Inverse participation ratio

Figure 12. Bottom panel Theoretical distributions of instantaneous frequencies for the uncoupled (F (co)) and coupled (Pc(to)) chromophores. Top panel Inverse participation ratios R(co) and Rm(w). Both panels are for H20 at room temperature.

Next we can consider the instantaneous eigenstates themselves At each time step, ic(f) is diagonalized by the orthogonal transformation BtkB. One can get a rough idea about over how many local-mode chromophores the eigenstates extend by considering the inverse participation ratio ... 

The degree of one-exciton state localization can be described by the inverse participation ratio (52-54) ... 

Figure 3 Solid line Inverse participation ratio of one-exciton states for models A-F. Dotted line Density of one-exciton states for models C-F. 

LRMT provides useful information on how the transition is approached when T(E) is less than 1 and energy is localized to a finite number of states on the energy shell. The extent of localization of molecular vibrations can be determined spectroscopically by the dilution factor, which is proportional to the inverse participation ratio for state n,... 

Ld is then defined as the inverse participation ratio associated with the distribution of populations ... 

The localization properties of the exeitons are usually described by means of the inverse participation ratio (IPR) defined as [19]... 

Fig. 15.4 a Electronic density of states and Inverse Participation Ratio (I PR, see text) of individual KS states in a model of trigonal GeTe with ad-hoc clustered (see text) Ge vacancies. The arrow indicates the Kohn-Sham orbital corresponding to a p lone pair of a twofold coordinated Te with four nearest neighbor vacancies. Inset Isosurface of the lone pair state under consideration, b The same of panel (a) for a two-fold coordinated Te atom in a 270-atom model of c-GST... 

The electronic structure is described by the electronic density of states (EDOS), projected density of states (PDOS), and inverse participation ratio (IPR) of each individual state. The EDOS is deflned as ... 

If solvolysis of CMP- NeuAc required nucleophilic participation of the carboxylate, this would proceed via a transient a-lactone, and in a second step give net retention to afford the p-anomcr. A direct displacement of CMP by solvent without carboxylate participation would yield the a-anomer, while a transition state that resulted in formation of a sialyl oxocarbenium ion would proceed with results ranging from inversion to racemization depending on whether the oxocarbenium ion lived long enough to equilibrate with solvent. Solvolysis of CMP-NeuAc in meth-anol/water mixtures at pH 5.0, resulted in 1 1 ratios of a- and p-methyl glycosides of NeuAc as determined by H-NMR.31 The a/p-methyl glycoside ratio was invariant when the mol fraction of methanol was increased by over 50%, which shows... 

The impressive gains illustrated in Fig. 6.1 for inverse vs traditional methods may not be met in practice when the details of a particular sequence are considered. Significant factors may include the different relaxation behaviour of participating spins or the presence of multiplet splittings that spread a resonance and so reduce the signal-to-noise ratio. However, even a realistic gain of a factor of four in correlations corresponds to a time saving... 

Jiang et al. [58] examined nut and seed consumption and inflammatory markers (C-reactive protein, interleukin-6, and fibrinogen) in the Multi-Ethnic Study of Atherosclerosis. This cross-sectional analysis included 6080 U.S. participants aged45-84 years. Nut and seed consumption was categorized as never/rare, less than once/week, one to four times per week, and five or more times/ week. Associations of nut and seed consumption with these biomarkers were not modified by BMI, waist to hip ratio, or race/ethnicity. Frequent nut and seed consumption was associated with lower levels of inflammatory markers, which may partially explain the inverse association of nut consumption with levels of C-reactive protein, interleukin-6, and fibrinogen. 

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