Related papers: On one class of quaternionic mappings
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as…
Among all the dynamical modular curves associated to quadratic polynomial maps, we determine which curves have infinitely many quadratic points. This yields a classification statement on preperiodic points for quadratic polynomials over…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii…
We provide a complete set of linearizability conditions for nonlinear partial difference equations de- fined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to…
We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional…
We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a…
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete…
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…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
Fractional $q$-extensions of some classical $q$-orthogonal polynomials are introduced and some of the main properties of the new defined functions are given. Next, a fractional $q$-difference equation of Gauss type is introduced and solved…
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…
Based on an original classification of differential equations by types of regular Lie group actions, we offer a systematic procedure for describing partial differential equations with prescribed symmetry groups. Using a new powerful…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…