THE METHOD OF MULTIPLE SCALES APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A TRUNCATED SHALLOW SPHERICAL SHELL OF VARIABLE THICKNESS WITH THE LARGE GEOMETRICAL PARAMETER

Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.

POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.

AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W^(m,p)t(Ω)

In the present paper the concept and properties of the residual functional in Sobolev space are investigated. The weak compactness, force condition, lower semi-continuity and convex of the residual functional are proved. In Sobolev space, the minimum principle of the residual functional is proposed. The minimum existence theoreomfor J(u) =0 is given by the modern critical point theory. And the equivalence theorem or five equivalence forms for the residual functional equation are also proved.

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

An impulsive control scheme of the Lur' e system and several theorems on stability of impulsive control systems was presented,these theorems were then used to find the conditions under which the Lur' e system can be stabilized by using impulsive control with varying impulsive intervals.The parameters of Lur' e system and impulsive control law are given,a theory of impulsive synchronization of two Lur' e system is also presented. A numerical example is used to verify the theoretical result.

On the conjunction practical stability and controllability of large-scale impulsive control systems

We studied the conjunction practical stability and controllability of large-scale impulsive control systems by using the comparison systems and vector Lyapunov fimctions. Then the less conservative sufficient conditions for conjunction practical stability and controllability of large-scale impulsive control system were obtained.

Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X1X2X3X4

To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

Using the matrix measure and delay differential inequality, the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay. These conditions are an improvement and extension of the results achieved in earlier papers presented by LIAO, LIU, ZHANG, SUN, et al.

ON MINIMAL IMMERSIONS OF R^2 INTO THE NEARLY KAHLER S^6

In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.

The 4-canonical Maps of 3-folds of General Type

The aim of this paper is to show that the 4-canonical maps of 3-folds of general type is birational when pg≥7 under some given conditions.

PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD

在这篇论文，明智的 NCP 功能为非线性的不平等被建议的有片的一个 QP 免费的可行方法抑制了优化问题。新 NCP 功能 arepiece 明智的线性合理的、常规伪 smooth 并且有好性质。这个方法是 KKT optimality 条件的方程重新阐述的线性系统的基于的在解决方案，由使用 thepiecewise NCP 函数。这个方法是没有假定严格的补充条件能、全球性会聚的工具，累积的孤立的海角指。而且，活跃限制的坡度没被请求线性地独立。可以被伪获得的次矩阵 -- 牛顿方法，没被请求一致地积极明确。初步的数字结果显示这个新 QP 免费的方法是相当有希望的。

Linear Error Equation on Field F_2

在这份报纸，我们将给一个方法在 F2 上解决线性错误 equationon，由使用地 F2 和分区理论上的线性代数学。

Two-parameters quasi-filled function algorithm for nonlinear integer programming

A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover, we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the pro- posed quasi-filled function algorithm.

ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

Binomial lattice for pricing Asian options on yields

An efficient binomial lattice for pricing Asian options on yields is established under the affine term structure model. In order to reconnect the path of the discrete lattice,the technique of D. Nelson and K. Ramaswamy is used to transform a stochastic interest rate process into a stochastic diffusion with unit volatility. By the binomial lattice and linear interpolation,the prices of Asian options on yields can be obtained. As the number of nodes in the tree structure grows linearly with the number of time steps, the computational speed is improved. The numerical experiments to verify the validity of the lattice are also provided.

Classification of (D_4, S^1-equivariant bifurcation problems up to topological codimension 2

The techniques from singularity theory are applied to the multiparameter bifurcation problem.The classification of (D4, S1)-equivariant bifurcation problems with topological codimension less than or equal to 2 is given. The corresponding recognition conditions are set up.

Strict Stability of Impulsive Differential Equations

In this paper, we will extend the strict stability to impulsive differential equations. By using Lyapunov functions, we will get some criteria for the strict stability of impulsive differential equations, and we can see that impulses do contribute to the system＇s strict stability behavior. An example is also given in this paper to illustrate the efficiency of the obtained results.

HOMOMORPHISMS BETWEEN CHEVALLEY GROUPS OF TYPES C_nAND G_2 OVER FINITE FIELDS

It is known that there exists an isogeny sort of Chevalley groups G (Σ, F) associated to any indecomposable root system Σ and any field F . In this paper the author determines all nontrivial homomorphisms from G(Σ, k) to G(Σ, K) when the root system Σ is of type C n or G 2 , and the fields k and K are finite fields of characteristic p .

equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

Under very weak condition 0 【 r(t)↑∞ , t→∞. we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.

ON THE FIRST CARTAN INVARIANT OF THE GROUP Sp(4, p^n)

The matrix C of Cartan invariants is one of the aspects in modular representation theory. The nature of the entries in C remains somewhat mysterious. One entry of C,in which we are mainly interested here, is C11, the first Cartan invariant of the Chevalley group of type B2 SP（4, pn） (the multiplicity of the trivial module in its projective cover,