一个条件不等式的图形证明与加强

一个条件不等式的图形证明与加强６４８５００四川武隆县中学夏中全本刊１９９５年第１０期Ｐ１２８出了下面试题：设０＜ｘ，ｙ，ｚ＜ｌ，证明：原文通过构造三角形给出了一个巧妙的图形证明，本文则通过相适正方形结出又一巧妙的图形证明．证如图是边长为１的正步形ＡＢ...     

巧用伸缩变换解决椭圆问题

在伸缩变换下,平面图形要发生相应的变化．如圆在伸缩变换下可变成椭圆,而椭圆在伸缩变换下又可变成圆．圆是我们相当熟悉的图形,它的许多性质的推导和证明都比较容易,在圆中研究图形的某种性质然后再还原到椭圆中,从而得到椭圆的相应性质,这往往要比直接在椭圆中进行计算和证明简单得多．     

关于1-序列商映射

引进了1-序列商映射，证明了1-序列商映射象保持sm-第一可数空间．作为这一结果的一个应用，本文证明了几乎开，闭映射保持度量空间，g-度量空间，sm-度量空间．此外本文还证明了度量空间上的1-序列商，紧映射是1-序列覆盖映射．这些结果改进并推广了广义度量空间映射象的有关理论．     

任意细分面具的级联算法对单个初始函数的收敛性

级联算法在计算机图形和小波分析中都有很重要的作用．对任意的初始函数φ0，一个级联序列(φ_n)_(n=1)~∞是由迭代产生的序列φ_n=C_aφ_(n-1)(n=1，2，…)，其中 C_a 定义为C_ag=sum from α∈Ζa(α)g(2·-α)，g∈L_p(R)．用函数序列和联合谱半径刻画了级联序列的收敛性．作为一个结果，证明了任意的级联收敛序列都有几何收敛速度，即‖φ_(n-1)-φ_n‖_[L_p(R)]=O((?)~n)对某个(?)∈(0，1)成立．不要求对面具的求和定则的条件．     

Banach空间奇摄动非线性微分方程的边值问题

对Banach空间中奇摄动非线性微分方程的边值问题，当空间弱序列完备时，证明存在单调序列{vn}和{un}分别一致收敛于两点边值问题的最大解和最小解．     

非等腰梯形映射族MSS序列的唯一性

本文研究非等腰梯形映射族ＭＳＳ序列的唯一性问题．我们证明在（约为０．３６１１０３…）时，对非等腰梯形映射族，给定一个ＭＳＳ序列Ａ，存在唯一的 ， 使     

立体几何中有关平行的证明

立体几何中有关平行的证明张强（湖北沙市一中４３４０００）在立体几何中，有关平行的问题是重点内容之一，也是学生推理论证时感到困难的图１线面平行的基本图形地方．本文提出两个基本图形，借以帮助学生快速找到解题的突破口，化解思维障碍，理顺思路．平行问题有三种...     

关注证明思路的获得还要关注对证明的理解——以“三角形内角和定理”的教学为例北大核心

三角形内角和定理是平面几何中最重要的三个定理之一．鉴于它的重要性,也是各级各类研究课常见的课题．通过现场听课和查阅文献,发现：大部分教师把本节课的教学重点定位在“让学生从拼图操作实验中获得证明的思路及三角形内角和定理的证明”,而证明三角形内角和定理的思路大多都是通过“实物拼图一留下痕迹一抽象图形一理解图形变化一分析提升”的途径获得．     

Bernoulli序列的无规则性定理的一种分析证法

本文的目的是要利用纯分析的方法，证明Bernoulli序列的无规则性定理．     

Bernoulli序列的无规则性定理的一种分析证法

本文的目的是要利用纯分析的方法，证明Ｂｅｒｎｏｕｌｉ序列的无规则性定理．     

Annihilators in Nonrepetitive Semigroups

It is well known that one can construct an infinite sequence on three or more symbols such that no two consecutive blocks are identical. In this paper we give a combinatorial characterization for those finite sequences which are maximal in the sense that appending to them even one more symbol yields two consecutive identical blocks.     

Measure for measure: Abell's narrative methods

This paper considers Abell's methods for analysis of narratives. I first consider the difference between the question of sequence pattern and the question of sequence generation, examining in paticular Abell's use of rational choice theory. I then consider some minor issues related to the choice of tolerances as foundations for homomorphisms among sequences. Finally, I analyze Abell's use of homomorphisms and propose replacing homomorphic reduaion of sequences with Levenshtein metrics defined on elementary operations like those Abell uses. This strategy could allow a more complete and parsimonious categorization than does Abell's present strategy.     

产生 M 序列的一个递推算法

§1.引言M 序列又称 de Bruijn 序列,是一类具有最长周期的非线性移位寄存器序列。本文研究产生 M 序列的算法。早在70年代万哲先等对构造 M 序列的方法已有系统的研究。此后有一系列的文章研究 M 序列的构造问题。最近 Fredricksen 对这方面的工作给出了一个很好的综述。产生 M 序列的一个常用方法是先由一个较简单的移位寄存器产生许多短圈,再用并圈法将这些短圈合并起来构成 M 序列。如在[1,6]中就已给出过一些将 n 级纯轮换移位寄存器(简记为 PCK_n)和 n 级补轮换移位寄存器(简记为 CCR_n)产生的圈合并为 M 序列的方法。与[1—7]不同,Fredricksen 给出一个将 PCR_n 产生的圈合并为 M 序列的递推算法。最近 Etzion 和 Lempe 在 Fredricksen 算法的基础     

The theory and computation of evolutionary distances: Pattern recognition

A method of finding pattern similarities between two sequences is given. Two portions, one from each sequence, are similar if they are close in the metric space of evolutionary distances. The method allows a complete list to be made of all pairs of intervals, one from each of two given sequences, such that each pair displays a maximum local degree of similarity, and, if the lengths of the given sequences are m and n, then the procedure takes on the order of mn computational steps. This result lends itself to finding similarities by computer between pairs of biological sequences, such as proteins and nucleic acids.     

On matching numbers of tree and bipartite degree sequences

We study the possible values of the matching number among all trees with a given degree sequence as well as all bipartite graphs with a given bipartite degree sequence. For tree degree sequences, we obtain closed formulas for the possible values. For bipartite degree sequences, we show the existence of realizations with a restricted structure, which allows to derive an analogue of the Gale–Ryser Theorem characterizing bipartite degree sequences. More precisely, we show that a bipartite degree sequence has a realization with a certain matching number if and only if a cubic number of inequalities similar to those in the Gale–Ryser Theorem are satisfied. For tree degree sequences as well as for bipartite degree sequences, the possible values of the matching number form intervals.     

An algebra of differential operators and generating functions on the set of univalent functions

With a method close to that of Kirillov [4], we define sequences of vector fields on the set of univalent functions and we construct systems of partial differential equations which have the sequence of the Faber polynomials (F_n) as a solution. Through the Faber polynomials and Grunsky coefficients, we obtain the generating functions for some of the sequences of vector fields.     

Slow Passage Through the Nonhyperbolic Homoclinic Orbit of the Saddle-Center Hamiltonian Bifurcation

Slowly varying Hamiltonian systems, for which action is a well-known adiabatic invariant, are considered in the case where the system undergoes a saddle center bifurcation. We analyze the situation in which the solution slowly passes through the nonhyperbolic homoclinic orbit created at the saddle-center bifurcation. The solution near this homoclinic orbit consists of a large sequence of homoclinic orbits surrounded by near approaches to the autonomous nonlinear nonhyperbolic saddle point. By matching this solution to the strongly nonlinear oscillations obtained by averaging before and after crossing the homoclinic orbit, we determine the change in the action. If one orbit comes sufficiently close to the nonlinear saddle point, then that one saddle approach instead satisfies the nonautonomous first Painlevé equation, whose stable manifold of the unstable saddle (created in the saddle-center bifurcation) separates solutions approaching the stable center from those involving sequences of nearly homoclinic orbits.     

A Formal Calculus for the Enumerative System of Sequences—I. Combinatorial Theorems

The enumeration of sequences plays an important part in combinatorial enumeration since sequences may be used as a means for encoding combinatorial structures. In the main, the enumeration of sequences has been treated by a collection of methods individually applied in particular cases. We present here a uniform constructive method for dealing with a large class of sequence problems. We obtain the generating function as the trace of an expression involving certain incidence matrices, expressions which are obtainable immediately from the combinatorial structure of a problem. The method relies on certain properties of matrices whose rank is equal to one. We demonstrate that these properties may be used to derive the required generating functions explicitly or, in more complex cases, as solutions to systems of linear equations. Results for permutations may be derived from those for sequences, and in certain frequently encountered special cases this operation may be carried out by a straightforward substitution. Applications of the method presented here will be given in Part II.     

Summation of almost convergent divergent sequences,topological methods

In this paper we give a characterization of the conservative matrices that sum only those divergent sequences which are not almost convergent. Such conditions are similar to those which are necessary and sufficient for a conservative matrix to sum no bounded divergent sequence (Agnew [1], Mazur-Orlicz [4], Wilansky-Zeller [6], and Zeller [7]). There are, however, some differences showing, that the results mentioned above cannot be transmitted without any restriction. Parts of this paper have been already developed by the author more detailed in [5].     

Scheduling Multiclass Packet Streams to Minimize Weighted Loss

We consider the problem of scheduling an arriving sequence of packets at a single server. Associated with each packet is a deadline by which the packet must be scheduled. Each packet belongs to one of a predetermined set of classes, and each class has an associated weight value. The goal is to minimize the total weighted value of the packets that miss their deadlines. We first prove that there is no policy that minimizes this weighted loss for all finite arrival sequences of packets. We then present a class of greedy scheduling policies, called the current-minloss throughput-optimal (CMTO) policies. We characterize all CMTO policies, and provide examples of easily implementable CMTO policies. We compare CMTO policies with a multiclass extension of the earliest-deadline-first (EDF) policy, called EDF+, establishing that a subclass of CMTO policies achieves no more weighted loss than EDF+ for any traffic sequence, and at the same time achieves a substantial weighted-loss advantage over EDF+ for some traffic sequences – this advantage is shown to be arbitrarily close to the maximum possible achievable advantage. We also provide empirical results to quantify the weighted-loss advantage of CMTO policies over EDF+ and the static-priority (SP) policy, showing an advantage exceeding an order of magnitude when serving heavy-tailed aggregations of MPEG traces.