scholarly journals The Laplace transform on a class of Boehmians

1992 ◽  
Vol 46 (2) ◽  
pp. 347-352 ◽  
Author(s):  
Dennis Nemzer
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Proper Subspace ◽  
Basic Properties ◽  
The Laplace Transform ◽  
Abelian Theorem ◽  
The One

The one-sided Laplace transform is defined on a space of generalised functions called transformable Boehmians. The space of one-sided Laplace transformable distributions is shown to be a proper subspace of transformable Boehmians. Some basic properties of the Laplace transform are investigated. An inversion formula and an Abelian theorem of the final type are obtained.

scholarly journals Flexural dynamic response of monopile foundations under linear wave loads

2020 ◽  
Vol 4 (1) ◽  
pp. 44-50
Author(s):  
Theofanis Giotis ◽  
◽  
Dimitrios Pavlou ◽  
Keyword(s):  
Dynamic Response ◽  
Laplace Transform ◽  
Linear Wave ◽  
Wave Loads ◽  
Cylindrical Structures ◽  
Double Laplace Transform ◽  
Static Solutions ◽  
The Laplace Transform ◽  
Analytical Result ◽  
The One

An analytical solution for the dynamic response of submerged slender circular cylindrical structures subjected to linear wave loads is presented. A double Laplace transform with respect to temporal and spatial variables is applied both to motion equation and boundary conditions. The dynamic deflection of the beam is obtained by inversion of the Laplace transform. The latter with respect to spatial variable is obtained analytically, while the one concerning the temporal variable is numerically calculated using Durbin numerical scheme. Results in the case of a representative example for a monopile foundation subjected to Airy waves are presented and discussed, and the analytical result is compared against numerical dynamic and static solutions.

scholarly journals A Sharp Abelian Theorem for the Laplace Transform

2015 ◽  
pp. 67-92
Author(s):  
Maëva Biret ◽  
Michel Broniatowski ◽  
Zansheng Cao
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform ◽  
Abelian Theorem

Some fluctuation identities for Lévy processes with jumps of the same sign

2004 ◽  
Vol 41 (04) ◽  
pp. 1191-1198 ◽  
Author(s):  
Xiaowen Zhou
Keyword(s):  
Laplace Transform ◽  
Lévy Process ◽  
Joint Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Exit Problem ◽  
The Laplace Transform ◽  
The One

We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

scholarly journals Some results on the complete monotonicity of Mittag-Leffler functions of Le Roy type

2019 ◽  
Vol 22 (5) ◽  
pp. 1284-1306 ◽  
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela ◽  
Roberto Garrappa
Keyword(s):  
Laplace Transform ◽  
Complete Monotonicity ◽  
Wright Function ◽  
Completely Monotonic ◽  
Completely Monotone ◽  
The Laplace Transform ◽  
Alpha Beta ◽  
The One ◽  
Open Question

Abstract The paper [5] by R. Garrappa, S. Rogosin, and F. Mainardi, entitled “On a generalized three-parameter Wright function of the Le Roy type” and published in Fract. Calc. Appl. Anal. 20 (2017), 1196–1215, ends up leaving the open question concerning the range of the parameters α, β and γ for which Mittag-Leffler functions of Le Roy type $\begin{array}{} F_{\alpha, \beta}^{(\gamma)} \end{array}$ are completely monotonic. Inspired by the 1948 seminal H. Pollard’s paper which provides the proof of the complete monotonicity of the one-parameter Mittag-Leffler function, the Pollard approach is used to find the Laplace transform representation of $\begin{array}{} F_{\alpha, \beta}^{(\gamma)} \end{array}$ for integer γ = n and rational 0 < α ≤ 1/n. In this way it is possible to show that the Mittag-Leffler functions of Le Roy type are completely monotone for α = 1/n and β ≥ (n + 1)/(2n) as well as for rational 0 < α ≤ 1/2, β = 1 and n = 2. For further integer values of n the complete monotonicity is tested numerically for rational 0 < α < 1/n and various choices of β. The obtained results suggest that for the complete monotonicity the condition β ≥ (n + 1)/(2n) holds for any value of n.

Some fluctuation identities for Lévy processes with jumps of the same sign

2004 ◽  
Vol 41 (4) ◽  
pp. 1191-1198 ◽  
Author(s):  
Xiaowen Zhou
Keyword(s):  
Laplace Transform ◽  
Lévy Process ◽  
Joint Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Exit Problem ◽  
The Laplace Transform ◽  
The One

We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

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