Deconvolution procedure

A deconvolution procedure to separate carbonyl spectra of species A and species B has been performed, and It has been shown that species B Is associated with rotational wings above and below 2140 cm l. These wings Indicate that species B undergoes llbratlonal and rotational motions It Is undoubtedly very much like C0(1), as shown by the comparison made In Fig. 12. Here the spectrum of a freely rotating C0(g) molecule at 80K Is compared to C0(i), also at 80K. 

Experimentally, the EMD function p(q) can be reconstructed from a set of Compton profiles J qz ) s, and B( r) from the EMD. However, A Air) is not a direct experimental product. By combining the experimental B(r) with theoretical B aik (r), we need to derive a semiexperimental AB(r). Since the atomic image is very weak, many problems must be cleared in experimental resolution, in reconstruction (for example, selection of a set of directions and range of qzs), in various deconvolution procedures and so on. First of all, high resolution experiments are desirable. 

For solution-phase libraries that are composed of mixtures of compounds, the difficulty of analysis escalates with increasing numbers of compounds. Typically, large mixtures of compounds are not analyzed before screening, whereas small ones may be analyzed for reaction completeness using mass spectrometry, HPLC, NMR, or combinations thereof. The identification and analysis of active compounds from these mixtures is painstakingly tedious, and often complete characterization is possible only after deconvolution procedures and resynthesis of the active compound. For solid-phase libraries, the methods currendy developed are discussed below. 

To derive S(t), a deconvolution procedure is required. The transducer function is easily obtained by running an experiment where the photoactive species decays with x 1/v, which is the case of the photoacoustic calibrants mentioned. Recall... 

We will not concern ourselves here with problems associated with line broadening, overlapping peaks, and background subtraction. There are, however, examples discussed later where both deconvolution and curve fitting procedures are shown to be essential in unraveling the contributions of differently bonded species of the same molecule to the total photoelectron yield. Carley and Joyner (14) have discussed recently deconvolution procedures for photoelectron spectra. 

Deconvolution Analysis of DSC. Data analysis was carried out using the DECONV section of the DA-2 software package. This software, which is based on the deconvolution procedure of Freire and Biltonen (4), allows deconvolution of differential heat-capacity peaks either as the result of simple addition of multiple independent transitions or as the result of more complex mathematical processes representing the combination of transitions that interact in such a way that an obligatory reaction sequence is imposed (sequential transitions). 

Calorimetric Deconvolution Models and the Reversibility or Irreversibility of Overall Denaturation Processes. The deconvolution procedures used to analyze the thermograms presented in this study are based on equilibrium models, even though the overall denaturation process seen over a cycle of heating to a temperature above T and then cooling to below is, depending on the pH, either completely or partially irreversible. There is ample precedent in the literature for the application of equilibrium models in such cases, however. Convincing evidence has been presented... 

Curve fitting and peak deconvolution procedures with non-linear regression methods have been applied several times with varying success. The non-linear regres-... 

For this work, the spectrometer function s(x) was determined by the method outlined in Section II.G.3 of Chapter 2. In digitizing the data, a sample density was chosen to accommodate about 70 samples taken across the full width at half maximum of s(x). A 25-point cubic polynomial smoothing filter was used in the deconvolution procedure to control high-frequency noise. Instead of the convolution in Eq. (13), the point-successive modification described in Section III.C.2 of Chapter 3 was employed. In Eq. (24) of Chapter 3, we replaced k with the expression... 

To calculate the pore size distributions we have constructed two kernels of theoretical isotherms in cylindrical channels corresponding to the metastable adsorption and equilibrium desorption branches. These kernels were employed for calculating pore size distributions from experimental isotherms following the deconvolution procedure described elsewhere [21, 24] In Figs 6-7 we present the pore size distributions of the enlarged MCM-41 samples [2-4] calculated from the experimental desorption branches by means of the desorption kernel and the pore size distributions calculated from the experimental adsorption branches by means of the adsorption kernel The pore size distributions obtained from the desorption and adsorption branches practically coincide, which confirms that the NLDFT quantitatively describes both branches on the adsorption-desorption isotherm. 

Methods for analysing the response of complex multicomponent-multifunctional systems will be needed. Global responses may be submitted to deconvolution procedures and multicomponent analysis [8.298], making use for instance of pattern recognition [8.238, 8.299], neural network [8.238, 8.300] and fuzzy logic [8.301] approaches. 

Figure 2 shows the results of the non-linear fitting procedure on a part of the equator, first and second layer lines of TMV. The diffraction pattern used was taken by Dr. S. Warren and Dr. G. Stubbs at the Max-Plank-Institut in Heidelberg, Germany. This pattern was taken on a Guinier camera and the arcsdue to disorientation are not circular. The natural coordinate system (3)of the camera (rather than polar coordi-nates)was used in the deconvolution procedure. The standard... 

Results. We have made a detailed study of the effect of using both the Jones and the Stokes corrections on crystallite size measurements obtained from the most crystalline samples of cellulose I and II, Ramie and Fortisan (18). Our conclusion was that the Jones corrections were always within 5% of the Stokes corrections for both half-width and integral breadth. Current practise is always to use a Stokes deconvolution procedure for the correction of all resolved peak profiles, evaluating an... 

In order to be effective, deconvolution procedures require that both the synthesis and assay of the library be rapid. The procedure is complicated when there is more than one active component in the library. In this case it is necessary to prepare and test all the possible compounds indicated by deconvolution in order to identify the most active compound in the library. 

Recently, attempts have been made to derive CD spectra of various p turns using deconvolution procedures (see below). Employing an approach termed convex constraint analysis, Perczel, Fasman, and others [58-61] have derived CD spectra for both types I and H turns. Three basis spectra were extracted for a data base of fourteen peptides which displayed either types I or II p turns. One basis spectrum for type I turns resembled a class C spectrum and the other a variation of a class B. The type II turn is said to display a classic class B spectrum [59-61],... 

In the last case, a special deconvolution procedure has to be followed, in order to identify the compound responsible for the biological activity, or other useful property. 

Since the development of the Fourier-transform deconvolution procedure for OHD-RIKES data by McMorrow and Lotshaw (22), the intermolecular dynamics of a wide range of liquids have been studied with this technique (26,52,65-85). Figure 13 illustrates representative OKE reduced spectral densities we have recorded in symmetric-top liquids, including acetonitrile, benzene, benzene-d6, carbon disulfide, chloroform, hexafluorobenzene, mesitylene, and 1,3,5-trifluorobenzene. Although there are conspicuous differences among these spectra, they are all broad and relatively featureless. Indeed, with rare exceptions the reduced spectral densities of simple liquids are devoid of sharp features, which makes it difficult to find an unambiguous interpretation of these spectra. 

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