Related papers: A note on the action-angle variables for the ratio…
The paper contains a description of a connection between diagonal actions and certain KMS weights on groupoid $C^{*}$-algebras. It furthermore contains the realization of a graph $C^{*}$-algebra of a countable graph as the groupoid…
Using the scattering transform for $n^{th}$ order linear scalar operators, the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner Poisson bracket for the KdV hierarchy, is computed on the scattering side.…
The canonical method of constrained system is discussed. The equations of motion for a free relativistic spinning particle are obtained without using gauge fixing conditions. The quantization of this model is discussed.
We propose a variant of the CCS process algebra with new features aiming at allowing multiscale modelling of biological systems. In the usual semantics of process algebras for modelling biological systems actions are instantaneous. When…
The causal set theory d'Alembertian has rational coefficients for which alternating expressions are known. Here, a combinatorial interpretation of these numbers is given.
A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on…
Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure is also exist…
We establish the boundedness character of solutions of a system of rational difference equations with a variable coefficient
Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…
Dynamic degrees of freedom and internal variables are treated in a uniform way. The unification is achieved by means of the introduction of a dual internal variable. This duality provides the corresponding evolution equations depending on…
The main point of the construction of spin Calogero type classical integrable systems based on dynamical r-matrices, developed by L.-C. Li and P. Xu, is reviewed. It is shown that non-Abelian dynamical r-matrices with variables in a…
Expressions for variables of the center of mass and relative motions for two-body system with different and equal masses in three-dimensional spaces of constant curvature are introduced in the terms of biquaternions. The problem of the…
We study free and compact group actions on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classical classification theory of…
Some systematic general features of y-scaling structure functions, which are essentially independent of detailed dynamics, are pointed out. Their physical interpretation in terms of general characteristics, such as a mean field description…
It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…
We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals which are invariant under the action of the corresponding rational Cherednik algebra…
This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…
The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic…
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…