“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.     

Generalizations of theorems of J. Aczél and R. Ger and T. Kochanek

Periodica Mathematica Hungarica - We present a result which generalizes a theorem proved by Aczél (Bull Am Math Soc 54:392–400, 1948). Hence we obtain generalizations of a theorem proved...     

Crystallographic classes on the minkowski space <Emphasis Type="Italic">R</Emphasis><Subscript>1,2</Subscript>. I. Theorems

Some preliminary statements are proved necessary for calculating the crystallographic groups in six crystallographic classes in the 3-dimensional Minkowski space. Three classes are determined by the unimodular subgroups of the general Lorentz group and three more classes, by subgroups unimodular in a certain isotropic coordinate system.     

Nina N. Uraltseva. On the occasion of her 75<Superscript>th</Superscript> birthday

It is a great pleasure for me to write about Nina N. Uraltseva who has been one of the most supportive persons during all my scientific career. I have learned from Nina very many things starting from the foundations of Mathematics to how to prepare Swedish gravad lax (salted salmon). Nina is one of the most wholly beautiful persons I have ever met and, together with all the contributors of these anniversary issues of “Problemy Matematicheskogo Analiza,” I wish her many healthy and active years ahead. Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 3–6.     

A note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée

The paper “Euclidean algorithms are Gaussian” [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331-386], is devoted to the distributional analysis of three variants of Euclidean algorithms. The Central Limit Theorem and the Local Limit Theorem obtained there are the first ones in the context of the “dynamical analysis” method. The techniques developed have been applied in further various works (e.g. [V. Baladi, A. Hachemi, A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs, Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 749-770; E. Cesaratto, J. Clément, B. Daireaux, L. Lhote, V. Maume, B. Vallée, Analysis of fast versions of the Euclid algorithm, in: Proceedings of Third Workshop on Analytic Algorithmics and Combinatorics, ANALCO'08, SIAM, 2008; E. Cesaratto, A. Plagne, B. Vallée, On the non-randomness of modular arithmetic progressions, in: Fourth Colloquium on Mathematics and Computer Science. Algorithms, Trees, Combinatorics and Probabilities, in: Discrete Math. Theor. Comput. Sci. Proc., vol. AG, 2006, pp. 271-288]). These theorems are proved first for an auxiliary probabilistic model, called “the smoothed model,” and after, the estimates are transferred to the “true” probabilistic model. In this note, we remark that “the smoothed model” described in [V. Baladi, B. Vallée, Euclidean algorithm are Gaussian, J. Number Theory 110 (2005) 331-386] is not adapted to this transfer and replaces it by an adapted one. However, the results remain unchanged.     

<Emphasis Type="Italic">Addendum by </Emphasis>L. Silberman To ¶"Random walk in random groups" by M. Gromov

((no abstract)) . Submitted: October 2002, Final version: December 2002.     

<Emphasis Type="Italic">A</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> theory,L.S. category,and strong category

Relations between category and strong category are studied. The notion of a homotopy coalgebra of order r over the Ganea comonad is introduced. It is shown that cat(X) =Cat(X) holds if a finite 1-connected complex X carries such a structure with r sufficiently large.