A NEW CHARACTERIZATION OF THE CLOSEDNESS OF THE SUM OF TWO SUBSPACES

In this article, a new characterization of the closedness of the sum of two closed subspaces of a Hilbert space is established.     

Tensor sum and dynamical systems

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.     

Divisibility tests for low-valued primes and their use as generators of simple proofs

This article considers a family of divisibility tests for low-valued primes and their place as activities which develop the use of proof both within school and in teacher training. The way in which these tests can be seen as developing one from another is seen as of value in encouraging students to produce their own proofs.     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅰ)

设随机变量Ｘ１，Ｘ２，…ｉｉｄ；称Ｕｎ＝１≤ｉ＜ｊ≤ｎＸｉＸｊ，为两两乘积之和，本文意在给出 Ｕｎ／ｎ~２→０即文中（０．３）式成立的充分必要条件．我们在这部分工作中虽未能彻底解决这个问题，但却揭示出这类条件与Ｓｎ／ｎ→０（Ｓｎ＝ｎｉ＝１Ｘｉ）之条件间的本质上的不同之处，就是说，这是一类不能完全用Ｘ１的矩来刻划的条件，它们要更为深层次地依赖于Ｘ１的尾分布性质．     

{Qs}{Q（＇）s} Molecular States in QCD Sum Rules

We systematically investigate the mass spectra of {Qs}{Q（＇）s} molecular states in the framework of QCD sum rules. The interpolating currents representing the molecular states are proposed. Technically, contributions of the operators up to dimension six are included in operator product expansion （OPE）. The masses for molecular states with various {Qs}{Q（＇）s} configurations are presented. The result 4.36 ± 0.08 Ge V for theDs＊ Ds0- ＊ molecular state is consistent with the mass 4350＋4.6 -5.1± 0.7 MeV of the newly observed X（4350）, which could support X（4350） interpreted as a D＊D＊so molecular state.     

Dedekind sums with a parameter in finite fields

We first introduce the multiple Dedekind–Rademacher sum with a parameter in finite fields and establish its reciprocity law. We then construct an analog of the higher-dimensional Apostol–Dedekind sums, and establish their reciprocity laws using the parameterized Dedekind sum.     

On the subset sum problem over finite fields

The subset sum problem over finite fields is a well-known NP-complete problem. It arises naturally from decoding generalized Reed–Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a mathematical point of view. In several interesting cases, we obtain explicit or asymptotic formulas for the solution number. As a consequence, we obtain some results on the decoding problem of Reed–Solomon codes.     

关于q-Bernstein多项式的加速问题

In this paper,we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f,q;x)to B∞(f,q;x)but also the convergence of their iterated Boolean sum.Using the methods of exact estimate and theories of modulus of smoothness,we get the respective estimates of the convergence rate,which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.     

Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros

We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros. As a corollary we obtain a new proof for a result of Carlitz which relates one- and two-dimensional Kloosterman sums. In addition, we count some power sums of Kloosterman sums over certain subfields.