The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried soil—pipelines oil or gas transportation. series 2D finite element simulations was employed to sample harmonic response a given geometry section. The inverse Laplace transform results allowed obtaining time domain evolution ...

In this paper, we deduce a fractional-order model based on skin effect for frequency dependent transmission line model. The voltages and currents at any location in transmission line can be calculated by the proposed fractional partial differential equations. Then the fractional ordinary differential equation can obtained from the transmission line fractional partial differential equations thro...

Wetting morphologies on solid substrates, which may be chemically or topographically structured, are studied theoretically by variation of the free energy which contains contributions from the substrate surface, the fluid– fluid interface and the three-phase contact line. The first variation of this free energy leads to two equations—the classical Laplace equation and a generalized contact line...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

Partial-post Laplace barriers have been postulated as a means to allow electrowetting transport and geometrical reshaping of fluids, followed by the preservation of fluid geometry after the electrowetting voltage is removed. Reported here is the first investigation of Laplace barriers with the arrayed electrodes and splitting/merging transport functions for an electrowetting lab-on-a-chip. Lapl...

We propose a standard approach to make inference for spatial generalized linear mixed models using Laplace approximation. Based on analysis of two datasets previous analysed in literature, we compare our approach with different approaches. The first the rhizoctonia root rot dataset is an example of Binomial SGLMM and the second rongelap dataset is an example of Poisson or Negative Binomial SGLM...

‎This paper presents a new mixture model via considering the univariate skew Laplace distribution‎. ‎The new model can handle both heavy tails and skewness and is multimodal‎. ‎Describing some properties of the proposed model‎, ‎we present a feasible EM algorithm for iteratively‎ ‎computing maximum likelihood estimates‎. ‎We also derive the observ...

1-type and biharmonic curves by using laplace operator in lorentzian 3-space arestudied and some theorems and characterizations are given for these curves.