Sentence examples for by the spectral data from inspiring English sources

Hence, the problem (1 - 7) is uniquely determined by the spectral data ({ lambda_{n},mu_{n} } ).

The success of the hydrazinolysis reaction was confirmed by the spectral data analysis of the diacid hydrazides 4a d.

Finally, we give an algorithm of the construction of the function Ω ( x ) by the spectral data { λ n, α n } ( n ∈ Z ).

Yurko has studied inverse problems for the Sturm-Liouville operator with the potential from (L 0, infty)) by the Weyl function and, in the self-adjoint case, by the spectral data.

The algorithm of the construction of the function Ω ( x ) by the spectral data { λ n, α n } ( n ∈ Z ) follows from the proof of the theorem: (1) By the given numbers { λ n, α n } ( n ∈ Z ) the functions F 0 ( x, t ) and F ( x, t ) are constructed, respectively, by (14) and (15).

We call the collection (( { V lambda)}_{lambda> 0}, { lambda_{k}, alpha_{k} } _{k = 1}^{P} )) the spectral data of L. Similarly to the scalar case (see [4]), the Weyl matrix can be uniquely determined by the spectral data M lambda) = int_{0}^{infty} frac{V(mu)}{lambda- mu},dmu+ sum_{k = 1}^{P} frac{alpha_{k}}{lambda- lambda_{k}},quad lambdainPibackslash Lambda'.

The subsequent statistical manipulations were performed by transferring the spectral data to Microsoft Excel 2010 program and SPSS.

In this section, we extend Theorem 1.3 by that the spectral data ({ lambda _{m},alpha_{m}}_{minmathbb{N}_{0}}) can be selected in terms of different Sturm-Liouville operators (L q,h_{0},h_{1})=:L(h_{0})) with (h_{0}) being different numbers in the boundary condition (1.2).

RGB (red-green-blue) color fluorescence images were synthesized from the spectral cube by mapping the spectral data into those color channels.

By analysing the spectral data set using the ANN, each spectrum was classified as being cancerous, healthy or un-identifiable.

The spectra were normalized by scaling the spectral data of all samples to achieve an equal total area for each spectrum.