Yielding the correct particle velocity. “ One third “ - P 1 ,“ two thirds” diffusion One of the purposes of this work is to give some physical support to the P 1/3 approximation. Asymptotic P 1 - The Basic Rationale Applying the Laplace transform to the time ...
Laplace transformFunctional equationsPartial differential equationsp-adic Volkenborn integralBy using the generating functions for the Bernstein basis functions, we derive various functional equations, differential equations and second order partial differential equations. By using these equations, we give new...
Laplce transform of a time function, expressing it as a function of the complex frequency variable s , but no mention has been made of the opposite process of deriving the time function corresponding to a given function of s . One of the main difficulties of the Laplace transform[translate...
By applying the Fourier transform and the Laplace transform to the generating functions, we derive series representations for the Bernstein basis functions. We also give the $p$-adic Volkenborn integral representations of the Bernstein basis functions....
We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.MSC: 14F10, 12D...
In this paper we use the one-dimensional axisymmelric Navier-Stokes equation for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one, two,...
In this paper we start with the one-dimensional axisymmetric Navier-Stokes equations for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one,...
Using second order partial differentia equation of the generating functions, we also obtain new derivative formulas for the Bernstein basis functions. By applying the Fourier transform and the Laplace transform to the generating functions, we derive series representations for the Bernstein basis functions...