In this article, we consider a stochastic PDE of parabolic type, driven by a space-time white-noise, and its numerical discretization in time with a semi-implicit Euler scheme. When the nonlinearity is assumed to be bounded, then a dissipativity assumption is satisfied, which ensures that the SDPE admits a unique invariant probability measure, which is ergodic and strongly mixing with exponenti...

We extend the results of Walters on the uniqueness of invariant measures with maximal entropy on compact groups to an arbitrary locally compact group. We show that the maximal entropy is attained at the left Haar measure and the measure of maximal entropy is unique.

We smoothly tune the dimensionality of pancake-shaped Li Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where EF/hνz 1, with EF the Fermi energy and hνz the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree wi...

magnetotelluric (mt) method is an electromagnetic technique that uses the earth natural field to map the electrical resistivity changes in subsurface structures. because of the high penetration depth of the electromagnetic fields in this method (tens of meters to tens of kilometers), the mt data is used to investigate the shallow to deep subsurface geoelectrical structures and their dimensions....

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .

Kolmogorov-Arnol’d-Moser Theory classically was mainly developed for conservative systems, establishing persistence results for quasi-periodic invariant tori in nearly integrable systems. In this survey we focus on dissipative systems, where similar results hold. In non-conservative settings often parameters are needed for the persistence of invariant tori. When considering families of such dyn...

In this paper, we introduce the concepts of partial-quasi k-metric spaces and strongly partial- quasi spaces, their relationship to metric are studied. Furthermore, obtain some results on fixed point theorems in spaces.

We consider the modified Surface Quasi-Geostrophic (mSQG) equation on 2D torus $\mathbb{T}^2$, perturbed by multiplicative transport noise. The admits white noise measure $\mathbb{T}^2$ as invariant measure. first prove existence of solutions to stochastic via method point vortex approximation, then, under a suitable scaling limit noise, we show that converge weakly unique stationary solution d...