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We consider sliced computer experiments where priori knowledge suggests that factors may have different levels of importance, and so some factors need to be paid more attention than others. A new clas...
While fundamental-mode discrete solitons have been demonstrated with both self-focusing and defocusing nonlinearity, high-order-mode localized states in waveguide lattices have been studied thus far o...
We introduce a two-dimensional discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensat...
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an...
In this work, we study two-dimensional Bose–Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal direction...
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derive...
In this work, we focus on the subject of nonlinear discrete self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation, ...
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate ...
The paper proposes Monte Carlo algorithms for the computation of the information rate of two-dimensional source / channel models. The focus of the paper is on binary-input channels with constraints...
In this paper we obtain the conditions of the strong law of large numbers for two-dimensional arrays of random variables which are blockwise independent and blockwise orthogonal. Some well-known re...
Some examples of translation invariant site percolation processes on the $Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the p...
Some examples of translation invariant site percolation processes on the $Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the p...

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