Benchmarking curriculum-based course timetabling: formulations,data formats,instances, validation,visualization, and results

We propose a set of formulations for the Curriculum-Based Course Timetabling problem, with the aim of “capturing” many real-world formulations, and thus encouraging researchers to “reduce” their specific problems to one of them, gaining the opportunity to compare and assess their results. This work is accompanied by a web application that maintains all the necessary infrastructures for benchmarking: validators, data formats, instances, reference scores, lower bounds, solutions, and visualizers. All instances proposed here are based on real data from various universities and they represent a variety of possible situations.     

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.     

Economies of scale,competitiveness, and trade patterns within the European community: Clarendon Press,Oxford, 1983, 193 pages, £20.00

We consider two queues in series with input to each queue, which can be controlled by accepting or rejecting arriving customers. The objective is to maximize the discounted or average expected net benefit over a finite or infinite horizon, where net benefit is composed of (random) rewards for entering customers minus holding costs assessed against the customers at each queue. Provided that it costs more to hold a customer at the first queue than at the second, we show that an optimal policy is monotonic in the following senses: Adding a customer to either queue makes it less likely that we will accept a new customer into either queue; moreover moving a customer from the first queue to the second makes it more (less) likely that we will accept a new customer into the first (second) queue. Our model has policy implications for flow control in communication systems, industrial job shops, and traffic-flow systems. We comment on the relation between the control policies implied by our model and those proposed in the communicationa literature.     

Cayley compositions,partitions, polytopes,and geometric bijections

In 1857, Cayley showed that certain sequences, now called Cayley compositions, are equinumerous with certain partitions into powers of 2. In this paper we give a simple bijective proof of this result and a geometric generalization to equality of Ehrhart polynomials between two convex polytopes. We then apply our results to give a new proof of Braun?s conjecture proved recently by the authors [15].     

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.     

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.     

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.     

Wave propagation in,layered, transversally isotropic,elastic media

Wave propagation in a transversally isotropic, elastic medium consisting of plane-parallel layers and half spaces is considered. A generalized matrix method is used to derive the dispersion equation of this medium and to find the coefficients of reflection and refraction. This method makes it possible to consider dispersion curves and the coeffients of reflection and refraction in a broader domain than with Haskell's method. The results obtained generalize to layers in which the elastic characteristics vary with depth according to an arbitrary law. For such layers it is possible to find matrices in the form of series which converge rapidly for low and high frequencies. Moreover, a rule is formulated which makes it possible on the basis of a known field in an isotropic medium to find the field in the corresponding transversally isotropic medium.     

Worms,gaps, and hydras

We define a direct translation from finite rooted trees to finite natural functions which shows that the Worm Principle introduced by Lev Beklemishev is equivalent to a very slight variant of the well‐known Kirby‐Paris' Hydra Game. We further show that the elements in a reduction sequence of the Worm Principle determine a bad sequence in the well‐quasi‐ordering of finite sequences of natural numbers with respect to Friedman's gapembeddability. A characterization of gap‐embeddability in terms of provability logic due to Lev Beklemishev is also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Complexity,Universal Libraries,dna Sequences

Complexity studies are burgeoning into an ever-increasing number of fields. This paper seeks to abstract from a large number of non-biological complexity areas some exemplar common thread representative of many complexity areas. One such common thread is identified, a thread leading immediately to the notion of Universal Library, as an additional complexity area, containing all possible texts and, correspondingly, encompassing all possible knowledge (amidst, naturally, a welter of partially and wholly senseless texts). This notion is then wedded to an elementary portion of number theory, to indicate where replicas of universal libraries exist and with what certain attributes. Next, a representative example of a biological complexity area—DNA sequences—is introduced. While DNA is often casually termed a library specifying the heritability machinery of individuals and species, this paper briefly explores whether explicit relations exist between DNA sequences and universal libraries, to help test, inter alia, the strength of the initially identified complexity thread to link non-biological and biological complexity areas. This theme of common linking threads has many interesting open research issues.     

Continue,quit, restart probability model

We discuss a new applied probability model: there is a system whose evolution is described by a Markov chain (MC) with known transition matrix on a discrete state space and at each moment of a discrete time a decision maker can apply one of three possible actions: continue, quit, and restart MC in one of a finite number of fixed “restarting” points. Such a model is a generalization of a model due to Katehakis and Veinott (Math. Oper. Res. 12:262, 1987), where a restart to a unique point was allowed without any fee and quit action was absent. Both models are related to Gittins index and to another index defined in a Whittle family of stopping retirement problems. We propose a transparent recursive finite algorithm to solve our model by performing O(n³) operations.     

Magnitude,Diversity, Capacities,and Dimensions of Metric Spaces

Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural and direct manner than in previous works by Leinster, Willerton, and the author. The new definition uncovers a previously unknown relationship between magnitude and capacities of sets. Exploiting this relationship, it is shown that for a compact subset of Euclidean space, the magnitude dimension considered by Leinster and Willerton is equal to the Minkowski dimension.     

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.     

Right-angularity, flag complexes, asphericity

The ??polyhedral product functor?? produces a space from a simplicial complex L and a collection of pairs of spaces, {(A(i), B(i))}, where i ranges over the vertex set of L. We give necessary and sufficient conditions for the resulting space to be aspherical. There are two similar constructions, each of which starts with a space X and a collection of subspaces, {X _i }, where ${i \in \{0,1. . . . , n\}}$ , and then produces a new space. We also give conditions for the results of these constructions to be aspherical. All three techniques can be used to produce examples of closed aspherical manifolds.     

Optimality,identifiability, and sensitivity

Around a solution of an optimization problem, an “identifiable” subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are “minimal”. This new notion lays a broad and intuitive variational-analytic foundation for optimality conditions, sensitivity, and active set methods.     

Hadamard matrices,Baumert-Hall units,four-symbol sequences,pulse compression,and surface wave encodings

If a Williamson matrix of order 4w exists and a special type of design, a set of Baumert-Hall units of order 4t, exists, then there exists a Hadamard matrix of order 4tw. A number of special Baumert-Hall sets of units, including an infinite class, are constructed here; these give the densest known classes of Hadamard matrices. The constructions relate to various topics such as pulse compression and image encodings.     

Real-World Contexts,Multiple Representations,Student-Invented Terminology,and Y-Intercept

One classroom using two units from a Standards-based curriculum was the focus of a study designed to examine the effects of real-world contexts, delays in the introduction of formal mathematics terminology, and multiple function representations on student understanding. Students developed their own terminology for y-intercept, which was tightly connected to the meaningfulness and implicit/explicit temporality of the contexts that students investigated as part of their classroom activities. This terminology held great promise for promoting the concept of y-intercept within a multiple representation environment. However, the teacher's interpretation of different activities and his assumptions about the transparency of different representations, as well as students' past experiences left the student-generated terminology and the concept of y-intercept disconnected from one another. This resulted in student-generated terminology that had limited applicability, a fragile understanding of y-intercept within different representations, and for some students, interference between their invented terminology and the concept of y-intercept itself.