Mittag

Mitt., abbrev. (Mitteilung) communication, Mittag, m. midday, noon south. Mittags-essen, n. noon meal, -kreis, m., -linie, /. meridian,... 

Nach-mittag, m. afternoon, -miihlenol, n. inferior olive oil from the marc, -musterfarben, n. dyeing to pattern. 

To assay the amount of LBP, first an excess amount of luciferin is added to the sample at pH 8 to saturate the binding site of LBP, and then the excess luciferin is removed by gel filtration using a small column of Sephadex G-25 (about 1 ml volume) also at pH 8. The luciferin-bound LBP is eluted at the void volume. To measure the amount of LBP, the following assay buffer is added to a small portion of the elu-ate 0.2 M phosphate, pH 6.3, containing 0.25 mM EDTA, 0.1 mg/ml of BSA, and luciferase (Morse and Mittag, 2000). The total light obtained represents a relative amount of LBP the absolute amount (the weight or the number of molecules) cannot be obtained because the quantum yield of the luminescence reaction is not known. 

Morse, D., and Mittag, M. (2000). Dinoflagellate luciferin-binding protein. Method. Enzymol. 305 258-276. 

W.Anselm, "Zerkleinerungstechnik und Staub , Deut Ing-Verlag, Diisseldorf (1950), 58pp (Crushing technology dust) 7)C.Mittag,... 

B. The Fractional Generalization of the Kramers Escape Problem Mittag-Leffler Decay of the Survival Probability... 

Appendix A A Primer on Levy Distributions Appendix B The Ubiquitous Mittag-Leffler Function References... 

Among the most striking changes brought about by fractional dynamics is the substitution of the traditionally obtained exponential system equilibration of time-dependent system quantities by the Mittag-Leffler pattern [44-46]... 

For systems that exhibit slow anomalous transport, the incorporation of external fields is in complete analogy to the existing Brownian framework which itself is included in the fractional formulation for the limit a —> 1 The FFPE (19) combines the linear competition of drift and diffusion of the classical Fokker-Planck equation with the prevalence of a new relaxation pattern. As we are going to show, also the solution methods for fractional equations are similar to the known methods from standard partial differential equations. However, the temporal behavior of systems ruled by fractional dynamics mirrors the self-similar nature of its nonlocal formulation, manifested in the Mittag-Leffler pattern dominating the system equilibration. 

Figure 3. Survival probability for absorbing boundary conditions positioned at x = 1, plotted for the subdiffusive case a = 1/2 and the Brownian case a = 1 (dashed curve). For longer times, the faster (exponential) decay of the Brownian solution, in comparison to the power-law asymptotic of the Mittag-Leffler behavior, is obvious.

Let us briefly examine the importance of the Mittag-Leffier function in relaxation modelling. The mathematical properties of the Mittag-Leffier function are compiled in Appendix B. Besides via the series representation, the Mittag-Leffier function is defined through its Laplace transform... 

In Refs. 80 and 81 it is shown that the Mittag-Leffier function is the exact relaxation function for an underlying fractal time random walk process, and that this function directly leads to the Cole-Cole behavior [82] for the complex susceptibility, which is broadly used to describe experimental results. Furthermore, the Mittag-Leffier function can be decomposed into single Debye processes, the relaxation time distribution of which is given by a mod-... 

The Mittag-Leffler function, or combinations thereof, has been obtained from fractional rheological models, and it convincingly describes the behavior of a number of rubbery and nonrubbery polymeric substances [79, 85]. The numerical behavior of the Mittag-Leffler function is equivalent to asymptotic power-law patterns that are often used to fit experimental data, see the comparative discussion of data from early events in peptide folding in Ref. 86, where the asymptotic power-law was confronted with the stretched exponential fit function. 

By comparison with Eq. (55), the Laplace inversion of Eq. (63) leads to the Mittag-Leffler shape [105]... 

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