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A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed t...
Abstract: Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A$, $B$ and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of norma...
Abstract: The Jaynes-Cummings-Gaudin model describes a collection of $n$ spins coupled to an harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each ...
Mechanical Normal Forms of Knots and Flat Knots     Mechanical Normal Forms  Knots  Flat Knots       font style='font-size:12px;'> 2010/11/24
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to iso...
Matrices over the ring of formal power series are considered. Normal forms wit respect to various sub-groups of the two-sided transformations are constructed. The construc-tion is based on the special...
On Urn Models, Non-commutativity and Operator Normal Forms     Urn Models  Non-commutativity  Operator Normal Forms       font style='font-size:12px;'> 2010/11/5
Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation rel...
The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrices is far from unifo...
Hermite normal forms with a given $\delta$-vector      Convex polytope  Ehrhart polynomial  -vector  Hermite normal form       font style='font-size:12px;'> 2010/12/14
Let (P) = (0, 1, . . . , d) be the -vector of an integral polytope P ⊂ RN of dimension d. By means of Hermite normal forms of square matrices,the problem of classifying the possible integra...
Conservation laws and normal forms of evolution equations     Conservation laws  normal forms  evolution equations       font style='font-size:12px;'> 2010/4/6
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Exampl...
The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for the admissible algebras with formal two-ray modules.
We describe di®erential rational normal forms of a rational function and their properties. Based on these normal forms, we present an algorithm which, given a hyperexponential function T (x), con...

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