We consider coupled map lattices of hyperbolic type, i.e., chains of weakly interacting hyperbolic sets (attractors) over multi-dimensional lattices. We describe thermodynamic formalism of the underlying spin lattice system and then prove existence, uniqueness, mixing properties, and exponential decay of correlations of equilibrium measures for a class of Holder continuous potential functions ...

The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF (q). When q is prime, we prove that Gn(q) is equal to the number Ln(q) of n-dimensional mod q lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice Z and having the property that given any point P in t...

The lattice of all permutations on a -element set has been shown to be bounded [5], which is a strong constructive property characterized by the fact that admits what we call an interval doubling scheme. In this paper we characterize all interval doubling schemes of the lattice , a result that gives a nice precision on the bounded nature of the lattice of permutations. This theorem is a direct ...

An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaunay tessellation of the medium. The dual sVoronoid tessellation is used to scale the elemental stiffness terms in a manner that renders the lattice elastically homogeneous. This property enables the accurate modeling of heterogeneity, as demonstr...

We investigate new generalizations of the Meixner polynomials on the lattice N, on the shifted lattice N + 1 − β and on the bi-lattice N ∪ (N + 1 − β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to the solutions of the fifth Painlevé equation PV. Initial conditions for different lattices can be transformed to the classical solu...

In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions lattice have been defined submodular property that is similar to submodularity of set functions. a further extended concept for functions lattice, which captures diminishing return property. Such find many applications in machine learning, social networks, wireless etc. The techniques ca...

The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of...

A strongly closed lattice of projections on a Hubert space is compact if the associated algebra of operators has a weakly dense subset of compact operators. If the lattice is commutative, there are necessary and sufficient conditions for compactness, one in terms of the structure of the lattice, and the other in terms of a measure on the lattice. There are many examples of compact lattices, and...

A major difficulty with logic programming is combinatorial explosion: since goals are solved with possibly indeterminate (i.e., branching) reductions, the resulting search trees may grow wildly. Constraint logic programming systems try to avoid combinatorial explosion by building in strong determinate (i.e., non-branching) reduction in the form of constraint simplification. In this paper, we pr...

The entire family of carefully oxygen-adjusted RBaCo2O5.5 or R2Ba2Co4O11 (R1⁄4Y, Ho–La) doubleperovskite oxides is systematically investigated for the lattice parameters, A-site cation disorder, and characteristic physical properties, i.e. the metal–insulator transition, ferromagnetic transition and socalled metamagnetic transition. With increasing size of the R constituent, the lattice paramet...