Sentence examples for fundamental operators from inspiring English sources
The fundamental operators play the main role in this model.
This paper shows the explicit fundamental operators for the LW approach when static analysis is investigated.
It consists of a convex combination of fundamental operators from mathematical morphology (MM) on complete lattices theory (CLT).
Such fundamental operators, expressed in the orthogonal curvilinear co-ordinate system, are obtained for the first time by the authors.
Problem specifics are confined to a limited part of the method and are addressed by means of assignment, sequencing, and route-evaluation components, which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities.
The main aim of this work is to determine the explicit fundamental operators that can be used not only for the Equivalent Single Layer (ESL) approach, but also for the Layer Wise (LW) approach.
In harmonic analysis, a fundamental operator is the Hardy-Littlewood maximal operator.
The most fundamental averaging operator is Hardy operator defined by mathcal{H}f(x):= frac{1}{x} int_{0}^{x}f(t),dt, where the function f is a nonnegative integrable function on (mathbb{R}^) and (x>0).
The Hamiltonian (2) is a quadratic model, hence, it can be diagonalized as H = ∑ q = 0 N v ω ( q ) ψ q † ψ q, (7 by means of a Bogoliubov transformation of the fundamental particle operators, a i †, a j.
The most fundamental averaging operator is the Hardy operator defined by H ( f ) ( x ) = 1 x ∫ 0 x f ( t ) d t, where the function f is a nonnegative integrable on R + = ( 0, ∞ ) and x > 0. A classical inequality, due to Hardy [1], states that ∥ H ( f ) ∥ L p ≤ p p − 1 ∥ f ∥ L p. holds for 1 < p < ∞, and the constant p p − 1 is best possible.
Finally, derive an abstract third Green identity invoking the resolvent (or fundamental solution operator (mathcal {G})) of A, the operator (T= T_+ oplus T_-), and abstract single and double layer operators constructed from (mathcal {G}).
