Related papers: The Ruijsenaars-Schneider Model
The aim of this paper is to clarify the relation between the following objects: $ (a) $ rank 1 projective modules (ideals) over the first Weyl algebra $ A_1(\C)$; $ (b) $ simple modules over deformed preprojective algebras $…
The issue of a Majorana, Dirac or pseudo-Dirac mass for gauginos must not be reduced to a question of an extension of the Minimal Supersymmetric Standard Model by extra states, parameters and phenomenological implications. On the contrary,…
The generalized Verlinde formulae expressing traces of mapping classes corresponding to automorphisms of certain Riemann surfaces, and the congruence relations on allowed modular representations following from them are presented. The…
In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere by so called rectangular diagrams. The formalism proved useful for comparing Legendrian knots. The aim of this paper is to…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
We elaborate the idea that the matrix models equipped with the gauge symmetry provide a natural framework to describe identical particles. After demonstrating the general prescription, we study an exactly solvable harmonic oscillator type…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion…
A mathematical model is a function taking certain arguments and returning a theoretical prediction of a feature of a physical system. The arguments to the mathematical model can be split into two groups; (a) controllable variables of the…
Clinical prediction models are developed widely across medical disciplines. When predictors in such models are highly collinear, unexpected or spurious predictor-outcome associations may occur, thereby potentially reducing face-validity and…
We present an elementary discussion of the Calogero-Moser model. This gives us an opportunity to illustrate basic concepts of the dynamical integrable models. Some ideas are also presented regarding interconnections between integrable…
A suitable choice of the four components of the metric tensor which are at our discretion allows to represent geodesically also the non-gravitational motions.
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
A pseudo-velocity concept, based on the extension of a linear body, is defined by a special relativity experiment. It suggests an analogy with the covariance properties of Wiener's process, ultimately implying that the scaling behavior of…
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
It is shown that spin Calogero-Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less then half of the dimension of the phase space. It is also shown that rational spin…
In this comment on arXiv:2308.07360 it is pointed out that though the authors raise an important question on the prevailing presentations of the unimodular gravity their own presentation is incomplete as well as confusing equating…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…