秩协方差分析及应用

吴占鹏．秩协方差分析及应用．数理统计与管理，１９９８，１７（３），７～１０．在随机区组试验中，区组内往往存在土壤梯度差异，使试验误差增大。为此，本文提出秩协方差分析方法，即把土壤差异εｉｊ分解成Δ·ｘｉｊ和δｉｊ两个成份，从中剔除土壤梯度差异Δ·ｘｉｊ对试验精度的影响，以提高试验结果的可靠性     

储层岩石周期性电渗流特性的微观机制

以双电层电位理论和电渗流动的动量方程为基础,结合储层岩石平行毛管束模型,推导出岩石孔隙内周期性电渗流的解析式,揭示了储层中电渗效应的微观机制,分析了非密闭储层岩石中宏观电渗Darcy速度及密闭储层中电渗压力系数频散特性的影响因素．数学模拟结果表明:储层岩石孔隙中,周期性电渗流速度剖面在频率较高时呈“波浪”状;孔隙度越大,电渗Darcy速度模值越大,其相位也越大,而电渗压力系数数值越小．储层岩石的溶液浓度越小或阳离子交换量越大,电渗Darcy速度模值和电渗压力系数数值越大,但对电渗Darcy速度的相位没有影响．     

用多指标正交试验的区间取值(RTV)综合评分法优化泥浆的配制

雷焕鸣等．用多指标正交试验的区间取值（ＲＴＶ）综合评分法优化泥浆的配制．数理统计与管理，１９９８，１７（４），１９～２３．雷焕鸣等．用多指标正交试验的区间取值（ＲＴＶ）综合评分法优化泥浆的配制．数理统计与管理，１９９８，１７（４），１９～２３．本文提出多指标正交法设计的一种综合评分方法。并将这种方法应用于钻井液——泥浆的配置之中，优选出的最优方案很受现场技术人员的好评，获得了良好的经济效益     

应用正交多项式设计法研究煤的粘附规律

丛茜等．应用正交多项式设计法研究煤的粘附规律．本文对影响煤与工作部件表面法向粘附力的二个主要因素：煤的含水量及所受正压力,进行了正交多项式回归设计,建立了显著的回归方程,并揭示了煤的粘附规律     

求解非线性互补问题的一个非精确信赖域方法

本文研究了基于非线性互补问题的等价非光滑优化问题的非精确依赖域方法，利用非线性规划的理论和方法，在一定条件下，获得了该方法的全局收敛性结果．     

均匀设计配制水泥基超细粉煤灰灌浆材料的研究

唐明，王继相．均匀设计配制水泥基超细粉煤灰灌浆材料的研究．数理统计与管理，１９９８，１７（４），１０～１９．唐明，王继相．均匀设计配制水泥基超细粉煤灰灌浆材料的研究．数理统计与管理，１９９８，１７（４），１０～１９．本研究用三因子多水平的均匀设计方法，研究了水泥基超细粉煤灰灌浆材料的性能，探索了组成材料对保水性和强度特性的影响规律，建立了相应的数学模型，优化求解对进一步开发该类材料，满足各种工程要求，提供了重要依据     

非光滑半无限多目标优化问题的Lagrange鞍点准则北大核心CSCD

本文研究了一类非光滑半无限多目标优化问题,并讨论它的鞍点准则．首先,定义了这类半无限多目标优化问题的标量和向量隋形的Lagrange函数和鞍点;其次,分别讨论了标量和向量情形的鞍点准则的必要性;最后,在非光滑（Ф,ρ）．不变凸性假设下给出这两种隋形的鞍点准则的充分性．     

处理污水的优化方案

李秀玲．处理污水的优化方案．数理统计与管理，１９９８，１７（４），１６～１８．     

非光滑多目标优化问题的最优性条件

本文利用极值原理在Fréchet次微分下研究了非光滑多目标优化问题的最优性条件.首先,研究了非光滑半无限多目标优化问题的必要性条件.随后,建立了非光滑多目标优化问题Henig真有效解的必要条件.     

非线性约束优化的光滑化平方根罚函数

介绍一种非线性约束优化的不可微平方根罚函数,为这种非光滑罚函数提出了一个新的光滑化函数和对应的罚优化问题,获得了原问题与光滑化罚优化问题目标之间的误差估计. 基于这种罚函数,提出了一个算法和收敛性证明,数值例子表明算法对解决非线性约束优化具有有效性.     

多目标优化正则条件的一个注记

给出带不等式约束的非光滑多目标优化问题正则条件的一个例子.通过该例,指出最近由Burachik和Rizvi利用线性化锥提出的可微多目标优化问题的正则条件不能利用Clarke导数推广到非光滑情形.     

First order approximations to nonsmooth mappings with application to metric regularity

The generalized Jacobian is used to examine various first order approximations to nonsmooth mappings between Banach spaces. As an application, we survey and extend various recently derived sufficient conditions for the metric regularity of(possibly infinite) systems of nonsmooth inequalities.     

Analysis of time discretization methods for Stokes equations with a nonsmooth forcing term

We consider a time dependent Stokes problem that is motivated by two-phase incompressible flow problems with surface tension. The surface tension force results in a right-hand side functional in the momentum equation with poor regularity properties. As a strongly simplified model problem we treat a Stokes problem with a similar time dependent nonsmooth forcing term. We consider the implicit Euler and Crank-Nicolson methods for time discretization. The regularity properties of the data are such that for the Crank-Nicolson method one can not apply error analyses known in the literature. We present a convergence analysis leading to a second order error bound in a suitable negative norm that is weaker that the $L^2$ -norm. Results of numerical experiments are shown that confirm the analysis.     

Optimality and Duality for Invex Nonsmooth Multiobjective programming problems

We consider nonsmooth multiobjective programming problems with inequality and equality constraints involving locally Lipschitz functions. Several sufficient optimality conditions under various (generalized) invexity assumptions and certain regularity conditions are presented. In addition, we introduce a Wolfe-type dual and Mond–Weir-type dual and establish duality relations under various (generalized) invexity and regularity conditions.     

On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential

The Cahn–Hilliard and viscous Cahn–Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved.     

Differentiability and regularity of Lipschitzian mappings

We introduce new differentiability properties of functions between Banach spaces and establish their relationships with graphical regularity of Lipschitzian single-valued and set-valued mappings. The proofs are based on advanced tools of nonsmooth variational analysis including new results on coderivative scalarization and normal cone calculus.

     

Regularity of functions smooth along foliations, and elliptic regularity

We produce two sets of results arising in the analysis of the degree of smoothness of a function that is known to be smooth along the leaves of one or more foliations. These foliations might arise from Anosov systems, and while each leaf is smooth, the leaves might vary in a nonsmooth fashion. One set of results gives microlocal regularity of such a function away from the conormal bundle of a foliation. The other set of results gives local regularity of solutions to a class of elliptic systems with fairly rough coefficients. Such a regularity theory is motivated by one attack on the foliation regularity problem.     

Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains

Global weighted Lp estimates are obtained for the gradient of solutions to nonlinear elliptic Dirichlet boundary value problems over a bounded nonsmooth domain. Morrey and Hölder regularity of solutions are also established, as a consequence. These results generalize various existing estimates for nonlinear equations. The nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation. The boundary of the domain, on the other hand, may exhibit roughness but assumed to be sufficiently flat in the sense of Reifenberg. Our approach uses maximal function estimates and Vitali covering lemma, and also known regularity results of solutions to nonlinear homogeneous equations.     

A Spline Collocation Method for Linear Volterra Integro-Differential Equations with Weakly Singular Kernels

The piecewise polynomial collocation method is discussed to solve linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. Using special graded grids, global convergence estimates are derived. The error analysis is based on certain regularity properties of the solution of the initial value problem.This revised version was published online in October 2005 with corrections to the Cover Date.     

Local existence, uniqueness and smooth dependence for nonsmooth quasilinear parabolic problems

We prove local existence, uniqueness, Hölder regularity in space and time, and smooth dependence in Hölder spaces for a general class of quasilinear parabolic initial boundary value problems with nonsmooth data. As a result the gap between low smoothness of the data, which is typical for many applications, and high smoothness of the solutions, which is necessary for the applicability of differential calculus to abstract formulations of the initial boundary value problems, has been closed. The theory works for any space dimension, and the nonlinearities in the equations as well as in the boundary conditions are allowed to be nonlocal and to have any growth. The main tools are new maximal regularity results (Griepentrog in Adv Differ Equ 12:781–840, 1031–1078, 2007) in Sobolev–Morrey spaces for linear parabolic initial boundary value problems with nonsmooth data, linearization techniques and the Implicit Function Theorem.