This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to da...

A Banaschewski function on a bounded lattice L is an antitone self-map of L that picks a complement for each element of L. We prove a set of results that include the following: • Every countable complemented modular lattice has a Banaschewski function with Boolean range, the latter being unique up to isomorphism. • Every (not necessarily unital) countable von Neumann regular ring R has a map ε ...

The 6-ring is a tubular surface of genus 13, obtained by gluing together twenty-four 12-gons which follows the regularity of the map R13.2′{12,3}. It is constructed from six rings of two Borromean rings, has the twenty-four elements of an oriented cube and matches nicely with the 6-coloring of R13.2′{12,3}. The 6-ring has minimal twists and geometrically equivalent sets of four 12-gons. We expl...

There is a close relation between comprehensive Gröbner bases and non-parametric Gröbner bases over commutative von Neumann regular rings. By this relation, Gröbner bases over a commutative von Neumann regular ring can be viewed as an alternative to comprehensive Gröbner bases. (Therefore, this Gröbner basis is called an “alternative comprehensive Gröbner basis (ACGB)”.) In the first part of th...

We show that cohopfian modules with finite exchange have countable exchange. In particular, a module whose endomorphism ring is Dedekind-finite and π-regular has the countable exchange property. We also show that a module whose en-domorphism ring is Dedekind-finite and regular has full exchange. Finally, working modulo the Jacobson radical, we prove that any module with the (C 2) property and a...

We show that ω-categorical rings with NIP are nilpotent-by-finite. We prove that an ω-categorical group with NIP and fsg is nilpotent-by-finite. We also notice that an ω-categorical group with at least one strongly regular type is abelian. Moreover, we get that each ω-categorical, characteristically simple p-group with NIP has an infinite, definable abelian subgroup. Assuming additionally the e...

A revised Marko-Siggia elastic model for DNA double helix [Macromolecules 27, 981 (1994)] is proposed, which includes the WLC bending energy and a new chiral twisting energy term. It is predicted that the mean helical repeat length (HRL) for short DNA rings increases with the decreasing of chain length; while for very long chains, their mean HRL is the same, independent of both the chain length...

Combining results on quadrics in projective geometries with an algebraic interplay between finite fields and Galois rings, we construct the first known family of partial difference sets with negative Latin square type parameters in nonelementary abelian groups, the groups Z 4 × Z4`−4k 2 for all k when ` is odd and for all k < ` when ` is even. Similarly, we construct partial difference sets wit...

Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [5] and [12]. It was shown that such graphs exist iff the corresponding group is isomorphic to Zpn ⊕Zpn , where p is an odd prime. In this paper we classify all strongly regular Cayley graphs over this group using Schur rings method. As a consequence we obtain a complete classification of strongly...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 → R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular triangular and ...