We show both experimentally and numerically, control over the acceleration of two-dimensional Airy beam propagating in optically induced photonic lattice. Varying the lattice strength and including various defects we can reach a state, where the acceleration is completely stopped. We find an additional class of discrete lattice beams, localized and defect modes observed with Airy beams propagat...

We prove the exponential localization of the eigenfunctions of the Anderson model in R in the regime of large coupling constant for the random potentials which values are independent and Bernoulli distributed. 2000 Math. Subj. Class. 82B44 (60H25, 81Q10, 82B10).

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this paper, we present several novel techniques to effectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important topological relations: contains, contained, overlap, and disjoint. We first present a novel fra...

Ray Singer torsion is a numerical invariant associated with a compact manifold equipped with a flat bundle, a Riemannian metric on the manifold and a Hermitian structure on the bundle. In this note we show how one can remove the dependence on the Riemannian metric and the Hermitian structure with the help of a base point and of an Euler structure, and obtain a topological invariant. A numerical...

We analyze the interaction between the massless Ramond-Ramond states with a dilaton in a type II superstring.By constructing vertex operators for massless Ramond-Ramond states and computing their correlation functions with a dilaton we find the RamondRamond part of the superstring low-energy effective action.Those RR terms appear in the action without the standard dilatonic factor (string coupl...

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.

This paper employs a contour integral method to derive and evaluate the infinite sum of Euler polynomial expressed in terms Hurwitz Zeta function. We provide formulae for several classes sums Riemann function fundamental mathematical constants, including Catalan’s constant. representation constant suggests it could be rational.

The Bernoulli boundary condition for traveling water waves is obtained from Euler’s equation for inviscid flow by employing two key reductions: (i) the traveling wave assumption, (ii) the introduction of a velocity potential. Depending on the order of these reductions, the Bernoulli boundary condition may or may not contain an arbitrary constant. This note shows the equivalence of the two formu...