陕西省“十一五”时期发明专利文献分析

专利数据是衡量区域创新能力的指标之一,可以反映出一个地区的技术水平和竞争力。以2006—2010年的陕西省发明专利为例,对发明专利申请量的时间、地区分布及IPC重点技术领域进行了统计分析,为陕西省的科技管理和专利战略制定提供基础资料和决策依据。     

弱化希尔伯特第16问题及其研究现状

V.I.Arnold多次提出如下问题:对于给定的自然数n≥2,所有n次多项式1-形式,沿一切可能的m≥3次闭代数曲线族的阿贝尔积分的孤立零点的最大个数Z(m,n)=?由Poincare-Pontryagin定理可知,当阿贝尔积分不恒为零时,A(n)=Z(n+1,n)给出n次Hamilton系统在n次多项式扰动下从原有周期环域分支出极限环的最大个数,因此Arnold把这个问题称为弱化的希尔伯特第16问题.30多年来,对此问题的研究取得了一定进展,也遇到了很大困难.本文拟对这个问题和相关研究工作做一个粗浅的介绍.     

Carpenter,tractors and microbes for the development of logical–mathematical thinking – the way 10th graders and pre-service teachers solve thinking challenges

The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical–mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers’ answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical–mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.     

Nonsmooth nonconvex optimization approach to clusterwise linear regression problems

Clusterwise regression consists of finding a number of regression functions each approximating a subset of the data. In this paper, a new approach for solving the clusterwise linear regression problems is proposed based on a nonsmooth nonconvex formulation. We present an algorithm for minimizing this nonsmooth nonconvex function. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate a good starting point for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or near global solution to the problem when the data sets are sufficiently dense. The algorithm is compared with the multistart Späth algorithm on several publicly available data sets for regression analysis.     

川东北南江地区灯影组三段岩石特征及沉积环境分析

南江地区位于上扬子地台东北缘,该区灯影组三段发育了一套以白云岩为主的沉积岩层。通过对杨坝剖面岩石学特征及沉积相的研究,结合前人的研究成果,认为该区灯影组三段可分为三个岩性段:下部以粉-微晶、泥微晶白云岩为主;中部以砂屑白云岩为主,局部可见角砾状泥微晶白云岩;上部以硅化细-粉晶白云岩、硅化叠层藻白云岩为主,部分层位发育角砾状粉微晶白云岩、中-细晶白云岩。岩层中主要发育纹层状、条带状、藻叠层及缝合线构造;并且认为研究区灯影组三段地层发育在碳酸盐台地-陆表海环境中,从底到顶可识别出泻湖、浅水碳酸盐砂滩、潮坪三种亚相的沉积。总体上为一海侵-海退的沉积旋回。     

An elementary and constructive solution to Hilbert's 17th Problem for matrices

We give a short and elementary proof of a theorem of Procesi, Schacher and (independently) Gondard, Ribenboim that generalizes a famous result of Artin. Let be an symmetric matrix with entries in the polynomial ring thbb{R}[x_1,\ldots,x_m]$">. The result is that if is positive semidefinite for all substitutions thbb{R}^m$">, then can be expressed as a sum of squares of symmetric matrices with entries in thbb{R}(x_1,\ldots,x_m)$">. Moreover, our proof is constructive and gives explicit representations modulo the scalar case.

     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by th-0002" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/e55bfe99-6125-4a44-a094-ed6ad998b2a6/mana201500183-math-0002.png">, is a graph with the same set of vertices as G such that two vertices are adjacent in th-0003" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/cf19f968-eb5b-45a3-bdd6-3467388f74f0/mana201500183-math-0003.png"> if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of th-0004" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/42f09283-da07-497a-8623-5970d769f4ec/mana201500183-math-0004.png"> and th-0005" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/52bbfbac-cde1-47ce-98aa-626afb1e9898/mana201500183-math-0005.png">. The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph th-0006" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/afb97c4f-7c69-4eb0-9726-b630ea1be77f/mana201500183-math-0006.png"> is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

一类流形的刚性定理

本文通过具有良好性质的子流形的存在性,证明了一类流形的一个刚性定理,并得到形如Ｂｏｎｎｅｔ－Ｍｙｅｒｓ定理的推论．我们还指出,在主要定理中全测地子流形的条件一般不能减弱为极小子流形．     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归模型Ｙ（ｎ）ｉ＝β·ｘ（ｎ）ｉ＋ｇ（ｔ（ｎ）ｉ）＋Ｅ（ｎ）ｉ,ｉ＝１,２,…,ｎ,本文由最小二乘法和一般加权方法定义的β、ｇ（ｔ）的估计量βｎ,ｇｎ（ｔ）,在误差为鞅差序列下获得了βｎ,ｇｎ（ｔ）的ｒ（≥２）阶平均相合性．     

提高经济技术开发区核心竞争力的主要对策

文章提出开发区核心竞争力由人才竞争力、制度竞争力、管理竞争力、资本竞争力、环境竞争力集合而成,其中人才竞争力为本;核心竞争力的营造需要一个过程,制度建设是经济技术开发区发展的根本,硬环境建设是经济技术开发区发展的基础和重要前提,软环境建设则是经济技术开发区能否加快发展的内在动因。三者密不可分,互为作用,是营造经济技术开发区核心竞争力的关键。