带有可测系数的二阶非线性抛物型方程组的初—混合边值问题

在多连通区域上研究带有可测系数的二阶非线性抛物型方程组的初－混合边值问题，首先我们将其化为复形式的方程组，并给出在一定条件下的上述初－这值问题解的先验估计，然后利用解的估计和列紧性原理，证明了这种初－边值问题解的存在性。在论证过程中，我们始终用复分析方法讨论文中所提出的问题，没有看到国外有人使用这种方法处理此类问题。     

Summation of arbitrary series by Riesz methods

It is known (theorem of Agnew and Darevskii) that for each divergent real sequence {s} and each real number c, there exists a T-method of summing {s_n} to c. In this note it is shown that for each divergent sequence which is bounded above or below we can take the T-method in the above theorem to be a Riesz method. We also study Riesz summability of unbounded (above and below) sequences.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 541–550, November, 1968.     

ON THE SYMPLECTIC REDUCTIONS

A symplectic reduction method for symplectic G-spaces is given in this paper without usingthe existence of momentum mappings.By a method similar to the above one,the arthorsgive a symplectic reduction method for the Poisson action of Poisson Lie groups on symplecticmanifolds,also without using the existence of momentum mappings.The symplectic reductionmethod for momentum mappings is thus a special case of the above results.     

ON THE SYMPLECTIC REDUCTIONS

A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.     

Oblique derivative problems for linear mixed equations of second order

Oblique derivative boundary value problems for the linear mixed (elliptic-hyperbolic) equation of the second order, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions are discussed. The representation of solutions for the above boundary value problem is given, the uniqueness and existence of solutions of the above problem are proved, and a priori estimates of the solutions of the above problem are obtained. Project supported by the National Natural Science Foundation of China.     

Oblique Derivative Problem for Quasilinear Mixed (Lavrentév-Bitsadze) Equations of Second Order in Two Connected Domains

In this article, we first give the representation of solutions for the oblique derivative problem of mixed (Lavrentév-Bitsadze) equations in two connected domains, afterwards prove the uniqueness of solutions of the above problem. Moreover, we prove the solvability of oblique derivative problem for quasilinear mixed (Lavrentév-Bitsadze) equations of second order, and obtain a priori estimates of solutions of the above problem. The above problem is an open problem proposed by Rassias.     

关于猝灭问题的一些结果及其应用

本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。     

AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献   

On complete Finslerian Yamabe solitons

Here it is shown that any Finslerian compact Yamabe soliton with bounded above scalar curvature is of constant scalar curvature. Furthermore, this extension of Yamabe solitons is developed for inequalities and among the others, it is proved that a forward complete non-compact shrinking Yamabe soliton has finite fundamental group and its first cohomology group vanishes, providing the scalar curvature is strictly bounded above.     

On estimation in multivariate linear calibration with elliptical errors

The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and give unbiased estimate of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution. From the unbiased estimate of risk, it is shown that a shrinkage estimator improves on the classical estimator under the loss function. Furthermore, from the extended Stein and Stein-Haff identities for our elliptically contoured distribution, the above result under normal errors is extended to the estimation problem under elliptical errors. We show that the shrinkage estimator obtained under normal models is better than the classical estimator under elliptical errors with the above loss function and hence we establish the robustness of the above shrinkage estimator.     

奇异三阶积分边值问题正解的全局分歧

研究带Riemann-Stieltjes积分边值条件的奇异三阶积分边值问题正解的全局分歧结构.首先,利用相关文献,获得了此类问题的格林函数并推证其满足的性质,同时可获得此类问题等价于一个全连续算子方程;其次,在满足所给的条件时,利用Krein-Rutmann定理建立了此类问题对应的线性问题存在简单的主特征值;最后,当非线性项在零和无穷远处满足非渐进线性增长条件、参数满足不同范围的值时,利用Dancer全局分歧定理、Zeidler全局分歧定理和序列集取极限的方法,建立了此类问题正解的全局结构,进而获得了正解的存在性.     

Boundary value problems for first-order mixed complex equations with degenerate curve

This article deals with some boundary value problems for quasilinear mixed (elliptic-hyperbolic) complex equations of first order with degenerate hyperbolic curve in a simply connected domain. First, we give the representation theorem and prove the uniqueness of solutions for the above boundary value problems. Then using the method of successive iteration, the existence of solutions for the above problems is proved.     

On the expected discounted penalty functions for two classes of risk processes under a threshold dividend strategy

In this paper, the discounted penalty (Gerber-Shiu) functions for a risk model involving two independent classes of insurance risks under a threshold dividend strategy are developed. We also assume that the two claim number processes are independent Poisson and generalized Erlang (2) processes, respectively. When the surplus is above this threshold level, dividends are paid at a constant rate that does not exceed the premium rate. Two systems of integro-differential equations for discounted penalty functions are derived, based on whether the surplus is above this threshold level. Laplace transformations of the discounted penalty functions when the surplus is below the threshold level are obtained. And we also derive a system of renewal equations satisfied by the discounted penalty function with initial surplus above the threshold strategy via the Dickson-Hipp operator. Finally, analytical solutions of the two systems of integro-differential equations are presented.     

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved.     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

A new bound for neighbor-connectivity of abelian Cayley graphs

For the notion of neighbor-connectivity in graphs, whenever a vertex is “subverted” the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. The main result of this paper is a sharpening of the bound for abelian Cayley graphs. In particular, we show by constructing an effective subversion strategy for such graphs, that neighbor-connectivity is bounded above by ⌈δ/2⌉+2. Using a result of Watkins the new bound can be recast in terms of κ to get neighbor-connectivity bounded above by ⌈3κ/4⌉+2 for abelian Cayley graphs.     

Tests for sphericity under correlated multivariate regression equations model

Summary In this paper, the authors investigated the asymptotic distribution theory connected with the likelihood ratio test (LRT)-like test statistic for sphericity under correlated multivariate regression equations (CMRE) model. An asymptotic expression is obtained for the null distribution of the above test statistic. Asymptotic nonnull distribution of the above test statistic under fixed alternatives is also derived. The above results are derived when the underlying distribution is multivariate normal. It was also shown that the above results are valid even when the joint distribution of the observations is elliptically symmetric. The authors also derived the asymptotic null distribution of the LRT-like test statistic when the observations on each variable are elliptically symmetric. This work was supported by the Air Force Office of Scientific Research under Contract F49620-82-K-0001. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article.a normalized biholomorphic mapping f defined on bounded starlike circular domain in C″is considered,where z=0 is a zero of order k 1 of f(z)(?) The sharp growth.covering theorems for almost starlike mappings of order a and starlile mappings of order wave established.Meanwhile,the construction of the above mappings on bounded starlike circular domain in C~n is also discussed,it provides the extremal mappings for the growth,covering theorems of the above mappings.     

Asymptotic behaviour of high Gaussian minima

We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high level is exceeded, the conditional shape of the process above the high level, and the location of the minimum of the process given that the sample path is above a high level.     

Superantichains in the Lattice of Partitions of a Set

A construction of superantichains in the lattice of partitions of finite sets is presented that works for set sizes above 10⁷. The construction refines Canfield's, which worked only for set sizes above 10²⁰, and provides a classification of the properties of partitions which allow such antichains to exist.