We consider a nearest-neighbor inhomogeneous p-adic Potts (with q ≥ 2 spin values) model on the Cayley tree of order k ≥ 1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p− adic) Gibbs measures of the model. We show that (i) if q / ∈ pN then there is unique Gibbs measure for any k ≥ 1 and ∀Jxy with |Jxy | < p . (...

The paper investigates completions in the context of finitely generated lattice-based varieties of algebras. In particular the structure of canonical extensions in such a variety A is explored, and the role of the natural extension in providing a realisation of the canonical extension is discussed. The completions considered are Boolean topological algebras with respect to the interval topology...

MODEL OF AN EXCITON-PHOTON SYSTEM INTERACTING WITH THE LATTICE

We consider the double-row (open) transfer matrix constructed from generic representations of various types of Hecke algebras. For different choices of boundary conditions for the relevant integrable lattice model we express the double-row transfer matrix solely in terms of generators of the corresponding Hecke algebra. We then expand the open transfer matrix and extract the associated Murphy e...

A lattice is called dual strongly perfect if both, the lattice and its dual, are strongly perfect. We show that there are no dual strongly perfect lattices of dimension 13 and 15.

Lattices have been used in mathematics going back at least to the 18th century. However, computational aspects of lattices were not investigated much until the early 1980s, when they were successfully employed for breaking several proposed cryptosystems (among many other applications). It was not until the late 1990s that lattices were first used in the design of cryptographic schemes, and the ...

Article history: Received 15 January 2013 Received in revised form 12 October 2013 Accepted 8 November 2013 Available online 22 November 2013

We construct two-dimensional (2-D) local cosine bases in discrete time. Solutions are offered both for rectangular and nonrectangular lattices. In the case of nonrectangular lattices, the problem is solved by mapping it into a one-dimensional (1-D) equivalent problem.

An integrable discretization of an inhomogeneous Volterra lattice is introduced. Some aspects of dynamics of a soliton affected by a random force are discussed.