单形内顶角的不等式及其应用

本文首先给出了单形内顶角的概念，建立了单形内顶角的不等式，以此为基础上得到涉及单及形体积的两个不等式。     

一线两等腰

<正>顶角是36°的等腰三角形具有一种特性,即经过它的某一顶点的射线可把它分成两个小等腰三角形.如图1,已知在△ABC中,AB=AC,∠A=36°,射线BD平分∠ABC,交AC于点D,此时△ABD和△BCD都是等腰三角形.如图2,很容易发现等腰直角三角形和含36°的等腰三角形都可以过顶角的顶点找到一条线将原三角形分割成两个新的等腰三角形.     

趣读畸形的等腰三角形

<正>如果将等腰三角形ABC的顶角顶点A分裂为两个点,记为A1、A2,连线A1A2与底边BC交于点D,仍保持两腰A1B和A2C相等,我们不妨把所得图形称为畸形的等腰三角形,如图1所示.特别地,若点D为底边BC的中点,则称A1A2D为畸形的等腰三角形的底边上的中线.若∠BA1D=∠CA2D,则称A1A2D为畸形的等腰三角形的顶角平分线.非常有趣的一个现象是等腰三角形的一些性质,也传给了畸形的等腰三角形.例如,等     

六顶角带色参数杨-Baxter方程的解

通过5个解变换,3组非退化基本解和若干组退化基本解,给出了精确可解统计模型理论中六顶角带色参数杨-Baxter方程的全部解,并说明由六顶角带色参数杨-Baxter方程的解可以得到六顶角带谱参数杨-Baxter方程的全部解.     

一道试题的分析与思考

一、考题(本题满分16分)如图1所示,公路AM、AN围成的是一块顶角为α的角形耕地,其中t anα=-2.在该块土地中P处有一小型建筑,经测量,它到公路AM、AN的距离分别为3km、5%姨km.现要过点P修建一条直线公路BC,将三条公路围成的区域ABC建成一个工业园.为尽量减少耕地占用,问:如何确定B点的位置,使得该工业园区的面积最小?并求最小面积.二、命题意图学生在学习直线与圆时,曾经做过这样的题目:“在     

一个新的黄金三角形

众所周知，顶角为36°的等腰三角形叫做黄金三角形，黄金三角形底与腰之比等于黄金数，且底角平分线与腰的交点为腰的黄金分割点．本文给出一个新的黄金直角三角形，即三边成等比数列的直角三角形，它止匕等腰黄金二三角形有更多与黄金数有关的美妙性质．黄金直角三角形有如下性质：性质1黄金直角三角形一税角正弦值等于黄金数．证明设为黄金直角三角形，且．性质2黄金直角三角形三边的公比为性质3黄金直角三角形外边上的垂线足为科边的黄金分割点．即p是AB的黄金分出点．性质4设CD是黄金直角三角形外边上的高，地ABC的面积，ABC的面积…     

数学问题解答

数学问题解答１９９６年４月号问题解答（解答由问题提供人给出）ＩＯＯ６在等腰凸ＡＢＣ中，顶角Ｂ—２０”，在边ＢＣ，ＡＢ上分别取点Ｄ，Ｅ，有ＺＤＡＣ＝６０“，ＺＡＣＥ＝５０”，求ＺＡＤＥ．一解设／＊＊Ｅ一。，则易知：凸ＡＤＥ面积凸ＢＤＥ面积凸＊＊Ｅ面积Ａ...     

正多边形的推广——"分数"多边形

1正多边形定义的推广———“分数”多边形图1将圆周五等分,画出正五边形和五角星.而五角星也是“五条边相等、五个顶角相等”的几何图形,它“符合”正多边形的定义中各边相等,各角相等的条件,但不是凸多边形.易求出它的顶角为36°.将36°代入正多边形内角公式:36°=(n-2)n×180°,则n=52.我们将五角星定义为“正25边形”:将圆周五等分,等分点为A,B,C,D,E.从等分点A开始,间隔2段弧,连接AC,依此类推,连接相应的等分点,形成五角星.我们将“正pq边形(q>2p,p,q为自然数)”定义为:将圆周q等分,得到q个等分点:A0,A1,A2,A3,…,Aq-2,Aq-1,(1)…     

椭圆特征焦点三角形的一个性质及应用

椭圆的两个焦点和其短轴的一个端点构成的等腰三角形称为椭圆的一个特征焦点三角形 .下面给出关于椭圆特征焦点三角形顶角的一个比较有用的性质及其应用 ,以引起同学们的注意 .性质　椭圆特征焦点三角形的顶角是椭圆上所有的点对椭圆两焦点所成张角中最大的角 .证　不妨设椭圆方程为ｘ2ａ2 + ｙ2ｂ2 =1 (ａ >ｂ>0 ) ,两焦点Ｆ1( -ｃ ,0 ) ,Ｆ2 (ｃ ,0 ) ,α为椭圆特征焦点三角形的顶角 ,Ｐ是椭圆上的任意一点 ,则 0 <α <π ,|ＰＦ1| + |ＰＦ2 | =2ａ ,|Ｆ1Ｆ2 | =2ｃ.当Ｐ与椭圆长轴的端点重合时 ,∠Ｆ1ＰＦ2 =0 ,显然α >∠Ｆ1ＰＦ2 .当Ｐ…     

圆锥曲线焦点三角形顶角平分线的性质探究

2010年高考数学安徽卷理科第19题考察椭圆焦点三角形顶角平分线的性质,视角独特,设计新颖.本文通过对第(2)(3)题的推广,探究出圆锥曲线的焦点三角形顶角平分线的一般方程及其对称性质.1试题回放     

Construction of MDS self-dual codes over Galois rings

The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79–95). We give a necessary and sufficient condition on which the building-up construction holds. We construct MDS self-dual codes of lengths up to 8 over GR(3²,2), GR(3³,2) and GR(3⁴,2), and near-MDS self-dual codes of length 10 over these rings. In a similar manner, over GR(5²,2), GR(5³,2) and GR(7²,2), we construct MDS self-dual codes of lengths up to 10 and near-MDS self-dual codes of length 12. Furthermore, over GR(11²,2) we have MDS self-dual codes of lengths up to 12.      

A Post-Optimality Analysis Algorithm for Multi-Objective Optimization

Algorithms for multi-objective optimization problems are designed to generate a single Pareto optimum (non-dominated solution) or a set of Pareto optima that reflect the preferences of the decision-maker. If a set of Pareto optima are generated, then it is useful for the decision-maker to be able to obtain a small set of preferred Pareto optima using an unbiased technique of filtering solutions. This suggests the need for an efficient selection procedure to identify such a preferred subset that reflects the preferences of the decision-maker with respect to the objective functions. Selection procedures typically use a value function or a scalarizing function to express preferences among objective functions. This paper introduces and analyzes the Greedy Reduction (GR) algorithm for obtaining subsets of Pareto optima from large solution sets in multi-objective optimization. Selection of these subsets is based on maximizing a scalarizing function of the vector of percentile ordinal rankings of the Pareto optima within the larger set. A proof of optimality of the GR algorithm that relies on the non-dominated property of the vector of percentile ordinal rankings is provided. The GR algorithm executes in linear time in the worst case. The GR algorithm is illustrated on sets of Pareto optima obtained from five interactive methods for multi-objective optimization and three non-linear multi-objective test problems. These results suggest that the GR algorithm provides an efficient way to identify subsets of preferred Pareto optima from larger sets.     

一类基于秩次的稳健线性回归估计与诊断方法

线性回归模型的误差项不服从正态分布或存在多个离群点时,可以将残差秩次的某些函数作为权重引入估计模型来减少离群点的不良影响。本文从参数估计、稳健性质、回归诊断等方面对基于残差秩次的一类稳健回归方法进行介绍.通过模拟研究和实例分析表明,R和GR估计是一种估计效率较高的稳健回归方法,其中GR估计可同时避免X与Y空间离群点,而高失效点HBR估计可通过控制某个参数在稳健性与估计效率之间进行折衷.     

Continuous optimization via simulation using Golden Region search

Simulation Optimization (SO) is a class of mathematical optimization techniques in which the objective function can only be numerically evaluated through simulation. In this paper, a new SO approach called Golden Region (GR) search is developed for continuous problems. GR divides the feasible region into a number of (sub) regions and selects one region in each iteration for further search based on the quality and distribution of simulated points in the feasible region and the result of scanning the response surface through a metamodel. Monte Carlo experiments show that the GR method is efficient compared to three well-established approaches in the literature. We also prove the asymptotic convergence in probability to a global optimum for a large class of random search methods in general and GR in particular.     

GR(4,m)上本原序列最高权位的密码特征

刻划了特征为4的Galois环上本原序列最高权位序列的相关函数、线性度和元素分布等密码特征。     

Symbol-Pair Distances of Repeated-Root Negacyclic Codes of Length 2s over Galois Rings

Negacyclic codes of length 2s over the Galois ring GR(2a,m) are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals <(x + 1)i>,0 ≤ i ≤ 2sa,of the chain ring GR(2a,m)[x]/.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m (i.e.,a =1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2s over F2m.     

Computing the field of values and pseudospectra using the Lanczos method with continuation

The field of values and pseudospectra are useful tools for understanding the behaviour of various matrix processes. To compute these subsets of the complex plane it is necessary to estimate one or two eigenvalues of a large number of parametrized Hermitian matrices; these computations are prohibitively expensive for large, possibly sparse, matrices, if done by use of the QR algorithm. We describe an approach based on the Lanczos method with selective reorthogonalization and Chebyshev acceleration that, when combined with continuation and a shift and invert technique, enables efficient and reliable computation of the field of values and pseudospectra for large matrices. The idea of using the Lanczos method with continuation to compute pseudospectra is not new, but in experiments reported here our algorithm is faster and more accurate than existing algorithms of this type.This work was supported by Engineering and Physical Sciences Research Council grants GR/H/52139 and GR/H/94528.     

Galois环上本原序列压缩映射的单性

设Ω是 Ｇａｌｏｉｓ环 ＧＲ（２~ｄ,ｒ）的 Ｔｅｉｃｈｍｕｌｌｅｒ代表集,则 ＧＲ（２~ｄ,ｒ）上每条序列ａ有唯一的权位分解,　其中ａ-ｉ是Ω上序列,同时也可自然视为有限域Ｆ-（２~ｒ）,上序列．设ｆ（ｘ）是环 ＧＲ（２~ｄ,ｒ）上强本原多项式,Ｇ（ｆ（ｘ））表示 ＧＲ（２~ｄ,ｒ）上以ｆ（ｘ）为特征多项式的序列的全体,是Ｆ-（２~ｒ）上一类ｄ－１元多项式, 　本文证明了压缩映射是单射,即对 ａ＝ ｂ当且仅当对所有 ａ,ｂ ∈ Ｇ（ｆ（ｘ））．     

分次模范畴上的分次循环同调

本文讨论了分次模范畴等价的两个分次代数的循环同调群之间的关系以及范畴gr-R,GR-R上的分次循环同调的形式.     

A universal building block for the approximate analysis of a shared buffer ATM switch architecture

A universal analytic approximation is proposed for the performance analysis of a general queueing model of a shared buffer ATM switch architecture with bursty arrivals. The forms of the joint, aggregate and marginal state probabilities are characterised via entropy maximisation. As an application, a continuous-time maximum entropy (ME) solution is implemented at equilibrium by assuming that the arrival process to each port of the ATM switch is modelled by a Compound Poisson Process (CPP) with geometrically distributed batches. Consequently, efficientz-transform-type recursive expressions of low computational cost are derived. Validation tests against simulation show that the ME approximation is credible with a very good error-level. Moreover, performance bounds for the mean queue length and cell-loss probability at each output port are experimentally defined over those generated by Interrupted Poisson Processes (IPPs) having the same first two interarrival-time moments.This work is sponsored by the Science and Engineering Research Council (SERC), UK, under grants GR/F 29271 and GR/H 18609.