Related papers: Multidimensional Laplace transforms over Cayley-Di…
In recent years, there is a growing interest in the studying octonions, which are 8-dimensional hypercomplex numbers forming the biggest normed division algebras over the real numbers. In particular, various tools of the classical complex…
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.
We consider Laplace transforms of the Picard-Fuchs differential equations of Calabi-Yau hypersurfaces and calculate their Stokes matrices. We also introduce two different types of Laplace transforms of Gel'fand-Kapranov-Zelevinski…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
The Laplace transform in Komatsu ultradistributions is considered. Also, conditions are given under which an analytic function is a Laplace transformation of an ultradistribution.
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation…
As is well-known, the real quaternion division algebra $ {\cal H}$ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra ${\cal O}$ can not be algebraically isomorphic to any matrix algebras…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Galilean transformation properties of different physical quantities are investigated from the point of view of four dimensional Galilean relativistic (non-relativistic) space-time. The objectivity of balance equations of general heat…
The split octonionic form of Dirac and Maxwell equations are found. In contrast with the previous attempts these equations are derived from the octonionic analyticity condition and also we use different basis of the 8-dimensional space of…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation…
In this work we are interested in the general problem of the determination of the normed division algebras. Our fundamental results are obtained in the particular subclass of those 8-dimensional quadratic flexible real division algebras. We…
The notion of Laplace invariants is transferred to the lattices and discrete equations which are difference analogs of hyperbolic PDE's with two independent variables. The sequence of Laplace invariants satisfy the discrete analog of…
Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of…
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…