The main objective of this work is to introduce a novel generalization double transformations called the triple Laplace–ARA–Sumudu transform (TLARAST). This hybrid transformation extends concepts Laplace–Sumudu, Laplace–ARA and ARA–Sumudu transforms into transform. article provides definition TLARAST investigates its fundamental properties, including existence, inverses related theorems. Furthe...

(0.1) F∞(u, U) := ‖|Du|‖L∞(U) among all such functions. Here |Du| is the Euclidean length of the gradient Du of u. We will also be interested in the “Lipschitz constant” functional as well. If K is any subset of IR and u : K → IR, its least Lipschitz constant is denoted by (0.2) Lip(u,K) := inf {L ∈ IR : |u(x)− u(y)| ≤ L|x− y| ∀ x, y ∈ K} . Of course, inf ∅ = +∞. Likewise, if any definition suc...

In this article, we have effectively used the Numerical Inversion of Laplace transform to study the time-dependent thin film flow of a second grade fluid flowing down an inclined plane through a porous medium. The solution to the governing equation is obtained by using the standard Laplace transform. However, to transform the obtained solutions from Laplace space back to the original space, we ...

STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces L i p ( a , Lp) and Zyg(a, L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, L M ) and Zygmund-Orlicz spaces Zyg (cp, L M ) and to the general function cp E P instead of the power function cp(t) = t a . Such results describe the behavior of the Lapl...

We study the enclosure method for the p-Calderón problem, which is a nonlinear generalization of the inverse conductivity problem due to Calderón that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, wh...

Abstract. In this paper, we consider the harmonic extension problem, which is widely used in many applications of machine learning. We formulate the harmonic extension as solving a LaplaceBeltrami equation with Dirichlet boundary condition. We use the point integral method (PIM) proposed in [14, 19, 13] to solve the Laplace-Beltrami equation. The basic idea of the PIM method is to approximate t...

An infinite dam with compound Poisson inputs and a statedependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.

We study N=2(4) superstring backgrounds which are four-dimensional nonKählerian with non-trivial dilaton and torsion fields. In particular we consider the case that the backgrounds possess at least one U(1) isometry and are characterized by the continual Toda equation and the Laplace equation. We obtain a string background associated with a non-trivial solution of the continual Toda equation, w...

Using a help system to make easier the CAS-user connection, we propose the problem of solving the equation of diffusion with variable coefficients. We transform the problem at the Laplace domain and we use the Bromwich integral and the residue theorem in order to do the inverse Laplace transform and then explicit solution is obtained.