两两NQD列的强收敛性质

本文讨论两两NQD随机变量列极限理论中的强收敛性质。首先建立了两两NQD随机变量列最大部分和的Bernstein型概率指数不等式;并在此基础上,给出了具有不同分布的两两NQD列在较弱矩条件下的Petrov型对数律与Wittmann型重对数律,将文献中相应内容从NA情形推广到两两NQD情形。     

两两NQD列的极限定理

本文主要研究了两两NQD列的完全收敛性和强大数定律.文中给出了两两NQD列的定义和推广的Kolmogorov型不等式,并利用推广的Kolmogorov型不等式,得到了两两NQD列的完全收敛性定理.本文构造了两个不增函数,利用不增函数的性质,得到了两两NQD列的强大数定律.本文得到的强大数定律与独立随机变量情况下的强大数定律相类似,进而推广了前人的研究成果.     

关于两两NQD序列的强收敛性

两两NQD随机变量序列是一类常见的随机变量序列,在理论与实际中有着广泛的应用.本文的主要目的是要研究一般两两NQD随机变量序列的强收敛性.利用两两NQD随机变量序列的三级数定理及其性质,通过巧妙的截尾方法,获得了两两NQD随机变量序列的一类强极限定理,同时给出一般例子说明本文结果改进和真推广了现有文献的一系列结果.     

佳能EOS500N QD相机使用体会

佳能EOS500NQD相机是佳能公司于去年9月推出的一款体积小巧、造型美观、使用方便、适应性强的自动对售单镜头反光照相机。从外表看，佳能EOS500NQD相机设计得典雅大方：机项和底盖呈银白色，机身部分则衬以黑色的饰皮，和以往绝大部分佳能EOS系列相机全黑的外观有所不同。在佳能目前所有的EOS系列相机中，EOS500NQD的体积与最小的EOS888一样；重量仅比最轻的EOS888重30克，为370克，与配套的28－80mm变焦镜头一起，总共才570克，不及重量相对较轻的EOS10QD机身重。但是，EOS500NQD的功能繁多，自动化程度高，操作也极为方…     

不同波前振幅分布对于斯特列尔比的影响

斯特列尔比SR（Strehl Ratio）是衡量一个光学系统光能强度分布优劣的重要评价指标。本文根据激光核聚变中利用修正SR模型,数学推导研究得出了波前位相及振幅信息,获取最大的SR比的两者匹配条件：即斯特列尔比与波前振幅分布和波前位相的指数函数分布的一致性成正比关系。并对该结论进行了计算机仿真验证。实验根据一有象差波面位相与一组不同的振幅分布函数进行匹配计算：当给定波前位相分布（PV〈1λ时,则不同的振幅分布得到的斯特列尔比从0．92-0．99之间变化。实验结果表明当波前振幅分布与波前位相的指数函数分布一致性越好,系统斯特列尔比越大,并且斯特列尔比主要由波前位相分布决定。该结论说明：虽然激光核聚变中振幅是高阶超高斯型分布的平顶光束,只有当波前位相的均方根趋于零相当于一平面波时则其指数分布与振幅分布达到了好的一致性,才能得到高的SR比。     

一类平稳高斯序列超过数点过程与部分和的联合极限分布

主要讨论了一类平稳高斯序列的超过数点过程与部分和的联合极限分布,同时说明了极值与部分和是渐近独立的。     

自聚焦透镜列阵象平面上照度分布的分析

研究了自聚焦透镜及其列阵象平面上的照度分布。讨论只限于近轴射线单位放大率成象的条件下。一列和二列的自聚焦透镜列阵在场扫描和线扫描光学成象系统中,象面上光强分布将有所不同。因此,我们作了分析,并对某些样品进行了测量。     

随机初始几何缺陷对柱列支撑受力的影响

采用蒙特卡罗方法,研究了柱子和水平撑杆初始几何缺陷的随机遇合对柱列支撑受力的有利影响。应用有限元程序ANSYS对带有不同初始几何缺陷分布的柱列纵向支撑体系进行了大量的仿真分析,得到了柱列纵向支撑体系的四种失稳模式;通过概率统计得到柱中水平撑杆所受内力的概率密度函数,确定了可用于实际工程设计的支撑力的大小。结果表明:柱子和水平撑杆初始几何缺陷的随机遇合作用导致柱中水平撑杆受压或拉力的随机性,降低了支撑力,比《钢结构设计规范》(GB50017-2003)中柱列支撑设计公式算得的支撑力小许多。     

NA列的随机足标和与首达时的完全收敛性

通过讨论NA列非随机足标和的完全收敛性的一系列等价条件，本文得到了NA列随机足标和的完全收敛性结果。并借以讨论“首选时”的完全收敛性．将Gut(1983)的结果从iid列的场合推广到更广泛的同分布NA列的场合．     

两两NQD序列下线性指数分布参数的经验Bayes检验

本文讨论了线性指数分布参数的经验Bayes单边检验问题。对于两两NQD样本序列,利用核函数估计方法给出了检验函数。证明了该检验函数是渐近最优的,并在适当的条件下得到其收敛速度。     

ρ混合序列加权和的Marcinkiewicz强大数定律

通过建立(ρ)混合序列加权和的Bernstein不等式,研究了(ρ)混合序列加权和线性统计量的Marcinkiewicz-Zygmund强大数定律,实质性的改进和推广了Z.D.Bai与P.E.Cheng的结果.最后讨论了一个实际例子,预测城市物价增长.     

Two applications of Weil-Serre's explicit formula

We apply Weil-Serre's explicit formula to produce non-trivial estimates of exponential sums along a curve and of the dual distance of subfield subcodes of algebraic-geometric (AG-)codes. These bounds work while the number of rational points of a curve is large when compared to its genus thus the Weil-Bombieri bound for exponential sums being trivial.Partly supported by Russian Fundamental Research Foundation (project N 93-012-458) and by the grant MPN000 from the International Science FoundationThe author is deeply grateful to Mme Aurélia Lozingot for her help in typing of the present paper.     

Character sum constructions of constrained error-correcting codes

We estimate parameters of constrained error-correcting codes constructed by means of additive and multiplicative characters. To get the bounds we derive estimates for some incomplete character sums.This work was supported in part by the Academy of Finland. The first-named author would also like to express his gratitude to the Department of Mathematics of the University of Turku for the hospitality during his visit in August, 1992.     

Hyper-Kloosterman Sums and their Applications to the Coding Theory

The dual code of the Melas code is called the Kloosterman code. The weights of its codewords can be expressed by the Kloosterman sums, and are uniformly distributed with respect to the Sato-Tate measure. In this paper, the hyper-Kloosterman code C _m (q), a generalization of the Kloosterman code is defined, and the uniform distribution property is deduced using the hyper-Kloosterman sums when m is even and p− 1|m. Finally we discuss doubly-evenness for the weights in the binary case. It shows that we can construct infinitely many doubly-even codes in a non-trivial way. Received: October 30, 2000; revised version: February 28, 2001     

Fractal digital sums and codes

The positivity of a special digital sum is proved and its fractal nature is discussed. The result is interpreted in terms of running digital sums of a special code. These authors were supported by the Austrian National Bank, project Nr. 4995     

Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables

Serre has obtained sharp estimates for the number of rational points on an algebraic curve over a finite field. In this paper we supplement his technique with divisibility properties for exponential sums to derive new bounds for exponential sums in one and several variables. The new bounds give us an improvement on previous bounds for the minimum distance of the duals of BCH codes. The divisibility properties also imply the existence of gaps in the weight distribution of certain cyclic codes, and in particular gives us that BCH codes are divisible (in the sense of H. N. Ward).The results of this paper were presented in the IEEE International Symposium on Information Theory, Budapest, Hungary, July 1991.This work was partially supported by the Guastallo Fellowship and the Israeli Ministry of Science and Technology under Grant 5110431.This work was partially supported by the National Science Foundation (NSF) under Grants DMS-8711566 and DMS-8712742.This work was partially supported by NSF Grants RII-9014056, the Component IV of the EPSCoR of Puerto Rico Grant, and U.S. Army Research Office through the Army Center of Excellence for Symbolic Methods in Algorithmic Mathematics (ACSyAM), of Cornell MSI. Contract DAAL03-91-C-0027.     

Fractal Digital Sums and Codes

The positivity of a special digital sum is proved and its fractal nature is discussed. The result is interpreted in terms of running digital sums of a special code. Received August 3, 1995; revised version December 14, 1995     

The Discrete Fourier Transform of a Recurrent Sequence

 We prove a theorem of H. A. Barker on the Fourier coefficients of the sequence obtained by applying a complex-valued function to a recurrent sequence over a finite field. It is shown to follow from a result on the modulus of certain character sums which are evaluated in terms of Gauss sums. Received: April 1, 1997; revised version: August 29, 1997