Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II

We calculate the pair correlation function and the magnetic susceptibility in the anisotropic Ising model on the lattice with one infinite and one finite dimension with periodic boundary conditions imposed along the second dimension. Using the exact expressions for lattice form factors, we propose formulas for arbitrary spin matrix elements, thus providing a possibility to calculate all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. We analyze passing to the scaling limit.     

On Stability of Solutions of a Certain Fourth—Order Functional Differential Equations

Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptoticstability of the zero solution of a certain fourth order functional differential equations.The resultgeneralizes the well known results.     

脉冲泛函微分方程关于两个测度的实际稳定性

利用Lyapunov,函数方法,建立了脉冲时滞微分方程关于两个测度的实际稳定的充分条件。     

On the Partial Equiasymptotic Stability in Functional Differential Equations

A system of functional differential equations with delay dz/dt = Z(t, z_t), where Z is the vector-valued functional is considered. It is supposed that this system has a zero solution z = 0. Definitions of its partial stability, partial asymptotical stability, and partial equiasymptotical stability are given. Theorems on the partial equiasymptotical stability are formulated and proved.     

脉冲泛函微分方程实用稳定性的一个比较定理

考虑一类脉冲泛函微分方程的实用稳定性，利用锥值李亚普诺夫函数方法，建立了脉冲泛函数微分方程与脉冲常微分方程的实用稳定性之间的比较定理。     

关于泛函微分方程的完全渐近稳定性定理

本文用两个李雅普诺夫V函数对泛函微分方程建立了完全渐近稳定性的一类判别定理.     

泛函微分方程的Lipschitz指数稳定性

提出泛函微分方程的Lipschitz指数稳定性概念,给出了利用Liapunov泛函数研究Lipschitz指数稳定性的条件。     

一阶迭代泛函微分方程的局部可逆解析解

本文研究迭代泛函微分方程x′(z)=1/(x(az+b/(x′(z)))),z∈C的解析解,其中a,b均为复常数.首先利用Schr(o|¨)der变换,把迭代泛函微分方程转化为不含迭代的泛函微分方程.针对Schr(o|¨)der变换中的常数α在单位圆上,不是单位根但满足Brjuno条件;α不但在单位圆上,而且是单位根;α在单位圆内三种情况,讨论了辅助方程的解析解.在此基础上,我们证明原方程局部可逆解析解存在,并且计算出解析解表达式.最后举例说明定理的应用.     

The exact boundaries of the stability domains of linear differential equations with distributed delay

For a differential equation with a distributed varying delay, sufficient criteria for the asymptotic and uniform stability of solutions are obtained. The constructed examples demonstrate exactness of the boundary of the obtained stability domain.     

用两个V函数判别泛函微分方程的完全渐近稳定性

本文用两个李雅普诺夫V函数对泛函微分方程建立了完全渐近稳定性的一类判别条件。     

线性泛函微分方程解的渐近表示

本文利用一类特殊方程的一致稳定性与收敛性定理研究Ｒ^ｎ中线性泛函微分方程解的渐近表示，在较弱的条件下得到了与文［１］同样的渐近积分公式．文中还讨论了一些特殊解的存在性、零解的吸引性等等     

On employment of semidefinite functions in stability of delayed equations

Four new stability theorems for nonautonomous delayed equations are established by the Lyapunov-Razumikhin approach with functions and its derivatives semidefinite. To do this, assume the collection of right-hand side translations in time has limit points which govern limiting equations. A corollary, which relates global asymptotic stability for the equation to that for limiting equations, and an illustrative example are given to show the applications of the established theorems.     

具有Monod-Haldane功能反应的一类食物链模型的动力学行为

该文研究了一个由食饵种群、捕食者种群和杂食者种群所构成的食物链系统, 其捕食功能反应为Monod-Haldane功能反应. 应用定性分析和Hopf分支理论, 得到了该系统边界平衡点的全局稳定性和周期解存在性的判别准则. 为了概括和归类这个系统的全局动力学行为,该文得到了具有不同动力学行为的参数区域. 应用MATLAB软件,该文提供了一个例子来展示这些结论, 并且表明: 这个系统能够产生非常复杂的动力学行为.     

STABILITY AND ALMOST PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

ＳＴＡＢＩＬＩＴＹＡＮＤＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＮＥＵＴＲＡＬＴＹＰＥＹｕａｎＲｏｎｇ（袁荣）（ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，北京师范大学，...     

On optimal control of functional differential systems

We use relaxed controls to derive optimality condition for control problems governed by functional differential systems. We include general boundary conditions, and the case of periodic trajectories is a special one.This research was supported by NSF Grant HRD-91-54077.     

一类二阶泛函微分方程的周期边值问题

讨论了一类二阶泛函微分方程的周期边值问题,给出了上、下解的一个新的概念,并且得到了一个新的比较结果.同时,修正了相关文献中的一个错误.     

Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.     

Differentiability of implicit functions: Beyond the implicit function theorem

The implicit function theorem (IFT) can be used to deduce the differentiability of an implicit mapping S:u?y$S:u?y$ given by the equation e(y,u)=0$e(y,u)=0$. However, the IFT is not applicable when different norms are necessary for the differentiation of e w.r.t. y   and the invertibility of the partial derivative _ey(y,u)$e_y(y,u)$. We prove theorems ensuring the (twice) differentiability of the mapping S which can be applied in this case. We highlight the application of our results to quasilinear partial differential equations whose principal part depends nonlinearly on the gradient of the state ∇y.