一类高阶拟线性椭圆型方程奇摄动边值问题

本文讨论了一类拟线性椭圆型方程奇摄动Dirichlet边值问题．在适当的条件下，利用不动点定理，研究了边值问题解的存在唯一性及其渐近性态．     

关于奇异二阶微分方程（Φ（X’））’＋f（t，X）＝0的某些可解准则

本文讨论了一类右端具有奇异性的二阶常微分方程的边值问题，证明了当ｆ（ｔ，ｘ）关于ｔ的奇异程度大于某值时，边值问题无解，而当奇异程度小于某值时，边值问题有解．关于ｕ在ｕ＝０的奇异程度没有限制．     

非线性四阶方程正解存在问题

本文讨论了一个四阶非线性方程在二类不同边界条件下正解的存在问题，即多点边值问题和积分型的边值问题．采用的方法是锥拉伸和压缩不动点定理，这里的结果推广了这类四阶方程边值问题的结果．     

二阶常微分方程及Thomas—Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．Ｄ．Ｌｕｎｉｎｇ的结果。     

二阶常微分方程及Thomas－Fermi方程的边值问题

本文利用上、下解方法推广了Ｍ．Ｌｅｅｓ关于半线性边值问题的结果，给出了另一类边值问题解的存在唯一性的一个充分条件；并利用所得的结果证明了Ｔｈｏｍａｓ－Ｆｅｒｍｉ方程的边值问题解的存在唯一性，从而推广了Ｃ．ＤＬｕｎｉｎｇ的结果．     

一类广义解析函数的Riemann边值逆问题

本文给出了一类有关广义解析函数Riemann边值逆问题的数学提法．在将此边值逆问题转化为边值问题的基础上，借助于广义解析函数边值问题的相关理论，分别获得了此边值逆问题在正则型和非正则型情况下的解．     

非正则型Hilbert边值问题

本文考虑了解析函数非正则型的Hilbert边值问题．利用对称扩张法将问题化为等价的正则型Riemann边值问题，获得了问题的通解及可解性条件，同时给出了问题可解的一个必要条件．     

一般区域上在边界退化的拟线性抛物方程的第—初边值问题

对有界域上拟线性抛物方程第一初边值问题，二阶退化拟线性抛物方程初边值问题已有丰富的成果，可见［１］，［２］，［３］，但对任意域上方程的工作则不多见．在此文中，我们讨论任意区域上在边界退化的拟线性抛物方程初边值问题的存在性．     

一维p-Laplacian方程边值问题多解的存在性

利用Clark定理，研究了一维p-Laplacian方程边值问题多解的存在性，得到了这类边值问题至少有n对非平凡解的充分条件．     

非线性项有非线性增长的高阶多点边值问题

本文考虑以下高阶多点边值问题：，其中关于f有非线性增长的情况，利用基于度理论的不动点定理，对上述边值问题建立了存在唯一性定理．     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Numerical methods for Hamilton Jacobi functional differential equations

Initial and initial boundary value problems for first order partial functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both the methods. It is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for implicit methods. There are implicit difference schemes which are convergent and corresponding explicit difference methods are not convergent. Error estimates for both the methods are construted.     

Determinant formulas with applications to designing when the observations are correlated

In the general linear model consider the designing problem for the Gauß-Markov estimator or for the least squares estimator when the observations are correlated. Determinant formulas are proved being useful for theD-criterion. They allow, for example, a (nearly) elementary proof and a generalization of recent results for an important linear model with multiple response. In the second part of the paper the determinant formulas are used for deriving lower bounds for the efficiency of a design. These bounds are applied in examples for tridiagonal covariance matrices. For these examples maximin designs are determined.Parts of the paper are based on a part of the author's Habilitationsschrift Bischoff (1993a).     

Mixtures of Global and Local Edgeworth Expansions and Their Applications

Edgeworth expansions which are local in one coordinate and global in the rest of the coordinates are obtained for sums of independent but not identically distributed random vectors. Expansions for conditional probabilities are deduced from these. Both lattice and continuous conditioning variables are considered. The results are then applied to derive Edgeworth expansions for bootstrap distributions, for Bayesian bootstrap distribution, and for the distributions of statistics based on samples from finite populations. This results in a unified theory of Edgeworth expansions for resampling procedures. The Bayesian bootstrap is shown to be second order correct for smooth positive “priors,” whenever the third cumulant of the “prior” is equal to the third power of its standard deviation. Similar results are established for weighted bootstrap when the weights are constructed from random variables with a lattice distribution.     

Invertibility and Spectrum of Hille–Tamarkin Matrices

Hille–Tamarkin matrices are investigated.Invertibility conditions and estimates for the norm of the inverse matrices are established. In addition, bounds for the spectrum are suggested. In particular, new estimates for the spectral radius are derived.     

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

Ｂ－ｖｅｘＦｕｚｚｙＭａｐｐｉｎｇｓａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎｔｏＦｕｚｚｙＯｐｔｉｍｉｚａｔｉｏｎＰｒｏｂｌｅｍｓ￥ＬｉｕＤｅｆｅｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＱｕａｎｔｉｔａｔｉｖｅＥｃｏｎｏｍｉｃｓ，ＤｏｎｇｂｅｉＵｎｉｖｅｒｓｉｔｙＯｆ...     

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.     

Constitutive Modelling of Resins in the Stiffness Domain

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.     

SOR-like Methods for Augmented Systems

Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.     

Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes

Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.