一类四阶奇异边值问题正解的存在性

该文利用不动点指数定理和Green函数的性质, 在较弱的条件下研究了四阶微分方程 奇异边值问题正解的存在性.     

Travelling wave solutions of nonlinear evolution equations by using the first integral method

In this paper, we established travelling wave solutions for some (2 + 1)-dimensional nonlinear evolution equations. The first integral method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The first integral method presents a wider applicability for handling nonlinear wave equations.     

Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.     

A splitting positive definite mixed element method for second‐order hyperbolic equations

In this article, we establish a new mixed finite element procedure, in which the mixed element system is symmetric positive definite, to solve the second‐order hyperbolic equations. The convergence of the mixed element methods with continuous‐ and discrete‐time scheme is proved. And the corresponding error estimates are given. Finally some numerical results are presented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Multiple positive solutions of a boundary value problem for a class of 2nth-order m-point singular integro-differential equations in Banach spaces

In this paper, we obtain the existence of multiple positive solutions of a boundary value problem for 2nth-order singular nonlinear integro-differential equations in a Banach space by means of fixed point index theory of completely continuous operators.     

Global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays

In this paper, by means of constructing the extended impulsive delayed Halanay inequality and by Lyapunov functional methods, we analyze the global exponential stability and global attractivity of impulsive Hopfield neural networks with time delays. Some new sufficient conditions ensuring exponential stability of the unique equilibrium point of impulsive Hopfield neural networks with time delays are obtained. Those conditions are more feasible than that given in the earlier references to some extent. Some numerical examples are also discussed in this work to illustrate the advantage of the results we obtained.     

Banach空间中非线性Sturm-Liouville问题的解

利用M(o)nch不动点定理,在更广泛的的条件下,证明了Banach空间中Sturm-Liouville问题解的存在性.     

Unified theory of augmented Lagrangian methods for constrained global optimization

We classify in this paper different augmented Lagrangian functions into three unified classes. Based on two unified formulations, we construct, respectively, two convergent augmented Lagrangian methods that do not require the global solvability of the Lagrangian relaxation and whose global convergence properties do not require the boundedness of the multiplier sequence and any constraint qualification. In particular, when the sequence of iteration points does not converge, we give a sufficient and necessary condition for the convergence of the objective value of the iteration points. We further derive two multiplier algorithms which require the same convergence condition and possess the same properties as the proposed convergent augmented Lagrangian methods. The existence of a global saddle point is crucial to guarantee the success of a dual search. We generalize in the second half of this paper the existence theorems for a global saddle point in the literature under the framework of the unified classes of augmented Lagrangian functions.     

Sliding mode synchronization controller design with neural network for uncertain chaotic systems

A sliding mode synchronization controller is presented with RBF neural network for two chaotic systems in this paper. The compound disturbance of the synchronization error system consists of nonlinear uncertainties and exterior disturbances of chaotic systems. Based on RBF neural networks, a compound disturbance observer is proposed and the update law of parameters is given to monitor the compound disturbance. The synchronization controller is given based on the output of the compound disturbance observer. The designed controller can make the synchronization error convergent to zero and overcome the disruption of the uncertainty and the exterior disturbance of the system. Finally, an example is given to demonstrate the availability of the proposed synchronization control method.     

命题逻辑中概率真度的相似度及伪距离

通过引入赋值密度函数、边缘密度函数等概念,给出了连续值命题逻辑系统中公式概率真度的定义,研究了概率真度的推理规则并证明了全体公式的概率真度之集在[0,1]中的稠密性,在此基础上给出了3种相似度,讨论了其性质及关系,并由此定义了3种伪距离,确定了三者之间的比例关系,为推理程度的数值化提供了依据.