奇完全数的两个猜想

运用初等方法讨论有关奇完全数的两个猜想.证明了:(i)如果n=p~αq_1~(2β_1)q_2~(2β_2)…q_s~(2β_s)是奇完全数,其中P,q_1,q_2,…,q_s是不同的奇素数,α,β_1,β_2,…,β_s是正整数,p≡α≡1(mood4),而且q_i≡-1(mod m)(i=1,2,…,s),m是大于2的正整数,则.1/2σ(p~α)必为合数;(ii)如果n=a~2~x+b~2~x,其中a,b,x是适合ab,gcd(a,6)=1,2|ab的正整数,则当x≥log_2log_2log_2 a时,n不是奇完全数.     

Characterizations of Best L_p(1≤p≤+ ∞) Approximation With Restricted Ranges of Derivatives

Let [a,b] be a compact set containing at least n + 1 points. If Φ_n = span(φ_1, φ_2,…, φ_n) is an n-dimensional subspace of L,[a, b] m φ_1~(s), φ_2~(s)…, φ_n~(s)exist (s≥0is an integer) and have a maximal linearly independent subset which is an extendedChebyshev system of order rs on [a,b], then write     

Toader型平均与几种经典平均的确界

给出了最佳参数α_1,α_2,α_3,β_1,β_2,β_3∈R,使得双向不等式α_1Q(a,b)+(1-α_1)G(a,b)0且a≠b成立.其中A(a,b)=(a+b)/2,H(a,b)=2ab/(a+b),G(a,b)=(ab)~(1/2),Q(a,b)=((a~2+b~2)/2)~(1/2),C(a,b)=(a~2+b~2)/(a+b),T(a,b)=2/π∫_0~(π/2)(a~2cos~2t+b~2sin~2)~(1/2)tdt分别是两个正数a和b的算术平均,调和平均,几何平均,二次平均,反调和平均和Toader平均.     

有限域上Carlitz方程的解数

设F_q是含有q个元素的有限域,其中q=p~t,t≥1,p是一个奇素数.研究了Carlitz方程的推广形式(a_1x_1~(m_1)+…+a_nx_n~(m_n)+a_(n+1)x_(n+1)~(m_(n+1))+…+a_(n+s)x_(n+s)~(m_(n+s)))~k=bx_1~(k_1)…x_n~(k_n),其中ai,b∈F_q~*,s≥1,n≥1.当方程变量的指数满足一定条件时,得到了方程的解数公式.     

关于时间序列线性预报问题的单纯形算法

本文考虑稳定时间序列的p阶线性预报问题,提出一个不受异常值影响的数学模型: 其中当k<1及k>n时ξ_k=0。进而将(1)归结为含有自由变量的线性规划问题 min1~Tδ~++1~Tδ~- (2) s.t.Aα+[E,-E][δ~(+T),δ~(-T)]=b,δ~+,δ~-≥0。其中α=[α_1,…,α_p]~T,b=[-ξ_2,…,-ξ_n,0,…,0]~T∈R~(p+n-1),1=[1,…,1]~T∈R~(p+n-1),A是(p+n-1)×p阶Toeplitz矩阵     

HIGHER C0MMUTATORS OF PSEUDODIFFERENTIAL OPERATORS

In this paper the following result is established: For a_i, f∈(R~K), i=1, …, n, and T (a, f) (x)=ω(x, D)(multiply from i=1 to n P_(mi)(a_i, x, ·)f(·)),it holds that ‖T(a, f)‖_q≤C‖f‖_(po) multiply from i=1 to n ~m_ia_i‖_(p_4),where a=(a_1, …, a_n), q~(-1)=p_0~(-1)+ sum from i=1 to n p_i~(-1)∈(O, 1), p_i∈(1, ∞)or i, p_i=∞, p_0∈(1, ∞),for an integer m_i≥0, P_(m_1)(a_i, x, y)=a_i(x)-∑ |β|相似文献   

COMMUTATORS OF MULTIPLIER OPERATORS

Denote M~l={ω∈C~∞(R~K\{0}:|ω~((β))(ξ)|≤C_β|ξ|~(l-|β|)},l is an integer.R_((-α))~((m))is the n-foldcomposition of Taylor series remainder operator,m=(m_1,…,m_n)∈Z~n.Z is the set ofnon-negative integers,α∈(R~K)n.DenoteThe main results are as follows:(i) If γ_1,γ_2∈Z~K and l is an integer such that |γ_1|+|γ_2|+l=|m|=m_1+…+m_n,0≤|γ_1|≤{m_4},and ω∈M~l,then we havewhereis a conseant.(ii)In the same sense of notation as in (i),but now|m|=1,we havewhereThese results extend the corresponding ones given by coifman-Meyer in [4] andCohen,J.in [2],and,in a sense,extend those given by Calderón,A.P.in [1].     

Galton-Watson过程收敛速率的一个充要条件

假设{Z_n}_(n=0)~∞为一Galton-Watson过程,Asmussen[1]给出了在EZ_1(logZ_1)~(α+1)∞条件下W-W_n=o(n~(-α)),a.s.的结果,这是一个充分条件.本文给出lim sup_(n→∞)n~α|W-W_n|∞,a.s.的充要条件.     

ON INTERPOLATION BY S_2~1(△_(m,n)~((2)))

Let △_(m,n)~(2)be a subdivision of D:[a,b]×[c,d](Fig.1),_1arelengths of[a,b]and[c,d]respectively,and h_1=_1/m,h_2=_2/n.     

一维问题的一种积分形式的流量重构算法

1引言我们考虑如下一维二阶椭圆边界值问题(-(β(x)p′)(x))′=f(x),x∈(a,b) p(a)=p(b)=0(1))其中β=β(x)是一恒正函数,且β∈H~1(a,b),f∈L~2(a,b)．事实上,在此条件下,我们可保证p∈H~2(a,b)(见[1],[2])．(1)之弱形式为：求p∈H_0~1(a,b)使得a(p,q)=(f,q),(?)q∈H_0~1(a,b),(2)其中a(p,q)=(?)_a~bβp′q′dx,(f,g)=(?)_a~bfqdx．给定(a,b)的一个分割α=x_0＜x_1＜…＜x_(n-1)＜x_n=b,令h=(?)(x_i-x_(i-1)),(?)_i表示通常相应于节点x_i的形状函数,即(?)_i是连续的分段线性函数且满足(?)_i(x_k)=δ_(ik),这里δ_(ik)=(?)i,k=0,1,…,n．又记V_h~0=span{(?)_1,(?)_2,…,(?)_(n-1)),取V_h~0作为p的逼近空间,则求解(1)的标准有限元格式为：求ph∈V_h~0使得     

On λ-Fold Equipartite Oberwolfach Problem with Uniform Table Sizes

We consider the following generalization of the Oberwolfach problem:”At a gathering there are n delegations each having m people. Is it possible to arrange a seating of mn people present at s round tables T ₁, T ₂, . . . , T _s (where each T _i can accommodate \( t_i\geq3 \) people and \( \sum t_i = mn \)) for k different meals so that each person has every other person not in the same delegation for a neighbor exactly λ times?” For λ= 1, Liu has obtained the complete solution to the problem when all tables accommodate the same number t of people. In this paper, we give the completesolution to the problem for \( \lambda\geq2 \) when all tables have uniform sizes t.     

Hamiltonian cycles and 2-dominating induced cycles in claw-free graphs

Let G = (V, E) be a connected graph. For a vertex subset , G[S] is the subgraph of G induced by S. A cycle C (a path, respectively) is said to be an induced cycle (path, respectively) if G[V(C)] = C (G[V(P)] = P, respectively). The distance between a vertex x and a subgraph H of G is denoted by , where d(x, y) is the distance between x and y. A subgraph H of G is called 2-dominating if d(x, H) ≤ 2 for all . An induced path P of G is said to be maximal if there is no induced path P′ satisfying and . In this paper, we assume that G is a connected claw-free graph satisfying the following condition: for every maximal induced path P of length p ≥ 2 with end vertices u, v it holds:

Edge-dominating cycles in graphs

A set S of vertices in a graph G is said to be an edge-dominating set if every edge in G is incident with a vertex in S. A cycle in G is said to be a dominating cycle if its vertex set is an edge-dominating set. Nash-Williams [Edge-disjoint hamiltonian circuits in graphs with vertices of large valency, Studies in Pure Mathematics, Academic Press, London, 1971, pp. 157-183] has proved that every longest cycle in a 2-connected graph of order n and minimum degree at least is a dominating cycle. In this paper, we prove that for a prescribed positive integer k, under the same minimum degree condition, if n is sufficiently large and if we take k disjoint cycles so that they contain as many vertices as possible, then these cycles form an edge-dominating set. Nash-Williams’ Theorem corresponds to the case of k=1 of this result.     

Paths and cycles of hypergraphs

Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given.     

Almost resolvable k‐cycle systems with

In this paper, we show that if and , then there exists an almost resolvable k‐cycle system of order for all except possibly for and . Thus we give a partial solution to an open problem posed by Lindner, Meszka, and Rosa (J. Combin. Des., vol. 17, pp. 404–410, 2009).     

Large cycles in 4-connected graphs

The first result states that every 4-connected graph G with minimum degree δ and connectivity κ either contains a cycle of length at least 4δ−κ−4 or every longest cycle in G is a dominating cycle. The second result states that any such graph under the additional condition δ≥α either contains a cycle of length at least 4δ−κ−4 or is hamiltonian, where α denotes the independence number of G. Both results are sharp in all respects.     

基于景气跟踪图的经济景气分析方法

首次将景气跟踪图方法引入中国经济景气分析中,并从宏观经济和行业分析两个维度对中国经济景气情况进行了分析.景气跟踪图方法基于时钟分析方法,对多个重要的经济时间序列指标的发展、运行进行跟踪,进而分析国民经济运行状态.景气跟踪图方法是一种新的景气分析方法,目前多用于宏观经济分析,作者尝试将其引入到行业分析中.针对直接采用原有景气跟踪图可能存在的问题,作者结合先行指标体系进行景气跟踪图分析,同时提出了基于景气跟踪图的经济持久期分析方法.中国经济的实证结果表明改进的景气跟踪图方法在宏观经济与行业分析中均有非常良好的表现,是现有景气分析方法的很好改进与补充.     

BIFURCATIONS OF LIMIT CYCLES FROM A HETEROCLINIC CYCLE OF HAMILTONIAN SYSTEMS

§１．ＮｏｒｍａｌＦｏｒｍｓｏｆＤｉｓｐｌａｃｅｍｅｎｔＦｕｎｃｔｉｏｎｓＣｏｎｓｉｄｅｒａｐｌａｎａｒＣ∞ｓｙｓｔｅｍｏｆｔｈｅｆｏｒｍｘ＝ｆ（ｘ）＋λｆ０（ｘ，δ，λ）≡ｆ（ｘ，δ，λ），（１．１）ｗｈｅｒｅｘ∈Ｒ２，λ∈Ｒ，δ∈Ｒｍ，ａｎｄｔｒ...     

循环分布图最大边数猜想的一个反例

令ｆ（ｎ）为恰有ｎ个顶点，任意两个循环长度都不相等的图的最多边数．１９７５年，Ｅｒｄｏｓ提出确定ｆ（ｎ）的问题（见［１］Ｐ２７４，Ｐｒｏｂｌｅｍ１１）．１９８６年，Ｙ．Ｓｈｉ证明了对任意自然数ｎ≥３，有ｆ（ｎ）≥ｎ＋８ｎ－２３＋１／２［］，且当３≤ｎ≤１７时，等号成立．进而猜想：对于任何自然数ｎ≥３，上述等式都成立．本文对该猜想给出一个反例．     

食饵种群具有常数收获率的捕食—食饵模型分析

本文研究食饵种群具有常数收获效的捕食－食饵模型：｛ｄｘ／ｄｔ＝ｂｘ＾２（１－ｘ／ｋ）－βｘｙ－ｈｄｙ／ｄｔ＝－ｃｙ＋ｄｘｙ讨论了极限环的存在性、唯一性和正平衡点的全局稳定性以及分界线环的存在性。