共查询到20条相似文献,搜索用时 31 毫秒
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文[1]给出了一个关于k√n的不等式猜想,文[2]指出该猜想的右侧不等式,即对于正整数n,k〉1,不等式k√n〈kn+(k-1)/k+1k√n-k(n-1)+(k-1)/k+1k√n-1在k=2时不成立,当k〉2时成立.本文研究了该猜想的左侧不等式,对于正整数n,k〉1,不等式 相似文献
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本文主要利用加性数论的理论考察整数和集,稚广了Vscvolod F.Lev的关于整数和的定理:设n≥1,B增包含[1,n],|B|〉n/4,k=|B|+1,则
(1)当1≤n≤2k-3时,有ia^s能写成两个不同B中元之和。
(2)当2k-2≤,1〈3k-3时,有ia^s能写成最多四个B中元之和。
(3)当3k-3≤n〈4k-4时,有ia^s能写成最多2h个B中元之和。
其中h=max[2k/4k-4-n],i=1,2,3,4,6 相似文献
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Jiong Sheng LI Jian Hua YIN 《数学学报(英文版)》2006,22(4):1133-1138
Let σ(k, n) be the smallest even integer such that each n-term positive graphic sequence with term sum at least σ(k, n) can be realized by a graph containing a clique of k + 1 vertices. Erdos et al. (Graph Theory, 1991, 439-449) conjectured that σ(k, n) = (k - 1)(2n- k) + 2. Li et al. (Science in China, 1998, 510-520) proved that the conjecture is true for k 〉 5 and n ≥ (k2) + 3, and raised the problem of determining the smallest integer N(k) such that the conjecture holds for n ≥ N(k). They also determined the values of N(k) for 2 ≤ k ≤ 7, and proved that [5k-1/2] ≤ N(k) ≤ (k2) + 3 for k ≥ 8. In this paper, we determine the exact values of σ(k, n) for n ≥ 2k+3 and k ≥ 6. Therefore, the problem of determining σ(k, n) is completely solved. In addition, we prove as a corollary that N(k) -= [5k-1/2] for k ≥6. 相似文献
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一、分析与研究
2010年高考上海卷理科第23题第(Ⅱ)问:
设直线L1:y=k1x+p交椭圆Г:x2/a2+y2/b2=1(a〉b〉0)于C,D两点,交直线L2:y=k2.x于点E.若k1·k2=-b2/a2,则E为CD中点。 相似文献
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Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
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Erdoes and Soes conjectured in 1963 that every graph G on n vertices with edge number e(G) 〉 1/2(k - 1)n contains every tree T with k edges as a subgraph. In this paper, we consider a variation of the above conjecture, that is, for n 〉 9/ 2k^2 + 37/2+ 14 and every graph G on n vertices with e(G) 〉 1/2 (k- 1)n, we prove that there exists a graph G' on n vertices having the same degree sequence as G and containing every tree T with k edges as a subgraph. 相似文献
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在Qp空间上建立了Jackson型不等式,即对任意f(z)=∑j=0 ^∞ αjz^j∈Qp,0≤p〈∞,α〉1及k-1∈N,有
||f(z)-Г(k)/Г(k+α)∑ j=0 ^k-1Г(k-j+α)/Г(k-j)αjz^j||Qp≤C(α)ω(1/k,f,Qp),其中ω(1/k,f,Qp)为Qp空间中的连续模,C(α)是仅与参数α有关的正常数. 相似文献
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引理设Pn,Pn+d,Pn+2d,…,Pn+(k-1)d是抛物线y=ax^2+vx+c(a,b,c为常数,a≠0)上的点列(注:本文用只表示函数图象上横坐标为t的点),则k边形Pn+dPn+2d…Pn+(k-1)d的面积S与n无关(即与点列的起始位置无关), 相似文献
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In this paper, by using superposition method, we aim to show that ∑^n i=1 (2/- 1)^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 (2i - 1)^2k is the product of n(2n - 1)(2n + 1) and a rational polynomial in (2n - 1)(2n + 1) with degree k - 1. Moreover, recurrence formulas to compute the coefficients of the corresponding rational polynomials are also obtained. 相似文献
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Linghai ZHANG 《数学年刊B辑(英文版)》2008,29(2):179-198
Let u=u(x,t,uo)represent the global solution of the initial value problem for the one-dimensional fluid dynamics equation ut-εuxxt+δux+γHuxx+βuxxx+f(u)x=αuxx,u(x,0)=uo(x), whereα〉0,β〉0,γ〉0,δ〉0 andε〉0 are constants.This equation may be viewed as a one-dimensional reduction of n-dimensional incompressible Navier-Stokes equations. The nonlinear function satisfies the conditions f(0)=0,|f(u)|→∞as |u|→∞,and f∈C^1(R),and there exist the following limits Lo=lim sup/u→o f(u)/u^3 and L∞=lim sup/u→∞ f(u)/u^5 Suppose that the initial function u0∈L^I(R)∩H^2(R).By using energy estimates,Fourier transform,Plancherel's identity,upper limit estimate,lower limit estimate and the results of the linear problem vt-εv(xxt)+δvx+γHv(xx)+βv(xxx)=αv(xx),v(x,0)=vo(x), the author justifies the following limits(with sharp rates of decay) lim t→∞[(1+t)^(m+1/2)∫|uxm(x,t)|^2dx]=1/2π(π/2α)^(1/2)m!!/(4α)^m[∫R uo(x)dx]^2, if∫R uo(x)dx≠0, where 0!!=1,1!!=1 and m!!=1·3…(2m-3)…(2m-1).Moreover lim t→∞[(1+t)^(m+3/2)∫R|uxm(x,t)|^2dx]=1/2π(x/2α)^(1/2)(m+1)!!/(4α)^(m+1)[∫Rρo(x)dx]^2, if the initial function uo(x)=ρo′(x),for some functionρo∈C^1(R)∩L^1(R)and∫Rρo(x)dx≠0. 相似文献
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Consider the following Neumann problem
d△u- u + k(x)u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,
where d 〉 0, B1 is the unit ball in R^N, k(x) = k(|x|) ≠ 0 is nonnegative and in C(-↑B1), 1 〈 p 〈 N+2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem (*) has no nonconstant radially symmetric least energy solution if k(x) ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that (*) has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k(x) ≡ 1 and nonconstant if k(x) ≠ 1. In particular, for k(x) ≡ 1, do can be expressed explicitly. 相似文献
d△u- u + k(x)u^p = 0 and u 〉 0 in B1, δu/δv =0 on OB1,
where d 〉 0, B1 is the unit ball in R^N, k(x) = k(|x|) ≠ 0 is nonnegative and in C(-↑B1), 1 〈 p 〈 N+2/N-2 with N≥ 3. It was shown in [2] that, for any d 〉 0, problem (*) has no nonconstant radially symmetric least energy solution if k(x) ≡ 1. By an implicit function theorem we prove that there is d0 〉 0 such that (*) has a unique radially symmetric least energy solution if d 〉 d0, this solution is constant if k(x) ≡ 1 and nonconstant if k(x) ≠ 1. In particular, for k(x) ≡ 1, do can be expressed explicitly. 相似文献
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用初等数论的思想方法研究Evans问题,可以证明:△ABC是以c为底的本原Evans三角形的充要条件是其三边由本原Heron数组公式所给出,且相应参数要满足(mt+ns)(ms-nt)│2mnst.当本原Heron数组公式中m=s=k,n=k-1,t=k+1(k∈N+,k≥2)时可以得到一类本原Evans三角形. 相似文献
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设σ(k,n)表示最小的正整数m,使得对于每个n项正可图序列,当其项和至少为m时,有一个实现含k 1个顶点的团作为其子图。Erdos等人猜想:σ(k,n)=(k-1)(2n-k) 2.Li等人证明了这个猜想对于k≥5,n≥(^k2))+3是对的,并且提出如下问题:确定最小的整数N(k),使得这个猜想对于n≥N(k)成立。他们同时指出:当k≥5时,[5k-1/2]≤N(k)≤(^k2) 3.Mubayi猜想:当k≥5时,N(k)=[5k-1/2]。在本文中,我们证明了N(8)=20,即Mubayi猜想对于k=8是成立的。 相似文献
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2013年高考江西卷理科第20题为:如图1,椭圆C:x2/a2+经过y2/b2=1(a〉b〉0)点P(1,3),离心率1e=,直线l的方程为x=4.22(1)求椭圆C的方程;(2)AB是经过右焦点F的任一弦(不经过点P),设直线AB与直线l相交于点M,记PA,PB,PM的斜率分别为k1,k2,k3.问:是否存在常数λ,使得k1+k2=λk3?若存在,求λ的值;若不存在,请说明理由.将该题推广可得: 相似文献
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我们知道,椭圆x2/a2+y2/b2=λ1(λ1〉0)与椭圆x2/a2+y2/b2=λ2(λ2〉0,λ2≠λ1)有相同的对称轴(x轴和y轴)和相等的离心率e=((2a-b2)/a)~(1/2),下面我们给出关联三个共轴等离心率椭圆的两个有趣性质.定理1给定两个共轴等离心率椭圆C1: 相似文献