The growth rate and dimension theory of beta-expansions

In a recent paper of Feng and Sidorov they show that for β∈(1,(1+5√)/2) the set of β-expansions grows exponentially for every x∈(0,1/(β−1)). In this paper we study this growth rate further. We also consider the set of β-expansions from a dimension theory perspective.

Toward a theory of semantic representation

We present an account of semantic representation that focuses on distinct types of information from which word meanings can be learned. In particular, we argue that there are at least two major types of information from which we learn word meanings. The first is what we call experiential information. This is data derived both from our sensory-motor interactions with the outside world, as well as from our experience of own inner states, particularly our emotions. The second type of information is language-based. In particular, it is derived from the general linguistic context in which words appear. The paper spells out this proposal, summarizes research supporting this view and presents new predictions emerging from this framework.

An example in Beurling's theory of generalised primes

In this paper we prove some connections between the growth of a function and its Mellin transform and apply these to study an explicit example in the theory of Beurling primes.

Lines of heavy elements and Fe II in the UV of CS 31082-001

The abundance of heavy r-elements may provide a better understanding of the r-process, and the determination of several reference r-elements should allow a better determination of a star`s age. The space UV region (lambda < 3000 angstrom) presents a large number of lines of the heavy elements, and in the case of some elements, such as Bi, Pt, Au, detectable lines are not available elsewhere. The extreme ""r-process star"" CS 31082-001 ([Fe/H] = -2.9) was observed in the space UV to determine abundances of the heaviest stable elements, using STIS on board Hubble Space Telescope.

Morphometric analysis of tracheary elements in four Portulaca species

This paper deals with the morphological features of the tracheary elements of the vegetative organs in four Portulaca species (Portulaca hirsutissima Camb., P. halimoides L., P. wedermannii Poelln. and P. mucronata Link.) occurring in Southeast and Northeast Brazil. The vessel elements are small (< 25 mu m) and with simple perforation plate. The pattern of wall thickening varied from bordered pitting (in roots) to scalariform and helicoidal (stem and leaves). Statistical methods show variation in vessel-element diameter in different vegetative organs; wider elements were observed in roots. Tracheids occurring in leaves of P. hirsutissima and P. wedermannii, have morphological features that are similar to terminal tracheids or tracheoid idiolasts frequently associated with xerophytes. The paedomorphic features (juvenlism) observed here may be related, in part, to aspects of water transport and storage as described in Cactaceae.

Contributions to the theory of magnetorotational instability and waves in a rotating plasma

The one-fluid magnetohydrodynamic (MHD) theory of magnetorotational instability (MRI) in an ideal plasma is presented. The theory predicts the possibility of MRI for arbitrary 0, where 0 is the ratio of the plasma pressure to the magnetic field pressure. The kinetic theory of MRI in a collisionless plasma is developed. It is demonstrated that as in the ideal MHD, MRI can occur in such a plasma for arbitrary P. The mechanism of MRI is discussed; it is shown that the instability appears because of a perturbed parallel electric field. The electrodynamic description of MRI is formulated under the assumption that the dispersion relation is expressed in terms of the permittivity tensor; general properties of this tensor are analyzed. It is shown to be separated into the nonrotational and rotational parts. With this in mind, the first step for incorporation of MRI into the general theory of plasma instabilities is taken. The rotation effects on Alfven waves are considered.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

Lie properties of symmetric elements in group rings

Let * be an involution of a group G extended linearly to the group algebra KG. We prove that if G contains no 2-elements and K is a field of characteristic p, 0 2, then the *-symmetric elements of KG are Lie nilpotent (Lie n-Engel) if and only if KG is Lie nilpotent (Lie n-Engel). (C) 2008 Elsevier Inc. All rights reserved.

ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS

We continue the investigation of the algebraic and topological structure of the algebra of Colombeau generalized functions with the aim of building up the algebraic basis for the theory of these functions. This was started in a previous work of Aragona and Juriaans, where the algebraic and topological structure of the Colombeau generalized numbers were studied. Here, among other important things, we determine completely the minimal primes of (K) over bar and introduce several invariants of the ideals of 9(Q). The main tools we use are the algebraic results obtained by Aragona and Juriaans and the theory of differential calculus on generalized manifolds developed by Aragona and co-workers. The main achievement of the differential calculus is that all classical objects, such as distributions, become Cl-functions. Our purpose is to build an independent and intrinsic theory for Colombeau generalized functions and place them in a wider context.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Effects of alloying elements on the cytotoxic response of titanium alloys

Titanium alloys, alloys, especially beta-type alloys containing beta-stabilizing elements, constitute a highly versatile category of metallic materials that have been under constant development for application in orthopedics and dentistry. This type of alloy generally presents a high mechanical strength-to-weight ratio, excellent corrosion resistance and low elastic modulus. The purpose of this study is to evaluate the cytotoxicity and adhesion of fibroblast cells on titanium alloy substrates containing Nb, Ta, Zr, Cu, Sn and Mo alloying elements. Cells cultured on polystyrene were used as controls. In vitro results with Vero cells demonstrated that the tested materials, except Cu-based alloy, presented high viability in short-term testing. Adhesion of cells cultured on disks showed no differences between the materials and reference except for the Ti-Cu alloy, which showed reduced adhesion attributed to poor metabolic activity. Titanium alloys with the addition of Nb, Ta, Zr, Sn and Mo elements show a promising potential for biomedical applications. (C) 2011 Elsevier B.V. All rights reserved.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.