Related papers: On Bers generating functions for first order syste…
We are studying here the classical operator creating secondary polynomials associated with an orthogonal system for a continuous probability density function on a real interval. We know it is possible with the coupling of Stietjes…
We construct a set of quaternionic metamonogenic functions (that is, in $\mbox{Ker}(D+\lambda)$ for diverse $\lambda$) in the unit disk, such that every metamonogenic function is approximable in the quaternionic Hilbert module $L^2$ of the…
A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bi-linear and commutative mapping on the solution space, is studied. This family of PDE's contains…
In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played…
We introduce to this paper new kinds of coherent states for some quantum solvable models: a free particle on a sphere, one-dimensional Calogero-Sutherland model, the motion of spinless electrons subjected to a perpendicular magnetic field…
We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are…
In this paper we present a new algebraic structure (a super hyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli…
The pseudopotential theory is extended to the Bogoliubov-de Gennes equations to determine the excess energy when one atom is added to the trapped superfluid Fermi system with even number of atoms. Particular attention is paid to systems…
We consider representations of quadratic $R$-matrix algebras by means of certain first order ordinary differential operators. These operators turn out to act as parameter shifting operators on the Gauss hypergeometric function and its limit…
Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on…
The main object of the paper is to reveal connections between Chebyshev polynomials of the first and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved by relating the respective (ordinary and exponential)…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
A cubic structure of polymer colloid complexes is studied. The technique of the research includes i) an analysis of well-known literature SAXS data; on this base, at some assumptions, ii) constructing a simple model to estimate geometric…
We suggest a systematic method of extension of quasi-exactly solvable (QES) systems. We construct finite-dimensional subspaces on the basis of special functions (hypergeometric, Airy, Bessel ones) invariant with respect to the action of…
Many aspects of pluripotential theory are generalized to quaternionic $m$-subharmonic functions. We introduce quaternionic version of notions of the $m$-Hessian operator, $m$-subharmonic functions, $m$-Hessian measure, $m$-capapcity, the…
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
Bayesian mechanics provides a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, elucidating the requisite generative models is essential for empirical applications to realistic…
We explore the question concerning the number of distinct resonant algebras depending on the generator content, which consists of the Lorentz generator, translation, and new additional Lorentz-like and translation-like generators. Such…
We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…