关于一个含参量的Hilbert型积分不等式

通过估算权函数及引入Beta函数,建立一个含参量的、具有最佳常数因子的Hilbert型积分不等式.同时建立它的两种最佳推广式及相应的等价形式.     

SOR矩阵■和Jacobi矩阵B的特征向量及特征值之间的关系

Young[1]中给出的基本特征值关系的定理,使得可以直接地建立SOR矩阵和Jacobi矩阵B的特征值之间的关系。但Young处理的只是下述形状的矩阵:其中,L及U分别为下及上三角矩阵。而且只建立了特征值之间的关系,而没有建立特征向量之间的关系。本文推广Young的结果,当Jacobi矩阵B是指标为P(≥2)的弱循环阵的法式时,来建立SOR矩阵和B的特征值及特征向量之间的关系。所用的方法只是直接推演。     

关于子区间逆向的Hilbert型积分不等式

本文研究了建立逆向Hilbert型不等式问题.引入两对共轭指数,应用权函数,实分析及参量化的方法,在积分子区间上建立逆向的具有最佳常数因子及一般齐次核的Hilbert型积分不等式,等价式及一些特殊核的不等式,推广了一些文献的结果.     

一个较为精密的Hilbert型不等式

本文通过引入独立参数λ与α,应用改进的Euler-Maclaurin公式,优化了权系数的估算方法,建立一个具有最佳常数因子的较为精密的Hilbert型不等式.作为应用,考虑了等价式及一些特殊情形将有助于估算及建立同类型的其它不等式.     

圆锥曲线中建立参数不等式的几种基本方法

<正>在圆锥曲线中,经常涉及到求最值及取值范围的问题,这类问题也是历年高考命题的热点,解决这类问题的关键和难点是如何准确建立相关不等式.因此,需要掌握建立相关不等式的几种基本方法.一、通过基本不等式建立不等式     

Hardy-Hilbert不等式的推广

引入参数A,B,C,λ及β函数,建立一个推广的、具有最佳常数因子的Hardy-Hilbert不等式,作为应用,建立该推广式的一个等价式．     

基于质量控制的供应链计划问题研究

为了研究基于质量控制的供应链计划问题,采用了优化建模的方法,分析了易腐物品生命周期函数的选用及拟合原则,建立起了质量衰减成本与时间之间的关系,考虑了涉及交通及天气情况的运输风险,最终建立了优化模型,以实现供应链运行总成本最小。最后,提出了动态规划的求解方法,并通过仿真实验证明了算法的有效性。     

屈曲特征值问题的边界元方法及收敛性分析

讨论了屈曲特征值问题的定解条件,建立了相应的具约束的积分方程组及带Lagrange乘子的边界变分方程,给出了解的存在唯一性定理。建立了相应的边界元方法并讨论了近似解的误差估计。文末给出了数值算例。     

p-凸函数与几类不等式

研究p-凸函数的一些新的性质及判别准则,并建立p-凸函数的Jensen型、Rado型及Hadamard型不等式.     

模糊综合评价法在科研选题中的应用

科研选题评价工作是一项复杂的系统工程,在武警部队院校目前尚未建立起科学的评价体系.由于科研选题的多因素性及评价因素的模糊性,可以用模糊数学建立综合评价模型.     

一般环之分式环

本文给出一般环R之分式环△^-1R的构造和△^-R的理想的一些性质,推广了现有中外教科书的结论．证明了（1）△^-1R中理想有且仅有形式△^-1I,其中△3R．（2）如果P是R的素理想,且△∩P=Ф,则△^-1P是△^-1R的素理想,且θ^-1（△^-1P）=P。     

Three Classes of Reaction-Diffusion Systems with Neumann Boundary Condition

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Enlargements of filtrations and path decompositions at non stopping times

Azéma associated with an honest time L the supermartingale and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic processes and in particular in the theory of progressive enlargements of filtrations. In this paper, we shall give an additive characterization for these supermartingales, which in turn will naturally provide many examples of enlargements of filtrations. We combine this characterization with some arguments from both initial and progressive enlargements of filtrations to establish some path decomposition results, closely related to or reminiscent of Williams' path decomposition results. In particular, some of the fragments of the paths in our decompositions end or start with a new family of random times which are not stopping times, nor honest times.     

Variational inequalities with nonmonotone operators

In this paper, existence results on variational inequalities and generalized variational inequalities for some nonmonotone operators over closed convex subsets of a real reflexive Banach space are proved. In particular, some surjectivity results and applications to complementarity and generalized complementarity problems are given.This work was partially supported by the National Science Council of the Republic of China under Contracts NSC 81-0208-M-007-34 and NSC 82-0208-M-110-023.     

Optimal control problems of hyperbolic systems with operator and nonoperator equality constraints

In the paper two kinds of optimal control problems of hyperbolic systems with additional equality constraints are considered: a problem with the operator equality constraint in the form of terminal condition and a problem with nonoperator equality constraint in the u(.)ε U where - some set. The extremum principles are proved: for the first problem - by using some specification of the Dubovitskii-Milyutin method in the case of n equality constraints in the operator form and for the second one - by using some generalization of the Dubovitskii-Milyutin theory     

Approximation by generalized MKZ-operators in polynomial weighted spaces

We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].     

OM AN INVERSE THEOREM OF APPROXIMATION

The author gives some disagreement to the following result, which is published in [1]. Let ${L_{n}(f)}$ be mass-concerntative,$\phi\rightarrow 0(n\rightarrow \infty), 0<\alpha\leq2$ and $$C^{-1}\leq \phi_{n+1}/\phi_{n}\leq C (n=1,2,\ldots)$$ for some constrant $C>0$. Then for any $f\in C[-2a,2a]$, $$\parallel L_{n}(f)-f\parallel_{C[ a,a]}= O(\phi^{\alpha}_{n})$$ inplies $f \in Lip^{*}\alpha$, where $$Lip*\alpha={f\in C[-2a,2a]|\omega_{2}(f,\delta)_{[-2a,2a]}=O(\delta^{\alpha})}.$$ Then some similar results on $C_{2\pi$ are given, and further some results on $C[-2a,2a]$ are established by adding some proper conditions.     

Frame wavelet sets in

In this paper, we try to answer an open question raised by Han and Larson, which asks about the characterization of frame wavelet sets. We completely characterize tight frame wavelet sets. We also obtain some necessary conditions and some sufficient conditions for a set to be a (general) frame wavelet set. Some results are extended to frame wavelet functions that are not defined by frame wavelet set. Several examples are presented and compared with some known results in the literature.

     

SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF A AUTONOMOUS DIFFERENTIAL SYSTEM

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