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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...
INEQUALITIES FOR THE H-AND FLAG H-VECTORS OF GEOMETRIC LATTICES
H-AND FLAG H-VECTORS GEOMETRIC LATTICES
2015/8/25
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...
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
$Top(X)$ within $\px$ ]{When lattices meet topology: $Top(X)$ within $\px$.}
$Top(X)$ within $\px$ lattices meet topology
2012/2/29
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...
On the Properties of Special Functions on the linear-type lattices
q-hypergeometric functions difference equations recurrence relations q-polynomials
2011/9/23
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...
Covolumes of nonuniform lattices in PU(n, 1)
Covolumes of nonuniform lattices Geometric Topology
2011/9/21
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...
Calderon couples of p-convexified Banach lattices
Calderon couples p-convexified Banach lattices Functional Analysis
2011/9/13
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...
Bose-Einstein condensates in optical lattices: mathematical analysis and analytical approximate formulae
Bose-Einstein condensates stability of ground states analytical approximate formulae repulsive or attractive interatomic interactions
2011/9/6
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, ...
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective...
Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices
Nonlinear localized modes dipolar Bose-Einstein condensates condensates optical lattices
2011/7/7
The modulational instability and discrete matter wave solitons in dipolar BEC, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instabilit...
Methods of exploring energy diffusion in lattices with finite temperature
lattices energy diffusion finite temperature
2011/7/7
We discuss two methods for exploring energy diffusion in lattices with finite temperature in this paper. The first one is the energy-kick (EK) method. To apply this method, one adds an external energy...
The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights
Toda Lattices Continuum Limit Random Matrices Odd Weights
2011/7/7
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/28
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Bounds for coefficients of cusp forms and extremal lattices
coefficients of cusp forms extremal lattices
2011/3/1
A cusp form f(z) of weight k for SL2(Z) is determined uniquely by its first ℓ := dim Sk Fourier coefficients. We derive an explicit bound on the nth coefficient of f in terms of its first ℓ...
Border Algorithms for Computing Hasse Diagrams of Arbitrary Lattices
Lattices Hasse diagrams border algorithms
2011/3/2
The Border algorithm and the iPred algorithm find the Hasse diagrams of FCA lattices. We show that they can be generalized to ar-bitrary lattices. In the case of iPred, this requires the identificatio...