Horo-tight spheres in hyperbolic space

We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by Cecil and Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

REIDEMEISTER TORSION AND ANALYTIC TORSION OF SPHERES

We provide a simple topological derivation of a formula for the Reidemeister and the analytic torsion of spheres.

Homotopy type of gauge groups of quaternionic line bundles over spheres

Let P be a principal S(3)-bundle over a sphere S(n), with n >= 4. Let G(p) be the gauge group of P. The homotopy type of G(p) when n - 4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295-297]. In this paper we extend his result anti we study the homotopy type of the gauge group of these bundles for all n <= 25. (C) 2008 Elsevier B.V. All rights reserved.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

UNIT VECTOR FIELDS ON ANTIPODALLY PUNCTURED SPHERES: BIG INDEX, BIG VOLUME

We establish in this paper a lower bound for the volume of a unit vector field (v) over right arrow defined ou S(n) \ {+/-x}, n = 2,3. This lower bound is related to the sum of the absolute values of the indices of (v) over right arrow at x and -x.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the kappa-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the kappa-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory. (C) 2008 Elsevier B.V. All rights reserved.

EXACT AND QUASI-EXACT MODELS OF STRANGE STARS

We construct and compare in this work a variety of simple models for strange stars, namely, hypothetical self-bound objects made of a cold stable version of the quark-gluon plasma. Exact, quasi-exact and numerical models are examined to find the most economical description for these objects. A simple and successful parametrization of them is given in terms of the central density, and the differences among the models are explicitly shown and discussed. In particular, we present a model starting with a Gaussian ansatz for the density profile that provides a very accurate and almost complete analytical integration of the problem, modulo a small difference for one of the metric potentials.

ON NONSYMMETRIC THEOREMS FOR (H, G)-COINCIDENCES

Let X be a compact Hausdorff space, phi: X -> S(n) a continuous map into the n-sphere S(n) that induces a nonzero homomorphism phi*: H(n)(S(n); Z(p)) -> H(n)(X; Z(p)), Y a k-dimensional CW-complex and f: X -> a continuous map. Let G a finite group which acts freely on S`. Suppose that H subset of G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set A(phi)(f, H, G) of (H, G)-coincidence points of f relative to phi.

Confinement-induced phase transition in a DNA-lipid hydrated complex

We study the effect of the soft confinement by fluid lipid bilayers on the spatial organisation of DNA molecules in a DNA-zwitterionic lipid hydrated lamellar complex. The confinement is increased by dehydrating the complex in a controlled way, which leads to a decrease of the water channel thickness separating the periodically stacked bilayers. Using grazing-incidence small-angle X-ray scattering on an oriented thin film, we probe in situ as dehydration proceeds the structure of the DNA-lipid complex. A structural phase transition is evidenced, where an apparently disordered phase of DNA rods embedded within the one-dimensionally ordered lipid lamellar phase observed at high hydration is replaced by a 2D hexagonal structure of DNA molecules intercalated between the lipid bilayers. Copyright (C) EPLA, 2010

Biomechanical effects of environmental and engineered particles on human airway smooth muscle cells

The past decade has seen significant increases in combustion-generated ambient particles, which contain a nanosized fraction (less than 100 nm), and even greater increases have occurred in engineered nanoparticles (NPs) propelled by the booming nanotechnology industry. Although inhalation of these particulates has become a public health concern, human health effects and mechanisms of action for NPs are not well understood. Focusing on the human airway smooth muscle cell, here we show that the cellular mechanical function is altered by particulate exposure in a manner that is dependent upon particle material, size and dose. We used Alamar Blue assay to measure cell viability and optical magnetic twisting cytometry to measure cell stiffness and agonist-induced contractility. The eight particle species fell into four categories, based on their respective effect on cell viability and on mechanical function. Cell viability was impaired and cell contractility was decreased by (i) zinc oxide (40-100 nm and less than 44 mu m) and copper(II) oxide (less than 50 nm); cell contractility was decreased by (ii) fluorescent polystyrene spheres (40 nm), increased by (iii) welding fumes and unchanged by (iv) diesel exhaust particles, titanium dioxide (25 nm) and copper(II) oxide (less than 5 mu m), although in none of these cases was cell viability impaired. Treatment with hydrogen peroxide up to 500 mu M did not alter viability or cell mechanics, suggesting that the particle effects are unlikely to be mediated by particle-generated reactive oxygen species. Our results highlight the susceptibility of cellular mechanical function to particulate exposures and suggest that direct exposure of the airway smooth muscle cells to particulates may initiate or aggravate respiratory diseases.

Formation of beta-nickel hydroxide plate-like structures under mild conditions and their optical properties

Nanostructural beta-nickel hydroxide (beta-Ni(OH)(2)) plates were prepared using the microwave hydrothermal (MH) method at a low temperature and short reaction times. An ammonia solution was employed as the coordinating agent, which reacts with [Ni(H(2)O)(6)](2+) to control the growth of beta-Ni(OH)(2) nuclei. A trigonal beta-Ni(OH)(2) single phase was observed by X-ray diffraction (XRD) analyses, and the crystal cell was constructed with structural parameters and atomic coordinates obtained from Rietveld refinement. Field emission scanning electron microscopy (FE-SEM) images revealed that the samples consisted of hexagonal-shaped nanoplates with a different particle size distribution. Broad absorption bands assigned as transitions of Ni(2+) in oxygen octahedral sites were revealed by UV-vis spectra. Photoluminescence (PL) properties observed with a maximum peak centered in the blue-green region were attributed to different defects, which were produced during the nucleation process. We present a growth process scheme of the beta-Ni(OH)(2) nanoplates. (C) 2011 Elsevier Inc. All rights reserved.

PACKMOL: A Package for Building Initial Configurations for Molecular Dynamics Simulations

Adequate initial configurations for molecular dynamics simulations consist of arrangements of molecules distributed in space in such a way to approximately represent the system`s overall structure. In order that the simulations are not disrupted by large van der Waals repulsive interactions, atoms from different molecules Must keep safe pairwise distances. Obtaining Such a molecular arrangement can be considered it packing problem: Each type molecule must satisfy spatial constraints related to the geometry of the system, and the distance between atoms of different molecules Must be greater than some specified tolerance. We have developed a code able to pack millions of atoms. grouped in arbitrarily complex molecules, inside a variety of three-dimensional regions. The regions may be intersections of spheres, ellipses, cylinders, planes, or boxes. The user must provide only the structure of one molecule of each type and the geometrical constraints that each type of molecule must satisfy. Building complex mixtures, interfaces, solvating biomolecules in water, other solvents, or mixtures of solvents, is straight forward. In addition. different atoms belonging to the same molecule may also be restricted to different spatial regions, in Such a way that more ordered molecular arrangements call be built, as micelles. lipid double-layers, etc. The packing time for state-of-the-art molecular dynamics systems varies front a few seconds to a few Minutes in a personal Computer. The input files are simple and Currently compatible with PDB, Tinker, Molden, or Moldy coordinate files. The package is distributed as free software and call be downloaded front http://www.ime.unicamp.br/similar to martinez/packmol/. (C) 2009 Wiley Periodicals. Inc. J Comput Chem 30: 2157-2164, 2009

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.