级数收敛的概念评注

从级数、函数列的收敛理论出发,建立数项级数和函数项级数的收敛理论,即数项级数的收敛归结为它的部分和数列收敛是数学分析(高等数学)教学中很重要的一个环节;本文就是从级数收敛的定义出发来分析和探讨级数收敛的概念的.     

The inveterate tinkerer

In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The eighth article in this series explores and demonstrates Kelvin–Helmholtz instability     

The inveterate tinkerer 9. Rayleigh–Taylor instability

In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The ninth article in this series explores and demonstrates Rayleigh–Taylor instability.     

The inveterate tinkerer 3. Experiments with vortex rings

In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The third article in this series is about vortex rings and some interesting experiments based on them.     

The inveterate tinkerer 10. Analog computing with soap films

In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via table-top experiments using low-cost or home-made instruments. The tenth article in this series demonstrates the use of the area-minimization property of soap films in the computation of analog solutions to mathematical problems.     

Effects of forced-choice runway variations on rats’ T-maze serial pattern learning

Rats learned an ordered RNR/RNN serial pattern task in a T-maze where they were shifted to a different runway on Trial 3 only in the RNR series (shift-win/stay-lose group) or only in the RNN series (stay-win/shift-lose group). The shift-win/stay-lose group developed faster speeds on Trial 3 of the RNR than on Trial 3 of the RNN series more easily than the stay-win/shift-lose group. This difference occurred whether all rats were forced onto the same runway on the first two trials (Experiment 1) or onto a different runway on Trial 2 from that on Trial 1 in each series (Experiment 2). Posttraining probe tests revealed that the shift-win/stay-lose group in each experiment relied on the runway shift event in Trial 3 or on the series position to anticipate the second reward within a series. Such reward expectancies were greater when the runway shift occurred in the same series position as during training. These probe tests revealed that the stay-win/shift-lose group relied only on the series position in Experiment 2. Our findings do not support predictions based on an associative predictive validity model. Rather, they reflect rats’ predisposition to spontaneously alternate choices in the T-maze, a tendency corresponding to their inherent win-shift foraging strategy. Rats in each group also reduced their speeds less on the nonrewarded Trial 2 when it preceded a rewarded rather than a nonrewarded Trial 3. This effect suggests that rats were able to determine which series contained a second rewarded trial. We discuss the theoretical implications of this Trial 2 speed effect in terms of rats’ uncertainty about where this second rewarded trial might occur in the RNR series.     

Students’ conception of infinite series

This is a report of a study of students’ understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be built so that we may uncover ways to help students improve their understanding. The theoretical framework consists of action–process–object–schema theory and the specific model of conceptions in Balacheff’s theory of conception, knowing, and concept. Approaching the problem from these two different theoretical perspectives allows us to provide different and at the same time complementary explanations of observed phenomena. The two different infinite series constructions are, briefly stated, series as an infinite unending process of addition and series as a sequence of partial sums. Students are found to have difficulty building an understanding of series as a sequence of partial sums and thus tend to have difficulty in problem situations that require this interpretation. The study uses semi-structured interviews with 10 graduate students. The interviews explore situations that might give insight into students’ notion of the sequence of partial sums.     

TV Production Techniques and Teaching Efficiency

Educators who venture into the realm of television immediately encounter this question: What equipment is required, and what can be done with it? This paper attempts to provide some basis for an intelligent answer. In designing the research from which this report derived, attention was focused upon basic television production techniques. A series of instructional segments were produced utilizing these techniques; a second series was subsequently produced with the same instructors and subject matter, but with more elaborate techniques. The two series were then presented for viewing by various student audiences. A control group viewed the first series; an experimental group was shown the second series. Preliminary knowledge of subject matter was determined by a pre-test; degree of learning and retention were measured by an immediate posttest, and a delayed post-test. Those data were then analyzed by means of standard statistical instruments. In collating and appraising the obtained results it was apparent that a one camera production, with true flat lighting, utilizing close-up camera coverage and a modicum of technical skill and imagination, was as effective as the more elaborate production in ordinary lecture-teaching situations.     

关于余切数论函数的级数表示

研究cotπz级数的有关性质，采用了解析数论中Γ函数和Zeta一函数相互联系的方法，给出了cotπz级数的表示公式，对于余切数论函数的内容研究有推进作用，也对级数研究提供了新的方法．     

关于余切数论函数的级数表示

研究cotπz级数的有关性质,采用了解析数论中Γ函数和Zeta-函数相互联系的方法,给出了cotπz级数的表示公式,对于余切数论函数的内容研究有推进作用,也对级数研究提供了新的方法.     

关于“钦州学院唱钦州”音乐实践活动的思考

在推动社会主义文化大发展大繁荣的新形势下,为打造地方本科院校音乐学专业办学特色和培养应用型创新人才,钦州学院拉开了＂唱响钦州,文化惠民＂慰问演出活动的序幕。这也激起了作者心中无数的遐想与思考,概括起来主要涉及到活动开展的意义、音乐学院学科建设与特色打造、音乐审美的基本原理、音乐创作的民族性等四个问题及其领域的一般探讨。     

Projectile motion with quadratic damping in a constant gravitational field

The motion of a projectile in a constant gravitational field is an age-old problem. If there is no resistive force, the problem is simple. However, with the intoduction of resistive forces, the complexity of the problem increases. Recently, there has been a growing interest in the problem of projectile motion under a resistive force proportional to the square of velocity. The problem for resistive force proportional to vv cannot be solved in closed analytical form. A series solution of the equation leads to divergent series for x (t) and y (t) for reasonable values of the initial speed and angle of projection. However, we demonstrate that by inverting the series for x (t), i.e., expressing t in terms of x, and substituting this in y (t) one can express y in terms of x which is a highly convergent series and one can obtain the path of projectile with a few terms of the series. We further demonstrate that one can obtain the path even with a few terms of the divergent series for x (t) and y (t) by using extrapolation methods.     

The inveterate tinkerer: Bubble raft

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The sixth article in this series explores crystalline defects and motion of dislocations using bubble rafts. Materials     

Handwriting Survey to Determine Grade Standards

Abstract

One purpose of this study was to determine whether a selected number of spelling series used high- frequency words for their lists when compared to a standard measure of word frequency. Another purpose was to determine whether students misspelled high-frequency words in their writing. Data collected from the spelling series were analyzed using a two-factor analysis of variance and the Tukey method of multiple comparisons. Data collected from children’s writing samples were analyzed using at test. Analysis showed differences in the number of high-frequency words among the series and within the grade levels. There also was a difference between the number of misspelled words in children’s writing at Grade 5 but not at Grade 3.     

平坦ΛCDM宇宙学模型下的光度距离级数解(英文)

宇宙学观测表明,目前宇宙的时空结构为平坦的且以暗能量(DE)为主要成分.光度距离对于研究宇宙的结构和演化具有重要意义,然而它在实际应用时需要进行繁重的数值求积过程.本文得到一个平坦ΛCDM宇宙学模型下的光度距离级数解.经过计算发现,在多项式阶数n=100,相对参数β∈[0,4](即0.2<ΩΛ<1,红移z>0.1)时,其相对误差低于0.36%.     

The Jasper experiment: An exploration of issues in learning and instructional design

The Jasper Woodbury Problem Solving Series is an example of a video-based instructional macrocontext for complex problem generation and problem solving. The Jasper series and curricular materials are described and illustrated in this article. The theoretical framework underlying the series includes assumptions about educational goals and the nature of learning, including the importance of generative activities and cooperative learning situations. The authors argue that the Jasper series affords generative and cooperative learning activities in a way that traditional mathematics problem-solving materials do not. However, whether these features are utilized depends on the teaching model at work in the classroom. Three models of teaching—basics first, structured problem solving, and guided generation—that can be applied to the Jasper series are outlined. The strengths and weaknesses of each are discussed, and associated assessment issues are raised. The article concludes by pointing to the need for research on the impact of differing instructional design decisions.Members of the Cognition and Technology Group at Vanderbilt who contributed to this paper are Linda Barron, John Bransford, Olin Campbell, Ben Ferron, Laura Goin, Elizabeth Goldman, Susan Goldman, Ted Hasselbring, Allison Heath, Charles Kinzer, James Pellegrino, Kirsten Rewey, Robert Sherwood, Nancy Vye, Susan Warren, Susan Williams.     

Āryabhata and axial rotation of earth

In the first part of this series, we discussed the celestial sphere and Aryabhata’s principle of axial rotation; in this part we shall discuss in detail the concept of sidereal day and then mention Aryabhata’s computations on the duration of sidereal day.     

Advice on life? Online fan forums as a space for peer-to-peer sex and relationships education

Previous research has pointed to the potential of entertainment media as a source of informal sex education for young people. New social media may offer additional potential in this respect. In this paper, we consider the pedagogical possibilities and limitations of online fan forums, via a case study of the forums of the controversial British teen drama series Skins. We analyse discussions of the realism of the series' representation of teenage life, and of specific issues (virginity, attractiveness and gay sexuality). We compare participants' discussions of their own experiences – in a section of the forum entitled ‘advice on life’ – with their discussions of the series and the characters. We find that the presentation of issues to do with sexuality sometimes challenges young people to engage in debate, and to move beyond established discourses. However, the value of the series in this respect depends crucially on its ‘openness’ – that is, its avoidance of fixed moral positions – and on its perceived plausibility and authenticity. The forum emerges as a new space for non-formal, peer-to-peer education that has limitations as well as new pedagogical possibilities.     

Reviews

Book review in this Article: Allington, R. and Krull, K. (1981) Beginning to Learn Alpha Books. Phases 7, 8, 9. Easy Readers series. John Murray The Laura Brewster Books. John Murray Kelley, Leo P. Galaxy 5 series. John Murray The Reporters series. Harrap Books. Melling, Frank E. Project Motor cross Collins English Library (1980) Collins The reading level of this series of 16 readers is assessed at Stage H, according to W. Body Jones, lewis (1979) Graded English puzzles. Collins Westrope, Anne (1981) Phonic Workshop. Henderson, E. E. Spell Well Work Books 3 and 4 Clemens, Gwen (1981) Shapes and Words. Brennan, Wilfred, Jackson, Jean and Reeve, Juliet (1981) Look Marrow, Keith (1980) Skills for Reading. Moon, Cliff and Raban, Bridie (1981) A Question of Reading Clay, Marie M. (1979). The Early Detection of Reading Difficulties: A Diagnostic Survey with Recovery Procedures (second edition).