Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations

We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the solutions to the time-harmonic Maxwell system in terms of series expansions involving spherical harmonics resp. spherical monogenics. Also, a thorough investigation for the series representation of the solutions in terms of eigenfunctions of Landau operators that encode $n-$dimensional spinless electrons is given. This new insight should lead to important investigations in the study of regularity and hypo-ellipticity of the solutions to Schr\"odinger equations with natural applications in relativistic quantum mechanics concerning massive spinor fields.Comment: Exposition improved; Some typos corrected; Accepted for publication in J.Phys.A (February 2011). http://www.mat.uc.pt/preprints/ps/p1047.pd

Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Fundamental solutions of Dirac type operators are introduced for a class of conformally. at spin manifolds. This class consists of manifolds obtained by factoring out the upper half-space of R-n by congruence subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincare type series

Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius

In this paper, we develop the basic concepts for a generalized Wiman-Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system . These functions are called monogenic or Clifford holomorphic inside the ball. We introduce growth orders, the maximum term and a generalization of the central index for monogenic Taylor series of finite convergence radius. Our goal is to establish explicit relations between these entities in order to estimate the asymptotic growth behavior of a monogenic function in a ball in terms of its Taylor coefficients. Furthermore, we exhibit a relation between the growth order of such a function f and the growth order of its partial derivatives

On a generalization of Valiron's inequality for k-hypermonogenic functions on upper half-space

We present some results on the asymptotic growth behavior of periodic k-hypermonogenic functions on upper half-space. A generalization of the classical Valiron inequality for this class of functions and some basic properties are discussed

Equilibrium relationships for non-equilibrium chemical dependencies

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually coincide with the equilibrium constant at any moment in time. This is established for batch reactors, and similar relations hold for steady-state plug-flow reactors, replacing astronomic time by residence time. Such relationships can be termed time invariants of chemical kinetics

The switching point between kinetic and thermodynamic control

In organic chemistry, the switching point between the kinetic and thermodynamic control regimes of two competitive, parallel reactions is widely studied. A new definition for this switching point is proposed: the time at which the rates of formation of the competing products are equal. According to this definition, the kinetic control regime is present from the beginning of the reaction, and is valid as long as the rate of formation of the kinetic product is larger than the rate of formation of the thermodynamic product. On the switching point, both rates of formation are equal, so, from this switching point the thermodynamic product has a larger rate of formation, and the thermodynamic control remains until the end of the reaction. A closed form expression is given for the proposed time of the switching point, as a function of the direct and inverse kinetic constants of both competing reactions, as well as the initial concentrations of the starting reagent and the competing products. The concept of competing control regimes is extended also to the case where the reactions start from two competitive reagents which decompose to produce a single product. (C) 2016 Elsevier Ltd. All rights reserved