Sentence examples for Following basis from inspiring English sources

We denote the power spectral density (PSD) of the unknown spectrum of the transmitted signal s by Φ s (f), which can be well approximated by the following basis expansion model [32] with N b sufficiently large: Phi_{s}(f)=sumlimits_{m=1}^{N_{b}}b_{m}(f){w}_{0m}=mathbf{b}_{0}^{T}(f mathbf{w}_{0} (91).

Then C 0 8 ( X 1 ) and C 1 8 ( X 1 ) are free abelian groups induced by the following basis, respectively: Hence we get the following short sequence: We may point out: Thus Z 1 8 ( X 1 ) = { 0 }.

Equation 3 can be seen as a decomposition of x t) in the vector space spanned by the following basis set: B = { 1 } ∪ { cos ω k t, k = 1, 2, … } ∪ { sin ω k t, k = 1, 2, … }. (4).

(3) The topology induced by the basis (mathcal{W}(p)) of neighborhoods of zero coincides with the topology induced by the following basis of neighborhoods of zero: mathcal{N}_{0}= bigl{ U varepsilon, lambda);lambdain 0, 1] bigr}, where U varepsilon, lambda)= bigl{ pinmathcal{V};upsilon_{p}( varepsilon)>1-lambda, lambdain 0, 1], varepsilon>0 bigr}.

Altogether, the socio-regulatory episodes coded represent a large proportion of the text transcribed: they cover 75.53% in activity 1 and 67.87% in activity 2. Each co-regulatory episode was also coded as either high- or low-content episode on the following basis.

It is obvious that (U_{h}subset U) and the test space (tilde{U}_{h}) is spanned by the following basis functions: phi_{z} x,y)=left { textstylebegin{array}{l@{quad}l} 1,& (x,y in V_{z}, 0, &mbox{elsewhere}, end{array}displaystyle right.

It can be recursively obtained as follows: Basis step: α 1 ( k ) = p H k p y 1 | H k, k = 1, 2, …, K. (9).

The dual matroid M∗ of M is defined as follows: the basis of M∗ are the complements of the basis of M.

This article is organized as follows: 'Theoretical basis of semitone mapping' section describes the theoretical basis of semitone mapping and explains why Smt mapping was chosen.

Whatever happens next, Donald Tusk's proposals are the urtext of the grand opera to follow, the basis (he and David Cameron hope) for agreement among the 28 member states at the EU summit on 18 February, and a referendum on 23 June, mandating the UK's continued membership.

Then we consider the random dynamical system φ as follows on the basis of the following uniform a priori estimates of the solution for the system (3.2 - 3.4 3.2 - 3.4