On Browkin''''s conjecture about the elements of order five in K_2(Q)

Based on the work of Lenstra, a succinct proof of Browkin's conjecture about the elements of order five in K2(Q) is given.     

The strength of sharply bounded induction

We prove that the sharply bounded arithmetic T⁰₂ in a language containing the function symbol ?x /2^y ? (often denoted by MSP) is equivalent to PV₁. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the decidability of exponential terms

In this paper we prove, modulo Schanuel's Conjecture, that there are algorithms which decide if two exponential polynomials in π are equal in ? and if two exponential polynomials in π and i coincide in ?. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A tropical nullstellensatz

We suggest a version of Nullstellensatz over the tropical semiring, the real numbers equipped with operations of maximum and summation.

     

一类多项式系统极限环的研究

讨论了系统dxdt=(-y y2-dx)(1-y)a-x2(1-y)a-1dydt=x[(1-y)a (ax)a]极限环的存在性和唯一性,其中α为正数.     

求矩阵最小多项式的初等变换方法

分别给出计算矩阵的最小多项式和向量关于矩阵的最小多项式的初等变换方法 .     

Legendre-Fourier级数部分和 对有界变差函数的逼近

本文讨论了Legendre-Fourier级数部分和对有界变差函数逼近的间题，发展了文献【1]R. Bojanic和M. Vuilleumier的结果.     

On a class of Szász-Mirakyan type operators

The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.     

Bandwidth choice for local polynomial estimation of smooth boundaries

Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.