, imposing strict differentiability for necessary conditions and differentiability for sufficient conditions and avoiding continuous differentiability. Convexity conditions are not imposed explicitly. The results make it clear when the envelope-like effect occurs and improve or include several recent existing ones. Examples are provided to show advantages of our theorems over some known ones in the literature.     

一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .