“Bricks-and-mortar” vs. “clicks-and-mortar”: An equilibrium analysis

The Internet has provided traditional retailers a new means with which to serve customers. Consequently, many “bricks-and-mortar” retailers have transformed to “clicks-and-mortar” by incorporating Internet sales. Examples of companies making such a transition include Best Buy, Wal-Mart, Barnes & Noble, etc. Despite the increasing prevalence of this practice, several fundamental questions remain: (1) Does it pay off to go online? (2) Which is the equilibrium industry structure? (3) What is the implication of this business model for consumers? We study these issues in an oligopoly setting and show that clicks-and-mortar arises as the equilibrium channel structure. However, we find that this equilibrium does not necessarily imply higher profits for the firms: in some cases, rather, it emerges as a strategic necessity. Consumers are generally better off with clicks-and-mortar retailers. If firms align with pure e-tailers to reach the online market, we show that a prisoner’s dilemma-type equilibrium may arise.     

‘Strong’-‘weak’ precedence in scheduling: Extensions to series-parallel orders

We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series-parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) [5]. Moreover, for series-parallel posets we establish new computational complexity results for strong precedence constraints for single- and multi-machine problems.     

‘Too Little’ or ‘Too Late’: The timing of supply chain demand collaboration

This study examines the supply chain demand collaboration between a manufacturer and a retailer. We study how the timing of collaboration facilitates production decision of the manufacturer when the information exchanged in the collaboration is asymmetric. We investigate two collaboration mechanisms: ‘Too Little’ and ‘Too Late’, depending on the timing of information sharing between the manufacturer and the retailer. Our research results indicate that early collaboration as in the ‘Too Little’ mechanism leads to a stable production schedule, which decreases the need of production adjustment when production cost information becomes available; whereas a late collaboration as in the ‘Too Late’ mechanism enhances the flexibility of production adjustment when demand information warrants it. In addition, the asymmetric demand information confounds production decisions all the time; the manufacturer has to provide proper incentives to ensure truthful information sharing in collaboration. Information asymmetry might also reduce the difference in production decision between the ‘Too Little’ and ‘Too Late’ collaboration mechanisms. Numerical analysis is further conducted to demonstrate the performance implications of the collaboration mechanisms on the supply chain.     

The difficulty of “length × width”: Is a square the unit of measurement?

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions were No (except for eighth (and ninth) graders in advanced sections of mathematics). The difficulty of “length × width” is explained in light of Piaget's theory, and educational implications are discussed.     

Les Récréations Mathématiques d'Édouard Lucas: quelques éclairages

The article is devoted to Edouard Lucas's contribution to the development of mathematical recreations in the France of the post 1870 war period. Lucas's name is associated to four volumes of Récréations mathématiques published between 1882 and 1894 (the last two having been published posthumously) and to a posthumous volume L'Arithmétique amusante, which appeared in 1895. The author analyzes the context of reform of science education in relation to which mathematical recreations appeared as a means of attracting a wider public to scientific activities and inspiring young people to study science. The article brings to light how the milieu of new associations which took shape to promote science (Association Française pour l'Avancement des Sciences, Société Mathématique de France) allowed the constitution of social groups internationally connected and quite active in the promotion and development of mathematical recreations. Lastly, the article suggests that this type of mathematical activity allowed the cultivation of fields that at the time the French academic milieu perceived as marginal such as number theory and analysis situs as well as their applications.     

Growth in Illyria: The role of meritocracy in the accumulation of human capital

In this paper we present a dynamic model of cooperative production with human capital accumulation. We assume CES preferences on consumption and leisure in each period. When agents do not care about future generations, sustained growth occurs iff the elasticity of substitution between consumption and leisure is larger or equal than one. Meritocracy always has a positive effect on output, but when the elasticity of substitution is less than one, is only a level effect. When agents care about future generations, under Cobb–Douglas preferences in each period and some extra conditions, there is constant growth at a rate that is larger than the one when future generations do not count. For any discount rate between generations, there is a unique level of meritocracy for which efficiency is achieved.     

“I’m not very good at solving problems”: An exploration of students’ problem solving behaviours

This paper reports one aspect of a larger study which looked at the strategies used by a selection of grade 6 students to solve six non-routine mathematical problems. The data revealed that the students exhibited many of the behaviours identified in the literature as being associated with novice and expert problem solvers. However, the categories of ‘novice’ and ‘expert’ were not fully adequate to describe the range of behaviours observed and instead three categories that were characteristic of behaviours associated with ‘naïve’, ‘routine’ and ‘sophisticated’ approaches to solving problems were identified. Furthermore, examination of individual cases revealed that each student's problem solving performance was consistent across a range of problems, indicating a particular orientation towards naïve, routine or sophisticated problem solving behaviours. This paper describes common problem solving behaviours and details three individual cases involving naïve, routine and sophisticated problem solvers.     

Homology of GL<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>: injectivity conjecture for GL<Subscript>4</Subscript>

The homology of GL _n (R) and SL _n (R) is studied, where R is a commutative ‘ring with many units’. Our main theorem states that the natural map H ₄(GL₃(R), k) → H ₄(GL₄(R), k) is injective, where k is a field with char(k) ≠ 2, 3. For an algebraically closed field F, we prove a better result, namely, is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the K-group K ₄(R).     

Optimal asset allocation aid system: From “one-size” vs “tailor-made” performance ratio

Optimal asset allocation well-fitting investors’ goals is a pressing challenge in risk management. Making a step forward to the Sharpe ratio, the parameter-dependent Sortino–Satchell, Generalized Rachev and Farinelli–Tibiletti performance ratios are suggested for personalizing asset allocation. Tailor-made optimal asset paths for five different investor risk profiles are traced over a rolling 12 month investing horizon. Our simulations show a satisfactorily good match between asset allocation and correspondent risk profile. Specifically, Generalized Rachev ratios outperform in personalized allocation for “extreme” risk profiles, i.e. conservative and aggressive investors, whereas Sortino–Satchell and Farinelli–Tibiletti ratios for those that are more moderate. Sharpe ratio confirms its ability in constructing steady-diversified portfolios, although underperformed.     

Acknowledgement of priority to: “Universal residuals: A multivariate transformation. Statistics & Probability Letters 27, 2007, 1473–1478”

This is an acknowledgement of priority about a paper that was published in 2007.     

<Literal>smt</Literal>: a Matlab toolbox for structured matrices

The full exploitation of the structure of large scale algebraic problems is often crucial for their numerical solution. Matlab is a computational environment which supports sparse matrices, besides full ones, and allows one to add new types of variables (classes) and define the action of arithmetic operators and functions on them. The smt toolbox for Matlab introduces two new classes for circulant and Toeplitz matrices, and implements optimized storage and fast computational routines for them, transparently to the user. The toolbox, available in Netlib, is intended to be easily extensible, and provides a collection of test matrices and a function to compute three circulant preconditioners, to speed up iterative methods for linear systems. Moreover, it incorporates a simple device to add to the toolbox new routines for solving Toeplitz linear systems.     

Discriminants of polynomials related to Chebyshev polynomials: The “Mutt and Jeff ” syndrome

The discriminants of certain polynomials related to Chebyshev polynomials factor into the product of two polynomials, one of which has coefficients that are much larger than the other?s. Remarkably, these polynomials of dissimilar size have “almost” the same roots, and their discriminants involve exactly the same prime factors.     

Self-interacting diffusions II: convergence in law

This paper concerns convergence in law properties of self-interacting diffusions on a compact Riemannian manifold.     

Flexible <Emphasis Type="Italic">versus</Emphasis> fixed timetabling: a case study

This case study presents the timetabling problem of the Flight Training Department at Embry-Riddle Aeronautical University. The problem consists of scheduling the flight resources to students to various time blocks. This problem represents a well-studied field in operations research, mainly adopting variations of mathematical programming models. This paper initially presents the efforts towards developing a fixed timetable using optimization models for the case under study. It is, however, demonstrated that implementation of optimum solutions obtained using this approach cannot be sustained, mainly because of the dynamic nature of the governing parameters. A flexible and dynamic timetable utilizing the university computer network, allowing the instructors and students to make their own decentralized flexible timetables, is proposed. A simulation study is initiated to compare the performance measures under both timetables. The analysis shows that implementation of a flexible system generates higher utilization of flight resources as well as improving key performance measures.