相关论文: Laplace transformation updated
We consider the conventional Laplace transform of $f(x)$, denoted by $\mathcal{L}[f(x); p]~\equiv~F(p)=\int_{0}^{\infty} e^{-p x} f(x) dx$ with ${\rm \mathfrak{Re}}(p) > 0$. For $0 < \alpha < 1$ we furnish the closed form expressions for…
We present a method derived from Laplace transform theory that enables the evaluation of fractional integrals. This method is adapted and extended in a variety of ways to demonstrate its utility in deriving alternative representations for…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.
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…
In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.
It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.
The Laplace transform is a valuable tool in physics, particularly in solving differential equations with initial or boundary conditions. A 2014 study by Tsaur and Wang (2014 \emph{Eur.~J.~Phys.} \textbf{35} 015006) introduced a…
Recently, it was found that a new set of simple techniques allow one to conveniently express ordinary integrals through differentiation. These techniques add to the general toolbox for integration and integral transforms such as the Fourier…
Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way…
In this paper, we solve Laplace equation analytically by using differential transform method. For this purpose, we consider four models with two Dirichlet and two Neumann boundary conditions and obtain the corresponding exact solutions. The…
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…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
It is shown that theories already presented as rigorous mathematical formalizations of widespread manipulations of Dirac's delta function are all unsatisfactory, and a new alternative is proposed.
Sources of uncertainties in perturbative calculations, tadpole improvement and its role in lattice perturbation theory, and six recent calculations are discussed.
Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is…
In this paper we comment the Post inversion formula for Laplace transform, and its possible application to the branch of Analytic Number theory (Arithmetical functions, RH and PNT), involving a condition in the form of iterated limit to…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
Inverse Laplace transform on the lattice spacing is introduced as a computational framework of the extrapolation of the strong coupling expansion to the scaling region. We apply the transform to the two-dimensional non-linear O(N) model at…
We introduce a transformation of linear Pfaffian systems, which we call the middle Laplace transform, as a formulation of the Laplace transform from the perspective of Katz theory. While the definition of the middle Laplace transform is…