Sentence examples for by using functional integral from inspiring English sources
By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions.
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs).
It is remarkable that many researchers pay attention to the study of the existence and attractiveness of solutions for fractional integral equations by using functional analysis methods such as the contraction principle, the Schauder fixed point theorem and a Darboux-type fixed point theorem involving a measure of noncompactness (see [25 33] and references therein).
By using an integral equation and functional equations of the generating functions and their partial differential equations (PDEs), we give a recurrence relation for the Apostol-Daehee polynomials.
A backstepping stable controller is designed by using the Integral Barrier Lyapunov Functionals (iBLF).
Several sufficient general conditions are derived for the robust passivity of delayed BAM NNs with reaction-diffusion terms by using Lyapunov functional method and Poincaré integral inequality, which are very convenient to verify.
In the present paper, we further extend Rice's integral by using Cauchy's integral formula.
The problem is solved by using the integral transform, singular integral equation methods and the theory of residues.
