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Convergent Quantum Normal Forms, ${\mathcal P}{\mathcal T}$-symmetry and reality of the spectrum
Convergent Quantum Normal Forms reality of the spectrum Mathematical Physics
2012/6/19
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...
Amalgamated Products of Groups II: Measures of Random Normal Forms
Amalgamated Products Measures of Random Normal Forms Group Theory
2011/9/15
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...
Classical Bethe Ansatz and Normal Forms in the Jaynes-Cummings Model
Classical Bethe Ansatz Normal Forms the Jaynes-Cummings Model
2011/7/28
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 ...
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...
Normal forms of matrices over the ring of formal series
Normal forms of matrices ring of formal series
2010/12/6
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
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...
Natural Density Distribution of Hermite Normal Forms of Integer Matrices
Natural density Hermite normal form integer lattices
2010/12/13
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
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
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...
NORMAL FORMS OF MODULES OVER ADMISSIBLE ALGEBRAS WITH FORMAL TWO_RAY MODULES
domestic algebra vector space category Aus\-lan\-der--Reiten sequence
2007/12/11
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.
Differential Rational Normal Forms and a Reduction Algorithm for Hyperexponential Functions
Normal forms Rational functions Hyperexponential functions Reduction algorithms
2013/9/3
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...