On I-fuzzy topologies derived from a decreasing family of I-topologies

The aim of this paper is to study I-fuzzy topologies (fuzzy topologies in ostak's sense) derived from decreasing families of I-topologies (fuzzy topologies in Chang's sense), defined on a set X.     

Embeddings and hyperplanes of the Lie incidence geometry of type E7,1

This paper continues a program to show that for most of the standard Lie incidence geometries, all geometric hyperplanes arise from a necessarily absolutely universal embedding, by addingE _7,1 to the list. It follows from [5, 12] that any projective embedding of this point line geometry is a homomorphic image of the one afforded by the 56-dimensional module for the groupE ₇(K).This work was supported by a grant from the National Science Foundation.     

How to work with one-dimensional quadratic maps

We analyse some identifiers which can univocally identify hyperbolic components and Misiurewicz points of one-dimensional quadratic maps. After seeing the equivalence among the different identifiers and how to go from one to another, we show which are the best for some specific tasks. Likewise, we present the analytic expressions, some of them shown for the first time in this paper, to calculate these identifiers. Some experimental considerations are taken into account.     

Ernest Julius Wilczynski (in Memoriam)

Ringrazio il collega dell'Università di Chicago di avermi permesso di pubblicare qui un breve sunto della commemorazione da lui scritta; e sono dolente che lo spazio concessomi non me ne abbia permesso la pubblicazione integrale.Guido Fubini     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

A multivalued version of Sharkovskiĭ’s theorem holds with at most two exceptions

A multivalued version of Sharkovskiĭ’s theorem is formulated for M-maps on linear continua and, more generally, for triangular M-maps on a Cartesian product of linear continua. This improves the main result of [AP1] in the sense that our multivalued analogue holds with at most two exceptions. A further specification requires some additional restrictions. For instance, 3- orbits of m-maps imply the existence of k-orbits for all k ? \mathbbNk \in {\mathbb{N}} , except possibly for k ?k \in {4, 6}. It is also shown that, on every connected linearly ordered topological space, an M-map with orbits of all periods can always be constructed. This demonstrates that Baldwin’s classification of linear continua in terms of admissible periods [Ba] is useless for multivalued maps.     

Evaluating the financial performance of bank branches

We evaluate the financial performance of most of the branch offices of a large European savings bank for a recent accounting period. We employ a complementary pair of nonparametric techniques to evaluate their financial performance, in terms of their ability to conserve on the expenses they incur in building their customer bases and providing customer services. We find variation in the ability of branch offices to perform this task, and agreement on the identity of the laggard branches. We then employ parametric techniques to determine that the list of indicators on which their financial performance is evaluated can be reduced without statistically significant loss of information to bank management. Both findings suggest ways in which the bank can increase the profitability of its branch network. A previous version of this paper was presented at CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium, where we received many helpful comments from the audience. We are grateful to three referees for their helpful comments as well.