一类新型时滞积分不等式及其应用

主要研究了一种新型时滞积分不等式u(t)≤a(t)+∫0α(t)f(t,s)w(u(s))ds+∫0α(t)g(t,s∫)0sh(s,τ)φ(u(τ))dτds up(t)≤a(t)+p/p-q∫0α(t)(f(t,s)uq(s)w(u(s))+g(t,s)uq(s))dsup(t)≤a(t)+p/p-q∫0α(t)f(t,s)uq(s)w(u(s))ds+p/p-q∫0tg(t,s)uq(s)w(u(s))ds这里p>q≥0是常数且t∈[0,∞).并且用此结果研究了时滞微分积分方程解的全局存在性和有界性.     

一类矩阵迹不等式的推广

利用平均值不等式 ,得到关于矩阵迹的不等式 :如果 A1 ,A2 ,… ,Am 皆为 n阶 Hermite半正定矩阵 ,且乘法两两可交换 ,0 相似文献   

基于模糊熵权优化的招标代理机构绩效评价研究

以《福建省工程招标代理机构信用等级评定暂行办法》、《黑龙江省工程招标代理机构信用评价暂行办法》等为依据,建立了招标代理机构绩效考核的三级评价指标体系,并运用AHP法确定绩效考核指标的主观权重值.然后,利用信息熵理论与模糊数学建立了熵权优化的绩效考核模糊综合评价模型.最后进行实例计算与分析,表明用此方法对招标代理机构进行绩效考核是科学的、合理可行的.通过将招标代理机构的收入与绩效考核结果挂钩,有利于促进其规范招标代理行为、提高服务质量.     

A NEW FAMILY OF FILTRATION S ＋ 5 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s ＋ 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s＋3hnhm∈Ext^s＋5,A ^t（Zp,Zp）in the Adams spectral sequence,where r=q（p^m＋p^n＋（s＋3）p^2＋（s＋2）p＋（s＋1））-5,t=p^mq＋p^nq＋（s＋3）p^2q＋（s＋2）pq＋（s＋1）q＋s,p≥7,m≥n＋2〉5,0≤s〈p-3,q=2（p-1）.     

Spaces of analytic functions represented by Dirichlet series of two complex variables

We consider the space X of all analytic functionsf(s1 ,s2) = ∞∑aminexp(s1λm+s2μtn)of two complex variables s1 and s2, equipping it with the natural locally convex topology and using thegrowth parmeter, the order of f as defined recently by the authors. Under this topology X becomes aFrechet space. Apart from finding the characterization of continuous linear functiors, linear transforma-tion on X, we have obtained the necesary and sufficient conditions for a double sequence in X to be a properbases.     

分支问题开折的强（r|s）稳定性与弱（r|s）稳定性

该文讨论了分支问题开折的强（r,s）稳定性及弱（r,s）稳定性,并给出了（r,s）无穷小稳定性、强（r,s）稳定性及弱（r,s）稳定性的等价性．     

中立型标量积分微分方程的周期解

本文考虑中立型标量方程x′(t)=a(t)x(t)+∫     

On a certain class of dirichlet series

For 0 1, let L(s,a) and L?(s,a) be the Dirichlet series L(s,a) = ∑ : cos (2πna)n^-s and L? [001](s,a) = ∑ sin (2πna)n^-s. We show that L(s,a) and L?(s,a[001]) have holomorphic extension in the whole complex plane. Values of L(s,a)andL?(s,a) at the negative integers are given. Moreover values of L?(s,a) at the intergers 0,2,4,... and values of L^?(s,a)at the integers 1,3,5,... are obtained. An exponential sums of certain recursion formulas are obtained by means of bernoulli numbers and Bernoulli polynomials     

Maximum Principle of Semi-Linear Distributed System (I)

In this paper, an optimal control problem of non-linear Volterra systems $x(\cdot)=h(t)+\int_0^t G(t,s)f(s,x(s),u(s))ds$ on Banach space X with a general cost functional $Q(u(\cdot)) = \int_0^T J(s,x(s,u(\cdot)),u(s))ds$ is discussed, where $G(t,s)\in \varphi(X)$ is strongly continuous in (t, s), h(\cdot)\in C([0,T],G),f(s,x,u):[0,T]*X*U \rightarrow X and J (s, x, u) : [0, T] *X*U \rightarrow R. The control region U is an arbitrary set in a Banach space. Under some other assumptions of f and J, we have proved the following Theorem. The optimal control u^*(\cdot) of the above problem satisfies max $H(t,u)=H(t,u^*(t))$ for a.e.t\in [0,T], Where $H(t,u)=-J(t,x^*(t),u)+(\phi(t),f(t,x^*(t),u))$, $\phi(t)=\int_t^T J_x(s,x^*(s),u^*(s))U(s,t)ds$ and $x^*(t)=x(t,u^*(\cdot)),U(s,t)\in \phi(X)$ is the solution of $U(s,t)=G(s,t)+\int _t^s G(s,w)f_x(w,x^*(w),u^*(w))U(w,t)dw$. We have applied the results to semi-linear distributed systems.     

Cartan-Fubini type extension of holomorphic maps respecting varieties of minimal rational tangents

A fundamental result in the theory of minimal rational curves on projective manifolds is CartanFubini extension theorem proved by Hwang and Mok,which describes the extensibility of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents(VMRT),under a mild geometric assumption on the second fundamental forms of VMRT’s.Hong and Mok have developed Cartan-Fubini extension for non-equidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold,under the assumptions that the map sends VMRT’s onto linear sections of VMRT’s and it satisfies a mild geometric condition formulated in terms of second fundamental forms on VMRT’s.In the current paper,we give a generalization of Hong and Mok’s result,under the same condition on second fundamental forms,assuming only that the holomorphic immersions send VMRT’s to VMRT’s.Our argument is different from Hong and Mok’s and is based on the study of natural foliations on the total family of VMRT’s.This gives a substantially simpler proof than Hong and Mok’s argument.