This report addresses and resolves several issues in the use of combinators for molecular computation. The issues include assumptions about binding sites and linking groups, “capping” of unused sites, replication and sharing of structures in a molecular context, creation of cyclic structures, disassembly of unneeded structures, representation of Boolean values and conditionals, representation o...

We develop an algebraic representation for ð1; 1Þ-knots using the mapping class group of the twice punctured torus MCG2ðTÞ. We prove that every ð1; 1Þ-knot in a lens space Lðp; qÞ can be represented by the composition of an element of a certain rank two free subgroup of MCG2ðTÞ with a standard element only depending on the ambient space. As notable examples, we obtain a representation of this t...

A constitutive multi-laminate based elastic-plastic model developed to be capable of accounting induced anisotropic behavior of granular material such as sand. The fabric feature or grain orientation characteristic effects through medium are considered in a rational way under any complex stress path, including cyclic loading. The salient feature of the developed model is a non-associative on pl...

Let R be a commutative finite chain ring of invariants (q ,s ). In this paper, the trace representation of any free cyclic R -linear code of length l, is presented, via the q -cyclotomic cosets modulo l, when gcd(l,q ) = 1. The lattice Cy(R,l);+,∩ of cyclic R -linear codes of length l, is investigated. A lower bound on the Hamming distance of cyclic R -linear codes of length l , is established....

A binary linear code C is a Z2-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z2[x]-module Z2[x]/(x r −1)×Z2[x]/(x − 1). We determine the structure of Z2-double cyclic codes giving the generator polynomials of these codes. ...

We study Hochschild and cyclic homology of finite type algebras using abelian stratifications of their primitive ideal spectrum. Hochschild homology turns out to have a quite complicated behavior, but cyclic homology can be related directly to the singular cohomology of the strata. We also briefly discuss some connections with the representation theory of reductive p–adic groups.