Interaction of Simple Particles in Soliton Cellular Automata

We consider a certain cellular automaton recently introduced by Park, Steiglitz, and Thurston. By introducing appropriate mathematical notation, the interaction of simple particles evolving according to this automaton rule is completely characterized analytically. It is found that: (1) If two particles have different speed and they interact, then they interact solitonically and, although they may interact a number of times, they finally separate with the faster particle moving in front of the slower one. (2) If two particles have the same speed and are close enough so that they interact, there exist two cases: either they will interact only once and then they will separate, travelling independently of each other, or they will form a new periodic configuration by interacting forever.     

Elements of Design‐Based Science Activities That Affect Students' Motivation

The primary purpose of this study was to examine the ways in which a 12‐week afterschool science and engineering program affected middle school students' motivation to engage in science and engineering activities. We used current motivation research and theory as a conceptual framework to assess 14 students' motivation through questionnaires, structured interviews, and observations. Students reported that during the activities they perceived that they were empowered to make choices in how to complete things, the activities were useful to them, they could succeed in the activities, they enjoyed and were interested in the hands‐on activities and some presentations, they felt cared for by the facilitators and received help when they were stuck or confused, and they put forth effort. Based on our examination of data across our three data sources, we identified motivating opportunities that were provided to students during the activities. These motivating opportunities can serve as examples to help both formal and informal science educators better connect motivation theory to practice so that they can create motivating opportunities for students. Furthermore, this study provides a methodological example of how students' motivation can be examined during the context of authentic science and engineering instruction.     

ON NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CARATHÉODORY SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS

Given two one-sided Markov chains, the authors illustrate a procedure for ascertaining whether they are essentially the same. Precisely, they show how one can determine whether they are block-isomorphic. An application to hydrology is investigated with an example.     

Why Expert Systems Fail

Although many papers have been published on the subject of expert systems, relatively few of them have been concerned with systems which failed.In this paper some of the major reasons why expert systems fail are described, along with some techniques for alleviating these problems.Expert system developments fail for the same reasons as conventional software systems. However, they may also fail because the problem they are dealing with is not or cannot be understood, because they require common sense or knowledge of the limitations of their knowledge, because they cannot be tested, or because they cannot or will not be trusted.     

Polynomial Convexity of Teichmuller Spaces

It is well known that finite-dimensional Teichmüller spacesare holomorphically convex, that is, they are domains of holomorphy.Moreover, the holomorphic convexity is fulfilled for all Teichmüllerspaces in a stronger form: they are complex hyperconvex. In this note we establish that, in fact, finite-dimensionalTeichmüller spaces possess a much stronger convexity property,namely, they are polynomially convex; in other words, they areRunge domains. Additionally, some geometric properties of Teichmüllerspaces are established.     

Felix Klein meets Napoléon

In this article we will show how, by teaching our students geometric transformations, we can help them see the way to the solution when faced with a challenging geometric problem. In this way they will understand that they should not let themselves be restricted by the tools they use.     

Mathematics Majors' Perceptions of Conviction,Validity, and Proof

In this paper, 28 mathematics majors who completed a transition-to-proof course were given 10 mathematical arguments. For each argument, they were asked to judge how convincing they found the argument and whether they thought the argument constituted a mathematical proof. The key findings from this data were (a) most participants did not find the empirical argument in the study to be convincing or to meet the standards of proof, (b) the majority of participants found a diagrammatic argument to be both convincing and a proof, (c) participants evaluated deductive arguments not by their form but by their content, but (d) participants often judged invalid deductive arguments to be convincing proofs because they did not recognize their logical flaws. These findings suggest improving undergraduates' comprehension of mathematical arguments does not depend on making undergraduates aware of the limitations of empirical arguments but instead on improving the ways in which they process the arguments that they read.     

Harmonic analysis on the Sierpiński gasket and singular functions

We study the restriction on [0,1] of harmonic functions on the Sierpiński gasket, proving they are singular functions whenever they are monotone. We show that their derivatives are zero or infinity on certain non-denumerable sets. Finally, we show they are among a wider class of functions that contains some already known and studied functions.     

如何成为一个合格的助课教师

每个学校的青年教师在登上三尺讲台前大都要经过助课阶段,经过了这个阶段,他们将知道如何完成教学任务．本文对助课工作的目标做些探讨,实现了助课目标也就成为了一个合格的助课教师．     

A Note on the Stefan-Boltzmann Problem for Heat Transfer in a Fin

A fin is traditionally thought of as an extension of a surface to facilitate the transfer of heat away from a larger body to which it is attached. In this paper, the authors study some mathematical properties of a nonlinear heat transfer model for a fin and its relation to an associated linear model. Specifically, they prove that the solution exists and is unique, and they determine bounds for the temperature. Further, they prove the monotonicity of the temperature distribution, and they obtain an estimate for the maximal difference between the temperatures as determined by the nonlinear and linear models.     

四维Clifford代数的相似与合相似

两四元数相似当且仅当它们有相同的实部和模,两四元数合相似当且仅当它们有相同的模.应用四维Clifford代数的矩阵表示,得到了四维Clifford代数中两元素相似或合相似的充分必要条件.     

Hypergeometric identities for 10 extended Ramanujan-type series

We prove, by the WZ-method, some hypergeometric identities which relate ten extended Ramanujan type series to simpler hypergeometric series. The identities we are going to prove are valid for all the values of a parameter a when they are convergent. Sometimes, even if they do not converge, they are valid if we consider these identities as limits.      

Accuracy of TSVD solutions computed from rank-revealing decompositions

Summary. Rank-revealing decompositions are favorable alternatives to the singular value decomposition (SVD) because they are faster to compute and easier to update. Although they do not yield all the information that the SVD does, they yield enough information to solve various problems because they provide accurate bases for the relevant subspaces. In this paper we consider rank-revealing decompositions in computing estimates of the truncated SVD (TSVD) solution to an overdetermined system of linear equations , where is numerically rank deficient. We derive analytical bounds which show how the accuracy of the solution is intimately connected to the quality of the subspaces. Received July 12, 1993 / Revised version received November 14, 1994     

遗传算法求解带容量限制的最小费用流问题

研究了带容量限制的带固定费用和可变费用的最小费用流问题,发现该问题是混合0-1整数规划问题,不存在多项式算法.在研究了最优解的结构后,结合最优解的结构特点为之设计了遗传算法,然后构造了一个100个节点的特殊网络,用计算机做了100例计算,验证了该算法具有很好的近似比和很快的收敛速度.     

Banach 空间中von Neumann-Jordan 型常数的一些性质

该文主要给出von Neumann-Jordan型常数的一些性质. 首先得到利用von Neumann-Jordan型常数来刻划一致非 方的等价条件. 其次介绍了von Neumann-Jordan型常数与正规结构的关系. 最后介绍了C_1'(X)与其他空间常数之间的关系, 例如C_1'(X)与C₁(X)之间的关系等等.     

A note on essentially convex orders

In this note, we determine precisely which partially ordered sets (posets) have the property that, whenever they occur as subposets of a larger poset, they occur there convexly, i.e., as convex subposets. As a corollary, we also determine which lattices have the property that, if they occur as sublattices of a finite distributive lattice L, then they also occur as closed intervals in L. Throughout, all sets will be finite.Dedicated to the memory of Ivan RivalReceived May 5, 2003; accepted in final form October 3, 2004.This revised version was published online in August 2005 with a corrected cover date.     

Characterizations of quadric and Hermitian Veroneseans over finite fields

In Hirschfeld and Thas [5] the most important characterizations of quadric Veroneseans are surveyed. However a few difficult cases were still open, in particular the even case. In [10, 11] Thas and Van Maldeghem not only solve all open cases, but they also generalize most of these characterizations in several ways: they do not restrict themselves to the quadric Veronesean of the plane PG, they allow ovals instead of conics, and they also characterize projections of quadric Veroneseans. Further, Cooperstein, Thas and Van Maldeghem [1] contains some properties of Hermitian Veroneseans over finite fields and also these varieties and some of their projections are characterized. All these results on Veroneseans will be surveyed here.     

一类时滞方程的谱与解展开

该文研究一类时滞方程解的展开问题. 研究的模型来自于实际高精密切割过程中具有时间延迟的机床振动问题. 对此模型,借助于泛函分析方法,将其写成抽象发展方程. 对系统确定的算子给出了较细致的谱分析,得到本征值的渐近表达式.同时证明相应的本征向量不能构成状态空间基, 但给出方程解的展开式.     

Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization

In the light, as said in Part I, of showing the main feature of image space analysis—to unify and generalize the several topics of optimization—we continue, in Part II, considering duality and penalization. In the literature, they are distinct sectors of optimization and, as far as we know, they have nothing in common. Here it is shown that they can be derived by the same “root.”