Fubini定理的推广

在计算付伦涅尔积分的过程中,我发觉一些分析教科书上现成的积分次序交换定理都不能引用,因此我建立一个新的积分次序交换定理。 在分析教科书上找到的定理是: 定理A 设二元函数f(x,y)满足条件:(1)在区域上连续; (2)integral from a to ∞(f(x,y)dx)关于y∈[α,β]一致收敛,integral from a to ∞(f(x,y)dy)关于x∈[a,b]一致收敛,β,b是任意给定的数:β>α,b>a;(3)integral from a to ∞(dx) integral from α to ∞(|f(x,y)|dy),integral from α to ∞(dy) integral from a to ∞(|f(x,y)dx)至少有一个存在(有限)。那末     

标准函数的积分

定义1.标准函数f(x)在(a,b)(?)~*R上有定义,如果 {n/integral from n=a_n to n f(x)dx存在且有限}∈U其中a=[a_n],b=[b_n],U为自然数集N的自由超滤子,integral from n=a_n to b_n f(x)dx是Riemann意义下的积分,则称f(x)在(a, b)(?)~*R上可积,称非标准数[integral from n=a_n to n f(x)dx]为f(x)在(a, b)(?)~*R上的积分,记作integral from n=(a.b) to f(x)dx。     

Riemann可积函数的一个性质

大家知道,如果f(x)在〔a,b〕上非负连续且integral from a to b(f(x)dx=0),则f(x)在〔a,b〕上恒等于0.但若把条件减弱为“f(x)在〔a.b〕上非负可积且integral from a to ∞b(f(x)dx=0)”,是否还能作出“在〔a,b〕     

卷首语

新年伊始,万象更新.回顾刚刚过去的一年,河北大学学报(自然科学版)在学校领导和全校教师、科研人员的大力支持下,在全国广大作者、读者的关心支持下,全体编辑同仁勤勤恳恳,辛勤工作,圆满地完成了各项编辑任务,并取得了新的进步.在进入2004年版核心期刊的基础上,去年我刊的稿源质量大大提高,全年基金论文率平均超过60%.我刊继2004年荣获第二届教育部优秀高校学报一等奖之后,在去年又获河北省新闻出版局、河北省期刊学会颁发的优秀期刊奖.我刊继获得两届华北地区优秀期刊奖后,又在去年中国首届北方期刊评比中荣获优秀期刊称号.今年我们要乘我…     

期刊中心开通网上在线投审稿系统

<正>《西安科技大学学报》(自然科学版)网址为http://xkxb.xust.edu.cn网站主要包括作者投稿系统、专家审稿系统和编辑办公系统3部分。作者可通过网站投稿并查询稿件处理状况,欢迎广大作者、读者,登录我刊网站。作者投稿步骤:登录西安科技大学期刊中心网站→点击"进入投稿系统"→《学报(自科版)》→注册→填写个人资料→登录"作者在线投稿"即可。此外,有关编辑部的活动通知也将通过网站发布。电子邮箱:2284180862@qq.com编辑     

The Mean Man''''s Party

The notorious (声名狼藉的) cheap skate (吝啬鬼) finally decided to have a party.Explanining to a friend how to find his apartment(公寓),he said,“Come up to 5M and ring the doorbell     

Frobenius问题的一种算法

设a1,a2,…,an(n≥2)都是正整数，且(a1,a2,…,an)=1.记线性型a1x1+a2x2+…+anxn当xi≥0且xi∈[WTHZ]Z[WTBX](i=1,2,…,n)时不可表出的最大整数为g(a1,a2,…,an).作者研究了g(a1,a2,…,an)的存在性及其解法问题也即一次不定方程a1x1+a2x2+…+anxn=N的Frobenius问题.利用初等而简便的方法，作者给出了Frobenius问题的一种算法，并由此得到了a1,a2,…,an满足特殊条件时g(a1,a2,…,an)的简便而有效的计算公式.     

Design of child’s safety management system based on ontology using context information of home network

This paper presents a system to alert of dangerous a child situation of a child by applying context information collected from a home network to ontology that is capable of inference. Radio frequency Identification (RFID) and sensors were used for the configuration of a home network, to obtain the raw data to convert into context information. To express the ontology, web ontology language (OWL) was used to provide the inference of context information. Then, simple object access protocol (SOAP) messages were used to notify of the dangerous situations that a child may be involved in via mobile devices. The proposed system consists of Context Manager, Service Manager, and Notification Manager. The child's safety management system can proactively detect the context data of a child on the basis of context awareness. In the experiment, the Jena 2.0 by ontology reasoner and the OSGi(Open Service Gateway initiative) Gateway developed using open source software Knopflerfish 1.3.3 were used to implement the service frame work.      

积分第一中值定理的一个简明的证明

本学报1979年第2期刊登了绍文同志《关于积分第一中值定理》一篇文篇,作者给出了定理的证明。本文就C∈(a,b)的问题再给出一个较为简明的证明,并给一个例子,说明连续的条件是必要的,即若f(x)在〔a,b〕上不连续时,则结论不再成立。这个定理是这样叙述的: 积分第一中值定理设在区间〔a,b〕上f(x)与g(x)都可积,且g(x)不变号,m≤f(x)≤M,则存在μ,m≤μ≤M,使下式成立 integral from n=a to b(f(x)g(x)dx)=μintegral from n=a to b(g(x)dx) (1)如果f(x)在〔a,b〕上连续,则可进一步证明,存在C∈(a,b),使 (?) (2) 为了叙述上的完整起见,把前一部分的证明也写上。证明:先证前一部分。由f(x)与g(x)在区间〔a,b〕上的可积性知(1)式左端的积分是存     

Ti leaching from activated ilmenite-Fe mixture at different milling energy levels

Mechanical activation processes on ilmenite concentrate were performed in three different energy levels. Iron powder as a reducing agent was added to ilmenite in the milling stage and the mechanically activated mixture was subjected to acid leaching. The leaching experiments were designed using the Taguchi method, and the optimum ranges were obtained. Furthermore, response surface methodology (RSM) was used to optimize the critical parameters in the leaching system to achieve the highest titanium (Ti) leachability. Based on the inductively coupled plasma-optical emission spectrometry (ICP-OES) results, maximum leaching recovery of Ti (80%) was obtained using activated Ti concentrates at a medium activation energy level, which is calculated to be 25.38 kJ/g, using 15vol% hydrochloric acid (HCl), a temperature of 70℃, leaching time of 3 h, and a solid-to-liquid ratio of 0.05 g·mL-1. Intensifying the milling energy from a low to high level led to a decrease in the mean crystallite size and also structure homogenization at the high energy level. According to the transmission electron microscopy (TEM) images, the mean grain size of the ilmenite/Fe nanocomposite was about 30 nm at the medium energy level sample. Finally, solvent extraction by tributyl phosphate (TBP) was performed on the leach liquor to separate dissolved Fe (the major impurity) from Ti, which led to 83% extraction recovery of Ti.