Sentence examples for complete basis for from inspiring English sources

It has been proved that this is the shortest possible single axiom that will give a complete basis for PIC with these transformation rules.

An even more economical complete basis for PIC contains the same transformation rules but the sole axiom[(p ⊃ q) ⊃ r] ⊃ [(r ⊃ p) ⊃ (s ⊃ p)].

The uniformly spaced infinite length sinc functions form a complete basis for the space of band-limited signals.

Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.

The set of orthonormal column vectors u j (j = 1, ···, NSV) constituting (i.e. ] and forms a complete basis for an arbitrary SV coefficient vector. Hence, it is expanded uniquely as. The scalar coefficients ß j are obtained by. Similarly, a flow coefficient vector m is expanded as, where V i is the orthonormal column vector of dimension NFL constituting V (i.e. and ).

Such wave-based architecture has been facilitated here by using a class of "isodiffracting pulsed beams" (PB) which not only provides simple wave-objects for local interrogation of a particular sub-environment in the global conglomerate, but also provides a complete basis for construction of arbitrary source-excited field in the global environment.

A complete basis of homogeneous solutions for the interior and exterior regions, corresponding to all possible Dirichlet boundary values at the interface, are calculated in a preprocessing step.

Petersson et al. Have developed a related series of methods, referred to as complete basis set (CBS) procedures, for the evaluation of accurate energies of molecular systems.

The results of these calculations are then extrapolated to the complete basis set limit and corrected for some smaller effects such as core-valence and relativistic effects.

The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams.

The reliability of the complete basis set ab initio method for computing those values, as well as using the ionization energies for determining the stabilities of the cations and using the electron affinities for determining the stabilities of carbanions were all discussed.