Initial Chain Algebras on Pseudotrees

We investigate a new class of Boolean algebra, called initial chain algebras on pseudotrees. We discuss the relationship between this class and other classes of Boolean algebras. Every interval algebra, and hence every countable Boolean algebra, is an initial chain algebra. Every initial chain algebra on a tree is a superatomic Boolean algebra, and every initial chain algebra on a pseudotree is a minimally-generated Boolean algebra.We show that a free product of two infinite Boolean algebras is an initial chain algebra if and only if both factors are countable.     

Some Remarks on Kernels

Kernel smoothing provides a simple way of finding a structure in data. Oneof the most popular settings where kernel smoothing ideas can be applied isthe simple regression model. In the context of kernel estimates of aregression function, the choice of a kernel from the different points ofview can be investigated. The aim of this paper is to present constructionsof minimum variance kernels and smooth kernels by means of the Legendrepolynomials and the Gegenbauer polynomials as well. Some of these kernelshave been introduced, e.g., in [2], [3], and [5], but here another approachby using the variational calculus is presented.     

Some Remarks on Orlicz-Lorentz Spaces

Spaces of Lorentz type called Orlicz-Lorentz spaces are studied. There are given necessary and sufficient conditions for the spaces to be order continuous, separable, KB-spaces and to contain isometric or isomorphic copy of l∞ or c₀. Moreover a criterion for strict convexity of these spaces is found.     

Some Remarks on Chung's Law

We discuss the notion of a "functional version of Chung's law of the iterated logarithm", and prove a result that incorporates both possible interpretations.     

关于拟本原p-块的一些说明

本文主要研究了拟本原p-块的性质,从而得到拟本原p-块与群中心结构的一些关系．     

极空间的注记

本文中我们提到的极空间的秩不必是有限的。得到的主要结果是，令S是一个不可约的极空间，如果p～q，p～q是S中的点，则有极空间是同构的，我们把它记作     

Some Remarks on Connected Coalgebras

In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category $ \mathcal{M} $ and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in the case when $ \mathcal{M} $ is the category of vector spaces over a field K. In particular we characterize when a 0-connected graded bialgebra is a bialgebra of type one.     

Some Remarks on Steiner Systems

The main purpose of this paper is to introduce Steiner systems obtained from the finite classical generalized hexagons of order q. We show that we can take the blocks of the Steiner systems amongst the lines and the traces of the hexagon, and we prove some facts about the automorphism groups. Also, we make a remark concerning the geometric construction of a known class (KW) of Steiner systems and we deduce some properties of the automorphism group.     

关于可信性模型的若干评注

可信性模型是经验费率厘定中最重要的方法，本文在简述可信性概念的发展简史并强调了有限扰动可信性和最精确可信性的区别后，重点剖析了最精确可信性的理论基础，且详尽地解释了导出（修正）Buehlmann单合同可信性模型的基本思路，在阶段性地展示了建立此模型基本假定的过程后，给出了风险保费与预测值的可信性估计的简明公式，现今最基础的Buehlmann-Straub可信性模型可视为由多个相互独立，且具有相同的结构函数的（修正）Buhlmann单合同模型相嵌而成，这种组嵌方式使得估计该模型的未知结构参数成为可能，本文最后概述了可信性模型的主要进展，全文的叙述是说明性的，不步及技术性证明过程，目的在于为理解可信性模型提供一个直观与清晰的思路。     

Some Remarks on Some Second-order Hyperbolic Differential Equations

We are concerned with the almost automorphic solutions to the second-order hyperbolic differential equations of type ü(s) + 2B ù(s) + Au(s) = f(s) (*), where A, B are densely defined closed linear operators acting in a Hilbert space H, and f : R |—> H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions, every solution to (*) is almost automorphic.     

Some Remarks on Relative Chebyshev Centers

In this work we study a relative Chebyshev center ofKwith respect toY, whereKis a closed bounded convex subset of a Hilbert spaceX, andYis a closed convex subset ofX. Some results of Amir and Mach [J. Approx. Theory40, (1984), 364–374] are extended.     

Some Remarks on p-Adic Analytic Groups

A theorem of Maranda [1, Section 30] states that if F is a finitegroup, p is a prime and p^e exactly divides |F|, then a Z_pF-latticeM is determined up to isomorphism by its finite quotient M/p^e+1M.If M is a free Z_p-module of rank d, this is equivalent to sayingthat representations of F in GL_d(Z_p) are determined up to equivalenceby their images modulo p^e+1. 1991 Mathematics Subject Classification20E18, 22E20.     

全纯二次微分的一些注记

记Q(X)为双曲黎曼曲面X上所有具有有限L^1-模的全纯二次微分所组成的Banach空间．本文讨论由V(φ)=|φ|/φ所定义的映射V：Q(x)→Q*(X)及其逆映射V^-1的连续性，并得到一些关于Teichmiiller空间几何的Lakic-型结果.     

Some Remarks on a Vibro-Impact Scheme

We consider a mechanical system subject to a unilateral constraint for which an impact law is defined. The impact process is considered to be instantaneous and the behavior at the impact is described through a restitution coefficient e. We solve this problem using an algorithm developed and used by Paoli and Schatzman. We show that this algorithm develops numerical instabilities related to the restitution coefficient used in the impact law. Finally, we propose a new scheme which introduces some numerical damping in order to avoid the numerical instabilities.     

Some Remarks on Differences between Totients

Mathematical Notes -