On the Newton polygons of twisted L-functions of binomials

Let χ be an order c multiplicative character of a finite field and $f(x)=x^d+\lambda x^e$ a binomial with $(d,e)=1$. We study the twisted classical and T-adic Newton polygons of f. When $p>(d-e)(2d-1)$, we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on $p\mathrm{mod}cd$.We conjecture that this condition holds if p is large enough with respect to $c,d$ by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for $e=d-1$.     

WEAK CONVERGENCE FOR NON-UNIFORM φ-MIXING RANDOM FIELDS

Let $\{\xi_{\bold t}, {\bold t} \in {\bold Z}^d\}$ be a nonuniform $\varphi$-mixing strictly stationary real random field with $E\xi_{\bold 0}=0, E|\xi_{\bold 0}|^{2+\delta}<\infty$ for some $0<\delta<1$. A sufficient condition is given for the sequence of partial sum set-indexed process $\{Z_n(A),\ A\in \Cal A\}$ to converge to Brownian motion. By a direct calculation, the author shows that the result holds for a more general class of set index ${\Cal A}$, where ${\Cal A}$ is assumed only to have the metric entropy exponent $r, 0相似文献   

Uniform bounds under increment conditions

We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.

     

NA列加权乘积和的完全收敛性

本文讨论了NA和几类加权部分和及加权乘积和的完全收敛性，其中部分结果要优于iid列的已知结论。     

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．     

On the average complexity of 3D-Voronoi diagrams of random points on convex polytopes

It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as Θ(n²). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyzing what occurs if the points are chosen from a 2-dimensional region in 3-dimensional space. As an example, we examine the situation when the points are drawn from a Poisson distribution with rate n on the surface of a convex polytope. We prove that, in this case, the expected complexity of the resulting Voronoi diagram is O(n).     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.     

Synthesis of molecular imprinted organic-inorganic hybrid polymer binding caffeine

Random copolymers of poly{(methacrylamide)-co-(vinyl trimethoxysilane)} and poly{(methacrylic acid)-co-(vinyl trimethoxysilane)} were synthesized via a free radical polymerization reaction. Acid catalyzed sol-gel process of tetraethylorthosilicate (TEOS) with aforementioned polymers in the presence of methyl xanthine class of alkaloid like caffeine resulted in the formation of highly transparent monoliths. Solvent extraction of the template leaves behind the recognition sites intact with high selectivity towards the print molecule. The ionic and non-specific adsorptions, which are considered to be the main disadvantages of the molecularly imprinted polymers (MIP), are prevented to a considerable extent by the end capping of surface silanol groups. The template binding efficiencies of MIP were determined by HPLC analysis.     

Prime divisors of sparse integers

We obtain a lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits. This revised version was published online in August 2006 with corrections to the Cover Date.