二元非乘积型Baskakov算子的某些逼近性质

该文利用多元分解技巧及一元的结果得出二元非乘积型算子V\-n的两个逼近性质定理.对f∈C\-0(T\+2),‖V\-n(f)-f‖≤cω\-2(f,[SX(]1[]n[SX)]); 对f∈C\+2(T\+2),lim[DD(X]n→∞[DD)]n(V\-n(f)-f)=[SX(]x(1+x)[]2[SX)]f\-\{11\}+[SX(]y(1+y)[]2[SX)]f\-\{22\}+[SX(]xy[]2[SX)]f\-\{12\}.     

BANACH空间有界线性算子A~((2))_(T,S)的表示

In this paper we extends the results in [1],[2],[3] and [4] to bounded linear operators in Banach spaces using matrix expression of a partitioned operator. For existence of the limit lim λ→0 (λI + GA)~(-1) G and lim λ→0 G(λI + AG)~(-1) it is necessary and sufficient condition that bounded linear operators A~((2))_(T,S) exist in Banach spaces. We get the integral representation: A(2)_(T,S)=∫∞0 exp(-GAt)Gdt.     

UNIFORM STRONG CONVERGENCE RATE OF NEAREST NEIGHBOR DENSITY ESTIMATION

Based on [3] and [4],the authors study strong convergence rate of the k_n-NNdensity estimate f_n(x)of the population density f(x),proposed in [1].f(x)>0 and fsatisfies λ-condition at x(0<λ≤2),then for properly chosen k_nlim sup(n/(logn)~(λ/(1 2λ))丨_n(x)-f(x)丨C a.s.If f satisfies λ-condition,then for propeoly chosen k_nlim sup(n/(logn)~(λ/(1 3λ)丨_n(x)-f(x)丨C a.s.,where C is a constant.An order to which the convergence rate of 丨_n(x)-f(x)丨andsup 丨_n(x)-f(x)丨 cannot reach is also proposed.     

關於有一無限極限的一個函數的窣锇Ъ墧祵墩笖悼偤托

<正> 1.我們已經證明開於有一無限極限的一個單調函數的福里哀級數對於负指數(c,r)總和性的情形的定理,很自然地,人們還要問起:對於正指數的情形是怎麼樣?現在進行討論如下.     

时间随机环境中一维紧邻随机游动的常返性质

设环境q={q(n)}∞0是取值于[0,1]上一列独立同分布的随机变量列,且Eq(0)=p;{Sn}∞0是随机环境q中取整数值随机游动,S0=0,且满足:对任意的整数xi(i≥0),x,y,P(Sn+1=y|S1=x1,…,Sn-1=xn-1,Sn=x,q)={q(n),y=x+1,1-q(n),y=x-1,0,其他.我们证明了:p>1/2时,Sn→+∞,a.e.,n→∞;p<1/2时,Sn→-∞,a.e.,n→∞;p=1/2时,-∞=(lim infSn)/(n→+∞)<(lim supSn)/(n→+∞)=+∞,a.e.,n→∞.     

A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée

The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331-386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749-770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271-288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331-386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged.     

环Z/p\+kZ上m阶交错矩阵的计数定理及其应用

设W\-m(R)是有限局部环R=Z/p\+kZ上所有m阶交错矩阵所构成的集合（p是素数,k>1）. 该文通过确定R上任意m阶交错矩阵的标准形,计算出W\-m(R)在线性群GL\-m(R)作用下的轨道数及n(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)]),其中W（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])(∑[DD(]l[]i=1[DD)]s\-i=t)表示不变因子为（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])的所有m阶交错矩阵构成的集合,n(2r,2t,（2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])表示其中的元素个数. 最后,作者利用有限局部环R上交错矩阵的标准形构作了一个Cartesian认证码,并计算出其全部参数.     

單葉函數的係數與開始多項式

<正> 以fk(z)表單位圓內的K次對稱單葉全純函數,亦即fk(z)=z+a_I~((k))z~(k+1)+a_2~((k))z~(2k+1)+…,|z|<1.以S_k表此種函數之全體.特別,書S以代S_1.     

一类非单调算法的收敛性质

1.搜索步长和搜索方向对于无约束最优化问题(?)f(x),其中f:R~n→R~1,f∈C~1,一般采用形如x_(k+1)=x_k+λ_kd_k(k=1,2,…)的迭代算法来求解,这里λ_k为搜索步长,d_k为搜索方向.     

Levinson定理证明的一些简化

<正> (一)1974年,Levinson N.证明了他的关于Riemann ζ-函数在直线σ=1/2上的零点个数的著名定理:对充分大的T有     

UNUNIQUENESS OF SOME HOLOMORPHIC FUNCTIONS

In the present paper, we show that there exist a bounded, holomorphic function $\[f(z) \ne 0\]$ in the domain $\[\{ z = x + iy:\left| y \right| < \alpha \} \]$ such that $\[f(z)\]$ has a Dirichlet expansion $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ in the halfplane $\[x > {x_f}\]$ if and only if $\[\frac{a}{\pi }\log r - \sum\limits_{{u_n} < r} {\frac{2}{{{u_n}}}} \]$ has a finite upperbound on $\[[1, + \infty )\]$, where $\[\alpha \]$ is a positive constant,$\[{x_f}( < + \infty )\]$ is the abscissa of convergence of $\[\sum\limits_{n = 0}^{ + \infty } {{d_n}{e^{ - {u_n}}}} \]$ and the infinite sequence $\[\{ {u_n}\} \]$ satisfies $\[\mathop {\lim }\limits_{n \to + \infty } ({u_{n + 1}} - {u_n}) > 0\]$. We also point out some necessary conditions and sufficient ones Such that a bounded holomorphic function in an angular(or half-band) domain is identically zero if an infinite sequence of its derivatives and itself vanish at some point of the domain. Here some result are generalizations of those in [4].     

Abstract Convexity,Some Relations and Applications

The aim of this article is to analyze the relationship between various notions of abstract convexity structures that we find in the literature, in connection with the problem of the existence of continuous selections and fixed points of correspondences. We focus mainly on the notion of mc -spaces, which was introduced in [J.V. LLinares (1998). Unified treatment of the problem of the existence of maximal elements in binary relations: a characterization. Journal of Mathematical Economics , 29 , 285-302], and its relationship with c -spaces [Ch.D. Horvath (1991). Contractibility and generalized convexity. Journal of Mathematical Analysis and Applications , 156 , 341-357], simplicial convexity [R. Bielawski (1987). Simplicial convexity and its applications. Journal of Mathematical Analysis and Applications , 127 , 155-171], order convexity (used in [Ch.D. Horvath and J.V. LLinares (1996). Maximal elements and fixed points for binary relations on topological ordered spaces. Journal of Mathematical Economics , 25 , 291-306]), B '-simplicial convexity and L -spaces [H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano and J.V. LLinares (1998). Abstract convexity and fixed points. Journal of Mathematical Analysis and Applications , 222 , 138-150]. Moreover, in the context of mc -spaces, a characterization result of nonempty finite intersection, in the line with the Knaster-Kuratowski-Mazurkiewicz Lemma, some consequences of it and some generalizations of Browder's existence of continuous selection and fixed point theorem are presented.     

一类Schrǒdinger算子的谱分析

本文研究了Hilbert空间L^2（R^2）上由势函数V（x）（V≥0,连续）给出的一类Schrǒdinger算子H=-△＋V的谱。本文的主要结果：（1）H的谱σ（H）不会出现本性谱与离散谱交替出现的情况,其谱要么是离散的,要么从infσcos（H）开始全是本性谱;（2）lim‖x‖→∞V（x）=∞是σcos（H）=φ的充要条件。（3）借助于讨论H的Zhis-lin谱,在一定的条件下。lim‖x‖→∞V（x）=0是σcos（H）=[∞,0）的充要条件。我们还提出了几个没有解决的问题。     

HOW BIG ARE THE LAG INCREMENTS OF A 2-PARAMETER WIENER PROCESS? (II)

The author investigated how big the lag increments of a 2-parameter Wiener process is in [1]. In this paper the limit inferior results for the lag increments are discussed and the same results as the Wiener process are obtained. For example, if $\[\mathop {\lim }\limits_{T \to \infty } \{ \log T/{a_T} + \log (\log {b_T}/a_T^{1/2} + 1)\} /\log \log T = r,0 \leqslant r \leqslant \infty \] $ then $\[\mathop {\lim }\limits_{\overline {T \to \infty } } \mathop {\sup }\limits_{{a_T} \leqslant t \leqslant T} \mathop {\sup }\limits_{t \leqslant s \leqslant T} \mathop {\sup }\limits_{R \in L_s^*(t)} |W(R)|/d(T,t) = {\alpha _r},a.s.,\] $ $\[\mathop {\lim }\limits_{\overline {T \to \infty } } \mathop {\sup }\limits_{{a_T} \leqslant t \leqslant T} \mathop {\sup }\limits_{R \in {{\tilde L}_T}(t)} |W(R)|/d(T,t) = {\alpha _r},a.s.,\] $ where $\alpha _r=(r/(r+1))^{1/2}$, $L*_s(t)$ and $\tider L_T(t)$ are the sets of rectangles which satisfy some conditions. Moreover, the limit inferior results of another class of lag increments are discussed.     

Algorithms for the single-source uncapacitated minimum concave-cost network flow problem

We investigate algorithms, applications, and complexity issues for the single-source uncapacitated (SSU) version of the minimum concave-cost network flow problem (MCNFP). We present applications arising from production planning, and prove complexity results for both global and local search. We formally state the local search algorithm of Gallo and Sodini [5], and present alternative local search algorithms. Computational results are provided to compare the various local search algorithms proposed and the effects of initial solution techniques.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

A class of norms of iterative methods for solving systems of linear equations

A new class of norms which generalize norms previously investigated by Young [9, 14], Sheldon [4, 5], Golub [1], Golub and Varga [2], Varga [6], Wachspress [7], Young and Kincaid [12], Young [14], and Kincaid [3] is introduced. Expressions for these norms applied to the matrices associated with various iterative methods are developed.Work on this paper was sponsored by NSF Grant GP-8442 and Army Grant DA-ARO(D)-31-124-G1050 at The University of Texas at Austin.     

关于矩阵乘法与整数卷积最佳算法运算量的估计

§1.引言 [1]通过构造一个大整数然后作整数乘除法给出了用于有理数矩阵相乘的算法,运算量为O(n~2),达到了矩阵乘法复杂性下界,是最佳算法。[2]曾指出[1]中忽略了不同字长有不同运算量这一事实。但对[1]中算法复杂性未作具体讨论和质疑。最近,[3]—[4]采用类似于[1]中的大整数乘除法分别提出整数向量卷积的算法,并认为运算量级为     

关于求解常微方程组的离散波形松驰方法的加速收敛

提出一种关于求解常微线性系统的离散波形松驰方法的新的加速收敛技巧。通过对系统矩阵A的分裂，该技巧使迭代矩阵（(zI M)^-1N）具有理想的较小谱半径。在LU分解的基础上给出了一个迭代算法以及用该法与Gauss-Seidel方不垢敛速进行比较的数值例子。