论p-Bergman,α-Bloch,小α-Bloch空间与Cesro平均

对于ｐ，α∈（０，∞）设Ａｐ，Ｂα和Ｂ０α分别是开单位圆盘上的ｐ－Ｂｅｒｇｍａｎ，α－Ｂｌｏｃｈ和小α－Ｂｌｏｃｈ空间本文首先给出Ａｐ，Ｂα和Ｂα０之间的进一步关系；其次，研究Ａｐ，Ｂα和Ｂα０中的Ｔａｙｌｏｒ级数之部分和的Ｃｅｓｒｏ平均；最后，讨论Ａｐ，Ｂα和Ｂα０中Ｔａｙｌｏｒ级数之系数的Ｃｅｓｒｏ平均     

涉及迹同伦范畴的几对伴随函子

Ｋ．Ａ．Ｈａｒｄｉｅ与Ｋ．Ｈ．Ｋａｍｐｓ研究过固定空间Ｂ上的迹同伦范畴（［１］）．他们引进了两对伴随函子ＰＢ┤ＮＢ与ｍ┤ｍ，此处ｍ：ＡＢ是固定映射，ＰＢ：ＨＢＨＢ与ｍ：ＨＡＨＢ是函子．我们在［２］中引进了分裂的范畴纤维化Ｌ：ＨｂＨＢ，并且证明了Ｌ┤Ｊ，Ｊ┤Ｌ．本文首先将ＰＢ┤ＮＢ推广到ＰＢｂ┤ＮＢｂ＃，其中ｂ：ＢＢ是任一固定映射，并且我们还得到涉及迹同伦范畴Ｈｂ与Ｈｂ的两对伴随函子，此处Ｈｂ是Ｈｂ的对偶．特别，Ｎｂ┤Ｐｂ不同于ＰＢ┤ＮＢ．     

Bent函数的一般构造法

本文用概率方法给出小项表示的布尔函数谱的性质,据此得到了Ｂｅｎｔ函数的特征矩阵的等价刻画,原则上给出了Ｂｅｎｔ函数的一般构造法,并为Ｂｅｎｔ函数的计数问题提供了一个模型。文中还提出了Ｂｅｎｔ矩阵的概念,考察了Ｂｅｎｔ矩阵的性质,并借助Ｂｅｎｔ矩阵得到由已知Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数的方法。     

数学问题解答

20 0 0年 1 2月号问题解答(解答由问题提供人给出 )1 2 86　直三棱柱ＡＢＣ———Ａ1 Ｂ1 Ｃ1 中 ,ＡＢ1 ⊥ＢＣ1 、ＢＣ1 ⊥ＣＡ1 、ＣＡ1 ⊥ＡＢ1 试证 :该棱柱是正棱柱 .(浙江省湖州市双林中学　李建潮　 31 30 1 2 )证明　先由ＡＢ1 ⊥ＢＣ1 、ＢＣ1 ⊥ＣＡ1 证ＡＢ =ＡＣ .在底面ＡＢＣ内作ＡＤ ⊥ＢＣ于Ｄ .∵底面ＡＢＣ ⊥侧面Ｂ1 ＢＣＣ1 ∴ＡＤ ⊥侧面Ｂ1 ＢＣＣ1 ①知Ｂ1 Ｄ是ＡＢ1 在侧面Ｂ1 ＢＣＣ1 上的射影 .∵ＢＣ1 ⊥ＡＢ1∴ＢＣ1 ⊥Ｂ1 Ｄ又在底面Ａ1 Ｂ1 Ｃ1 内Ａ1 Ｄ1 ⊥Ｂ1 Ｃ1 于Ｄ1 ,同理可证Ａ1 Ｄ1 ⊥侧面Ｂ1 ＢＣ…     

以三角形的三边构图的数学名题

题 1　 (拿破仑定理 )以△ＡＢＣ各边为边分别向外作等边三角形 ,则它们的中心构成一个等边三角形 .(此定理是法国皇帝拿破仑发现的 ,又叫拿破仑三角形 )图 1证明　如图 1,等边△Ａ′ＢＣ、△ＡＢ′Ｃ、△ＡＢＣ′的中心分别为Ｏ1 、Ｏ2 、Ｏ3,连结ＢＢ′ ,ＣＣ′ .∵　∠ＢＡＢ′ =∠ＣＡＣ′ =∠ＢＡＣ +60° ,∴　△ＢＡＢ′≌△Ｃ′ＡＣ .故　ＢＢ′ =ＣＣ′.同理可得　ＡＡ′ =ＢＢ′ =ＣＣ′.记△ＡＢＣ三边分别为ａ、ｂ、ｃ,连结ＢＯ1 、ＢＯ3,则ＢＯ1 =33 ａ ,　ＢＯ3=33 ｃ .∴　 ＢＯ1 ＢＯ3=ＢＣＢＣ′=ａｃ.又　∠Ｏ1 ＢＯ3=∠…     

直觉的误导

问题　已知ＰＡ⊥平面ＡＢＣ,如图1,我们称△ＡＢＣ是△ＰＢＣ在平面ＡＢＣ上的射影三角形,那么这两个三角形的顶角∠ＢＡＣ与∠ＢＰＣ哪一个大呢?　　这个问题看起来非常简单,凭直觉都认为∠ＢＡＣ>∠ＢＰＣ.事实并非如此,剖析如下.图2∠ＢＡＣ>∠ＢＰＣ的情形1)过Ａ作ＡＤ⊥ＢＣ.当垂足Ｄ在线段ＢＣ上时,因ＰＡ⊥平面ＡＢＣ,则ＰＤ⊥ＢＣ.在Ｒｔ△ＰＤＡ中,ＡＤ<ＰＤ.在ＰＤ上取一点Ａ′,使ＡＤ=Ａ′Ｄ.易证△Ａ′ＢＣ≌△ＡＢＣ,因此∠ＢＡ′Ｃ=∠ＢＡＣ,如图2.因∠ＢＡ′Ｄ>∠ＢＰＤ∠ＤＡ′Ｃ>∠ＤＰＣ∠ＢＡ′Ｃ>∠ＢＰＣ.从而∠ＢＡ…     

推导台体体积公式有新法

立几教材中推导台体体积公式的方法不是唯一的 ,因为用体积的割法可求出三棱台的体积 ,因此任意台体体积即可获解 .题 1　已知棱台Ａ′Ｂ′Ｃ′ ＡＢＣ中 ,设Ｓ△Ａ′Ｂ′Ｃ′=图 1　方法 1图Ｓ1 ,Ｓ△ＡＢＣ =Ｓ2 ,高为ｈ .试推导三棱台的体积公式 .解　 [方法 1]如图 1,连结ＡＣ′ ,ＡＢ′ ,ＣＢ′ .Ｖ台 =ＶＡ Ａ′Ｂ′Ｃ′ ＶＢ′ ＡＢＣ　 ＶＡ Ｂ′Ｃ′Ｃ=13Ｓ1 ｈ 13Ｓ2 ｈ　 ＶＡ Ｂ′Ｃ′Ｃ.ＶＡ Ｂ′Ｃ′ＣＶＢ′ ＡＢＣ=ＶＡ Ｂ′Ｃ′ＣＶＡ ＢＢ′Ｃ′=Ｓ△Ｂ′Ｃ′ＣＳ△ＢＢ′Ｃ=Ｂ′Ｃ′ＢＣ ,ＶＡ Ｂ′Ｃ′ＣＶＡ Ａ′…     

数学问题解答

20 0 0年 1 0月号问题解答(解答由问题提供人给出 )1 2 76　设Ｉ为△ＡＢＣ的内心 ,Ｋ、Ｌ、Ｍ分别为△ＡＢＣ的内切圆在ＢＣ ,ＣＡ ,ＡＢ上的切点 .过Ｂ且与ＭＫ平行的直线分别与直线ＬＭ及ＬＫ交于Ｒ及Ｓ ,点Ｊ在ＢＩ上 ,试证明 :∠ＲＪＳ是锐角 ,当且仅当ＢＪ >12 (ＡＢ ＢＣ-ＡＣ) .(山东枣庄市立新学校　孔令恩　 2 771 0 2 )证明　如图所示 ,ＩＢ⊥ＭＫＲＳ∥ＭＫ ＩＢ ⊥ＲＳ∠ＡＢＩ=∠ＣＢＩ ∠ＲＢＭ =∠ＳＢＫ∠ＲＭＢ =∠ＡＭＬ =90°- Ａ2∠ＢＳＫ =∠ＭＫＬ =90°- Ａ2 ∠ＲＭＢ=∠ＢＳＫ △ＲＢＭ ∽△ＳＢＫ ＢＲＢＫ …     

两道赛题的联系、深化和推广

１两道联赛题 例 １ 给定一圆内接△ＡＢＣ,设 Ａ＇Ｂ＇和Ｃ＇分别是连结Ａ＇Ｃ＇Ａ＇Ｂ＇分别交ＡＢ、ＡＣ于Ｄ、Ｅ．求证：ＤＥ//ＢＣ,且ＤＥ经过△ＡＢＣ的内心． 这是全俄第五届（１９６５年）数学竞赛的一道试题［１］,现给一简明的证法如下． 证明 连结 Ａ＇Ｂ、ＢＣ＇,设Ｆ是ＢＣ与Ａ＇Ｃ＇的交点,如图１．Ａ＇Ｂ＝Ａ＇Ｉ．同理 Ｃ＇Ｂ＝Ｃ＇Ｉ, Ａ＇Ｃ是线段ＢＩ的中垂线． ＢＩ平分 Ｂ, ＢＩ是ＤＦ的垂直平分线, ＤＢＦＩ是菱形, ＤＩ//ＢＦ,即 ＤＩ//ＢＣ． 同理可证 ＩＥ//ＢＣ, 故 ＤＥ//ＢＣ,且ＤＥ过△ＡＢＣ的内…     

一道竞赛题的多种证法

2002年全国初中数学竞赛中有这样一道几何题 :△ＡＢＣ内 ,∠ＢＡＣ =6 0° ,∠ＡＣＢ =40° ,Ｐ、Ｑ分别在ＢＣ、ＣＡ上 ,并且ＡＰ、ＢＱ分别是∠ＢＡＣ、ＡＢＣ的角平分线 .求证 :ＢＱ +ＡＱ =ＡＢ +ＢＰ .下面给出它的几种证法 .图 1证法 1　延长ＡＢ到Ｄ ,使ＢＤ =ＢＰ ,连结ＤＰ(如图 1 ) ,则∠Ｄ =∠ＢＰＤ .∵　∠ＡＢＣ =1 80°-(∠ＢＡＣ +∠ＡＣＢ) =80° ,∴　∠Ｄ =∠ＢＰＤ=40° ,∴　∠Ｃ =∠Ｄ .∵　∠ 1 =∠ 2 ,　ＡＰ =ＡＰ ,∴　△ＡＣＰ≌△ＡＤＰ ,∴　ＡＣ =ＡＤ ,即ＡＱ +ＣＱ =ＡＢ +ＢＤ .又∵　∠ 3=12 ∠ＡＢＣ =…     

Generalized symmetry of graphs — A survey

Symmetry of graphs has been extensively studied over the past fifty years by using automorphisms of graphs and group theory which have played and still play an important role for graph theory, and promising and interesting results have been obtained, see for examples, [L.W. Beineke, R.J. Wilson, Topics in Algebraic Graph Theory, Cambridge University Press, London, 2004; N. Biggs, Algebraic Graph Theory, Cambridge University Press, London, 1993; C. Godsil, C. Royle, Algebraic graph theory, Springer-Verlag, London, 2001; G. Hahn, G. Sabidussi, Graph Symmetry: Algebraic Methods and Application, in: NATO ASI Series C, vol. 497, Kluwer Academic Publishers, Dordrecht, 1997]. We introduced generalized symmetry of graphs and investigated it by using endomorphisms of graphs and semigroup theory. In this paper, we will survey some results we have achieved in recent years. The paper consists of the following sections.

1. Introduction

2. End-regular graphs

3. End-transitive graphs

4. Unretractive graphs

5. Graphs and their endomorphism monoids.

Moment information for probability distributions,without solving the moment problem,II: Main-mass,tails and shape approximation

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev–Stieltjes–Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented.     

Splitting up value: A critical review of residual income theories

This paper deals with the notion of residual income, which may be defined as the surplus profit that residues after a capital charge (opportunity cost) has been covered. While the origins of the notion trace back to the 19th century, in-depth theoretical investigations and widespread real-life applications are relatively recent and concern an interdisciplinary field connecting management accounting, corporate finance and financial mathematics (Peasnell, 1981, 1982; Peccati, 1987, 1989, 1991; Stewart, 1991; Ohlson, 1995; Arnold and Davies, 2000; Young and O’Byrne, 2001; Martin, Petty and Rich, 2003). This paper presents both a historical outline of its birth and development and an overview of the main recent contributions regarding capital budgeting decisions, production and sales decisions, implementation of optimal portfolios, forecasts of asset prices and calculation of intrinsic values. A most recent theory, the systemic-value-added approach (also named lost-capital paradigm), provides a different definition of residual income, consistent with arbitrage theory. Enfolded in Keynes’s (1936) notion of user cost and forerun by Pressacco and Stucchi (1997), the theory has been formally introduced in Magni (2000a,b,c; 2001a,b; 2003), where its properties are thoroughly investigated as well as its relations with the standard theory; two different lost-capital metrics have been considered, for value-based management purposes, by Drukarczyk and Schueler (2000) and Young and O’Byrne (2001). This work illustrates the main properties of the two theories and their relations, and provides a minimal guide to construction of performance metrics in the two approaches.     

关于群中乘积元素的阶

讨论群中两个元素a,b的阶不相等时其乘积ab的阶的一类计算问题.设ㄧaㄧ=m,ㄧ bㄧ=n,若(m,n)=1,且存在k∈N使a=bk,则有ㄧabㄧ=mn/d1d2,其中d1=(m,k+1),d2=(n,k+1).若m≠n,ab=ba,且(m,n)ㄧm/(m,n),或(m,n)ㄧn/(m,n),则有ㄧabㄧ=[m,n].     

The permanence and extinction of a nonlinear growth rate single-species non-autonomous dispersal models with time delays

In this paper, we consider the effect of diffusion on the permanence and extinction of a non-autonomous nonlinear growth rate single-species dispersal model with time delays. Firstly, the sufficient conditions of the permanence and extinction of the species are established, which shows if the growth rate and dispersal coefficients is suitable, the species is permanent, on the contrary, it is extinction. Secondly, an interesting result is established, that is, if only the species in some patches even in one patch is permanent, then it is also permanent in other patches. Finally, some examples together with their numerical simulations show the feasibility of our main results.     

A Sequent Calculus for Propositional Dynamic Logic for Agents with Interactions

We consider a propositional dynamic logic for agents with interactions such as known commitment, no learning, and perfect recall. For this logic, we present a sequent calculus with a restricted cut rule and prove the soundness and completeness for the calculus.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 261–269, April–June, 2005.     

互连网络的向量图模型

n-超立方体,环网,k元n超立方体,Star网络,煎饼(pancake)网络,冒泡排序(bubble sort)网络,对换树的Cayley图,De Bruijn图,Kautz图,Consecutive-d有向图,循环图以及有向环图等已被广泛的应用做处理机或通信互连网络.这些网络的性能通常通过它们的度,直径,连通度,hamiltonian性,容错度以及路由选择算法等来度量.在本文中,首先,我们提出了有向向量图和向量图的概念;其次,我们开发了有向向量图模型和向量图模型来更好地设计,分析,改良互连网络;我们进一步证明了上述各类著名互连网络都可表示为有向向量图模型或向量图模型;更重要的是该模型能够使我们设计出了新的互连网络---双星网络和三角形网络.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。