# differential operator

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## differential operator

[‚dif·ə′ren·chəl ′äp·ə‚rād·ər]
(mathematics)
An operator on a space of functions which maps a function ƒ into a linear combination of higher-order derivatives of ƒ.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The matrix a above is AH domain differential operator , which can be considered as the similar time-domain operator d/dt or frequency-domain operator j[omega] and respective identity matrix I is for 1.
Moreover, the second-order differential equation also can be considered as a product of two first-order differential operators and the spinor wave function related to the differential equation that is expressed in terms of Rodrigues representations related to the orthogonal polynomials.
where [alpha],[beta], [gamma] [member of] (0,1], [R.sup.i], [N.sup.i], i = 1,2,3, denote linear differential operators and nonlinear differential operators, respectively, and [g.sup.i] (x, t) are the source terms.
Let [u.sub.n](x) = [w.sub.n]([x.sub.1])[u.sub.1]([x.sub.2]), where [u.sub.1] is the first eigenfunction of the one-dimensional second-order differential operator on [L.sup.2]((0, a)) which is identically equal to 1.
We now try to decompose the differential operator [L.sup.2.sub.[alpha]] into differential operators [L.sub.A(r)] and [L.sub.B(r)] of first order such that
In this section, we give some theorems that estimate resolvent of an differential operator on a Hilbert space.
Moreover, let we choose [mathematical expression not reproducible] and A to be differential operator with generalized Wentzell-Robin boundary condition defined by
Using convolution, we here define the differential operator [D.sup.(n]) analogue of the operator defined in (8), n [member of] [N.sub.0], by
The external differential operator in (5) is [[partial derivative].sub.i].
This is an evolutionary algorithm specializing in the mutation process through a differential operator. After performing the mutation, a cross or recombination process also takes place.
We considered the general form of inhomogeneous nonlinear partial differential equations with initial conditions as given below Equations the remaining linear operator represents a general nonlinear differential operator and was source term.

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