Strong／weak limits and strong／weak differentials of multi-variable indeterminate forms. II： Supplementary annotations and analysis

Supplementary annotations on special forms 1to 4, discussion on the general characteristics of K(t) and K(t,t′), and analyses on two noticeable limits are presented in this part. It is demonstrated that strong and weak parabolic transforms can beemployed to change the standard form of a multi-variable indeterminate form into χ^mK type, hence to derive the standardformulae of the limit and the differential.     

On closed weak supplemented modules

INTRODUCTION In recent years theory of extending modules and rings has come to play an important role in the theory of rings and modules. A module is called an extending module (or CS-module) if every submodule is essen- tial in a direct summand, or equivalently, every closed submodule is a direct summand. Although this gen- eralization of injectivity is extremely useful, it does not satisfy some important properties. For example, direct sums of extending modules need not be ex- tending;…     

Global dimension of weak smash product

INTRODUCTION In (Auslander, 1995), the author established the relationship of homological dimension between skew group algebra ΛG and Λ. Recall from Corollary 4.7 and Corollary 4.10 in (Auslander, 1995) that gl.dim(ΛG)=gl.dim(Λ) where ΛG is a skew group algebra with the order of G invertible in Λ. Recently, more and more mathematicians have studied homological dimension for Hopf algebra. Yang (2002) gave the relationship of homological dimension between smash product algebra A#H…     

Rudiment of weak Doi-Hopf π-modules

The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in （Boehm, 2000）, also as a generalization of a Doi-Hopfπ-module introduced in （Wang, 2004）. Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.     

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. III: Transformations

1SimplificationinsphericalcoordinatesInthesphericalcoordinatessystem,??y?x=rsinθcosφ,z=rsinθsinφ,=rcosθ,???00≤θ<π,≤θ<2π.Setk=?tanφ,yandK=?zcotθ,then,xxcosφcotθu=r0K(t,t')istransformedintor=r0K(tanφ,cos),φandis,whenφ=0,simplifiedintoatruncatedcurver=r°K(0,cotθ).Thelatteriseasiertoberesolvedandcanreverttotheformerthroughturningaroundfor180°.Example.Thereexistsu=z2=(rcosθ)2x2+y2+z2r2=r°cos2θ?φ°,0≤θ≤π,0≤φ<2π.AsshowninFig.1,XX′isthediameteroftheunitcircle,OP0i…     

Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. I: Deduction and geometric illustration

1. Introduction In 1696, the French mathematician L. Hospital published a thesis titled Infinitesimal Analysis which dealt with differential and integral calculus created by Newton and Leibniz. The thesis attracted much worldwide attention on its appearance, especially Hospital抯 creation so called 揹ifferential solution method for unitary indeterminate form?is till popular. The author acquired in early 1936 that 22xyzxy=+ is the indeterminate form when P(x,y) O (0,0), and that dtandyykxxa…     

Some stationary weak solutions to inhomogeneous Landau-Lifshitz equations in three dimensions

In this paper, we describe several stationary conditions on weak solutions to the inhomogeneous Landau-Lifshitz equation, which ensure the partial regularity. For certain class of proper stationary weak solutions, a compactness result of the solutions, a finite Hausdorff measure result of the t-slice energy concentration sets and an asymptotic limit result of the Radon measures are proved. We also present a subtle rectifiability result for the energy concentration set of certain sequence of strong stationary weak solutions.     

自主／体验／开放

《语文课程标准》明确提出了“努力建设开放而有活力的语文课程”的目标,这反映了近年来语文教学改革的开放趋向。学生语文能力的形成,必须靠大量的语文实践活动来实现;同时,学生道德品质、健康个性、正确价值观的形成,又必须靠语文实践过程中的潜移默化、熏陶感染来实现。过去的语文学习,往往与生活脱节,与生存的世界脱节,把语言文字从活生生的现实世界中抽取出来肢解,进行“纯粹”的学习,大搞文字游戏。走出封闭的象牙塔面向广阔的天地,在大自然中汲取无穷无尽的知识,在山川河谷中陶冶性情,再也不见那“高墙内四角的天空”,这是一种多么美好的学习。真正拓宽学生学语文、用语文的领域,构建开放而有活力的语文课堂,成为我的追求。因此,对于语文实践,在教学中我努力从这四点着手：     

／A里AB／新论

半个世纪以来，语言学界一般认为／Ａ里ＡＢ／是汉语形容词的一种构形变化，表达语法意义。实际上，／Ａ里ＡＢ／＜／Ａ里八Ｂ／＜／Ａ七八Ｂ／，“里”只是“七八”的变异形式的残余，属于构词语素；Ａ在第三音节出现，不是为了同第一音节构成重叠式，而是为了使这一格式的语义的主要负荷者／ＡＢ／作为一个相连的整体在格式中出现，以克服／Ａ七八Ｂ／与／Ａ里八Ｂ／格式的内部矛盾造成的在形义两方面的不稳定性。     

CTAB／正丁醇／正戊烷／水微乳液体系结构参数的测定

采用稀释法计算了CTAB／正丁醇／正戊烷／水的微乳体系的结构参数和醇由连续相转移到界面层的自由能变化．结果表明：随着随ω的增大,水内核半径Rw、界面层厚度,以及表面活性荆和醇在微乳粒子表面的平均聚集数n^-增加,而醇转移自由能-△G c→i、分散相所占总界面面积Ad和颗粒总数心减小．     

vt／2和vs／2

匀变速直线运动中，常常用到中间时刻速度vt／2和中间位移速度vs／2，现分别讨论如下．     

整体感知／质疑设问／明理析例／循环教学

在新课程理念下,课堂教学是一个让学生充分展示自我、教师实现自我的大舞台,是对学生法制教育的主阵地。我在进行《公民私有财产的继承权受法律保护》的课堂教学过程中,运用“整体感知、质疑设问、明理析例、循环教学”的四步教学法,激发了学生学习的积极性,取得了较理想的教学效果,有利于学生法律意识的培养,综合能力的提高。     

Mother＇s Day／／母亲节

母亲节原是美国人的节日，但是现在很多国家也都庆祝这个节日，母亲节定在每年5月的第二个星期日，这是一个感谢母亲的日子，那一天，母亲们通常都会收到鲜花和贺卡，卡片上，孩子们都会写着“谢谢您，妈妈”，“献给世界上最好的妈妈”，“母亲节快乐”等等祝福的语言。     

长尾林鸮／／Strix uralenses

长尾林鸮为中型猛禽，体长约45～60cm，重约500g～700g。长尾林鸮面盘显著，眼线为黑褐色，其余部分为灰白。背部为褐色，飞羽深褐色，杂以灰褐横斑。其腹部淡灰褐色，杂有褐色羽干纹。腿上有污灰色绒羽，并有浅褐色斑点。喙黄色，爪褐色。雌雄羽色相似。长尾林鸮常栖息于针叶阔叶混交林中，喜独居，夜间活动，食物以鼠类为主，也食小鸟、蛙、昆虫等。每年5～6月繁殖，在树洞营巢，雌雄常常成对活动。     

否定构词“不／非／没／未／无＋X”的语义关系

由“不／非／没／耒／无＋X”构成的双音合成词并不罕见,但它们之间的语义关系尚未引起学界关注。在封闭考察的基础上,将否定构词的语义关系分为语义相关和语义无关两类,并对语义相关细分小类,同时简释其成因及否定构词在本体和教学中的研究价值。     

浅谈高职学生听／说／读／写能力的培养

培养学生的听、说、读、写能力是高职语文课堂的基本目标,是高职学生步入社会的必修课。培养学生的语文能力是一个系统工程,教学中必须要有周密的计划,合理的安排,分步骤、分阶段、分层次的进行,训练学生具有适应经济与社会发展需要的听、说、读、写等运用语言工具的能力。     

断肠人／在天涯？还是断肠／人在／天涯？

在中国幼年期的曲坛上,马致远的《天净沙·秋思》用不甚美丽的外形,缘合流动的情思,为美打开了一扇模糊的窗口,引领人们去寻求作家艺术世界里的独特光彩,去发现作家意象森林里每片树叶的朝向,去咀嚼意象与意象之间不可触摸的疼痛。王国维赞誉其“寥寥数语,深得唐人绝句之妙境”。周德清称其为“秋思之祖”。这首《天净沙·秋思》被收人人教版初中语文义务教育课程标准实验教科书中,     

是3／16还是3／8

牛的黑毛和棕毛是一对相对性状，并且黑毛(B)对棕毛(b)是显性。已知两只黑牛交配，生了一只棕毛牛。问：如果连生两牛，是一黑一棕的几率?     

蒙古语／r／辅音的声学分析

本文用声学分析、统计分析等方法，说明了蒙古语／ｒ／辅音不但有［ｒ］［ｘ］［ｒ］等三个变体，而且主要（典型）变体不是颤音［ｒ］，而是闪音［ｒ］。现代蒙古语里［ｒ］音的出现频率很低。     

从CLIENT／SERVER到BROWSE／SERVER

本文主要讨论了当前正在迅猛发展的从胖客户应用程序向瘦客户应用程序的转变,同时概括地讨论了使用ＨＴＭＬ及ＶＢＳｃｒｉｐｔ进行Ｗｅｂ－数据库存取的一般方法并以实例加以说明。