Banach空间中i.i.d.随机变量中偏差的下限不等式

本文得到了Ｂａｎａｃｈ空间中ｉ．ｉ．ｄ．随机元序列部份和Ｓｎ满足中偏差下限不等式的充要条件，讨论了开凸集上的中偏差问题。     

Percolation in invariant Poisson graphs with?i.i.d.?degrees

Let each point of a homogeneous Poisson process in ℝ ^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution μ on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution μ. Leaving aside degenerate cases, we prove that for any μ there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme which is a natural extension of Gale–Shapley stable marriage, we give sufficient conditions on μ for the absence and presence of infinite components.     

具有非负i.i.d.新息的AR（p）模型的参数估计

一、引言 Bell和Smith讨论了正值AR(1)模型的参数估计问题，所谓正值AR(1)模型是指     

i.i.d情况下非参数回归模型的误差密度估计的收敛性质

本文研究了i．i．d情况下非参数回归的误差密度估计的一致收敛和均方收敛，给出了一定条件下误差密度的估计量f^n(x)的一致收敛速度和均方收敛速度。     

A sharp inequality for the tail probabilities of sums of i.i.d. r.v.’s with dominatedly varying tails

Let F be a distribution function supported on (-∞, ∞) with a finite mean μ. In this note weshow that if its tail F = 1 - F is dominatedly varying, then for any γ＞ max{μ, 0}, there exist C(γ) ＞ 0 and D(γ) ＞ 0 such thatC(γ)nF(x) ≤ Fn*(x) ≤ D(γ)nF(x),for all n ≥ 1 and all x ≥γn. This inequality sharpens a classical inequality for the subexponential distributioncase.     

On uniform closeness of local times of Markov chains and i.i.d. sequences

In this paper we consider the field of local times of a discrete-time Markov chain on a general state space, and obtain uniform (in time) upper bounds on the total variation distance between this field and the one of a sequence of $n$ i.i.d. random variables with law given by the invariant measure of that Markov chain. The proof of this result uses a refinement of the soft local time method of Popov and Teixeira (2015).     

Translation surfaces in the 3-dimensional space satisfying Δ III r i = μ i r i

In this paper we study the translation surfaces in the 3-dimensional Euclidean and Lorentz-Minkowski space under the condition ${\Delta ^{III}r_{i} = \mu _{i}r_{i},\mu _{i} \in \mathbb{R}}$ , where Δ ^III denotes the Laplacian of the surface with respect to the third fundamental form III. We show that in both spaces a translation surface satisfying the preceding relation is a surface of Scherk.     

A Note on the Difference Equation x n +1 = ∑ i =0 k α i x n − i p i

In this note we improve Theorem 2 in Ref. [3] , about the difference equation x n +1 = ~ i =0 k f i x n m i p i , n =0,1,2,..., where k is a positive integer, f i , p i ] (0, X ) for i =0,..., k , and the initial conditions x m k , x m k +1 ,..., x 0 are arbitrary positive numbers.     

Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying Δr i ?=?λ i r i

In this paper we classify the factorable surfaces in the three-dimensional Euclidean space ${\mathbb{E}^{3}}$ and Lorentzian ${\mathbb{E}_{1}^{3}}$ under the condition ??r _i ?=??? _i r _i , where ${\lambda_{i}\in\mathbb{R}}$ and ?? denotes the Laplace operator and we obtain the complete classification for those ones.     

i．i．d随机变量随机和的数字特征

讨论了i．i．d的随机变量随机和的数学期望和方差、特征函数以及矩母函数的计算公式。并对求和个数服从几何分布和Possion分布，随机变量服从指数分布时给出了直接结果．     

Helicoidal surfaces in the three-dimensional Lorentz�CMinkowski space satisfying �� II r i ?=?�� i r i

In this paper, we study helicoidal surfaces without parabolic points in the 3-dimensional Lorentz?CMinkowski space under the condition ?? ^II r _i ?=??? _i r _i where ?? ^II is the Laplace operator with respect to the second fundamental form and ?? _i is a real number. We prove that there are no helicoidal surfaces without parabolic points in the 3-dimensional Lorentz?CMinkowski space satisfying that condition.     

Cyclic and simultaneous iterative methods to matrix equations of the form A i X B i = F i

This paper deals with a general type of linear matrix equation problem. It presents new iterative algorithms to solve the matrix equations of the form A _i X?B _i = F _i . These algorithms are based on the incremental subgradient and the parallel subgradient methods. The convergence region of these algorithms are larger than other existing iterative algorithms. Finally, some experimental results are presented to show the efficiency of the proposed algorithms.     

Exponential asymptotics of bi-oscillatory integrals. Application to the problem of persistence of homoclinic connections for the (iω0)2iω1 resonance

We explain in this Note how to obtain an exponentially small equivalent of a bioscillatory integral when it involves solutions of a nonlinear differential equation. The method proposed in this Note enables us to study the problem of existence of homoclinic connections for vector fields admitting a (iω₀)²iω₁ resonance at the origin. This problem could not be solved by a direct application of the classical Melnikov method since the Melnikov function is given in this case by an exponentially small bi-oscillatory integral.     

尤拉公式e~(θi)=cosθ+i sin θ

引言在这篇短文里,我們向讀者介紹一种新的建立尤拉公式的方法。我們不用一般数学分析里所用的方法,而用一个人家熟知的重要极限来建立尤拉公式。同时,我們考虑到尤拉公式的应用很广泛,也很重要,因此,順便列举了一些应用。其中特别請大家注意应用4和5,显然这样做是不够严格的,但我們想借此向讀者說明:当在复数城里研究初等函数时会出現实数城里沒有的有趣性质,从而帮助我們更深地理解初等实函数。这对中学数学教师是有帮助的。§1.尤拉公式e~(θi)=cosθ+isinθ的推导在数学分析里已經証明了一个重要极限 e~θ=(?)(1+θ/n)~n,这里θ为任意实数。推广这个結果于θi,得 e~(θi)=(?)(1+θi/n)~n (1)这里θ为任意实数,而i为虚数单位。現在我們来計     

(i1i)*(b12k0)及(i1i)*(b31k0)在π*V(1)中的收敛性

对连通有限型谱X,y,存在Adams谱序列{Es,tr,dr},满足(1)dr:Es,t,r→Es+r,t+r-1,r是谱序列的微分, (2)Es,t,2≌Exts,t,A(H*X,H*y),(3)收敛到[∑t-sY,X].当X分别是球谱S,Moore谱M,Toda-smith谱V(1)时,(πt-X)p分别是S,M,V(1)的稳定同伦群.利用Adams 谱序列,证明了(i1i)*(62,1k0)及(i1i)*(b3,1k0)是永久循环但不是边缘,因此收敛到π*V(1)中的非零元,其中P为奇索数,q=2p-2.     

关于图Kn-H2n+i(i=1,2)的升分解

Yousef.Alavi等人在文献[1]中定义了一种新分解(Ascending Subgraph Decomposition),即"升分解",并且猜想:任意有正整数条边的图都可以升分解.本文证明了下面两个结论:1. Kn-H2n+1可以升分解,其中H2n+1为含有2n+1条边的Kn的子图;2. Kn-H2n+2可以升分解,其中H2n+2为含有2n+2条边的Kn的子图.