Sentence examples for formulas concerning from inspiring English sources

Three biorthogonality formulas concerning the wave wrap functions are obtained.

This means that the difference between indiscernibility and I(A,x,y) is minimized at least to the extent that, for a sufficiently rich language such as L, the valid formulas concerning indiscernibility (i.e., the formulas true in every model of what is termed below 'the pure L-theory with identity') coincide with the valid formulas concerning I(A,x,y).

Their characteristics are investigated by means of harmonic analysis method, matrix theory and operator theory, and three orthogonality formulas concerning the wavelet packets are presented.

In previous works by Emami-Razavi [5, 6], it has been demonstrated that, by employing a reformulated model in QFT proposed by Darewych [7, 8], formulas concerning relativistic n-body wave equations for scalar particles and/or antiparticles can be obtained (see also [9]).

Nothing is more American, whether catastrophic or amiable, than that Emersonian formula concerning power: "it resides in the moment of transition from a past to a new state, in the shooting of a gulf, in the darting to an aim".

Moreover, an overview on Fermat polynomials and some new formulae concerning these polynomials are presented.

Before stating the quadratic recurrence formula for the Apostol-Bernoulli polynomials, we begin with a summation formula concerning the quadratic recurrence of the Apostol-Bernoulli polynomials.

Thus, we obtain the following formula concerning the optimal emission: F ' e * = n α ∂ ψ ∂ c 1 d | ϵ j l * = 1 n.

As in the proof of Theorem 3.4, we need the following summation formula concerning the quadratic recurrence of mixed Apostol-Bernoulli and Apostol-Euler polynomials.

As in the proof of Theorem 2.3, we need the following formula concerning the mixed Apostol-Bernoulli and Apostol-Euler polynomials.

In order to give the quadratic recurrence formula for the Apostol-Euler polynomials, it is routine to present a summation formula concerning the quadratic recurrence of the Apostol-Euler polynomials.