共查询到20条相似文献,搜索用时 109 毫秒
1.
高维空间中半线性波动方程的Sobolev指数 总被引:6,自引:0,他引:6
赖绍永 《数学年刊A辑(中文版)》1997,(5)
GustavoPonce与ThomasC.Sideris[4]猜测对一些具有特殊非线性项的半线性波动方程,如ut-△u=uk(Du)α(x∈Rn,k∈Z+,l=|α|2),其中Sobolev指数会在n2与(n2+1)之间.文[4]中,在x∈R3时,回答了这一问题.本文在n3维空间中,得到了半线性波动方程ut-△u=uk(Du)α(x∈Rn,k∈Z+,l=|α|2)的Sobolev指数为max{n2+12,(n2-1)·l-3l-1+2},此数确实在区间[n2+12,n2+1]中. 相似文献
2.
Jacobi多项式零点为结点的Lagrange插值多项式之逼近 总被引:1,自引:0,他引:1
对于可微函数f∈Cq[-1,1],本文研究以Jacobi多项式J(α,β)n(x)的零点为结点组之Lagrange插值多项式对f及其导数的同时逼近,证明不等式L(s)n(f,α,β,x)-f(s)(x)=O(1)Δ-sn(x)Δqn(x)ω(f(q),Δn(x))logn{+(1-x+n-1)-α-12n-qω(f(q),n-1)},在[0,1]上对于s=0,1,2,…,q一致成立,其中Δn(x)=n-11-x2+n-2 相似文献
3.
本文建立了关于欧拉常数γ的一个不等式:∑nk=11k-ln(n)-12n+112n2-1120n4<γ<∑nk=11k-ln(n)-12n+112n2-1120n4+1252n6,改进了文献[1],[2],[3]的结果 相似文献
4.
张秉儒 《纯粹数学与应用数学》1997,(1)
记δn=k≤nkn-k,在本文中证明了:r∈N,若i∈{1,2,…,r},qi(>5)都是素数,并且[(δqi-1-1)!+1]/δqi-1是正整数,则图簇Kn-Ek0P3∪k1Pq1-1∪k2Pq2-1∪…∪krPqr-1是色唯一的,推广了文[1]的结果 相似文献
5.
§1. IntroductionIn1908,E.Landauintroducedthefollowingwellknownsequenceofoperators[1]Ln[f(t);x]=Kn∫1-1f(t)[1-(t-x)2]ndt, (1.1)where Kn=[∫1{-1(1-t2)ndt]-1~nπ (n→∞).(1.1)wasusedintheproofoftheWeierstrassTheorem.Sincethen,theapproximationprop-ert… 相似文献
6.
7.
恰有t行含对称正元的布尔方阵的幂敛指数的估值 总被引:1,自引:0,他引:1
设Dn,2(t)为恰有t行含对称正元的n阶布尔方阵的集合,2≤t≤n。本文证明了,对于任给A∈Dn,2(t),幂敛指数k(A)≤∫(n-t-1)^2+1,3n-t-2,当t≤n-[3+√8n-7/2]当t〉n-[3+√8n-7/2],这里[x]表示不小于x的最小整数。同时,我们还证明了这个界是可以达到的,并且对Dn,2(t)的极矩阵集合作了部分刻划。 相似文献
8.
张秉儒 《纯粹数学与应用数学》1997,13(1):61-67
记δn=Σ↓k≤n(^kn-k),在本文中证明了:A↓r∈N,若A↓∈N,若A↓∈{1,2,…,r},qi(〉5)都是素数,并且[(δqi-1-1)!+1]/δqi-1是正整数,则图簇Kn-E(k0P3∪k1Pq1-1∪…∪krPqr-1)是色唯一的,推广了文[1]的结果。 相似文献
9.
《数学的实践与认识》2017,(22)
根据二元叠加码(Binary Superimposed Code)M_q(n,k,d)的定义研究了这个BSC码任意两个码字的汉明(Hamming)距离上下界,并由此给出了它的平均汉明距离和均方差的界. 相似文献
10.
“mp2型“伪素数的性质与存在 总被引:1,自引:1,他引:0
定义 若n是合数,且2n-1=1(mod n),则称n是伪素数. 文[1]证得 10932及 35112这两个数是伪素数,从而否定了陈历功等提出的“伪素数不含平方数因数”的猜想.记p是奇素数,mN,本文将讨论“mP2型”伪素数的性质与存在的实例.先引入以下的 引理[2]设使同余式:2r=1(mod m)成立的最小正整数为r,则 2a=1(mod m)的充要条件是r(注引理即文[2]第七章定理1的推过2) 定理1 设p是奇素数,如果n是含有因数P2的伪素数,则P2是伪素数. 证明 记n=mp2(m N),则由伪… 相似文献
11.
设U (n)是具有n个顶点的所有单圈图的集合,G(3; n- 3)是由一个三角形C3粘上一条悬挂路P_(n-3)得到的单圈图.本文将证明当n 5时具有最大度距离的单圈图是G(3; n - 3). 相似文献
12.
移位交换网的最优路由算法 总被引:1,自引:1,他引:0
移位交换网是重要的互联网络之一 ,在并行计算中有着广泛应用 .然而 ,它缺少任意点对间的最短路由算法 .已有的路由算法都不能保证其任意节点对间都是最短路由 .文中给出了一个最短路由算法 ,也是最优路由算法 ,它使得从源节点到目的节点的任何信息都是沿最短路由传输 .同时 ,我们还得到了任意节点对间的距离公式 相似文献
13.
Qi Guo 《Discrete and Computational Geometry》2005,34(2):351-362
Given a convex body $C\subset R^n$ (i.e., a compact convex set with nonempty
interior), for $x\in$ {\it int}$(C)$, the interior, and a hyperplane $H$ with $x\in H$,
let $H_1,H_2$ be the two support hyperplanes of $C$ parallel to $H$. Let $r(H, x)$
be the ratio, not less than 1, in which $H$ divides the distance between
$H_1,H_2$. Then the quantity
$${\it As}(C):=\inf_{x\in {\it int}(C)}\,\sup_{H\ni x}\,r(H,x)$$
is called the Minkowski measure of asymmetry of $C$. {\it As}$(\cdot)$ can be viewed as a real-valued function defined on the family of
all convex bodies in $R^n$. It has been known for a long time that {\it As}$(\cdot)$
attains its minimum value 1 at all centrally symmetric convex bodies and maximum
value $n$ at all simplexes. In this paper we discuss the stability of the
Minkowski measure of asymmetry for convex bodies. We give an estimate for the
deviation of a convex body from a simplex if the corresponding Minkowski measure
of asymmetry is close to its maximum value. More precisely, the following result
is obtained: Let $C\subset R^n$ be a convex body. If {\it As}$(C)\ge n-\varepsilon$ for some $0\le
\varepsilon < 1/8(n+1),$ then there exists a simplex $S_0$ formed by $n+1$
support hyperplanes of $C$, such that
$$(1+8(n+1)\varepsilon)^{-1}S_0\subset C\subset S_0,$$
where the homethety center is the (unique) Minkowski critical point of $C$. So
$$d_{{\rm BM}}(C,S)\le 1+8(n+1)\varepsilon$$
holds for all simplexes $S$, where $d_{{\rm BM}}(\cdot,\cdot)$ denotes the Banach-Mazur distance. 相似文献
14.
For the affine distance d(C,D) between two convex bodies C, D(?) Rn, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) < n1/2 if one is an ellipsoid and another is symmetric, d(C, D) < n if both are symmetric, and from F. John's result and d(C1,C2) < d(C1,C3)d(C2,C3) one has d(C,D) < n2 for general convex bodies; M. Lassak proved d(C, D) < (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies. 相似文献
15.
实Hilbert空间中点到有限余维子空间的距离问题 总被引:2,自引:0,他引:2
本文讨论实Hilbert空间中一点到有限余维子空间的距离,将一点到超平面的距离公式推广到一点到余维n子空间M以及仿射集Q的距离公式,并对M或Q闭的情形表示出最佳逼近元。 相似文献
16.
《数学季刊》2016,(2):111-117
Let D(G) = (dij )n×n denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vertices vi and vj in G. A graph is called distance integral if all eigenvalues of its distance matrix are integers. In 2014, Yang and Wang gave a su?cient and necessary condition for complete r-partite graphs Kp1,p2,··· ,pr =Ka1·p1,a2·p2,··· ,as···ps to be distance integral and obtained such distance integral graphs with s = 1, 2, 3, 4. However distance integral complete multipartite graphs Ka1·p1,a2·p2,··· ,as·ps with s>4 have not been found. In this paper, we find and construct some infinite classes of these distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with s = 5, 6. The problem of the existence of such distance integral graphs Ka1·p1,a2·p2,··· ,as·ps with arbitrarily large number s remains open. 相似文献
17.
假定Γ是一个有限的、单的、无向的且无孤立点的图,G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.结果为:设图Γ含有一个阶为pn(p是素数,n≥2)的自同构群,且G有一个极大子群循环,则Γ是G-边传递的,当且仅当Γ同构于下列图之一1)pmK1,pn-1-m,0≤m≤n-1;2)pmK1,pn-m,0≤m≤n;3)pmKp,pn-m-1,0≤m≤n-2;4)pn-mCpm,pm≥3,m<n;5)2n-2K1,1;6)pn-1-mCpm,pm≥3,m≤n-1;7)2pn-mCpm,pm≥3,m≤n-1;8)2pn-mK1,pm,0≤m≤n;9)pn-mK1,2pm,0≤m≤n;10)pn-mK2,pm,0<m≤n;11)C(2pn-m,1,pm);12)pkC(2pm-k,1,pn-m),0<k<m,0<m≤n;13)(t-s,2m)C(2m 1/(t-s,2m),1,2n-1-m),其中0≤m≤n-1,2n-2(s-1)≡0(mod 2m),t≡1(mod 2),s(≠)t(mod 2m),1≤s≤2m,1≤t≤2n-1;14)∪p i=1 Ci p n-1,其中Ci p n-1=Ca1a1 [1 (i-1)pn-2]a 1 2[1 (i--1)p n-2]…a 1 (pn-1-1)[1 (i-1)p n-2]≌Cp n-1,i=1,2,…,p;15)∪2 i=1 Ci 2n-1,其中Ci 2n-1=Ca1a 1 [1 (i-1)(2n-2-1)]a1 2[1 (i-1)(2n-2-1)]…a1 (2n-1-1)[1 (i-1)(2n-2-1)]≌C2n-1,i=1,2. 相似文献
18.
Привалов定理的拓广 总被引:1,自引:0,他引:1
<正> 设Ω是 m 个实变数 u_1,…,u_m 空间中的-p 维可定向流形Ω:(?)Ω称为属于 C~e 类(e是非负的整数),如果实函数 f_1,…,f_(m-p)皆有e次连续偏微商.Ω称为平滑的,如Ω属于 C~1 类并且矩阵 相似文献
19.
<正> 最近几年来,关于同伦群的研究,特别是球面同化群的计算有很大的进步,但是关于更一般的空间的同伦群的计算,就作者所知道的文献来说,似乎没有相应的进展,在这一方面的工作,最早也是最主要的是 Hurewicz 定理,Serre 在[15]中利用所谓 C同构的概念,把 Hurewicz 定理推广到所谓(n-1)维 C 连通空间中,但是也和 Hure-wicz 定理一样,只能讨论 n 维同伦群和 n 维同调群的关系.张素诚,Hilton 及 Barrat 相似文献
20.
Rigid frameworks in some Euclidean space are embedded graphs
having a unique local realization (up to Euclidean motions) for
the given edge lengths, although globally they may have several.
We study the number of distinct planar embeddings of minimally
rigid graphs with $n$ vertices. We show that, modulo planar rigid
motions, this number is at most ${{2n-4}\choose {n-2}} \approx
4^n$. We also exhibit several families which realize lower bounds
of the order of $2^n$, $2.21^n$ and $2.28^n$.
For the upper bound we use techniques from complex algebraic
geometry, based on the (projective) Cayley--Menger variety
${\it CM}^{2,n}(C)\subset P_{{{n}\choose {2}}-1}(C)$ over the complex
numbers $C$. In this context, point configurations are represented
by coordinates given by squared distances between all pairs of
points. Sectioning the variety with $2n-4$ hyperplanes yields at
most $deg({\it CM}^{2,n})$ zero-dimensional components, and one finds
this degree to be $D^{2,n}=\frac{1}{2}{{2n-4}\choose {n-2}}$.
The lower bounds are related to inductive constructions of
minimally rigid graphs via Henneberg sequences.
The same approach works in higher dimensions. In particular, we
show that it leads to an upper bound of $2 D^{3,n}=
{({2^{n-3}}/({n-2}})){{2n-6}\choose{n-3}}$ for the number of
spatial embeddings with generic edge lengths of the $1$-skeleton
of a simplicial polyhedron, up to rigid motions.
Our technique can also be adapted to the non-Euclidean case. 相似文献