共查询到20条相似文献,搜索用时 359 毫秒
1.
Alexander A. Razborov 《Proceedings of the Steklov Institute of Mathematics》2011,274(1):247-266
Fon-Der-Flaass (1988) presented a general construction that converts an arbitrary [(C)\vec]4\vec C_4 -free oriented graph Γ into a Turán (3, 4)-graph. He observed that all Turán-Brown-Kostochka examples result from his construction,
and proved the lower bound $\tfrac{4}
{9}
$\tfrac{4}
{9}
(1 − o(1)) on the edge density of any Turán (3, 4)-graph obtainable in this way. In this paper we establish the optimal bound $\tfrac{3}
{7}
$\tfrac{3}
{7}
(1 − o(1)) on the edge density of any Turán (3, 4)-graph resulting from the Fon-Der-Flaass construction under any of the following
assumptions on the undirected graph G underlying the oriented graph Γ: (i) G is complete multipartite; (ii) the edge density of G is not less than $\tfrac{2}
{3} - \varepsilon $\tfrac{2}
{3} - \varepsilon for some absolute constant ε > 0. We are also able to improve Fon-Der-Flaass’s bound to $\tfrac{7}
{{16}}
$\tfrac{7}
{{16}}
(1 − o(1)) without any extra assumptions on Γ. 相似文献
2.
具$p$-Laplacian 算子的多点边值问题迭代解的存在性 总被引:1,自引:0,他引:1
利用单调迭代技巧和推广的Mawhin定理得到下述带有p-Laplacian算子的多点边值问题迭代解的存在性,{(Фp(u'))' f(t,u, Tu)=0, 0(≤)t(≤)1,u(0)=q-1∑i=1γiu(δi),u(1)=m-1∑i=1ηiu(ξi),其中Фp(s)=|s|p-2s,p>1;0<δi<1,γi>0,1(≤)i(≤)q-1;0<ξi<1,ηi(≥)0,1(≤)i(≤)m-1且q-1∑i=1γi<1,m-1∑i=1ηi(≤)1;Tu(t)=∫t0k(t,s)u(s)ds,k(t,s)∈C(I×I,R ). 相似文献
3.
Let M be a 3-manifold, F= {F1 , F2 , . . . , Fn } be a collection of essential closed surfaces in M (for any i, j ∈ {1, ..., n}, ifi≠j, Fi is not parallel to Fj and Fi ∩Fj = φ) and0 M be a collection of components of M. Suppose M-UFi ∈FFi×(-1, 1) contains k components M1 , M2 , . . . , Mk . If each M i has a Heegaard splitting ViUSiWi with d(Si) > 4(g(M1 ) + ··· + g(Mk )), then any minimal Heegaard splitting of M relative to 0M is obtained by doing amalgamations and self-amalgamations from minimal Heegaard splittings or -stabilization of minimal Heegaard splittings of M1 , M2 , . . . , Mk . 相似文献
4.
For p>1,many improved or generalized results of the well-known Hardy's inequality have been established.In this paper,by means of the weight coefficient method,we establish the following Hardy type inequality for P=-1:n∑i=1(1/ii∑j=1aj)-1<2n∑i=1(1-π2-9/3i)ai-1,Cn such that the inequality ∑ni=1(1/i∑ij=1 aj)-1≤Cn∑ni=1ai-1 holds.Moreover,by means of the Mathematica software,we give some examples. 相似文献
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6.
对一列独立同分布平方可积的随机变量序列{Xn,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和Tn(a)的随机乘积的渐近正态性质,其中Tn(a)=Sn-Sn(a),n=1,2,…,Sn(a)=n∑ j=1 XjI{Mn-a<Xj≤Mn},a为某一大于零的常数'Mn=max 1≤k≤n{Xk}. 相似文献
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9.
设α是环R的一个自同态,称环R是α-斜Armendariz环,如果在R[x;α]中,(∑_(i=0)~ma_ix~i)(∑_(j=0)~nb_jx~j)=0,那么a_ia~i(b_j)=0,其中0≤i≤m,0≤j≤n.设R是α-rigid环,则R上的上三角矩阵环的子环W_n(p,q)是α~—-斜Armendariz环. 相似文献
10.
Let G(V, E) be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V(Cm). The G - E(Cm) are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui : i = 1, 2 , m}. Let κ = ec+1. Forj = 1,2,...,k- 1, let δij = max{dv : dist(v, ui) = j,v ∈ Ti}, δj = max{δij : i = 1, 2,..., m}, δ0 = max{dui : ui ∈ V(Cm)}. Then λ1(G)≤max{max 2≤j≤k-2 (√δj-1-1+√δj-1),2+√δ0-2,√δ0-2+√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 (G) is the largest eigenvalue of the adjacency matrix of G. 相似文献
11.
An infinite integer sequence {1 ≤ a1 〈 a2 〈 ... } is called A-sequence, if no ai is sum of distinct members of the sequence other than ai. We give an example for the A-sequence, and the reciprocal sum of elements is∑1/ai〉 2.065436491, which improves slightly the related upper bounds for the reciprocal sums of sum-free sequences. 相似文献
12.
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
13.
设{X_(ni):1≤i≤n,n≥1}为行间NA阵列,g(x)是R~+上指数为α的正则变化函数,r>0,m为正整数,{a_(ni):1≤i≤n,n≥1}为满足条件(?)|a_(ni)|=O((g(n))~1)的实数阵列,本文得到了使sum from n=1 to ∞n~(r-1)Pr(|■multiply from j=1 to m a_(nij) X_(nij)|>ε)<∞,■ε>0成立的条件,推广并改进了Stout及王岳宝和苏淳等的结论。 相似文献
14.
设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设K是实Banach空间E中非空闭凸集,{Ti}i=1^N是N个具公共不动点集F的严格伪压缩映像,{αn}包括于[0,1]是实数例,{un}包括于K是序列,且满足下面条件(i)0〈α≤αn≤1;(ii)∑n=1∞(1-αn)=+∞.(iii)∑n=1∞ ‖un‖〈+∞.设x0∈K,{xn}由正式定义xn=αnxn-1+(1-αn)Tnxn+un-1,n≥1,其中Tn=Tnmodn,则下面结论(i)limn→∞‖xn-p‖存在,对所有p∈F;(ii)limn→∞d(xn,F)存在,当d(xn,F)=infp∈F‖xn-p‖;(iii)lim infn→∞‖xn-Tnxn‖=0.文中另一个结果是,如果{xn}包括于[1-2^-n,1],则{xn}收敛,文中结果改进与扩展了Osilike(2004)最近的结果,证明方法也不同。 相似文献
15.
Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ(x_i)= ayi,σ(y_i)= a~-1x_i,where a ∈ F.In this paper,we describe the explicit generator of the ring of modular vector invariants of F[V]~G.We prove that F[V]~G = F[l_i = x_i + ay_i,q_i = x_iy_i,1 ≤ i ≤ n,M_I = X_I + a~-I-Y_I],where I∈An = {1,2,...,n},2 ≤-I-≤ n. 相似文献
16.
Let be either the real, complex, or quaternion number system and let be the corresponding integers. Let be a vector in . The vector has an integer relation if there exists a vector , , such that . In this paper we define the parameterized integer relation construction algorithm PSLQ, where the parameter can be freely chosen in a certain interval. Beginning with an arbitrary vector , iterations of PSLQ will produce lower bounds on the norm of any possible relation for . Thus PSLQ can be used to prove that there are no relations for of norm less than a given size. Let be the smallest norm of any relation for . For the real and complex case and each fixed parameter in a certain interval, we prove that PSLQ constructs a relation in less than iterations.
17.
图G的顶点集V(G)的一个二部划分V_1和V_2叫做平衡二部划分,如果||V_1|-|V_2||≤1成立.Bollobas和Scott猜想:每一个有m条边且最小度不小于2的图,都存在一个平衡二部划分V_1,V_2,使得max{e(V_1),e(V_2)}≤m/3,此处e(V_i)表示两顶点都在V_i(i=1,2)中的边的条数.他们证明了这个猜想对正则图(即△(G)=δ(G))成立.颜娟和许宝刚证明了每个(k,k-1)-双正则图(即△(G)-δ(G)≤1)存在一个平衡二部划分V_1,V_2,使得每一顶点集的导出子图包含大约m/4条边.这里把该结论推广到最大度和最小度相差不超过2的图G. 相似文献
18.
The number $\[A({d_1}, \cdots ,{d_n})\]$ of solutions of the equation
$$\[\sum\limits_{i = 0}^n {\frac{{{x_i}}}{{{d_i}}}} \equiv 0(\bmod 1),0 < {x_i} < {d_i}(i = 1,2, \cdots ,n)\]$$
where all the $\[{d_i}s\]$ are positive integers, is of significance in the estimation of the number $\[N({d_1}, \cdots {d_n})\]$ of solutiohs in a finite field $\[{F_q}\]$ of the equation
$$\[\sum\limits_{i = 1}^n {{a_i}x_i^{{d_i}}} = 0,{x_i} \in {F_q}(i = 1,2, \cdots ,n)\]$$
where all the $\[a_i^''s\]$ belong to $\[F_q^*\]$. the multiplication group of $\[F_q^{[1,2]}\]$. In this paper, applying the inclusion-exclusion principle, a greneral formula to compute $\[A({d_1}, \cdots ,{d_n})\]$ is obtained.
For some special cases more convenient formulas for $\[A({d_1}, \cdots ,{d_n})\]$ are also given, for
example, if $\[{d_i}|{d_{i + 1}},i = 1, \cdots ,n - 1\]$, then
$$\[A({d_1}, \cdots ,{d_n}) = ({d_{n - 1}} - 1) \cdots ({d_1} - 1) - ({d_{n - 2}} - 1) \cdots ({d_1} - 1) + \cdots + {( - 1)^n}({d_2} - 1)({d_1} - 1) + {( - 1)^n}({d_1} - 1).\]$$ 相似文献
19.
Zhi-Wei Sun 《Proceedings of the American Mathematical Society》2001,129(10):3129-3131
Let 1)$"> be sets. By a simple graph-theoretic argument we show that any set of distinct representatives of can be extended to a set of distinct representatives of in more than ways. This yields a natural induction proof of the well-known theorem of P. Hall.
20.
Miodrag Zivkovic. 《Mathematics of Computation》1999,68(225):403-409
For a positive integer let and let . The number of primes of the form is finite, because if , then is divisible by . The heuristic argument is given by which there exists a prime such that for all large ; a computer check however shows that this prime has to be greater than . The conjecture that the numbers are squarefree is not true because .