On Necklaces inside Thin Subsets of R

On T-codes and necklaces

This paper describes a newly discovered aspect of T-codes, a family of variable length codes first described by Titchener in the 1980s. We show that the constant-length subsets of codewords generated during the Tcode construction process constitute sets of necklaces. Moreover, we show that these sets are complete except for a small subset which we characterize. Bounds on the number of constant-...

SOME REMARKS ON GENERALIZATIONS OF MULTIPLICATIVELY CLOSED SUBSETS

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...

Splitting Necklaces and a Generalization of the Borsuk-ulam Antipodal Theorem

We prove a very natural generalization of the Borsuk-Ulam antipodal Theorem and deduce from it, in a very straightforward way, the celebrated result of Alon [1] on splitting necklaces. Alon’s result says that t(k− 1) is an upper bound on the number of cutpoints of an opened t-coloured necklace so that the segments we get can be used to partition the set of vertices of the necklace into k subset...

The Immunomodulatory Effect of Cyclophosphamide on Regulation of T-Cell Subsets and Antigen Presenting Cells.

Center--like subsets in rings with derivations or epimorphisms

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.