Related papers: An arithmetic study of the formal Laplace transfor…
Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional…
A modified version of this paper is under process and with a new title and abstract. Hence, this version of the article is completely withdrawn.
In this revised version, we add some expository material and references and make some minor corrections.
We survey the classical results of the Dirichlet Approximation Theorem.
This paper has been withdrawn by the author. A much more revised version is available as arXiv:0909.4238.
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.
Summarizing results from Joseph Mecke's last fragmentary manuscripts, the generating function and the Laplace transform for nonnegative random variables are considered. The concept of thickening of a random variable, as an inverse operation…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
This paper has been withdrawn by the author, since now all four parts of the review are available as a single file 0804.1639. I also made some revision of the text in order to avoid misprints and some inaccurate expressions.
This paper has been withdrawn by the author. This paper is now obsolete. For a solution please see: arXiv:/1205.4265.
Motivated by the new Laplace transforms for the Kummer's confluent hypergeometric functions $_1F_1$ obtained recently by Kim et al. [Math $\&$ Comput. Modelling, 55 (2012), pp. 1068--1071], the authors aim is to establish so far unknown…
this paper has been withdrawn. A crucial estimate on a Lipschitz variant of the Kakeya maximal function has an incomplete proof.
This paper describes a general formalism for obtaining localized solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems. This class includes the important cases of Schr\"odinger's…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
This paper has been withdrawn by the author. It will be replaced, substantially modified, by sections of the author's completed PhD thesis.
This is a survey on recent results on the Loewner theory in one and several complex manifolds
This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.