Long-range dependence has usually been defined in terms of covariance properties relevant only to second-order stationary processes. Here we provide new definitions, almost equivalent to the original ones in that domain of applicability, which are useful for processes which may not be second-order stationary, or indeed have infinite variances. The ready applicability of this formulation for categorizing the behaviour for various infinite variance models is shown.
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.
Long-range dependence has usually been defined in terms of covariance properties relevant only to second-order stationary processes. Here we provide new definitions, almost equivalent to the original ones in that domain of applicability, which are useful for processes which may not be second-order stationary, or indeed have infinite variances. The ready applicability of this formulation for categorizing the behaviour for various infinite variance models is shown.
Jeans mass is regarded as a crucial factor in the study of nebula collapse. Astronomical data shows that Jeans mass is larger in theory than it is in observation. Someone mentioned that Jeans mass can be modifed by using the generalized uncertainty principle. However, different physical backgrounds lead to different forms of GUP expression. In order to make the theoretical values of Jeans mass and
its observed values match better, we used three distinct types of generalized uncertainty principles to correct Jeans mass in this paper. And we find that the corrected Jeans masses are smaller than the uncorrected ones, where the Pedram corrected Jeans mass is the minimum and is close to the observed value. Additionally, we also consider the impact of temperature T and the generalized uncertainty principle parameters ( \eta, \beta , and \gamma ) for the corrected Jeans mass.
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