Sentence examples for in a given basis from inspiring English sources

A brief review of major approaches that are suggested for the third step was given in Section 2. A signal x ∈ R n may be sparse in a given basis but not sparse in a different basis.

The most important advantage of having (mathbf {D}) explicitly is that there is no need to go from one basis to another (normally monomial) to differentiate a polynomial in a given basis.

When the Hilbert space is of infinite dimension, state vectors can be represented by functions, the so-called 'wave functions.' In any given basis, there is a unique wave function that corresponds to the state vector in that basis.

It is important to mention that the performance of these methods, however, is strongly dependent on the key assumption that the source signals have a sparse representation in some given basis.

A shareholder who guarantees the debt of an S corporation will only be given basis in that debt when the shareholder actually pays the guarantee.

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented by random coefficients in a given deterministic basis.

In this case, it might be beneficial to adapt our approach such that (i) the modes for the Green function decomposition are expanded in a given nonideal basis and (ii) the compressed sensing algorithm seeks for a minimum number of decomposition modes.

Nevertheless, the 2.5% higher accuracy obtained by PreTect HPV-Proofer and the favourable effects of using five types instead of nine types regarding cost and the follow-up in a low-resource setting give basis to prefer PreTect HPV-Proofer over a nine mRNA-type assay.

Currently, damage models are either probabilistic (define the occurrence, growth or death of pits as probability functions) or empirical (define a single relationship between mass loss in a given state on the basis of measured data) in nature, but new experimental and modelling research is being undertaken to develop first-principle models of corrosion under established oxide films.

We conclude that it remains impossible to predict the number of QTLs in a given context on the basis of trait variability and prior knowledge on genetic parameters.

In order to assess the radon risk in buildings in a given area on the basis of soil radon or of radon-related variables, it is necessary to set up indexes accounting for the effective radioactivity levels as well as for the physical properties of solids through which radon transfer occurs.