On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.     

Generalizations of Polya's urn Problem

We consider generalizations of the classical Polya urn problem: Given finitely many bins each containing one ball, suppose that additional balls arrive one at a time. For each new ball, with probability p, create a new bin and place the ball in that bin; with probability 1–p, place the ball in an existing bin, such that the probability that the ball is placed in a bin is proportional to $ m^\gamma $, where m is the number of balls in that bin. For p=0, the number of bins is fixed and finite, and the behavior of the process depends on whether is greater than, equal to, or less than 1. We survey the known results and give new proofs for all three cases. We then consider the case p>0. When =1, this is equivalent to the so-called preferential attachment scheme which leads to power law distribution for bin sizes. When >1, we prove that a single bin dominates, i.e., as the number of balls goes to infinity, the probability that any new ball either goes into that bin or creates a new bin converges to 1. When p > 0 and < 1, we show that under the assumption that certain limits exist, the fraction of bins having m balls shrinks exponentially as a function of m. We then discuss further generalizations and pose several open problems.AMS Subject Classification: 05D40, 60C05, 60G20, 68R10, 91C99.     

Some Generalizations of the Pinwheel Tiling

We introduce a new family of nonperiodic tilings, based on a substitution rule that generalizes the pinwheel tiling of Conway and Radin. In each tiling the tiles are similar to a single triangular prototile. In a countable number of cases, the tiles appear in a finite number of sizes and an infinite number of orientations. These tilings generally do not meet full-edge to full-edge, but can be forced through local matching rules. In a countable number of cases, the tiles appear in a finite number of orientations but an infinite number of sizes, all within a set range, while in an uncountable number of cases both the number of sizes and the number of orientations is infinite. Received April 9, 1996, and in revised form September 16, 1996.     

On Some Generalizations and Refinements of a Ky Fan Inequality

In this paper, a Ky Fan inequality and an inequality by Wu and Wang [10] will be generalized. Some new and improved refinements of the Ky Fan inequality will be put forward.AMS Subject Classification (2000) 26D15     

关于Hilbert积分不等式新的改进和推广

本文通过引入一些常数，运用一些分析技巧和Young不等式，给出了Hilbert积分不等式的一些新的改进和推广。     

Some Generalizations of the Notion of Length

Two numerical characteristics of a nonrectifiable arc generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums , where are the lengths of segments of a polygonal line inscribed in the curve and is a given function. On the other hand, the length of is the norm of the functional in the space ; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve implies its generalized analytic rectifiability.     

Some Generalizations of Semimartingales in the Plane

51.IntroductionTwo(parametersemi-martingaleswereinvestigated,forexample,inthepaperbyBrennan[21,Cairoli[3]andZakai[81.Inthispaperwegeneralizetheconceptofatwo-parametersemimartingaleandinvestigatesomepropertiesofthegeneralizedsemi-martingaoes.Wealsodefineaclassofpositivemeasuresassociatedwiththegeneralizedsemi-martingales.InSectionII,followingtheterminologygivenin[21,wedefinestrongandweakA--processesoforderp,alsofor15p相似文献   

A Combinatorial Algorithm for the Minimum (2, r)-Metric Problem and Some Generalizations

be a graph with nonnegative integer capacities c(e) of the edges , and let μ be a metric that establishes distances on the pairs of elements of a subset . In the minimum 0-extension problem (*), one is asked for finding a (semi)metric m on V such that m coincides with μ within T, each is at zero distance from some , and the value is as small as possible. This is the classical minimum (undirected) cut problem when and , and the minimum (2, r)-metric problem when μ is the path metric of the complete bipartite graph . It is known that the latter problem can be solved in strongly polynomial time by use of the ellipsoid method. We develop a polynomial time algorithm for the minimum (2, r)-metric problem, using only ``purely combinatorial' means. The algorithm simultaneously solves a certain associated integer multiflow problem. We then apply this algorithm to solve (*) for a wider class of metrics μ, present other results and raise open questions. Received: June 11, 1998     

Krasnoselskii定理几种新的推广

利用随机不动点指数,研究了随机半闭1-集压缩算子方程的随机解,同时,从不同角度推广了著名的Krasnoselskii定理,得出若干新的结果.     

广义双拟变分不等式的推广*

本文引出和研究了一类新型双拟变分不等式解的存在性问题.本文的结果统一、改进和发展了有关变分不等式问题许多最新的结果.     

Lehmer问题的两个推广

设素数P>2,整数C与P互素．对任意整数1≤a≤P-1,存在惟一的整数 1≤b≤P-1满足ab≡c mod P．Lehmer建议我们研究a与b的奇偶性不同的情形．本文给出了这一问题的两个推广,并获得了两个有趣的混合均值公式．     

关于分离性和同胚关系的一些推广

1963年Norman Levine引入了半开集和半连续函数的概念。1972年S.Gene Crossley等又引入不定函数和前半开函数,定义了半同胚,讨论了一系列的半拓扑性质。以后出现了不少有关半开集和半同胚方面的论文。作者拟在这里进一步引入两类分离性和几种新的同胚,并且指出在一定意义下有些名称应当改变。 首先,我们在这里利用半开集,产生一种分离手段——半开集分离性,从而定义一系列新的拓扑空间,它们之间及它们与T_(i-)型拓扑空间(i=0,1,2,3,4)之间有着一定的联     

一类积分不等式的推广

对一些基本的积分不等式进行了推广，给出了含有n个无关变元的更广泛的非线性积分不等式．利用所得的不等式讨论了某些非线性积分方程解的有界性．     

On Generalizations of Commutativity

This note is concerned with generalizations of commutativity. We introduce identity-symmetric and right near-commutative, and study basic structures of rings with such ring properties. It is shown that if R is an identity-symmetric ring, then the set of all nilpotent elements forms a commutative subring of R. Moreover, identity-symmetric regular rings are proved to be commutative. The near-commutativity is shown to be not left-right symmetric, and we study some conditions under which the near-commutativity is left-right symmetric. We also examine the near-commutativity of skew-trivial extensions, which has a role in this note.     

一道考研题的推广及其几种证法

针对一道研究生入学考试题进行了推广,并对推广的命题给出了四种证明方法.