浅谈数列的周期及应用

对于给定的数列{a_n},若存在一个为自然数的常数T,使得对任意自然数n,恒有 a_(n T)=a_n (n=1,2,3,…)则我们称T为数列{a_n}的周期。数列{a_n}称为周期数列。对周期数列,不难得如下简单的性质。性质1 若T是数列{a_n}的周期,则2T、3T、…、nT、…都是数列{a_n}的周期。由此知,周期数列的周期有无穷多个,我们把最小的一个称为最小正周期。     

一类多滞量周期扰动非线性系统的周期解

研究一类具有多个滞量的周期扰动非线性系统的T周期解.利用拓扑度的方法得到了系统存在T周期解的充分条件.作为应用,证明了具有滞后的单种群对数模型在一定条件下存在正周期解.     

Fibonacci数列的模数列的周期的一个性质

Fibonacci数列的模数列是周期数列,并且是纯周期数列.利用模数列的定义,讨论了Fibonacci数列的模数列的周期的一个性质,证明了下列结果:假设m1与m2为不同的正整数,Fibonacci数列{Fn}的模数列{an(m1)}与{an(m2)}的最小正周期分别为T1与T2,则模数列{an([m1,m2])}的最小正周期为[T1,T2].     

每个点都是链回归点的树映射

设f是端点数为n的树T上的连续自映射且T上的每一点都是f的链回归点.本文证明了: (1)如果T的某个端点是f的不动点,那么,T上的每个点都是f的周期为r≤n-1的周期点,或存在自然数r ≤ n-1,使得fr含有湍流; (2)如果f的不动点都在T的内部,那么,T上的每个点都是f的周期为r≤n的周期点,或存在自然数r≤n,使得,fr含有湍流.     

利用单位根给出一般周期数列的通项公式

首先回顾周期数列的定义:给定数列{an},如果存在不为0的正整数T,使得ai=ai+T对一切自然数i都成立,则称数列{an}称为周期数列,称T为这个数列的周期.例如a,b,c,a,b,c,…,一般要写出这个简单周期数列的通项并不困难,通常可以用分段通项公式来确定.但     

求解三角函数最小正周期的常见策略

<正>周期性是函数的一个重要性质,也是高考命题的一大热点.本文通过实例介绍几种求三角函数最小正周期的常见策略,仅供同学们参考.一、定义法首先,我们来看周期的定义:如果对于定义域内的任一自变量x,都存在常数T,使f(x+T)=f(x)恒成立,那么T为函数f(x)的一个周期.通常高中所指的周期是最小正周期.根     

“旋转数列”简论(续完)

四、旅转数列周期性的讨论有些无穷数列具有周期现象,即{A_n}满足条件:A_(x T)=A_x,(x∈N,常数T≠0),例如常数列{A_n}:A_1,A_2,…的周期T=1,正k次圆周型旋转数列[A_n,(P_0,θ)]的周期T=k(k>1)等。 (1)旋转数列通项计算公式     

周期数列的几种形式

数列是一种特殊的函数,所以数列中也存在周期的问题,且以各种形式给出的周期函数问题在数列中同样成立.定义对于数列{an},若存在一个(固定的)自然数T,使得对一切自然数n≥N,都有an T=an成立,则称数列{an}为从第N项起的周期为T的周期数列.若N=1,则称数列{an}为纯周期数列,否则称     

新题征展(113)

A 题组新编 1.(袁保金)在数列{an}中,如果存在非零常数T,使得am+T＝am对于任意的非零自然数m均成立,那么就称数列{an}为周期数列,其中T为数列{an}的周期.     

周期参数扰动的T混沌系统周期轨道分析

本文研究了一类周期参数扰动的T混沌系统的周期轨道问题.利用次谐波Melnikov方法,获得了具有广义Hamilton结构的周期参数扰动的慢变系统的振荡周期轨道和旋转周期轨道.     

关于Banach空间中渐近非扩张型半群的不动点的存在性

设C是具有弱一致正规结构的Banach空间X的非空弱紧凸子集, T={T(t):t∈S}是渐近非扩张型半群, 且每个T(t)在C上连续. 该文证明了如下结论:(i) 若X是一致凸的, 则F(T) 非空;(ii) 若T={T(t):t∈S}满足lim inf_{t→∞,t in S}|‖T(t)‖|<+∞, 且在C上弱渐近正则, 则F(T)非空, 其中|‖T(t)‖|是T(t)的精确的Lipsch itz常数,F(T)是T(t),t∈S的所有公共不动点之集.     

Lp Contraction Semigroups for Vector Valued Functions

Let be a contraction semigroup on the space of vector valued functions ( is a Hilbert space). In order to study the extension of to a contaction semigroup on , Shigekawa [Sh] studied recently the domination property where is a symmetric sub-Markovian semigroup on . He gives in the setting of square field operators sufficient conditions for the above inequality. The aim of the present paper is to show that the methods of [12] and [13] can be applied in the present setting and provide two ways for the extension of to We give necessary and sufficient conditions in terms of sesquilinear forms for the contractivity property as well as for the above domination property in a more general situation.     

A$\mathcal{T}$-algebras and extensions of A$\mathbb{T}$-algebras

Lin and Su classified A$ \mathcal{T} $ \mathcal{T} -algebras of real rank zero. This class includes all A$ \mathbb{T} $ \mathbb{T} -algebras of real rank zero as well as many C*-algebras which are not stably finite. An A$ \mathcal{T} $ \mathcal{T} -algebra often becomes an extension of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra. In this paper, we show that there is an essential extension of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra which is not an A$ \mathcal{T} $ \mathcal{T} -algebra. We describe a characterization of an extension E of an A$ \mathbb{T} $ \mathbb{T} -algebra by an AF-algebra if E is an A$ \mathcal{T} $ \mathcal{T} -algebra.     

一类本质正规算子的稳定不变子空间

在本文中 ,我们给出了一类本质正规算子的稳定不变子空间的特征 .即 ,T∈ L( H2 ( Ω;μ) )且满足1 ) T是本质正规算子 ;2 )σ( T) =Ω,σe( T) = Ω,σp( T) =Ω ;3) ind( T-z) =n,z∈Ω;4 ) minind( T-z) =0 ,z∈ Ω.M是 T的非平凡的不变子空间 ,则 M是 T的稳定不变子空间当且仅当 dim M<∞ and dim M⊥ =∞     

反对角算子矩阵及其平方的(ω)性质的摄动

设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体.若σ_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.     

A Tree-valued Markov Process Associated with an Admissible Family of Branching Mechanisms

Let E?R be an interval. By studying an admissible family of branching mechanisms{ψt,t ∈E} introduced in Li [Ann. Probab., 42, 41-79(2014)], we construct a decreasing Levy-CRT-valued process {Tt, t ∈ E} by pruning Lévy trees accordingly such that for each t ∈E, Tt is a ψt-Lévy tree. We also obtain an analogous process {Tt*,t ∈E} by pruning a critical Levy tree conditioned to be infinite. Under a regular condition on the admissible family of branching mechanisms, we show that the law of {Tt,t ∈E} at the ascension time A := inf{t ∈E;Tt is finite} can be represented by{Tt*,t∈E}.The results generalize those studied in Abraham and Delmas [Ann. Probab., 40, 1167-1211(2012)].     

Regular Subsets of Semigroups Related to their Idempotents

For a subsemigroup T of a semigroup S, we let Reg(T) and reg(T) denote respectively the set of all regular elements of T and the set of all elements of T which are regular in S. We characterize semigroups with Reg(T)=reg(T), where T runs over one of the following families of subsemigroups: {Se | e ∈ E(S)}, {eS | e ∈ E(S)}, {eSf | e,f ∈ E(S)}.     

Kolmogorov complexity and characteristic constants of formal theories of arithmetic

We investigate two constants c _T and r _T , introduced by Chaitin and Raatikainen respectively, defined for each recursively axiomatizable consistent theory T and universal Turing machine used to determine Kolmogorov complexity. Raatikainen argued that c _T does not represent the complexity of T and found that for two theories S and T , one can always find a universal Turing machine such that $c_\mathbf {S}= c_\mathbf {T}$. We prove the following are equivalent: $c_\mathbf {S}\ne c_\mathbf {T}$ for some universal Turing machine, $r_\mathbf {S}\ne r_\mathbf {T}$ for some universal Turing machine, and T proves some Π₁‐sentence which S cannnot prove. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

上三角算子矩阵Browder定理稳定性的判定

用σ(T)和σ_w)分别表示算子T的谱与weyl谱,π_(00)(T)={λ∈isoσ(T),0dimN(T-λI)∞},若σ(T)\σ_w(T)■π_(00)(T)成立,则就认为T满足Browder定理.主要研究了2×2上三角算子矩阵的Browder定理在紧摄动下的稳定性,并给出了判定稳定性的等价条件.     

ON THE SPECTRAL RADIUS OF IRREDUCIBLE AND WEAKLY IRREDUCIBLE OPERATORS IN BANACH LATPICES

Abstract

If T is an operator on a Banach lattice E we call T weakly irreducible if E contains no non-trivial T-invariant bands. We prove that if E is order complete and if the weakly irreducible operator T > 0 is in (E′_oo ? E)^⊥⊥ then T has positive spectral radéus. Prom this follows that Jentesch's theorem holds in arbitrary Banach function spaces.

If [Ttilde] denotes the restriction of T′ to E′_oo, 0 ? T an order continuous operator, then T is weakly irreducible if and only if [Ttilde]: E′_oo→E′_oo is weakly irreducible.

Finally we show that the majorizing, irreducible operator T ≥ 0, has positive spectral radius if either Tⁿ is weakly compact or E has property (P) or T is strongly majorizing.