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1.
马驷良 《计算数学》1989,11(1):104-106
熟知,Kreiss矩阵定理在差分法稳定性理论中占有十分重要的位置.定理的证明相当复杂,[2]中收入的证明虽经Morton和Schechter作了适当处理,但是被称为证明核心的(R)?(S)的过程仍然繁琐.本文给出一种简单直观的新证明.在证明回路(A)?(R)?(S)?(H)?(A)中,(A)?(R)和(H)?(A)沿用[2]的证明,一并给出.顺便指出,新证明并不影响[2]中对另一重要定理(Buchanan准则)证明的简化,  相似文献   

2.
褚玉明 《数学进展》2003,32(3):375-376
Let D be a bounded domain in R~2 and c(≥1)be a constant.We say that D is a c-Johndomain if there exists x_0∈D such that for any x∈D,there must be a rectifiable curve γDwhich joins x and x_0,satisfying l(γ(x,y))≤cd(y,D)for any y ∈γ,where l(γ(x,y))denotesthe Euclidean length of the subcurce γ between x and y,d(y,D)is the Euclidean distance fromy to the boundary D of D.We say that D is a John domain if D is a c-John domain for some  相似文献   

3.
一个不等式的证明及引伸推广   总被引:1,自引:0,他引:1  
贵刊 2 0 0 2年第 2期数学问题第 3题是 :设a、b、c ∈R ,且abc =1,求证 :a3(c b) (a c) b3(b c) (b a) c3(c a) (a b) ≥ 34( 1)一、关于不等式 ( 1)的证明原证明是在假定a≥b≥c的前提下运用排序不等式给出的 ,但由于不等式 ( 1)的左端不是关于a、b、c的对称式 ,故原证明有不妥之处 ,下面我们给出不等式 ( 1)的一个证明 .证明 :记不等式 ( 1)的左端为M ,由平均值不等式得a3(c b) (a c) c b8 a c8≥ 33 a364 =3a4,即 a3(c b) (a c) ≥ 5a -b-2c8.同理 ,b3(b c) (b a) ≥ 5b -c-2a8,c3(c a) (a b) ≥ 5c-2a -b8,以上三个不等式…  相似文献   

4.
陈强 《数学通讯》2003,(17):18-20
1 一个例题文 [1 ]中钱亦青老师举到如下例题 :求函数 f(a ,b ,c) =1a3(b +c) + 1b3(c+a)+ 1c3(a +b) 在条件a >0 ,b >0 ,c >0 ,abc =1之下的最小值 .该题变式为 :命题 1 已知a >0 ,b>0 ,c>0且abc=1 ,求证 :1a3(b+c) + 1b3(c+a) + 1c3(a +b) ≥32 ( 1 )现采用文 [2 ]构造函数的方法证明不等式( 1 ) .证 为了书写方便 ,设U =1a3(b +c) +1b3(c+a) + 1c3(a+b) ,V =1a+ 1b+ 1c.构造函数g(x) =xaa(b +c) -a(b+c) 2  + xbb(c+a) -b(c+a) 2  + xcc(a +b) -c(a +b)2=x21a3(b +c) + 1b3(c+a)  + 1c3(a+b)  - 2x 1a+ 1b+ 1c + [a(b +c)  +b(c…  相似文献   

5.
两个关于三角形边角关系的结论   总被引:2,自引:0,他引:2  
定理 1 设a、b、c为△ABC的三边 ,当an,bn,cn(n∈N+,n <5 )组成等差数列时∠B≤ 60°.证明 当n=1时 ,2b=a+c由cosB =a2 +c2 -b22ac=a2 +c2 - 14(a+c) 22ac =34× a2 +c22ac - 14≥12  即B ≤ 60°当n =2时 ,2b2 =a2 +c2cosB =a2 +c2 -b22ac=a2 +c2 - 12 (a2 +c2 )2ac =12 ·a2 +c22ac ≥ 12  即B≤ 60°当n =3时 ,12 (a3+c3)≥ ( a+c2 ) 3 (a3+c3) 3≥ ( a3+c32 ) 2 (a+c) 3 (a+c) 3(a2 +c2 -ac) 3≥ ( a3+c32 ) 2 (a+c) 3 (a2 +c2 -ac)≥ ( a3+c32 ) 2 (a2 +c2 -ac)≥ ( a3+c32 ) 23 a2 +c2 -ac≥b2 B ≤ 60°当n =4时 ,(a-c) 4 …  相似文献   

6.
例  ( a b c) 10 的展开式共有几项 ?本题的传统解法如下 :解 ∵  ( a b c) 10 =[( a b) c]10    =C010 ( a b) 10 C110 ( a b) 9c C210 ( a b) 8c2 … C1010 c10 ,而  C010 ( a b) 10的展开式共有 1 1项 ,C110 ( a b) 9c的展开式共有 1 0项C2  相似文献   

7.
吴春雪  张琳 《大学数学》2007,23(4):50-52
研究了平均非扩张型映射T:‖Tx-Ty‖≤a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖,(x,y∈K,a,b,c≥0,a+b+c≤1)的公共不动点的存在性和唯一性.得到平均非扩张型映射T1和T2满足T1T2=T2T1,则T1T2存在唯一的不动点,并且T1和T2存在唯一的公共不动点.本文结果是近期相关文献结果的推广.  相似文献   

8.
研究小规律巧解竞赛题   总被引:4,自引:0,他引:4  
成功的解题 ,往往体现在 :寻找规律 ,应用规律 .而规律性的解题研究 ,常可以从一些不引人注意的小规律开始 .我们不难得如下呈现规律性的恒等式 :2 ( a2 b2 ) =( a b) 2 ( a - b) 2 ( 1 )3( a2 b2 c2 ) =( a b c) 2 ( a - b) 2 ( b - c) 2 ( c - a) 2 ( 2 )4( a2 b2 c2 d2 ) =( a b c d) 2 ( a - b) 2 ( a - c) 2 ( a - d) 2 ( b- c) 2 ( b - d) 2 ( c - d) 2 ( 3)这三个恒等式的配方推证并不难 ,这里主要是研究其奇妙的解题应用 .1 恒等式 ( 1 )的巧用例 1 设 c是直角三角形的斜边 ,a,b是两条直…  相似文献   

9.
一位名师一道题   总被引:1,自引:0,他引:1  
问题 :实数a ,b,c满足 (a +c) (a+b+c) <0 .求证 :(b -c) 2 >4a(a +b+c) .分析与解 要证的式子与二次方程的判别式形式相似 .故可构造辅助函数y=ax2 + (b-c)x + (a+b +c) .当a≠ 0时 ,二次函数过点P1( 0 ,a+b+c)及P2 ( -1 ,2 (a+c) ) .显见 ,y1y2 =2 (a+b +c) (a +c) <0 (已知条件 ) .即P1、P2 中有一点在x轴上方 ,另一点在x轴下方 .为此二次函数的图像与x轴相交 .所以 Δ =(b -c) 2 -4a(a +b +c) >0 .即得  (b-c) 2 >4a(a+b+c) .当a=0时 ,由已知条件得c(b+c) <0 ,即b≠c,(b -c) 2 >0 ,结论也成立 .原命题得证 .构造二次函数来解题是一…  相似文献   

10.
一、选择题 1.在空间中,若命题“a⊥b,b∥c’则a⊥c”成立,那么字母a,b,c分别表示( )。 (A)a,b各表示直线,c表示平面 (B)a,b各表示平面,c表示直线 (C)a,b,c都表示直线 (D)a,c各表示平面,b表示直线 2.下列命题中正确的是( )。  相似文献   

11.
Some Liouville type theorems for harmonic maps from Kähler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (exceptR IV(2)) to any Riemannian manifold with finite energy has to be constant.  相似文献   

12.
《随机分析与应用》2013,31(4):1121-1130
Abstract

A position dependent random map is a dynamical system consisting of a collection of maps such that, at each iteration, a selection of a map is made randomly by means of probabilities which are functions of position. Let f* be an invariant density of the position dependent random map T. We consider a model of small random perturbations 𝔗? of the random map T. For each ? > 0, 𝔗? has an invariant density function f ?. We prove that f ? → f* as ? → 0.  相似文献   

13.
A random map is discrete-time dynamical system in which one of a number of transformations is randomly selected and applied at each iteration of the process. Usually the map τk is chosen from a finite collection of maps with constant probability pk. In this note we allow the pk's to be functions of position. In this case, the random map cannot be considered to be a skew product. The main result provides a sufficient condition for the existence of an absolutely continuous invariant measure for position dependent random maps on [0,1]. Geometrical and topological properties of sets of absolutely continuous invariant measures, attainable by means of position dependent random maps, are studied theoretically and numerically.  相似文献   

14.
3维双曲空间中曲面的双曲Gauss映照和法Gauss映照   总被引:3,自引:0,他引:3  
史淑国 《数学学报》2004,47(1):1-10
本文导出了3维双曲空间中曲面的双曲Gauss映照和法Gauss映照的关系,发现了一般的曲面由双曲Gauss映照和平均曲率函数唯一确定,并证明了双曲Gauss映照所满足的二阶线性椭圆方程,给出了两种形式的关于双曲Gauss映照的三阶非线性偏微分方程(组)的一个解.  相似文献   

15.
It is shown that every unimodal map is realized as a restriction of a simple map defined on the unit disc to a part of its boundary. Our two-dimensional map is called a full-folding map, which is defined generally on a compact metric space. It is a generalization of the full tent map in that it has two homeomorphic inverse maps and thus every non-critical point has two inverse images.  相似文献   

16.
The author studies the minimization of an energy functional which is introduced in the study of ferromagnets and antiferromagnets. It is proved that the map u0=(u01,u02,0) is a minimizer by setting up the uniform gradient estimate where (u01,u02) is a p-harmonic map.  相似文献   

17.
Let S be a smooth minimal projective surface of general type with p_g(S) = q(S) = 1,K_S~2= 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface.  相似文献   

18.
J.E. Graver and M.E. Watkins, Memoirs Am. Math. Soc. 126 (601) ( 5 ) established that the automorphism group of an edge‐transitive, locally finite map manifests one of exactly 14 algebraically consistent combinations (called types) of the kinds of stabilizers of its edges, its vertices, its faces, and its Petrie walks. Exactly eight of these types are realized by infinite, locally finite maps in the plane. H.S.M. Coxeter (Regular Polytopes, 2nd ed., McMillan, New York, 1963) had previously observed that the nine finite edge‐transitive planar maps realize three of the eight planar types. In the present work, we show that for each of the 14 types and each integer n ≥ 11 such that n ≡ 3,11 (mod 12), there exist finite, orientable, edge‐transitive maps whose various stabilizers conform to the given type and whose automorphism groups are (abstractly) isomorphic to the symmetric group Sym(n). Exactly seven of these types (not a subset of the planar eight) are shown to admit infinite families of finite, edge‐transitive maps on the torus, and their automorphism groups are determined explicitly. Thus all finite, edge‐transitive toroidal maps are classified according to this schema. Finally, it is shown that exactly one of the 14 types can be realized as an abelian group of an edge‐transitive map, namely, as ?n × ?2 where n ≡ 2 (mod 4). © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 1–34, 2001  相似文献   

19.
20.
The allowed patterns of a map on a one-dimensional interval are those permutations that are realized by the relative order of the elements in its orbits. The set of allowed patterns is completely determined by the minimal patterns that are not allowed. These are called basic forbidden patterns.In this paper, we study basic forbidden patterns of several functions. We show that the logistic map Lr(x)=rx(1−x) and some generalizations have infinitely many of them for 1<r≤4, and we give a lower bound on the number of basic forbidden patterns of L4 of each length. Next, we give an upper bound on the length of the shortest forbidden pattern of a piecewise monotone map. Finally, we provide some necessary conditions for a set of permutations to be the set of basic forbidden patterns of such a map.  相似文献   

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