Regularization procedure

With a predictive maintenance strategy, long-term plans typically involve as few as only two regular procedures ... 

Titterington, D.M., 1985, General structure of regularization procedures in image reconstruction, Astron. Astrophys. 144, 381... 

Since the NJL model is not renormalizable, we need some regularization procedure to get a meaningful finite value for the vacuum contribution. Consider the sum of the negative energy over the Dirac sea,... 

The reaction rate in differential theories of bimolecular reactions is always the product of the reactant concentrations and the rate constant, does not matter whether the latter is truly the constant or the time-dependent quantity. In integral theories there are no such constants at all they give way to kernels (memory functions) of integral equations. However, there is a regular procedure that allows reduction the integral equations to differential equations under specificconditions [34,127]. This reduction can be carried out in full measure or partially, but the price for it should be well recognized. 

Following the regular procedure described in Section IV.A and employed in Section VI.B, the IET equations (3.777) were transformed to their UT analogs, valid when / = 0 [275] ... 

Analysis of the TEB decay curves was carried out using both the cumulants and the regularization procedures. From the cumulants results, we plotted against C and obtained D = 7.4 sec , as shown in figure 5. 

O Leary, D.P. and Simmons, J.A., A bidiagonalization — regularization procedure for large scale discretizations of ill-posed problems, SIAM J. Sci. Stat. Comput., 2, 474-489, 1981. 

In this section, we consider briefly the accuracy and convergence aspects of the multi-mode models derived by the L-S method. We also illustrate the regularization procedure used for the local equation(s) to increase the region of convergence of the multi-mode models. 

Here, we use the example of the Taylor dispersion problem discussed Section III to illustrate the regularization procedure. For simplicity, we illustrate this only for the case of PeT —> oo (negligible axial diffusion). In this case, the global equation is given by... 

And yet, on looking into the history of science, one is overwhelmed by evidences that all too often there is no regular procedure, no logical system of discovery, no simple, continuous development. The process of discovery has been as varied as the temperament of the scientist. 

Although it is fairly easy to draw Lewis structures for most compounds formed by nonmetals, it is a good idea to follow a regular procedure. The following steps should be used to determine Lewis structures. 

It is apparent that such dependence is possible at varying surface coverage of the heterogeneous surface, since reactivity of the sites reduces as 0 increases. An approach for calculation of the surface distribution functions on In A and on values from chemisorption kinetic isotherms measured at different temperatures has been developed in [70,130,131]. Distribution functions on Ink at different T can be found, for example, using the regularization procedure or expressions from Table 4. If In A and E values are connected by Eq. (60), the expression connecting cumulant of Ink distribution with the sum of cumulants of In A and E distributions is changed for cumulants of the second order as [132] ... 

The regularization procedure takes a different form for each method of statistical learning. When training hidden Markov models, the derived probabilities do not only take the observed sequences into account but also use so-called prior distributions that formulate some hypothesis on the occurrence of output characters in the case that we have no additional information (such as the observed sequences). An expected background distribution of amino acids or nucleotides is a natural starting point for such a prior distribution. 

As a regular procedure, the manufacturer controls the dextrose equivalent, which is a measure of the degree of conversion. He also controls the Baume, which is an empirical function of the density and reasonably defines the dry substance content, although this relationship varies slightly with the dextrose equivalent. 

E is the adsorption energy, y is a constant Qg and Qp are the adsorption heat on flat surface and in pores, respectively z = p/po i n is the number (noninteger) of statistical mono-layers of adsorbate molecules and its maximal value for a given is equal to (Rp - (Tgl2)ltn, is the colhsion diameter equal to the average size of nitrogen and surface atoms and Rg is the gas constant. Desorption data were utilized to compute flie / pj distributions with Equations (38.2)-(38.4) and the modified regularization procedure [27]... 

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