Sentence examples for the classical approximation from inspiring English sources

This provides a 'Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler.

Numerical results for 1st-order terms indicate a good agreement of the classical approximation (with properly formulated Navier Stokes and Fick's equations) with the Maxwell Müller system, in the studied cases.

Moreover, the classical approximation theorem [11] tells lim N → ∞ ∥ f N − f ∥ p = 0. for p > 1.

In molecule 3, the allyl head groups are symmetric, and the TSM error mainly arises from the classical approximation of the intercellular interactions.

By the best-known classical approximation, Eq. (1) can be simplified as Blake et al. (2011) suggested { Pr }(f) = prodlimits_{s = 1}^{n} {Pr } left( {f_{text{s}} |f_{{eta_{text{s}} }} } right) (2 where (f_{{eta_{s} }} = { f_{r} left| {r in eta_{s} } right.}) stands for the set of state values at the cells neighboring s.

This can be explained by the fact that in the quasi-classical approximation the electron staying on the quinone corresponds to a non-equilibrium state of the system: in this case, electromagnetic wave in the result of non-resonant interaction can excite oscillations in the electron subsystem of the particles of protein molecule of RC, which is partially ordered.

In this short paper, we give a generalization of the classical Korovkin approximation theorem (Korovkin in Linear Operators and Approximation Theory, 1960), Volkov-type theorems (Volkov in Dokl. Akad. Nauk SSSR 115:19579, 1957), and a recent result of (Taşdelen and Erençin in J. Math. Anal. Appl. 331(1):7200735, 2007).

In this paper, the interference models based on classical approximation or on other distributions are assumed to be independent from the useful term.

It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.

The one approximation especially suited for studies of weakly interacting cold atomic gases is the classical field approximation, where we replace the quantum field operator of the effective field theory ψ ˆ (z ) by a classical field ψ (z )   [8].

This is the parabolic analogue of the classical harmonic approximation lemma of De Giorgi [11, 12] and allows to approximate functions with solutions to parabolic systems with constant coefficients in a similar way as the classical harmonic approximation lemma does with harmonic functions.