Related papers: Alternative Mathematical Technique to Determine LS…
Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often…
We provide an explicit algorithm to calculate invariant tensors for the adjoint representation of the simple Lie algebra $sl(n)$, as well as arbitrary representation in terms of roots. We also obtain explicit formulae for the adjoint…
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
An ab initio method for calculating electron-phonon coupling parameters is presented. The method is an extension of the plane-wave-based linear-response method for the calculation of lattice dynamics. Results for the mass enhancement…
The continuous spectrum to the spectral side of the Arthur-Selberg trace formula is described in terms of intertwining operators, whose normalising factors involve quotients of $L$-functions. In this paper, we derive two expressions in the…
Transformation matrices of the weights of the atomic wave functions in jj coupling to the relevant weights of LS coupling are considered for a shell of equivalent electrons. Their use allows one to preserve main part of relativistic effects…
Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…
Relativistic tunnel ionization of atoms by intense, elliptically polarized light is considered. The relativistic version of the Landau-Dykhne formula is employed. The general analytical expression is obtained for the relativistic…
In the first order of the perturbation theory, the correction to the electronic terms of a diatomic molecule is calculated taking into account the Pauli principle.
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…
Using Selberg's integral formula we derive all Leutwyler-Smilga type sum rules for one and two flavors, and for each of the three chiral random matrix ensembles. In agreement with arguments from effective field theory, all sum rules for…
The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined…
We study a number of issues related to the emission and absorption radiation by non-relativistic electrons within the framework of a Lorentz-breaking electrodynamics in (3+1) dimensions. Our main results concern how Planck-like spectrum law…
We show that the spectral theorem -- which we understand to be a statement that every self-adjoint matrix admits a certain type of canonical form under unitary similarity -- admits analogues over other $*$-algebras distinct from the complex…
Let $L$ be the $n$-th order linear differential operator $Ly = \phi_0y^{(n)} + \phi_1y^{(n-1)} + \cdots + \phi_ny$ with variable coefficients. A representation is given for $n$ linearly independent solutions of $Ly=\lambda r y$ as power…
The supersymmetric standard model with supergravity-inspired soft breaking terms predicts a rich pectrum of sparticles to be discovered at the SSC, LHC and NLC. Because there are more supersymmetric particles than unknown parameters, one…
Two properties of the radiation emitted by a relativistic electron in an external field, in the classical approximation, are presented in details: 1) spectral sum rules and their relationship with the sum rules for oscillator strength in…
A new parameter choice rule for inverse problems is introduced. This parameter choice rule was developed for total variation regularization in electron tomography and might in general be useful for $L^1$ regularization of inverse problems…