Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.

     

A uniform refinement property for congruence lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tuma. In a previous paper, we constructed a distributive algebraic lattice with compact elements that cannot be obtained by Schmidt's construction. In this paper, we show that the same lattice cannot be obtained using the Pudlák, Tischendorf, Tuma approach.

The basic idea is that every congruence lattice arising from either method satisfies the Uniform Refinement Property, that is not satisfied by our example. This yields, in turn, corresponding negative results about congruence lattices of sectionally complemented lattices and two-sided ideals of von Neumann regular rings.

     

Countable Products of Čech-scattered supercomplete spaces

We prove by using well-founded trees that a countable product of supercomplete spaces, scattered with respect to ech-complete subsets, is supercomplete. This result extends results given in [1], [5], [6], [19], [26] and its proof improves that given in [19].     

均匀磁场中带电粒子的四类升降算子

用因式分解法求出带电粒子在垂直于均匀磁场的平均面内运动体系的四类升降算子,并了相应的选择定则和守恒量子数。     

UNIFORM BOUNDEDNESS AND UNIFORM STABILITY OF A KIND OF DELAY──DIFFERENTIAL EQUATIONS

ＵＮＩＦＯＲＭＢＯＵＮＤＥＤＮＥＳＳＡＮＤＵＮＩＦＯＲＭＳＴＡＢＩＬＩＴＹＯＦＡＫＩＮＤＯＦＤＥＬＡＹ──ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＺｈｅｎｇＢｕｎａｎ（ＧｕａｎｇｘｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａ...     

Waiting time problems for a sequence of discrete random variables

Let X ₁, X ₂,... be a sequence of nonnegative integer valued random variables.For each nonnegative integer i, we are given a positive integer k _i . For every i = 0, 1, 2,..., E _i denotes the event that a run of i of length k _i occurs in the sequence X ₁, X ₂,.... For the sequence X ₁, X ₂,..., the generalized pgf's of the distributions of the waiting times until the r-th occurrence among the events % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaiWabeaacaWGfbWaaSbaaSqaaiaadMgaaeqaaaGccaGL7bGaayzF% aaWaa0baaSqaaiaadMgacqGH9aqpcaaIWaaabaGaeyOhIukaaaaa!43D8!\[\left\{ {E_i } \right\}_{i = 0}^\infty\]are obtained. Though our situations are general, the results are very simple. For the special cases that X's are i.i.d. and {0, 1}-valued, the corresponding results are consistent with previously published results.This research was partially supported by the ISM Cooperative Research Program (90-ISM-CRP-11) of the Institute of Statistical Mathematics.     

Uniform Growth of Polycyclic Groups

We prove that polycyclic groups have uniform exponential or polynomial growth.     

MSE's of prediction in growth curve model with covariance structures

We consider the growth curve model with covariance structures: positive-definite, uniform covariance structure and serial covariance structure. Two types of prediction problems are studied in this paper. One is called the conditional prediction problem and the other is called the extended prediction problem. For both types of prediction problems, the mean squared error for a serial covariance structure is obtained for the estimates based on the conditional expectation: the mean squared error for an unrestricted covariance structure is compared with the mean squared error for a uniform covariance structure or a serial covariance structure. These results are exemplified by two sets of real data.This research was supported in part by Grant-in-Aid for general Scientific Research, The Ministry of Education, Science and Culture under Contract Number 03640239.     

Numerical algorithms for uniform Airy-type asymptotic expansions

Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.     

Distance—Stability of Nonlinear Discrete Systems

In this paper,the distance-sability of nonlinear discrete system is investigated by meansof the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.