We consider the multidimensional generalised stochastic Burgers equation in the space-periodic setting: $ \partial \mathbf{u}/\partial t+$ $(\nabla…

The present issue of the series <<Modern Problems in Mathematical Physics>> represents the Proceedings of the Students Training Contest Olympiad in M…

For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, Lanczos bidiagonalization base…

We present a mathematical theory of time-harmonic wave propagation and reflection in a two-dimensional random acoustic waveguide with sound soft boun…

We analyze long range wave propagation in three-dimensional random waveguides. The waves are trapped by top and bottom boundaries, but the medium is …

We prove well-posedness of time-dependent Ginzburg--Landau system in a nonconvex polygonal domain, and decompose the solution as a regular part plus …

We introduce {\em vector diffusion maps} (VDM), a new mathematical framework for organizing and analyzing massive high dimensional data sets, images …

We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimension…

We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The…

This section is devoted to proving Theorems 3.2 and 3.3. Firstly, we show a technical result.

This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this par…

We study a class of discrete focusing nonlinear Schr{\"o}dinger equations (DNLS) with general nonlocal interactions. We prove the existence of onsite…

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage t…

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