Bessel beams (BBs) have gained prominence thanks to their diffraction-free propagation and self-healing properties. These are conventionally generated using different approaches, namely by transforming a narrow circular beam with lens, axicons or holographic beam-shaping techniques. methods involve space-consuming optics. To overcome this limitation, in the past, efforts been made create BBs di...

We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by linear partial differential operator (PDO) of order smaller than Laplacian. show that one can uniquely recover coefficients PDO from Dirichlet-to-Neumann (DN) map associated to perturbed FSE. This is proved two classes coefficients: which belong certain spaces Sobolev multipliers and bounded...

In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method pos...

Convergence results for optimized Schwarz methods (OSM) applied as solvers Poisson's equation in a bounded rectangular domain with Dirichlet (physical) boundary conditions and zeroth-order (Robin) artificial transmission between subdomains are presented. The analysis presented applies to continuous formulation on an arbitrary number of cross points. Both synchronous asynchronous versions OSM di...

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a planar three-dimensional channel with smoothly varying, axis-symmetric periodic side walls is investigated. Here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry...

Dispersive deformations of the Monge equation uu = uux are studied using ideas originating from topological quantum field theory and the deformation quantization programme. It is shown that, to a high-order, the symmetries of the Monge equation may also be appropriately deformed, and that, if they exist at all orders, they are uniquely determined by the original deformation. This leads to eithe...

This paper considers stochastic convex optimization problems with two sets of constraints: (a) deterministic constraints on the domain variable, which are difficult to project onto; and (b) or that admit efficient projection. Problems this form arise frequently in context semidefinite programming as well when various NP-hard solved approximately via relaxation. Since projection onto first set i...

Let G(n; m) be a connected graph without loops and multiple edges which has n vertices and m edges. We ÿnd the graphs on which the zeroth-order connectivity index, equal to the sum of degrees of vertices of G(n; m) raised to the power − 1 2 , attains maximum.

In this paper we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of difficult non-convex problems, and under the challenging setti...