相关论文: Hyperbolic complex numbers in two dimensions

We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural…

Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its…

We prove a generalization of the Hermitian version of the Helton-Vinnikov determinantal representation of hyperbolic polynomials to the class of semi-hyperbolic polynomials, a strictly larger class, as shown by an example. We also prove…

Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.

We study strictly hyperbolic partial differential operators of second order with non-smooth coefficients. After modelling them as semiclassical Colombeau equations of log-type we provide a factorization procedure on some…

We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of invariant sets) associated to analytic hyperbolic systems.…

Hyperbolic cross approximation is a special type of multivariate approximation. Recently, driven by applications in engineering, biology, medicine and other areas of science new challenging problems have appeared. The common feature of…

This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the…

The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its relativistic generalization. We prove new product formulas for…

In this paper, we define two types of partitions of an hyperbolic interval: weak and strong. Strong partitions enables us to define, in a natural way, a notion of hyperbolic valued functions of bounded variation and hyperbolic analogue of…

The present paper is a continuation of our work [11], where we introduced a fractional operator calculus related to a fractional ${\psi}-$Fueter operator in the one-dimensional Riemann-Liouville derivative sense in each direction of the…

The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for…

We propose a geometric explanation for the observation that generic quadratic polynomials over split quaternions may have up to six different factorizations while generic polynomials over Hamiltonian quaternions only have two. Split…

A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…

We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order…

New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently,…