The minimal spanning tree and the upper box dimension

We show that the -weight of an MST over points in a metric space with upper box dimension has a bound independent of if d$"> and does not have one if .

     

A generic method for measuring the potential number of structure‐preserving transformations

In many fields of psychology, it may be interesting to measure the potential number of structure‐preserving transformations that exist between succeeding structures. The aim of this article is to present a methodology for measuring the potential number of structure‐preserving transformations between succeeding structures and to illustrate the applicability of the methodology through a case study. The article concludes by discussing the lessons and implications of the proposed methodology for microgenetic research. © Wiley Periodicals, Inc. Complexity, 2012     

Synthesis and Reactivity of Allylic and Propargylic Trichloromethanesulfinates

Abstract

The synthesis and rearrangement of the title compounds to sulfones are discussed. A facile isomerization of the allylic trichloromethyl sulfones to the corresponding vinyl sulfones is also described.     

The transfer point location problem

In this paper, we introduce the transfer point location problem. Demand for emergency service is generated at a set of demand points who need the services of a central facility (such as a hospital). Patients are transferred to a helicopter pad (transfer point) at normal speed, and from there they are transferred to the facility at increased speed. The general model involves the location of p helicopter pads and one facility. In this paper, we solve the special case where the location of the facility is known and the best location of one transfer point that serves a set of demand points is sought. Both minisum and minimax versions of the models are investigated. In follow up papers we investigate the general model using the results obtained in this paper.     

Orlicz–Young Structures of Young Measures

The paper examines the integration of Young functions applied to Young measures and identifies Orlicz-like structures in the space of Young measures. In particular, a convergence intermediate between the weak convergence of measures and the variational norm is determined; it serves in the completion of the Orlicz space of functions when interpreted as degenerate Young measures. Partial linear operations are defined on Young measures with respect to which the linear operations in the Orlicz space of functions are continuously embedded in the space of Young measures. This leads to a definition of convexity-type structures in the space of Young measures via a limiting procedure. These structures enable applications of Young functions arguments to Young measures. Applications to optimal control and to well posedness of minimization in function spaces with respect to convex functions are provided.     

Averaging of time-varying differential equations revisited

Employing comparison of integrals on a fast time scale, we offer a new criterion and simple proofs of the averaging principle for time-varying ordinary differential equations. The method allows straightforward extensions and generalizations. Comparisons with available criteria and estimates, along with examples and applications, are offered.