复射影空间CPn+p中的全实2-调和子流形

本文研究了复射影空间中的全实2 -调和子流形问题.利用活动标架法,获得了这类子流形成为极小子流形的关于第二基本形式模长的Pinching定理及一个积分不等式.此外还得到关于全实2-调和伪脐子流形的一些刚性定理,推广了CPn中全实2-调和子流形的一些相应结果.     

3—Sasakian流形的3—C—全实子流形

引入并研究了３－Ｓａｓａｋｉａｎ流形的３－Ｃ－全实子流形，借助了第二基本形式的长度，给出了单位球面Ｓ＾４ｍ＋３－Ｃ－全实子流形的一个Ｐｉｎｃｈｉｎｇ定理。     

复空间形式中全实2-调和子流形

本文研究了复空间形式中的全实2-调和子流形,获得了关于此类子流形的一些性质和一个Simons型积分不等式,并研究了其Pinching现象.     

复空间形式中具有常数量曲率的全实子流形

本文研究了复空间形式中具有常数量曲率的全实子流形.利用一种自伴算子,得到了这类子流形关于第二基本形式模长平方的积分不等式.     

复射影空间中具有常数量曲率的完备全实子流形

本文研究了复射影空间中具有常数量曲率的完备全实子流形的问题.利用丘成桐的广义极大值原理和自伴随算子,获得了这类子流形的某些内蕴刚性定理.     

关于复射影空间的一般极小子流形

设N是具殆复结构J的Kaehler流形,M是等距浸入N的实子流形,若M上每点的法空间被J变换到读点的切空间中,则M称为N的一般子流形(generic submanifold).特别当codim M=1时,就是实超曲面,而当codim M=dim M时便得到全实子流形.关于实极小超曲面和全实极小子流形,已有文献[3,6,8,10].最近A.Bejancu.M.Kon和 K.Yano等对一般极小子流形也作了某些讨论.     

复n维射影空间的全实n维极小子流形

1.引言 设CP~n是具有Fubini-Study度规的复n维射影空间,它的常数全纯截面曲率等于4,M是CP~n的子流形。如果M上每点的切空间被CP~n的复结构J映射到该点的M的法空间中,则称M是全实子流形。又若M的平均曲率向量恒消失,则M称为全实极小子流形。Chen和Ogiue曾经证明:     

复射影空间中极小子流形的几个整体pinching定理

本文利用对复射影空间中紧致极小子流形的第二基本形式长度平方进行积分形式的估计方法,证明了复射影空间中紧致复子流形和紧致全实极小子流形的几个整体pinching定理。     

关于全实极小子流形的谱几何

本文研究复射影空间中紧致全实极小子流形的谱几何,给出了一个基本谱不等式。     

复射影空间的2-调和全实子流形

研究了复射影空间中2-调和全实子流形,得到了这类子流形的一个积分公式,讨论了伪脐条件下的情形,通过计算第二基本形式模长平方的Laplacian得到一个刚性定理.     

Bipolarization of posets and natural interpolation

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of n[0,1]. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy.A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme.Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.     

Middle-school students’ concept images of geometric translations

This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.     

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Vibrations of a beam can be described as an Euler-Bernoulli beam,or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.     

The prediction of sequences

The problem of predicting the short-term future behavior of a sequence, after observing it as long as we please, so as to achieve a specified reliability against all possible sequences is considered. For a particular problem, namely, predicting when in a sequence of 0's and 1's the pair (1, 0) in that order is not coming next, a reliability of 3/4 can be approximated as closely as we please, but not achieved. This article appeared as a Research Memorandum of the Rand Corporation, RM-1570, 12 October 1955.     

Sequential entry and exit decisions with an ergodic performance criterion

We consider a variant of an optimisation problem involving sequential entry and exit decisions that has emerged in the economics literature as a real option model. The problem that we solve aims at maximising an ergodic, or long-term average, performance criterion in a pathwise as well as in an expected sense. Such a performance index is probably better suited to decision making within a sustainable economic environment. Our results include a complete characterisation of the optimal strategy, which can take qualitatively different forms depending on the problem's data, as well as explicit expressions for the maximal value of the associated performance index.     

An evolving framework for describing student engagement in classroom activities

Student engagement in classroom activities is usually described as a function of factors such as human needs, affect, intention, motivation, interests, identity, and others. We take a different approach and develop a framework that models classroom engagement as a function of students’ conceptual competence in the specific content (e.g., the mathematics of motion) of an activity. The framework uses a spatial metaphor—i.e., the classroom activity as a territory through which students move—as a way to both capture common engagement-related dynamics and as a communicative device. In this formulation, then, students’ engaged participation can be understood in terms of the nature of the “regions” and overall “topography” of the activity territory, and how much student movement such a territory affords. We offer the framework not in competition with other instructional design approaches, but rather as an additional tool to aid in the analysis and conduct of engaging classroom activities.     

社会网络分析方法在管理民间信仰活动的应用研究

民间信仰活动是一种复杂的社会现象,其信众群体是一个独特的社会关系网络。本文在国内首次运用社会网络分析的思维和方法,在对冀南地区民间信仰抽样调查的基础上,建立网络模型,通过对民间信仰主体和客体各结点的中心性、凝聚性等进行量化分析,进而探究民间信仰网络的社会结构及其属性,得出信众群体特征、信仰动因、活动特点、社会心态等有益结论,为民间信仰活动的社会治理和政府管理提供科学依据.     

Engineering design and the development of knowledge for teaching among preservice science teachers

The goal of this article is to inform professional understanding regarding preservice science teachers’ knowledge of engineering and the engineering design process. Originating as a conceptual study of the appropriateness of “knowledge as design” as a framework for conducting science teacher education to support learning related to engineering design, the findings are informed by an ongoing research project. Perkins’s theory encapsulates knowledge as design within four complementary components of the nature of design. When using the structure of Perkins’s theory as a framework for analysis of data gathered from preservice teachers conducting engineering activities within an instructional methods course for secondary science, a concurrence between teacher knowledge development and the theory emerged. Initially, the individuals, who were participants in the research, were unfamiliar with engineering as a component of science teaching and expressed a lack of knowledge of engineering. The emergence of connections between Perkins’s theory of knowledge as design and knowledge development for teaching were found when examining preservice teachers’ development of creative and systematic thinking skills within the context of engineering design activities as well as examination of their knowledge of the application of science to problem‐solving situations.