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).
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).
(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.
After I reached twelve points, I was offered admission to the New Jersey Driver Improvement Program, on the following voluntary basis: enroll or lose your license.
One of the main safety goals is to achieve indefinite cooling following design basis accidents (DBAs) using atmosphere air as ultimate heat sink.
Simulated datasets were tested for combinations of the following parameters: basis function, global scaling, low-pass filter, high-pass filter and autoregressive modeling of serial autocorrelation.
The coating paste was formulated on the following weight basis: polymer-encapsulated PGAP 22%%, glycerol 1 %, DM-5268 3%%, urea 0.3 %, FWO-B 4 %, DM-5218 23.7 %, and distilled water 50%%.
We assume (16) Therefore, we get the following fuzzy basis functions (17) The T S fuzzy model in (15) is to interpolate L linear systems to approximate the non-linear system in (4) via the fuzzy basis functions.
