Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

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Not AvailableHistamine poisoning occurs when temperature-abused marine fish containing elevated levels of histamine are consumed. Histamine-producing bacteria found in fish can colonize processing surfaces and form biofilms. In this study, the biofilm-forming abilities of histamine-producing bacteria from Indian mackerel (Rastrelliger kanagurta) and the effect of hypochlorite treatment on biofilm formation were studied. The isolates of this study produced histamine in the range of 471 to 2,126 ppm. The histidine decarboxylase gene hdc was detected in all isolates producing histamine except in one strain each of Psychrobacter pulmonis and Proteus vulgaris. All isolates tested in this study produced moderate biofilms under control conditions, whereas exposure to 1 and 3 ppm of sodium hypochlorite significantly enhanced biofilm formation. However, exposure to 5 ppm of sodium hypochlorite showed an inhibitory effect on biofilm formation by all the isolates except Klebsiella variicola. The results of this study suggest that histamine-producing bacteria can form stable biofilms and that this activity may be enhanced by the application of low levels of sodium hypochlorite, a phenomenon that might influence the persistence of histamine-producing bacteria in fish processing areas.Not Availabl