Sentence examples for by using the generating from inspiring English sources
By using the generating functions, we obtain functional equations related to a generalized partial Hecke operator and Euler-type polynomials and numbers.
The purpose of this paper is to present a systemic study of some families of higher-order generalized -Genocchi numbers and polynomials attached to by using the generating function of those numbers and polynomials.
By using the generating functions of the Bernoulli, Euler and Genocchi polynomials, we construct unification of the L-functions.
In this paper, by using the generating function and nonlinear differential equations, we deduce the explicit expression of degenerate Daehee numbers as the inversion formula of [1].
Despite their differences, generalized linear systems have two fundamental operations: vector addition ⊕ and scalar multiplication ⊗, which are defined by using the generating function as follows: xoplus y=phi^{-1}left[phi(x)+phi y)right] (12).
By using the generating function of P n, N ( M ) ( x ), we get ∑ n = 0 ∞ ∑ k = 0 a − 1 ( ∏ j = 1 M e 2 π i k N j ) P n, N ( M ) ( x + k a ) t n n !
The robustness evaluation process enables an updating of the timetable by using the generated dispatching schedules.
Optimal search for the best match is then performed by using the generated FVs inside an adaptive search window.
The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method.
By using the generated machining know-how database, the machining operation planning will be automated by its counterpart system the machining operation planner.
