Generalized susceptibility definition

However, from the point of view of linear response theory, the definitions (174) or (178) suffer from several drawbacks. Actually, the function X ( , tw) as defined by Eq. (174) is not the Fourier transform of the function X (, x), but a partial Fourier transform computed in the restricted time interval 0 < x < tw. As a consequence, it does not possess the same analyticity properties as the generalized susceptibility x( ) defined by Eq. (179). While the latter, extended to complex values of co, is analytic in the upper complex half-plane (Smoo > 0), the function Xi ( - tw) is analytic in the whole complex plane. As a very simple example, consider the exponentially decreasing response function... 

Still, it is extremely difficult to define the constitutional factor in language which conveys a definite meaning or to say how or why one person differs from another, with respect to the general property of susceptibility to disease.. . . 7... 

In addition to the underlying disease, there are many potential susceptibility factors (499,519). There is as yet no definitive evidence that age, sex, dose, and duration of treatment play an important role in the development of thyroid disorders. However, patients with previous thyroid abnormalities are predisposed to develop more severe thyroid disease (SEDA-20, 328). The incidence of thyroid disease was not different between natural and recombinant interferon alfa. Although this should be taken into account, a previous familial or personal history of thyroid disease was generally not considered a major risk factor. Finally, only pre-treatment positivity or the development of thyroid antibodies during treatment seem to be strongly associated with the occurrence of thyroid dysfunction. 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

The plan of the article is as follows —In section 2 the systematic definitions of the susceptibilities and (hyperjpolarizabilities are described section 3 briefly derives the standard SOS formulae in section 4 the general theory of the field induced second... 

Researchers have devised numerous extraction and fractionation schemes to deal with the heterogeneous nature of humic substances. Traditionally, the operational definition of humic substances as used by the International Humic Substances Society (Hayes et al., 1989) is based on the solubility in a series of acids and bases. In this scheme, humic substances are classified into three chemical groupings (1) fulvic acid, soluble in both alkali and acid solutions, has the lowest molecular weight and is generally considered the most susceptible to microbial degradation (2) humic acid, soluble in alkali but not in acid, is intermediate in molecular weight and decomposability and (3) humin, insoluble in both alkali and acid solutions, is the most... 

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