Key distribution patterns (KDPs) are finite incidence structures satisfying a certain property which makes them widely used in minimizing the key storage and ensuring the security of communication between users in a large network. In this paper we discuss the close connection between resolvable designs and KDPs, and convert the constructions of KDPs into the constructions of resolvable designs....

We introduce a ZFC method that enables us to build spaces (in fact special dense subspaces of certain Cantor cubes) in which we have ”full control” over all dense subsets. Using this method we are able to construct, in ZFC, for each uncountable regular cardinal λ a 0-dimensional T2, hence Tychonov, space which is μ-resolvable for all μ < λ but not λ-resolvable. This yields the final (negative) ...

‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull&apos;s intersection theorem of fuzzy ideals by using concept $mu$-adic...

The resolvability of combinatorial designs is intensively investigated because of its applications. This research focuses on resolvable designs with an additional property—they have resolutions which are mutually orthogonal. Such designs are called doubly resolvable. Their specific properties can be used in statistical and cryptographic applications. Therefore the classification of doubly resol...

This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970’s but never published. This article “Suspensions of homology spheres” presents the initial solutions of the fabled Double Suspension Conjecture. The article “Approximating certain cell-like maps by homeomorphisms” presents the definitive theorem on the recognition of ma...

LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...