OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION:THE METHOD OF A-HARMONIC APPROXIMATION

In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.

On Nonhomogeneous Singular Elliptic Systems with Critical C-K-NExponent

Abstract： In this paper, we are interested in the existence and multiplicity results ofnontrivial solutions to nonhomogeneous singularelliptic systems with critical C-K-N exponent（λ1,λ2）.With the help of the Nehari manifold and under sufficient conditions on the parameters λ1 and λ2, we prove some existence results.

Stochastic Stabilization for Nonhomogeneous Markovian Jump Discrete-Time Singular Systems

Stochastic stability analysis and control synthesis problems are studied for a class of nonhomogeneous Markovian jump discretetime singular systems( MJDSS). The time-varying character is considered to be the model in a polytopic sense. Based on the parameter dependent stochastic Lyapunov functional and the matrix analysis techniques, sufficient criteria are derived to ensure regularity, causality and stochastic stability of the closed-loop singular system in terms of linear matrix inequalities. Finally,one example is provided to illustrate the effectiveness of our results.

Positive solutions of second-order differential systems with nonhomogeneous boundary conditions

This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal HSlder exponent for the derivative of a weak solution on its regular set.

PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

In this article, we consider the partial regularity of stationary Navier-Stokes system under the natural growth condition. Applying the method of A-harmonic approximation,we obtain some results about the partial regularity and establish the optimal Holder exponent for the derivative of a weak solution on its regular set.

The Method of A-Harmonic Approximation and Boundary Regularity for Nonlinear Elliptic Systems under the Natural Growth Condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.

SOLUTION OF A CLASS OF NONHOMOGENEOUS ELLIPTIC SYSTEM INVOLVING CRITICAL SOBOLEV EXPONENT

In this paper, we discuss the problem of solving a class of nonhomogeneous semilinear elliptic system with critical Sobolev exponent changing into one of critical points of some given functional. Using Nehari technique, the given functional attain its minimum by adding suitable constraints, and the minimal point becomes a critical point of the original functional after eliminating the added constraints, thus the solution of the nonhomogeneous elliptic system is obtained.

逐步优化灰导数白化值的GM(1,1)直接建模法

在GM (1,1)直接建模法以差商作为灰导数白化值的基础上 ,提出了一种逐步优化灰导数白化值的方法 .结果表明 ,这一方法不仅保持了原方法的升 (降 )凹 (凸 )一致性、线性变换一致性 ,而且具有渐近白指数律重合性和线性收敛速度 .弥补了原方法不具有白指数律重合性的缺陷 ,突破了当发展系数的绝对值较大时GM(1,1)不能应用的禁区 。

毫米通道内氯苯-水非均相体系混合效果研究

以氯苯-水体系为对象,研究了毫米通道内液液非均相流体在不同流速下的流动形态及其混合传质效果。通过对子弹流型、子弹单滴混合流型、三相并行流型的观察分析,以流动雷诺数、毛细数、韦伯数为评价参数,讨论了流体流动表面力与流型形成的关系。以混合传质前后水相中醋酸浓度的变化为分析依据,探究了流体流型、流速对液液非均相体系传质效率与总体积传质系数的影响。结果表明:界面张力是子弹流型、子弹单滴混合流型形成的主导控制力,流动惯性力则促进三相并流的产生;随着流速的增加和流型的转变,扩大了二相传质界面积,提高了混合过程的总体积传质系数和传质效率。

房柱式开采煤柱系统失效的模糊理论研究

针对大同矿区房柱式开采坚硬顶板大面积冒落的特征和冒落机理,考虑到煤柱规格尺寸和分布间距的无规律性以及煤柱个体之间强度的差异性等带来的煤柱支承状况的随机、非均和不确定性,引入模糊集理论研究了非均因素对煤柱群体支承能力弱化过程、失效系数的影响。给出了表征煤柱个体间支承状况非均性的隶属函数和支承煤柱模糊失效系数的条件隶属函数关系式,并讨论了隶属函数的取值原则。

劣化系统周期预防性维修策略的优化

以长期运行费用率为评估指标,研究了劣化系统的周期预防性维修策略。假定开展的周期预防性维修介于最小维修和完全维修之间,维修间隔期间的故障过程用非齐次泊松过程进行描述,在此基础上采用比例寿命回退模型对预防性维修效果进行建模,给出了最佳预防性维修周期T和预防性维修次数N的计算方法以及参数应当满足的条件,同时结合实际情况给出了(N,T)策略的优化求解算法,最后通过数值算例,验证了所提方法的可行性。

刚性联接裙板式基础系统的破坏包络面研究

对于刚性联接裙板式基础系统在竖向荷载V、水平荷载H与弯矩M复合加载条件下的稳定性进行系统的平面应变有限元分析,主要探讨基础间距与宽度之比、地基土不排水抗剪强度的非均质性对于基础系统在不同荷载平面与V-H-M三维荷载空间内的破坏包络面的影响,并与单个基础的相应包络面形状进行对比。对比结果表明,裙板式基础系统的归一化V-H包络面形状与单个基础基本一致,但V-M、H-M包络面形状则出现显著差异。根据有限元得到的裙板式基础系统在单向加载情况下的失稳破坏模式,分别给出竖向、水平及弯矩承载力系数的塑性极限分析上限解。基于计算结果,建议了刚性联接裙板式基础系统的三维破坏包络面方程,该方程可以用来估计给定间距范围内的基础系统在复合加载条件下的承载力。

基于Chebyshev多项式函数系的齐次扩容精细算法

基于Chebyshev多项式函数系的特点,设计了求解非齐次线性自治系统的一种新的精细算法———基于Chebyshev正交多项式系的齐次扩容精细算法(HHPDC)。这一算法不仅避免了HPD-F算法中的矩阵求逆,还克服了HHPDF算法中对右端激励的周期性要求,从而适合于任意形式的右端激励;不仅计算量小、设计合理,还易于推广和实现。理论与算例表明,HHPD-C算法十分有效。

任意随机序列关于随机选择系统的一类强极限定理

主要研究任意随机序列在随机选择系统中的随机条件概率其调和平均的强极限定理。在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。作为推论,得到m重非齐次马氏链的一个强极限定理,并将已有的结果加以推广。

样本相对熵率与一类关于随机选择系统的强偏差定理

将样本相对熵率和随机选择系统的概念引入任意整值随机变量序列的研究,在样本空间的子集上把样本相对熵率作为任意整值随机变量序列与非齐次马氏链之间偏差的一种度量,给出了一类关于随机选择系统的强偏差定理.

一类非齐次马氏信源关于随机选择系统的广义Shannon-McMillan定理

通过构造相容分布和非负上鞅的方法,研究非齐次马氏信源关于赌博系统的一类广义Shannon-Mcmillan定理.并由此得出已有的非齐次马氏信源的Shannon-Mcmillan定理,推广了前人的结果.

二阶非齐次马氏信源关于广义随机选择系统的一类Shannon-McMillan定理

文中通过构造相容分布和非负上鞅的方法,研究了二阶非齐次马氏信源关于广义赌博系统的一类广义Shannon-Mcmillan定理.并由此得出已有的非齐次马氏信源、无记忆信源的一类Shannon-Mcmillan定理,推广了前人的结果.

弹性模量随深度变化的有限厚层轴对称问题的通解

本文通过资料分析,简要阐明了研究弹性模量随深度呈指数规律变化的有限厚层轴对称问题的必要性。联合运用Hankle和Laplace积分变换,对此问题进行求解。并将之退化为均质线弹性问题的解,从而验证了它的正确性。其通解适用于有限厚或无限深空间问题,并可推广到多层体系的分析中。