Related papers: Quaternion Analysis
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
In this paper we define and study properties and applications of a, b, x0, x1 elements in some special cases.
It is shown that the Stokes-Mueller formalism can be reformulated in terms of quaternions, and the quaternion approach is more suitable for the formalism of Mueller-Jones states that we have recently described. In terms of quaternions it…
Some recent issues in the theory of heavy quarkonium are discussed. Many of these deal with the need to extend the description of charmonium and bottomonium states beyond the simple quark-antiquark picture. Some recent progress on radiative…
An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…
Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.
The determinant for complex matrices cannot be extended to quaternionic matrices. Instead, the Study determinant and the closely related $q$-determinant are widely used. We show that the Study determinant can be characterized as the unique…
We aim at studying automorphic forms of bounded analytic conductor in the division quaternion algebra setting. We prove the equidistribution of the universal family with respect to an explicit and geometrically meaningful measure. It leads…
We show that the classical algebra of quaternions is a commutative $\Z_2\times\Z_2\times\Z_2$-graded algebra. A similar interpretation of the algebra of octonions is impossible.
Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…
In this paper we review the topological model for the quaternions based upon the Dirac string trick. We then extend this model, to create a model for the octonions - the non-associative generalization of the quaternions.
Recent results in Quarkonia are reviewed, including updates on spectroscopy and $\alpha_s$, and a first look at quarkonium annihilation decays.
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
I review briefly the recent status of research on neutrino oscillations, such as three and four flavor analysis of atmospheric neutrinos and solar neutrinos, and prospects of present and future long baseline experiments.
Two complementary approaches to the theory of heavy quarkonia are discussed. The nonrelativistic potential models give amazingly accurate predictions, but lack a theoretical justification. The expansion in powers of $v/c$ is theoretically…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
The singularity analysis is carried out for a system of four first-order quadratic ODEs with a parameter, which was proposed recently by Golubchik and Sokolov. A transformation of dependent variables is revealed by the analysis, after which…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…