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.

Comparison of biological behavior between early-stage adenocarcinoma and squamous cell carcinoma of the uterine cervix

Objectives: (1) To compare the anatomopathological variables and recurrence rates in patients with early-stage adenocarcinoma (AC) and squamous cell carcinoma (SCC) of the uterine cervix; (2) to identify the independent risk factors for recurrence. Study design: This historical cohort study assessed 238 patients with carcinoma of the uterine cervix (113 and IIA), who underwent radical hysterectomy with pelvic lymph node dissection between 1980 and 1999. Comparison of category variables between the two histological types was carried out using the Pearson`s X-2 test or Fisher exact test. Disease-free survival rates for AC and SCC were calculated using the Kaplan-Meier method and the curves were compared using the log-rank test. The Cox proportional hazards model was used to identify the independent risk factors for recurrence. Results: There were 35 cases of AC (14.7%) and 203 of SCC (85.3%). AC presented lower histological grade than did SCC (grade 1: 68.6% versus 9.4%; p < 0.001), lower rate of lymphovascular space involvement (25.7% versus 53.7%; p = 0.002), lower rate of invasion into the middle or deep thirds of the uterine cervix (40.0% versus 80.8%; p < 0.001) and lower rate of lymph node metastasis (2.9% versus 16.3%; p = 0.036). Although the recurrence rate was lower for AC than for SCC (11.4% versus 15.8%), this difference was not statistically significant (p = 0.509). Multivariate analysis identified three independent risk factors for recurrence: presence of metastases in the pelvic lymph nodes, invasion of the deep third of the uterine cervix and absence of or slight inflammatory reaction in the cervix. When these variables were adjusted for the histological type and radiotherapy status, they remained in the model as independent risk factors. Conclusion: The AC group showed less aggressive histological behavior than did the SCC group, but no difference in the disease-free survival rates was noted. (C) 2006 Elsevier Ireland Ltd. All rights reserved.

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.

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].

Study of electrochemical behavior of azoles for AISI 430 stainless steel in H(2)SO(4) 1 mol L(-1)

Corrosion is an undesirable process that occurs in metallic materials. Studied was the effect of inhibiting Benzotriazole (BTAH), Benzimidazole (BZM) and Indole in different concentrations-for the stainless steel (SS) AISI 430 in H(2)SO(4) mol The techniques employed this research were: anodic potenciostatic polarisation, electrochemical impedance spectroscopy, optical microscopy and scanning electron microscopy The curves of anodic polarisation showed that BTAH, BZM and Indol act as corrosion inhibitors for 430 SS, at concentrations of 1x10(-3) and 5x10(-4) mol L(-1) but do not inhibit corrosion for concentrations equal to or less than 1x10(-4) mol L(-1). The in-crease of the efficiency in relation to the inhibitory substances studied followed this order: Indol

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.