Exact(1)
Ashford gets a lot of respect for his abilities as a designer, but he has so far not been able to transform respect into solid financial backing.
Similar(59)
The solutions are found using the Laplace transform with respect to time, the Hankel transform with respect to the radial coordinate, the finite Fourier transform with respect to the angular coordinate, and the exponential Fourier transform with respect to the spatial coordinate.
Operating a Fourier transform with respect to space and a Laplace transform with respect to time on Eqs.
Governing equations are solved by applying the methods of the Laplace transform with respect to time and the Fourier transform with respect to a longitudinal space variable.
The method first performs Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate to convert the set of partial differential equations into a system of algebraic equations.
The Laplace transform with respect to time t and the finite sin-Fourier transform with respect to the spatial coordinate x have been used.
end{aligned} (32) As above, the new function u is introduced according to (12), and the Laplace transform with respect to time t and the finite sin-Fourier transform with respect to the spatial coordinate x give the solution in the transform domain: widetilde{u}^ (xi_{k},s ) =ac_{0} xi_{k} frac{1}{s (s^{alpha} + axi_{k}^{2} + frac {v^{2}}{4a} )}.
A Laplace transform with respect to the time variable and a generalized integral transform technique with respect to the spatial variable are first performed to convert the transient governing partial differential equations into an algebraic equation.
The model equations are analytically solved by using the Laplace transform with respect to time.
Let F ′ denote the Fourier transform with respect to x ′ = ( x 1, …, x n − 1 ).
After taking the inverse Fourier transform with respect to (see (8)), we obtain.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com