半参数回归模型的两步估计——差分法和样条函数法

本文考虑半参数回归模型yi =XTiβ g(ti) ei(i =1 ,2 ,… ,n) .先利用差分的方法估计 ^β ,接着用样条函数的方法定义 ^g(T) ,最后讨论 ^g(t)的性质 .     

Minimal Covers of Q +(2n + 1, q) by (n − 1)-Dimensional Subspaces

A t-cover of a quadric is a set C of t-dimensional subspaces contained in such that every point of is contained in at least one element of C.We consider (n – 1)-covers of the hyperbolic quadric Q ⁺(2n + 1, q). We show that such a cover must have at least q ^{n + 1} + 2q + 1 elements, give an example of this size for even q and describe what covers of this size should look like.     

一类高阶有理差分方程解的收敛性(英文)

本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解.     

Constructions of External Difference Families and Disjoint Difference Families

External difference families (EDFs) are a type of new combinatorial designs originated from cryptography. In this paper, some earlier ideas of recursive and cyclotomic constructions of combinatorial designs are extended, and a number of classes of EDFs and disjoint difference families are presented. A link between a subclass of EDFs and a special type of (almost) difference sets is set up.     

Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the finite simple group classification

Davenport’s Problem asks:What can we expect of two polynomials,over Z,with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport,Lewis and Schinzel.By bounding the degrees,but expanding the maps and variables in Davenport’s Problem,Galois stratification enhanced the separated variable theme,solving an Ax and Kochen problem from their Artin Conjecture work.Denef and Loeser applied this to add Chow motive coefficients to previously introduced zeta functions on a diophantine statement.By restricting the variables,but leaving the degrees unbounded,we found the striking distinction between Davenport’s problem over Q,solved by applying the Branch Cycle Lemma,and its generalization over any number field,solved by using the simple group classification.This encouraged Thompson to formulate the genus 0 problem on rational function monodromy groups.Guralnick and Thompson led its solution in stages.We look at two developments since the solution of Davenport’s problem.Stemming from MacCluer’s 1967 thesis,identifying a general class of problems,including Davenport’s,as monodromy precise.R(iemann)E(xistence)T(heorem)’s role as a converse to problems generalizing Davenport’s,and Schinzel’s (on reducibility).We use these to consider:Going beyond the simple group classification to handle imprimitive groups,and what is the role of covers and correspondences in going from algebraic equations to zeta functions with Chow motive coefficients.     

Dimension polynomials of difference local algebras

We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal.     

The complexity of minimum difference cover

The complexity of searching minimum difference covers, both in Z⁺ and in Z_n, is studied. We prove that these two optimization problems are NP-hard. To obtain this result, we characterize those sets—called extrema—having themselves plus zero as minimum difference cover. Such a combinatorial characterization enables us to show that testing whether sets are not extrema, both in Z⁺ and in Z_n, is NP-complete. However, for these two decision problems we exhibit pseudo-polynomial time algorithms.     

Reconstruction from local discrete averages on the plane

The aim of the paper is to construct a solution for the equation f?μ=g, where f?μ is the convolution of f and μ given by , g is an arbitrary continuous function and μ is a finitely supported measure on the plane.