Related papers: Relations between angular and Cartesian orientatio…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…
In this paper, we present a mathematical model for the angular projection of a rectangular arrangement of points in a grid. This simple, yet interesting problem, has both a scholarly value and applications for data extraction techniques to…
An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the…
We use the multipole technique to derive four equivalent expressions for the bipolar expansion of the inverse distance, valid in all the regions of configuration space. Using the first-order perturbation theory, we calculate the overlap…
The operator product expansion in four-dimensional superconformal field theory is discussed. The OPE takes a particularly simple form for chiral operators, in $N=1$ and $N=2$, and for analytic operators, in $N=2$ and $N=4$. It is argued…
Cartesian differential categories are categories equipped with a differential combinator which axiomatizes the directional derivative. Important models of Cartesian differential categories include classical differential calculus of smooth…
All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then…
Expansions of Lie algebras are the opposite process of contractions. Starting from a Lie algebra, the expansion process goes to another one, non-isomorphic and less abelian. We propose an expansion method based in the Casimir invariants of…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
In a recent paper, Cohl and Costas-Santos derived a number of interesting multi-derivative and multi-integral relations for associated Legendre and Ferrers functions in which the orders of those functions are changed in integral steps.…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
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 mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
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…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components…
A method for calculating coefficient functions of the operator product expansion, which was previously derived for the non-singlet case, is generalized for the singlet coefficient functions. The resulting formula defines coefficient…