Search results for " math"

Excitation energies and photoabsorption oscillator strengths of the Rydberg series in CF3Cl. A linear response and quantum defect study.

2007

Vertical excitation energies of the CF(3)Cl molecule have been obtained from a response function approach with a CC reference function to determine absolute photoabsorption oscillator strengths in the molecular-adapted quantum defect orbital formalism (MQDO). The present work covers more highly excited Rydberg states than have been experimentally reported. Assessing of the reliability of the present calculations is provided through a comparative analysis between the results of the molecule and the Cl atom. This can be used to allow for predictions of the same type of properties in other analogous systems.

Non-Stationary Probabilistic Response of Linear Systems Under Non-Gaussian Input

1991

The probabilistic characterization of the response of linear systems subjected to non-normal input requires the evaluation of higher order moments than two. In order to obtain the equations governing these moments, in this paper the extension of the Ito’s differential rule for linear systems excited by non-normal delta correlated processes is presented. As an application the case of the delta correlated compound Poisson input process is treated.

Champs de vecteurs analytiques commutants, en dimension 3 ou 4: existence de zeros communs

1992

One proves the existence of a common zero for any two ℝ-analytic commuting vector fields on a 4-dimensional manifold with not zero Euler characteristic. A local version of this result remains true on 3-manifolds.

A Stieltjes Approach to Static Hedges

2014

Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be exte…

Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that

2016

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.

On Taylor coefficients of entire functions integrable against exponential weights

2001

Jacobi Fields, Conjugate Points

2001

Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.

Representation of Stationary Multivariate Gaussian Processes Fractional Differential Approach

2011

In this paper, the fractional spectral moments method (H-FSM) is used to generate stationary Gaussian multivariate processes with assigned power spectral density matrix. To this aim, firstly the N-variate process is expressed as sum of N fully coherent normal random vectors, and then, the representation in terms of HFSM is used.

Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media

1981

SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.

THE ARITHMETIC BOHR RADIUS

2007

We study the arithmetic Bohr radius of Reinhardt domains in ℂ n which was successfully used in our study of monomial expansions for holomorphic functions in infinite dimensions. We show that this new Bohr radius is different from the radii invented by Boas and Khavinson and Aizenberg. It gives an explicit formula for the n-dimensional hypercone (which means n-dimensional variants of classical results of Bohr and Bombieri), and moreover asymptotically corrects upper and lower estimates for various types of convex and non-convex Reinhardt domains.