Selecting families and their applications

Selecting families and their applications

Deguire and Lassonde [P. Deguire, M. Lassonde, Familles sélectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261–269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obt...

Disjoint difference families and their applications

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and...

Stereoscopic families of permutations, and their applications

A stereoscopic family of permutations maps an mdimensional mesh into several 1-dimensional lines, in a way that jointly preserves distance information. Specifically, consider any two points and denote their distance on the m-dimensional mesh by d. Then the distance between their images, on the line on which these images are closest together, is O(dm). We initiate a systematic study of stereosco...

Magentotactic bacteria and their applications

Magentotactic bacteria are the types of bacteria capable of orientation in an external magnetic field because of the ability to produce structures called magnetosomes. Magnetosomes, nanometer-scale structures, are present in most of the magnetotactice bacteria. They are intracellular organelles composed of magnetic iron mineral crystals individually surrounded by a phospholipid layer. Because o...

Sequential Methods and Their Applications