一个包含广义Euler函数φ3(n)方程的解

令φ_e(n)为广义Euler函数,e为正整数.利用已有的φ_3(n)的计算公式,以及分类讨论的方式,讨论了方程φ_3(n)=2~(ω(n))3~(ω(n))的正整数解,给出了正整数n=2~m3~αq_1~(β_1)q_2~(β_2…)q_t~(β_t)除α∈[0,1],且q_i≡2(mod3)中的α=0,m=1情况外该方程的正整数解,其中q_i为异于3的奇素数,i=1,…,t.     

用于复合型裂纹问题的一个开裂准则

利用两个基本假设:(1)裂纹启裂方向沿裂尖距其近旁等应变能密度线最近的方向;(2)当裂纹尖端近旁材料的有效应力达到1型平面应变裂纹开裂的临界应力时即发生启裂,由引给出了复合型裂纹的基于应变能和应力的混合型开裂准则,第一个假设,开裂角方程可以写成[(1—k)sinθ_0+sin2θ_0]K_Ⅰ~2+2[2cos2θ_0+(1—k)cosθ_0]K_ⅠK_Ⅱ-[(1—k)sinθ_0+3sin2θ_0]K_Ⅱ~2=0。该方程与Sih等人的复合型裂纹的S准则的结论相同。而Sih的S准则的开裂角经大量实验证明是有效的、较为准确的。本文的假定(1)有明确的理论基础,完全不同于S准则中的应变能密度因子。由第二个假定,开裂条件可以写成C_(11)K_Ⅱ~2+2C_(12)K_ⅠK_Ⅱ+C_(22)K_Ⅱ~2+C_(33)K_Ⅲ~2+=K_(IC)~2式中C_(ij)=3/4b_(ij)(θ_0);θ_0就是由第一个假设给出的开裂角,b_(ij)是θ的函数(见王锋,断裂力学)。     

三角函数的周期问题

本文探讨函数的周期性、三角函数的周期等问题,最终推出函数f(x)=Asin(ω_1x+φ_1)+Bcos(ω_2x+φ_2)在一定条件之下的最小正周期公式。     

二维Lotka-Volterra型反应扩散系统正平衡点的全局稳定性

考虑如下齐次Neumann初、边值问题其中D_1、D_2>0为扩散常数,a_(ij),b_i(i,j=1,2)为常数,Q为R~n中有界开集,Ω为Ω之光滑边界,我们证明了: 如果问题有一个正平衡点u~*=(u_1~*,u_2~*)>0满足并且>0,a_(11)<0,a_(22)<0,则对任给正光滑初值函数φ_1(x),φ_2(x),问题有唯一解u(t,x)=(u_1(t,x),u_2(t,x))并且有 u(t, x)=u~*     

铊膜DC-SQUID磁强计研制成功

高温超导体铊膜DC-SQUID(直流-超导量子干涉仪)磁强计已于1992年12月8日通过专家鉴定。整机磁通灵敏度(稳定值)达到9.3×10~4φ_0/Hz~(1/2),最佳值为3.8×10~(-4)φ_0/Hz~(1/2),磁场分辨率为9pT/Hz~(1/2),为目前同类仪器的国际先进水平。除具有极高灵敏度和广泛应用前景外,因为可以在液氮温度工作,高温超导磁强计比低温超导磁强计使用起来更方便。     

与广义Euler函数有关的一方程的解

设m是一正整数,讨论了一个与广义Euler函数有关的方程φ_2(m)=2~(ω(m))3~(ω(m))的可解性,利用初等方法及广义Euler函数的性质,给出了该方程的一切解,其中ω(m)为m的互异的质因数个数。     

考察极端元素寻求最简算法

1　试题解法引出一个问题在今年我市的直属中学初中毕业统一考试中 ,有一道数学试题 ,难住了 1/3强的学生。这一现象引起了我们毕业班许多数学教师的注意。这道试题是这样的 :在平面直角坐标系中 ,有两点 A( 2 ,8) ,( 4,4) ,已知直线y=kx与线段 AB相交 ,求 k的取值范围。这一试题有不止一种的解法 ,但以下面的解法最简捷。解 :若直线 y=kx经过点 A( 2 ,8)则　 8=2 K　从而 k=4则　 4=4K　从而 k=1注意到线段 AB上的点是连续的 ,∴ k取以 1至 4的全体实数即　 1≤ k≤ 4这种解法的特点是考虑了问题的两种极端情况 ,从而获解。2　例析在解…     

带有一般非线性项的一类p拉普拉斯型方程基态解的存在性

研究p拉普拉斯型非线性椭圆方程:{Δ_pu+|u|~(p-2)u=f(u)于R~N,u∈W~(1,p)(R~N),p≥2.其中非线性项f∈C并且满足类似于文献[1]的非线性项条件。我们无须借助于Nehari流形即证明了上述方程的基态解的存在性。证明的方式主要是基于变分方法。本文的结果是文献[1]中的半线性椭圆方程的结果在p拉普拉斯型方程中的推广。     

谈数学题中的隐含条件

数学题中的隐含条件是潜藏在题目背后的隐蔽条件 ,若发掘出来能迅速获得解题的思路和途径 ,否则不注意题中的隐含条件 ,就会造成无法解答或得出错误结论。1　挖掘隐含条件寻求解题思路和途径例 1　已知定义在实数集 R上的奇函数 f( x)满足 f( x 1 ) =f( x- 2 )且 f( 1 ) =2 ,求 f( 1 991 )值。思路 :由函数满足 f( x 1 ) =f( x- 2 ) ,得到函数f( x)的周期为 3的隐含条件 ,从而 f( 1 991 )的值容易求出。解 :f( 1 991 ) =f( 3× 664- 1 ) =f( - 1 ) =- 2。例 2　已知 a>0 ,f( x) =a( x2 1 ) ,g( x) =( 1 -2 a) x,,则当 f( x)≥ g( x)时 …     

低压配电线路的单相接地保护

低压配电设计规范规定:配电线路应装设短路保护,过负载保护和接地故障保护。并在规范说明中说明(针对单相接地保护)是为了防止人身直接接触带电和间接接触保护,这种保护是人身安全问题,随着用电水平的提高上述保护是必须保证的。规范又规定单相接地保护是有一定指标的,当人体接触到带电(因为单相接地引起的)的导体时,其接触电压(身体接触部分到脚下的电位差或另一处接触的电位差)要≤50V,且带电时间≤5S。要满足这个要求,除了在开关电器的保护要满足外,还要求等电位连结上考虑,只有双管齐下才能有效地实施保护。而在实际工作中由于种种原因…     

Low doses of a red wine ingredient figh diabetes in mice

Aresearch group led by Prof. ZHAI Qiwei from the Institute for Nutritional Sciences under the CAS Shanghai Institutes for Biological Sciences has discovered that even relatively low doses of resveratrol--a chemical found in the skins of red grapes and in red wine--can improve the sensitivity of mice to the hormone insulin, according to a report in the October,2007 issue of Cell Metabolism. As insulin resistance is often characterized as the most critical factor contributing to the development of Type 2 diabetes, the findings“provide a potential new therapeutic approach for preventing or treating” both conditions, the researchers said.     

Students' Reactions to the Introduction of Videoconferencing for Classroom Instruction

This study examined how students who had no prior experience with videoconferencing would react to the use of videoconferencing as an instructional medium. Students enrolled in seven different courses completed a questionnaire at the beginning of the semester and again at the end of the semester. Students at the origination and remote sites did not differ in their reactions toward videoconferencing but there was a significant difference for gender. Women reacted less favorably to videoconferencing. Compared to the beginning of the semester, students reported significantly less positive attitudes toward taking a course through videoconferencing at the end of the semester. There were no significant differences in students' attitudes toward videoconferencing across courses at the beginning of the semester but there were significant differences across the courses at the end of the semester. The results suggest the need for better preparation for both students and instructors.     

Cooler temperatures inductive to locust outbreaks

Ajoint study by Prof. ZHANG Zhibin from the CAS Institute of Zoology and his co-workers from Norway, US and Swiss have indicated that historical outbreaks of migratory locusts in China were associated with cold spells, suggesting that China＇s projected climate warming could decrease the pest＇s numbers. The study was published in Proceedings of theNational Academy of Sciences on 17 September, 2007.     

Exploring Multiplexity: Social Network Structures in a Computer-Supported Distance Learning Class

A computer-mediated group is a complex entity whose members exchange many types of information via multiple means of communication in pursuit of goals specific to their environment. Over time, they coordinate technical features of media with locally enacted use to achieve a viable working arrangement. To explore this complex interaction, a case study is presented of the social networks of interactions and media use among members of a class of computer-supported distance learners. Results show how group structures associated with project teams dominated who communicated with whom, about what, and via which media over the term, and how media came to occupy their own communication niches: Webboard for diffuse class-wide communication; Internet Relay Chat more to named others but still for general communication across the class; and e-mail primarily for intrateam communication. Face-to-face interaction, occurring only during a short on-campus session, appears to have had a catalytic effect on social and emotional exchanges. Results suggest the need to structure exchanges to balance class-wide sharing of ideas with subgroup interactions that facilitate project completion, and to provide media that support these two modes of interaction.     

To serve and promote science development via innovation

CAS should stick to the principle of rendering service to, and giving impetus for, the development of China＇s science enterprise by making S＆T innovations, said CAS President LU Yongxiang. The CAS president made the remarks in a recent talk to communicate the gist of the winter session of the Party＇s Leading-member Group at CAS, which was held from 7 to 11 January in Beijing.     

Molecular motor assembly of a biomimetic system

Active biological molecules and functional structures can be fabricated into a bio-mimetic system by using molecular assembly method. Such materials can be used for the drug delivery, disease diagnosis and therapy, and new nanodevice construction.     

The Role of Intermediating Institutions in the Diffusion of Electronic Data Interchange (EDI): How Industry Associations Intervened in Denmark, Finland, and Hong Kong

Electronic data interchange (EDI) provides means for interorganizational communication, creates network externalities, requires an advanced information technology (IT) infrastructure, and relies on standards. In the diffusion of such innovations, institutional involvement is imperative. Such institutions contain governmental agencies, national and global standardization organizations, local government, and nonprofit private organizations like industry associations. The last type of organizations we call intermediating institutions. They intermediate or coordinate ("inscribe") the activities of a group of would-be adopters. Unfortunately, little is known of how these organizations shape the EDI diffusion trajectory. In this article we examine one specific type of intermediating organizations?industry associations?and how they advanced the EDI diffusion process in the grocery sectors of Hong Kong, Denmark and Finland. We identify six institutional measures, placed into a matrix formed by the mode of involvement (influence vs. regulation) and the type of diffusion force (supply push vs. demand pull), that can be mobilized to further the EDI diffusion. Industry associations were found to be active users of all these measures to varying degrees. Their role was critical especially in knowledge building, knowledge deployment, and standard setting. Furthermore, institutional involvement varied due to policy and cultural contingencies and power dependencies.     

Tracing the origin and early radiation of birds——Paleornithologist ZHOU Zhonghe

With great care, Dr. ZHOU Zhonghe takes out a package wrapped by cotton tissue from a drawer and says: "This is the gem of our collections: the fossil of a bird that lived 125 million years ago!" Then, pointing at a tiny mound, he explains: "Look, this is the claw and that is the head. It was in the egg shell and ready to hatch ... The species fell into a family of waterside inhabitants."     

How Electronic Publishers are Protecting Against Piracy: Doubts About Technical Systems of Protection

The increasing prospects of digital piracy has prompted the perceived need by electronic publishers to adopt technical systems of protection, and governments to reform their copyright laws. This article is a preliminary study of the management of intellectual property by electronic publishers, defined as those involved in the production of online databases, and CD-ROMs. It focuses on three main issues: (1) how electronic publishers view the increasing threat of piracy; (2) the methods of protection employed to protect intellectual property in digital format; and (3) the importance of technological protection of intellectual property in electronic publications. The analysis is based on a sample of 23 UK electronic publishers. The interviews revealed an interesting assortment of protection methods and did not show that technological protection was a preferred way. Instead, the means of protection, in addition to copyright law, comprised niche markets, pricing, trust, bad publicity, and nontechnical and technical means.     

The Information Environment and Universal Service

This essay focuses on universal service and the Internet as means to support social and political participation. The emphasis on access to telecommunications systems in conventional approaches to universal service is contrasted with access to content. A model of the information environment is described that accounts for the roles of content and conduit, both of which are necessary conditions to achieve true access. A method is outlined for employing information indicators to observe or measure the information environment.