Geometrically uniform hyperbolic codes

In this paper we generalize the concept of geometrically uniform codes, formerly employed in Euclidean spaces, to hyperbolic spaces. We also show a characterization of generalized coset codes through the concept of G-linear codes.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

Fitting hyperbolic universes to Cayon-Smoot spots in COBE maps

On the possibility that the universe's matter density is low (Ohm(0) < 1), cosmologies can be considered with the metric of Friedmann's open universe but with closed hyperbolic manifolds as the physical three-space. These models have nontrivial spatial topology, with the property of producing multiple images of cosmic sources. Here a fit is attempted of 10 of these models to the physical cold and hot spots found by Cayon & Smoot in the COBE/DMR maps. These spots are interpreted as early, distant images of much nearer sources of inhomogeneity. The source for one of the cold spots is seen as the seed of a known supercluster.

Mapping deformed hyperbolic potentials into nondeformed ones

In this work we introduce a mapping between the so-called deformed hyperbolic potentials, which are presenting a continuous interest in the last few years, and the corresponding nondeformed ones. As a consequence, we conclude that these deformed potentials do not pertain to a new class of exactly solvable potentials, but to the same one of the corresponding nondeformed ones. Notwithstanding, we can reinterpret this type of deformation as a kind of symmetry of the nondeformed potentials. © 2005 Elsevier B.V. All rights reserved.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

On superfield covariant quantization in general coordinates

We propose a natural extension of the BRST-antiBRST superfield covariant scheme in general coordinates. Thus, the coordinate dependence of the basic tensor fields and scalar density of the formalism is extended from the base supermanifold to the complete set of superfield variables. © Springer-Verlag.

Sharp Turán inequalities via very hyperbolic polynomials

We present new sharp inequalities for the Maclaurin coefficients of an entire function from the Laguerre-Pólya class. They are obtained by a new technique involving the so-called very hyperbolic polynomials. The results may be considered as extensions of the classical Turán inequalities. © 2010 Elsevier Inc.

Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.

One-nucleon-induced nonmesonic hypernuclear decay in laboratory coordinates

We present a formalism for the computation of one-nucleon-induced nonmesonic weak hypernuclear decay rates in laboratory coordinates, within an independent-particle shell model framework, with a view to its generalization to the case of two-nucleon-induced transitions. © 2013 AIP Publishing LLC.

Simultaneous linearization of a class of pairs of involutions with normally hyperbolic composition

In this paper we obtain a result on simultaneous linearization for a class of pairs of involutions whose composition is normally hyperbolic. This extends the corresponding result when the composition of the involutions is a hyperbolic germ of diffeomorphism. Inside the class of pairs with normally hyperbolic composition, we obtain a characterization theorem for the composition to be hyperbolic. In addition, related to the class of interest, we present the classification of pairs of linear involutions via linear conjugacy. © 2012 Elsevier Masson SAS.

Approximation of hyperbolic tangent activation function using hybrid methods

Artificial Neural Networks are widely used in various applications in engineering, as such solutions of nonlinear problems. The implementation of this technique in reconfigurable devices is a great challenge to researchers by several factors, such as floating point precision, nonlinear activation function, performance and area used in FPGA. The contribution of this work is the approximation of a nonlinear function used in ANN, the popular hyperbolic tangent activation function. The system architecture is composed of several scenarios that provide a tradeoff of performance, precision and area used in FPGA. The results are compared in different scenarios and with current literature on error analysis, area and system performance. © 2013 IEEE.