When is an L(B, m, n, r, s, t, z, w) loop SRAR?

In [5, 6], the second author and D. A. ROBINSON initiated a study of non-Moufang Bol loops with the property that over a field, necessarily of characteristic 2, their loop rings satisfy the right, but not the left, Bol identity. They called such loops SRAR and showed that the family of SRAR loops includes those Bol loops which have a unique non-identity commutator/associator. In [4, 2], the current authors presented a construction for a new class of Bol loops denoted L(B,m,n,r,s,t,z,w) with initial data a given (possibly associative) Bol loop B, elements, r, s, t, z and w in the centre of B, and integers m and n.     

基于区间数据分析的期刊发展现状分析

采用CSSCI数据库中收录的全部期刊数据,通过相关分析、区间数据主成分分析等方法建立模型,客观地对整个数据库中期刊的整体特征进行全面、系统的分析,探寻其中的特征、规律以及原因,提出了办好学术期刊的一些方式方法.     

Woodhouse, babbage, peacock, and modern Algebra

In a recent article, J. M. Dubbey [Historia Mathematica 4 (1977), 295–302] showed that George Peacock's A Treatise on Algebra (1830) was similar to an unpublished work written by Charles Babbage in 1821. Evidently perplexed about the absence of a dispute over priority, Dubbey concluded that Peacock had unconsciously assimilated Babbage's ideas, and that Babbage was too busy with other activities to be concerned. The thesis of this article is that the innovative aspects of the work of both Babbage and Peacock are extensions of ideas put forth in 1803 by Robert Woodhouse, and that probably neither Babbage nor Peacock was overly concerned with acknowledgments because their approach to algebra was not unique at Cambridge.     

A three-stage, VSVO, Hermite-Birkhoff-Taylor, ODE solver

The new variable-step, variable-order, ODE solver, HBT(p) of order p, presented in this paper, combines a three-stage Runge-Kutta method of order 3 with a Taylor series method of order p-2 to solve initial value problems , where y:R→R^d and f:R×R^d→R^d. The order conditions satisfied by HBT(p) are formulated and they lead to Vandermonde-type linear algebraic systems whose solutions are the coefficients in the formulae for HBT(p). A detailed formulation of variable-step HBT(p) in both fixed-order and variable-order modes is presented. The new method and the Taylor series method have similar regions of absolute stability. To obtain high-accuracy results at high order, this method has been implemented in multiple precision.     

Kepler, Kugeln, Cluster, Katastrophen

Zusammenfassung. Dieser Überblick skizziert Theorie und Anwendungen von Kugelpackungen, ausgehend von den klassischen Problemen von Kepler und Newton. Der weitaus wichtigste Bereich der regelmäßigen, gitterförmigen Kugelpackungen einschließlich der Anwendungen auf Codes wird kurz gehalten, weil es dazu ausgiebig Literatur gibt. Dagegen wird ausführlicher auf die in den letzten Jahren stark entwickelten endlichen Kugelpackungen eingegangen, die gute Modelle für die in der Nanotechnik wichtigen Microcluster sind. In jeder der relativ knapp gehaltenen Sektionen wird das zum Verständnis Unerlässliche an Theorie angegeben, sowie mindestens ein überraschendes oder im Wortsinn merkwürdiges Phänomen. Außerdem wird auf weiterführende Literatur verwiesen. Für Einsteiger sei insbesondere M. Leppmeiers Buch [L] empfohlen.     

Segments,rectangles, contours

Two sets H and V of horizontal and vertical segments, respectively, determine a subdivision M of the plane into regions. A nontrivial region is one whose boundary contains an end-portion of nonzero length of at least one segment, and the nontrivial contour of M is the collection of boundaries of nontrivial regions. In this paper we consider several problems pertaining to H and V, such as the construction of the nontrivial contour of M, of the external contour of M, and of a path between two points in the plane avoiding the segments (route-in-a-maze). We show that, if |H| + |V| = n, all of these problems are solved in time O(n log n), by making use of a static data structure, called the adjacency map, which can be searched in time O(log n) and can be constructed in time O(n log n). The algorithms for the nontrivial and external contour are shown to be optimal.     

Quasi-symmetric designs,codes, quadrics,and hyperplane sections

It is proved that a quasi-symmetric design with theSymmetric Difference Property (SDP) is uniquely embeddable as a derived or a residual design into a symmetric SDP design. Alternatively, any quasi-symmetric SDP design is characterized as the design formed by the minimum weight vectors in a binary code spanned by the simplex code and the incidence vector of a point set in PG(2m-1, 2) that intersects every hyperplane in one of two prescribed numbers of points. Applications of these results for the classification of point sets in PG(2m-1, 2) with the same intersection properties as an elliptic or a hyperbolic quadric, as well as the classification of codes achieving the Grey-Rankin bound are discussed.     

Efficiency analysis, shortage functions, arbitrage, and martingales

This paper shows that standard tools of efficiency analysis, directional distance functions, can be used to characterize the investment-returns technology. That ability to characterize the investment-returns technology and fundamental duality relationships imply that directional distance functions can be used to detect the presence of an arbitrage, to value financial assets in the absence of an arbitrage lying in the span of the market and to place bounds on the no-arbitrage values of assets lying outside the span of the market.     

Development of elementary teachers' science,technology, engineering,arts, and mathematics planning practices

The purpose of this instrumental case study was to understand elementary teachers' planning of Science, Technology, Engineering, Arts, and Mathematics (STEAM) curriculum during a two-year professional development experience. This research was guided by the following question: What planning practices developed or changed during a professional development experience? Analysis of 25 teachers' planning documents indicated growth in the following areas: (a) tighter alignment to fewer standards, (b) more meaningful integration and broader definitions of arts and technology, and (c) increased use of formative assessment but persistent difficulties in summatively assessing the multiple disciplines of STEAM. The growth in teachers' STEAM instruction from the beginning to the end of this two-year professional development was important in building our understanding of what constitutes sound design of STEAM inquiries.     

Simulation,Gaming and Training in a Competitive,Multimodal, Multicompany,Intercity Passenger-transportation Environment

This paper presents a microcomputerized simulation game designed as an analysis, experimentation and training tool in the field of intercity passenger-transportation planning and management. The simulation deals with different transportation modes and companies in a competitive environment, whether it be regulated or not. The background, philosophy and objectives of the game are discussed in relation to the intrinsic complexity of decision-making and the state of development of modelling in transportation.     

On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

The research is focused on the question of proportional development in economic growth modeling. A multilevel dynamic optimization model is developed for the construction of balanced proportions for production factors and investments in a situation of changing prices. At the first level, models with production functions of different types are examined within the classical static optimization approach. It is shown that all these models possess the property of proportionality: in the solution of product maximization and cost minimization problems, production factor levels are directly proportional to each other with coefficients of proportionality depending on prices and elasticities of production functions. At the second level, proportional solutions of the first level are transferred to an economic growth model to solve the problem of dynamic optimization for the investments in production factors. Due to proportionality conditions and the homogeneity condition of degree 1 for the macroeconomic production functions, the original nonlinear dynamics is converted to a linear system of differential equations that describe the dynamics of production factors. In the conversion, all peculiarities of the nonlinear model are hidden in a time-dependent scale factor (total factor productivity) of the linear model, which is determined by proportions between prices and elasticities of the production functions. For a control problem with linear dynamics, analytic formulas are obtained for optimal development trajectories within the Pontryagin maximum principle for statements with finite and infinite horizons. It is shown that solutions of these two problems differ crucially from each other: in finite horizon problems the optimal investment strategy inevitably has the zero regime at the final stage, whereas the infinite horizon problem always has a strictly positive solution. A remarkable result of the proposed model consists in constructive analytical solutions for optimal investments in production factors, which depend on the price dynamics and other economic parameters such as elasticities of production functions, total factor productivity, and depreciation factors. This feature serves as a background for the productive fusion of optimization models for investments in production factors in the framework of a multilevel structure and provides a solid basis for constructing optimal trajectories of economic development.     

Entropy,Universal Coding,Approximation, and Bases Properties

We shall present here results concerning the metric entropy of spaces of linear and nonlinear approximation under very general conditions. Our first result computes the metric entropy of the linear and m-terms approximation classes according to a quasi-greedy basis verifying the Temlyakov property. This theorem shows that the second index r is not visible throughout the behavior of the metric entropy. However, metric entropy does discriminate between linear and nonlinear approximation. Our second result extends and refines a result obtained in a Hilbertian framework by Donoho, proving that under orthosymmetry conditions, m-terms approximation classes are characterized by the metric entropy. Since these theorems are given under the general context of quasi-greedy bases verifying the Temlyakov property, they have a large spectrum of applications. For instance, it is proved in the last section that they can be applied in the case of L _p norms for R ^d for 1 < p < \infty. We show that the lower bounds needed for this paper in fact follow from quite simple large deviation inequalities concerning hypergeometric or binomial distributions. To prove the upper bounds, we provide a very simple universal coding based on a thresholding-quantizing constructive procedure.     

Factorizations,denseness, separation,and relatively compact objects

Some of the relationships among the topological notions: ‘Hausdorff’, ‘compact’, ‘perfect’, and ‘closed’ are abstracted to a more general categorical setting, where they are shown to remain intact. An investigation is made of factorization structures (especially for single morphisms) and their relationships to strong limit operators and to the Pumplu¨n-Ro¨hrl Galois correspondence between classes of objects and classes of morphisms in any category. Many examples as well as internal characterizations of Galois-closed classes are provided.     

A finite algorithm to fit geometrically all midrange lines, circles, planes, spheres, hyperplanes, and hyperspheres

Summary. The algorithm proved here solves the problem of orthogonal distance regression for the maximum norm with hyperplanes and hyperspheres. For each finite set of points in a Euclidean space of any dimension, the algorithm determines – through finitely many arithmetic operations – all the hyperplanes and hyperspheres that minimize the maximum Euclidean distance measured perpendicularly from the data. The algorithm finds all the slabs (bounded by parallel hyperplanes) and all the spherical shells (bounded by concentric hyperspheres) that contain all the data and are “rigidly supported” by the data (for which there does not exist any other pair of parallel hypersurfaces of the same type that intersect the data at the same points.) The computational complexity of the algorithm increases as the number of data points raised to the dimension of the ambient space. The solutions are then the midrange hyperplanes in the thinnest slabs, and the midrange hyperspheres in the thinnest shells. Their sensitivity to perturbations of the data is of the order of a power of the reciprocal of the smallest angle between two median hyperplanes separating two pairs of data points. The methods of proof consist in showing that if a pair of parallel hyperplanes or hyperspheres is not rigidly supported but encompasses all the data, then there exists a projective shift of their common projective center producing a thinner slab or shell that still contains all the data. Received December 14, 1999 / Revised version received August 30, 2000 / Published online September 19, 2001     

Ceva, Menelaus, and Selftransversality

The purpose of this paper is to state and prove a theorem (the CMS Theorem) which generalizes the familiar Ceva's Theorem and Menelaus' Theorem of elementary Euclidean geometry. The theorem concernsn -acrons (generalizations of n-gons) in affine space of any number of dimensions and makes assertions about circular products of ratios of lengths, areas, volumes, etc. In particular it contains, as special cases, many results in this area proved by earlier authors.     

Puzzles,tableaux, and mosaics

We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, easy proof of the Littlewood-Richardson rule. Finally we discuss how our operation is related to other known constructions, particularly jeu de taquin.     

Contractualism, Politics, and Morality

Rawls developed a contractualist theory of social justice and Scanlon attempted to extend the Rawlsian framework to develop a theory of rightness, or morality more generally. I argue that there are some good reasons to adopt a contractualist theory of social justice, but that it is a mistake to adopt a contractualist theory of rightness. I begin by illustrating the major shared features of Scanlon and Rawls’ theories. I then show that the justification for these features in Rawls’ theory, the centrality of cooperative fairness to social justice, cannot be used to defend their use in Scanlon’s. Finally, I argue that Scanlon has not provided an adequate alternative defense of these features, and show that they create problems when contractualists try to explain major features of our common-sense morality.     

Discontinuous Solutions of Linearized, Steady-State, Viscous, Compressible Flows

In thIs paper we prove the existence and uniqueness of the solution to a linearized, two dimensional, steady state, viscous, compressible Navier-Stokes equations in a strip. We obtain a regularity result and a new a priori estimate of the solution. We establish the discontinuity of the solution when the boundary data of pressure have a jump discontinuity. We also derive a formula for the discontinuous part and show that the remainder is smooth in the strip.     

Randomness,chaos, and structure

We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex dynamics regularities and patterns emerge. © 2009 Wiley Periodicals, Inc. Complexity 2009