The roller bearing characteristic frequencies contain very little energy, and are usually overwhelmed by noise and higher levels of structural vibrations. Therefore, envelope spectrum analysis is widely used to detection bearing localized fault. In order to overcome the shortcomings in the traditional envelope analysis in which manually specifying a resonant frequency band is required, a new ap...

The purpose of this document is to summarize main points of the paper, “Numerical Inversion of Laplace Transforms of Probability Distributions”, and provide R code for the Euler method that is described in the paper. The code is used to invert the Laplace transform of some popular functions. Context Laplace transform is a useful mathematical tool that one must be familiar with, while doing appl...

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.

This note presents the explicit form of the Laplace transform of the state transition matrix in the case of a system matrix being a companion matrix. Starting from this special case, we show how to compute the Laplace transform of the state transition matrix for any system matrix.1

This paper gives a generalization of the Pseudo-Laplace transform. In the special cases of semirings, the pseudo-exchange formula is proved. Also, for these semirings the forms of the Pseudo-Laplace transform and inverse operator are given. The results can be applied in dynamical programming for finding the maximum and minimum of the utility functions. AMS Mathematics Subject Classification (19...

We present a form of the discrete dipole approximation for electromagnetic scattering computations in time domain. We show that the introduction of complex frequencies, through the Laplace transform, significantly improves the computation time. We also show that the Laplace transform and its inverse can be combined to extract the field inside a scatterer at a real resonance frequency.

This paper is on the solutions of fuzzy initial value problems for fourth-order fuzzy differential equations with positive and negative fuzzy coefficients by fuzzy Laplace transform. Examples are solved. Conclusions are given.