We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation.

Abstract In this article, we continue the structural study of factor maps between symbolic dynamical systems and relative thermodynamic formalism. Here, one is studying a map from shift finite type X (equipped with potential function) to sofic Z , equipped shift-invariant measure $\nu $ . We equilibrium states, that is, measures on push forward under which maximize pressure: entropy plus integr...

Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that increasing the computation load in the Map phase by a factor of r can create coded multicasting opportunities to reduce the communication load in the Reduce...

Saliency map generation in synthetic aperture radar (SAR) imagery has become a promising research area, since it has a close relationship with quick potential target identification, rescue services, etc. Due to the multiplicative speckle noise and complex backscattering in SAR imagery, producing satisfying results is still challenging. This paper proposes a new saliency map generation approach ...

Let $\bigwedge_\sigma V=\bigoplus_{k\geq 0}\bigwedge_\sigma^kV$ be the quantum exterior algebra associated to a finite-dimensional braided vector space $(V,\sigma)$. For an $\mathfrak{A}$, we consider convolution product on graded $\bigoplus_{k\geq 0}\mathrm{Hom}\big(\bigwedge_\sigma^kV,\bigwedge_\sigma^kV\otimes \mathfrak{A}\big)$. Using this product, define notion of minor determinant map fro...