共查询到20条相似文献,搜索用时 15 毫秒
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A number of problems of finding the shape of a thin curvilinear rod (the support element of an artificial lens) of constant cross-section and specified length with its ends at specified points and under specified loading conditions with maximum compliance for characteristic types of end restraint and loading are considered. It is shown that the boundary-value problem arising for the non-linear Euler equation may have a set (possibly denumerable) of solutions, one of which gives the absolute maximum compliance, and the others the local maxima. The problem is analysed in detail, analytical solutions are obtained and the corresponding shapes are constructed in a number of important cases. 相似文献
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Yoshinori Shimizu 《ZDM》1999,31(6):190-194
The findings of the TIMSS Videotape Classroom Study include aspects of mathematics lessons showing a strong resemblance between Germany and the US in difference to Japan. This paper discusses some of the features that appear to make Japanese lessons different from the other two countries. In particular, the paper examines the goals of lessons described by Japanese teachers, how lessons are structured and implemented, and the emphasis on alternative solutions to a problem in the teaching and learning processes. The characteristics of Japanese lessons identified by the TIMSS Videotape Classroom Study can naturally be interpreted as indications of teachers' efforts to foster students' mathematical thinking in the classroom. 相似文献
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In a decision process (gambling or dynamic programming problem) with finite state space and arbitrary decision sets (gambles or actions), there is always available a Markov strategy which uniformly (nearly) maximizes the average time spent at a goal. If the decision sets are closed, there is even a stationary strategy with the same property.Examples are given to show that approximations by discounted or finite horizon payoffs are not useful for the general average reward problem. 相似文献
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In this article, we aim to examine the features of mathematics classroom instruction excellence valued in China. The popular approach to pursuing mathematics classroom instruction excellence through exemplary lesson development is also investigated to demonstrate the nature of teaching culture that has been advocated and nurtured in China. Features of an exemplary lesson are analyzed in detail, and the practicing teacher’s experience through participating in the development of the exemplary lesson is examined as well. Finally, the implications of developing exemplary lessons for pursuing excellence in mathematics classroom instruction as a culturally valued approach in China are also discussed. 相似文献
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G. Gutin 《Graphs and Combinatorics》1994,10(2-4):225-230
For a graph G, letG′(G″) denote an orientation ofG having maximum (minimum respectively) finite diameter. We show that the length of the longest path in any 2-edge connected (undirected) graph G is precisely diam(G′). LetK(m l ,m 2,...,m n) be the completen-partite graph with parts of cardinalitiesm 1 m2, …,m n . We prove that ifm 1 = m2 = … =m n = m,n ≥ 3, then diam(K″(m1,m2,...,mn)) = 2, unless m=1 andn = 4. 相似文献
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Vasso Anagnostopoulou Karla Díaz-Ordaz Oliver Jenkinson Catherine Richard 《Bulletin of the Brazilian Mathematical Society》2012,43(2):285-302
Let T be the angle-doubling map on the circle $\mathbb{T}$ , and consider the 1-parameter family of piecewise-linear cosine functions $f_\theta :\mathbb{T} \to \mathbb{R}$ , defined by $f_\theta (x) = 1 - 4d_\mathbb{T} (x,\theta )$ . We identify the maximizing T-invariant measures for this family: for each ?? the f ?? -maximizing measure is unique and Sturmian (i.e. with support contained in some closed semi-circle). For rational p/q, we give an explicit formula for the set of functions in the family whose maximizing measure is the Sturmian measure of rotation number p/q. This allows us to analyse the variation with ?? of the maximum ergodic average for f ?? . 相似文献
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Sigrid Blömeke Lynn Paine Richard T. Houang Feng-Jui Hsieh William H. Schmidt M. Teresa Tatto Kiril Bankov Tenoch Cedilllo Leland Cogan Shin Il Han Marcella Santillan John Schwille 《ZDM》2008,40(5):749-762
The study "Mathematics Teaching in the 21st Century (MT21)" focuses beyond others on the measurement of teachers’ general pedagogical knowledge (GPK). GPK is regarded as a latent construct embedded in a larger theory of teachers’ professional competence. It is laid out how GPK was defined and operationalized. As part of an international comparison GPK was measured with several complex vignettes. In the present paper, the results of future mathematics teachers’ knowledge from four countries (Germany, South Korea, Taiwan, and the US) with very different teacher-education systems are presented. Significant and relevant differences between the four countries as well as between future teachers at the beginning and at the end of teacher education were found. The results are discussed with reference to cultural discourses about teacher education. 相似文献
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Let be a bounded domain satisfying a Hayman-type asymmetry condition, and let D be an arbitrary bounded domain referred to as an “obstacle”. We are interested in the behavior of the first Dirichlet eigenvalue .First, we prove an upper bound on in terms of the distance of the set to the set of maximum points of the first Dirichlet ground state of Ω. In short, a direct corollary is that if
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is large enough in terms of , then all maximizer sets of are close to each maximum point of .Second, we discuss the distribution of and the possibility to inscribe wavelength balls at a given point in Ω.Finally, we specify our observations to convex obstacles D and show that if is sufficiently large with respect to , then all maximizers of contain all maximum points of . 相似文献
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The portfolio selection problem with one safe andn risky assets is analyzed via a new decision theoretic criterion based on the Recourse Certainty Equivalent (RCE). Fundamental results in portfolio theory, previously studied under the Expected Utility criterion (EU), such as separation theorems, comparative static analysis, and threshold values for inclusion or exclusion of risky assets in the optimal portfolio, are obtained here. In contrast to the EU model, our results for the RCE maximizing investor do not impose restrictions on either the utility function or the underlying probability laws. We also derive a dual portfolio selection problem and provide it with a concrete economic interpretation.Research partly supported by ONR Contracts N0014-81-C-0236 and N00014-82-K-0295, and NSF Grant SES-8408134 with the Center for Cybernetic Studies, The University of Texas at Austin.Partly supported by NSF Grant DDM-8896112.Partly supported by AFOSR Grant 0218-88 and NSF Grant ECS-8802239 at the University of Maryland, Baltimore Campus. 相似文献
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Numerical Algorithms - This paper is motivated by results of extensive comparative study of three-point methods for solving nonlinear equations presented in the paper (C. Chun, B. Neta, Comparative... 相似文献
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Arzu Aydogan Yenmez Ayhan Kursat Erbas Erdinc Cakiroglu Cengiz Alacaci Bulent Cetinkaya 《International Journal of Mathematical Education in Science & Technology》2017,48(6):895-912
Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers’ difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers’ knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers’ knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle. 相似文献