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The entropy of coupled map lattices with respect to the group of space-time translations is considered. We use the notion of generalized Lyapunov spectra ([11]) to prove the analogue of Ruelle inequ...
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r +1) geometric lattice L, then the for all i ≤ r...
In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is ...
We study the evolution of rotational response of a statistical mechanical model of two-component superfluid with a nondissipative drag interaction as the system undergoes a transition into a paired su...
In this thesis we summarize the classical cases of one-dimensional oligomers and two dimensional plaquettes, respecting the parity-time (PT ) symmetry. We examine different types of solutions of such ...
We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-...
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
We investigate static properties of laser-driven, ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of squa...
Abstract: We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear diff...
Abstract: We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limitin...
Abstract: This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume l...
Abstract: We numerically investigate the heat conduction behavior of one-dimensional momentum-conserved lattice systems with {\it asymmetric} interactions. The heat conductivity is measured by couplin...
Abstract: We deal with the question of whether or not the p-convexified couple (X_0^{(p)},X_1^{(p)}) is a Calderon couple under the assumption that (X_0,X_1) is a Calderon couple of Banach lattices on...
Abstract: We show that the Gross-Pitaevskii equation with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, ...

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