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.     

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.     

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.     

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.     

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．     

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.     

On the factor-web $$ {\boldsymbol{\bar{ W}}} $$ ( ρ, r,r) of the three-web W( r,r, r)

The notion of the factor-web [`(W)] \bar{W} (ρ, r, r) (1 ≤ ρ < r) is defined for the three-web W(r, r, r) formed on a 2r-dimensional differentiable manifold by three r-dimensional smooth foliations. Embedding of the factor-web in the initial web W(r, r, r) is constructed. This construction is a well-known geometric analog of the canonical extension of a Lie group of transformations to its parameter group.     

Diffusions réfléchies réversibles dégénérées

On a domain D in ^d, for a smooth enough probability density and a diffusion matrix which can degenerate, we construct the law Q ^s of a (x)d -symmetric reflecting process in D with matrix . Therefore, we use the associated Dirichlet form and a sequence of approximating processes already used by Pardoux and R. Williams in [23]. Under mild conditions on the boundary ofD (finite Minkowski content), we prove that Q ^s is the law of a semi-martingale and provide its decomposition. Comparing with the decomposition in additive functionals, we conclude that the process is reflected in the conormal direction ^* n where n denotes Chen's normal (cf [10]), that is, the reflection direction of the Brownian motion in Kuramochi compactification.     

多目标规划的r—有效解和r—最优

本文引入有限维向量空间的r-序类概念,讨论了它们的基本性质。在此基础上,定义了多目标规划的r-有效解和r-最优解,研究了它们与其它有关解之间的关系。     

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.     

Lokale Konvergenzbedingugen für trigonometrische Reihen und für Potenzreihen

Ohne ZusammenfassungHerrnFriedrich Lösch zum 60. Geburstag am 10. Dezember 1963 gewidmetDie Arbeit wurde unterstützt durch den National Research Council of Canada, als der Verfasser an der University of Western Ontario war.     

Integralgleichungen für einige Randwertprobleme für Gebiete mit Ecken

Summary Concerning conformal mapping and problems of the theory of elasticity, the classical integral equations are modified in order to treat the cases of not smooth boundary curves. As the kernels are still bounded, no difficulties of numerical computation arise.     

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.     

图Kn—E（k0P3（∪↑r↓i=1kiPqi—1））的色唯一性

记δｎ＝Σ↓ｋ≤ｎ（＾ｋｎ－ｋ），在本文中证明了：Ａ↓ｒ∈Ｎ，若Ａ↓∈Ｎ，若Ａ↓∈｛１，２，…，ｒ｝，ｑｉ（〉５）都是素数，并且［（δｑｉ－１－１）！＋１］／δｑｉ－１是正整数，则图簇Ｋｎ－Ｅ（ｋ０Ｐ３∪ｋ１Ｐｑ１－１∪…∪ｋｒＰｑｒ－１）是色唯一的，推广了文［１］的结果。     

Varför Tunneldioder?

In the last two years the electronic industry has shown a great interest in tunnel diodes. This article gives a short explanation of the basic effect and summarizes the more important features of the device. The general fabrication technique is outlined, and some associated problems are discussed.     

Le régulateur p-adique

For all $n\in {\mathbf{N}}^1$, we define a p-adic regulator $R_p:K_{2n+1}({\mathbf{Q}}_p)\to {\mathbf{Q}}_p$ given by an explicit formula and we show that $R_p$ is non-trivial for $n=1$. The main ideas come from a Note published in 2000 for the transcendental case. To cite this article: N. Hamida, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Existenzfragen für Strahlensysteme

Ohne ZusammenfassungHerrn Professor Dr.Wolfgang Haack zum 60. Geburtstag gewidmet