Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model

Methodology and Computing in Applied Probability - In the failure dependent proportional hazard model, it is assumed that identical components work jointly in a system. At the moments of...     

Analytic families of semihyperbolic generalized polynomial-like mappings

We show that the Hausdorff dimension of Julia sets in any analytic family of semihyperbolic generalized polynomial-like mappings (GPL) depends in a real-analytic manner on the parameter. For the proof we introduce abstract weakly regular analytic families of conformal graph directed Markov systems. We show that the Hausdorff dimension of limit sets in such families is real-analytic, and we associate to each analytic family of semihyperbolic GPLs a weakly regular analytic family of conformal graph directed Markov systems with the Hausdorff dimension of the limit sets equal to the Hausdorff dimension of the Julia sets of the corresponding semihyperbolic GPLs.     

Transversality family of expanding rational semigroups

We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a d$d$-parameter family of such semigroups satisfies the transversality condition, then for almost every parameter value the Hausdorff dimension of the Julia set is the minimum of 2 and the zero of the pressure function. Moreover, the Hausdorff dimension of the exceptional set of parameters is estimated. We also show that if the zero of the pressure function is greater than 2$2$, then typically the 2-dimensional Lebesgue measure of the Julia set is positive. Some sufficient conditions for a family to satisfy the transversality conditions are given. We give non-trivial examples of families of semigroups of non-linear polynomials with the transversality condition for which the Hausdorff dimension of the Julia set is typically equal to the zero of the pressure function and is less than 2$2$. We also show that a family of small perturbations of the Sierpinski gasket system satisfies that for a typical parameter value, the Hausdorff dimension of the Julia set (limit set) is equal to the zero of the pressure function, which is equal to the similarity dimension. Combining the arguments on the transversality condition, thermodynamical formalisms and potential theory, we show that for each a∈C$a\in \mathbb{C}$ with |a|≠0,1$\left|a\right|\ne 0,1$, the family of small perturbations of the semigroup generated by {z²,az²}$\{z^2,a{z}^2\}$ satisfies that for a typical parameter value, the 2-dimensional Lebesgue measure of the Julia set is positive.     

Influence of terbium on structure and luminescence of nanocrystalline TiO2 thin films

In this work analysis of the structural and optical properties of TiO₂ thin films doped with terbium has been described. Samples were prepared by a high energy reactive magnetron sputtering process under low pressure of oxygen plasma. X-ray diffraction results have shown that different TiO₂ crystal forms have been produced, depending on the amount of Tb dopant. The undoped matrix had rutile structure with crystallites with a size of 8.7 nm, while incorporation of 0.4 at. % of Tb into the film during the sputtering process resulted in anatase structure with bigger crystallites (11.7 nm). Increasing the amount of terbium up to 2 at. % and 2.6 at. % gave rutile structure with crystallites with a size of 6.6 nm for both films. However, Raman spectroscopy has revealed that in the case of TiO₂:(2 at. % Tb), except for the rutile form, the presence of fine-crystalline anatase was observed. Moreover, the lack of Raman peaks shift attests to the lack of stress in the titania lattice of all of the TiO₂:Tb films. This fact indicates localization of Tb3+ ions on the surface of TiO₂ nanocrystals. In the case of optical investigation, results have shown that doping with terbium has a significant influence on the properties of TiO₂, but it does not decrease the high transparency of the matrix. The observed changes of the transmission characteristics were produced only due to modification of the TiO₂:Tb structure. Photoluminescence measurements have shown that emission of light from TiO₂:Tb films occurs when the amount of terbium is 2.6 at. %. Based on the obtained results a scheme of direct energy transfer from titanium dioxide matrix (with rutile structure) to Tb³⁺ ions has been proposed.     

Structural properties of transparent Ti-V oxide semiconductor thin films

Transparent oxide semiconducting thin films based on mixed Ti-V oxides were prepared using a modified reactive magnetron sputtering method. Based on structural investigations performed with the help of x-ray diffraction and transmission electron microscopy analysis, two distinct regions in the prepared thin film have been observed: a nanocrystalline TiO₂-V₂O₃-V₂O₅ mixed composition, and a thin layer consisting of amorphous phase and nanocystalline TiO₂ phase deposited directly at the substrate. Optical measurements show excellent transmission in the visible spectral range of 73%, on average. Resistivity of the thin film was found at the order of 10⁵ Ω cm at room temperature. The preparation of mixed Ti-V oxides provides a combination of high transparency and semiconducting properties.     

Integrating DNA Photonic Wires into Light‐Harvesting Supramolecular Polymers

An approach combining DNA nanoscaffolds with supramolecular polymers for the efficient and directional propagation of light‐harvesting cascades has been developed. A series of photonic wires with different arrangements of fluorophores in DNA‐organized nanostructures were linked to light‐harvesting supramolecular phenanthrene polymers (SPs) in a self‐assembled fashion. Among them, a light‐harvesting complex (LHC) composed of SPs and a photonic wire of phenanthrene, Cy3, Cy5, and Cy5.5 chromophores reveals a remarkable energy transfer efficiency of 59 %. Stepwise transfer of the excitation energy collected by the light‐harvesting SPs via the intermediate Cy3 and Cy5 chromophores to the final Cy5.5 acceptor proceeds through a Förster resonance energy transfer mechanism. In addition, the light‐harvesting properties are documented by antenna effects ranging from 1.4 up to 23 for different LHCs.     

Colloidal liquid crystal type assemblies of spheroidal polystyrene core/polyglycidol‐rich shell particles (P[S/PGL]) formed at the liquid‐silicon‐air interface by a directed dewetting process

A method for the preparation of stripe‐like monolayers of microspheroids is described. The particles were obtained from polystyrene core/polyglycidol‐rich shell microspheres by stretching poly (vinyl alcohol) films that contain embedded particles. The stretching was performed under controlled conditions at temperatures above the T_g of the films and particles. The elongated films were dissolved in water, and the microspheroids were subsequently removed and purified from the poly (vinyl alcohol). The aspect ratio (AR) of the particles, which denotes the ratio of the lengths of the longer to shorter particle axes, was determined by the film elongation. The AR values were in the range of 2.9‐7.7. Spheroidal particles with various ARs were deposited onto silicon wafers from an ethanol (EtOH) suspension. The particle concentration and volume of the suspension were the same in each experiment. Evaporation of the EtOH yielded stripes of spherical particles packed into nematic‐type colloidal crystals and assembled into monolayers. The orientation of the stripes after ethanol evaporation was perpendicular to the triphasic (silicon‐ethanol‐air) interface along the silicon substrate. The adsorbed stripes on the wafers were characterized in terms of their interstripe distance (ID), stripe width, and crystal domain size. Nematic‐type spheroid arrangements in the stripes were the dominant structure, which enabled denser packing of the particles into colloidal crystals than that allowed by the smectic‐type arrangements. Furthermore, the number of spheroids adsorbed per surface unit of the silicon wafers was similar for all ARs, but the width and frequency of the spheroid stripes adsorbed on the wafers were different.     

Ergodic Theory of Parabolic Horseshoes

In this paper we develop the ergodic theory for a horseshoe map f which is uniformly hyperbolic, except at one parabolic fixed point ω and possibly also on W ^s (ω). We call f a parabolic horseshoe map. In order to analyze dynamical and geometric properties of such horseshoes, by making use of induced maps, we establish, in the context of σ-finite measures, an appropriate version of the variational principle for continuous potentials with mild distortion defined on subshifts of finite type. Staying in this setting, we propose a concept of σ-finite equilibrium states (each classical probability equilibrium state is a σ-finite equilibrium state). We then study the unstable pressure function , the corresponding finite and σ-finite equilibrium states and their associated conditional measures. The main idea is to relate the pressure function to the pressure of an embedded parabolic iterated function system and to apply the developed theory of the symbolic σ-finite thermodynamic formalism. We prove, in particular, an appropriate form of the Bowen-Ruelle-Manning-McCluskey formula, the existence of exactly two σ-finite ergodic conservative equilibrium states for the potential –t ^u log |Df|E ^u | (where t ^u denotes the unstable dimension), one of which is the Dirac δ-measure supported at the parabolic fixed point and the other being non-atomic. We also show that the conditional measures of this non-atomic equilibrium state on unstable manifolds, are equivalent to (finite and positive) packing measures, whereas the Hausdorff measures vanish. As an application of our results we obtain a classification for the existence of a generalized physical measure, as well as a criteria implying the non-existence of an ergodic measure of maximal dimension. The research of the first author was supported in part by the NSF Grant DMS 0400481. The research of the second author was supported in part by the National Science Foundation under Grant No. EPS-0236913 and matching support from the State of Kansas through Kansas Technology Enterprise Corporation.     

Structural investigations of TiO2:Tb thin films by X-ray diffraction and atomic force microscopy

In this work, structural investigations of TiO₂ thin films doped with Tb at the amount of 0.4, 2 and 2.6 at.% have been outlined. Thin films were deposited on Si and SiO₂ substrates by high energy reactive magnetron sputtering from mosaic Ti-Tb target. The influence of Tb dopant amount, post-annealing treatment and kind of applied substrate on microstructure has been discussed. Thin films were investigated by means of X-ray diffraction (XRD) and atomic force microscopy (AFM). XRD analysis revealed the existence of crystalline TiO₂ in anatase and rutile forms, depending on Tb amount in examined samples. AFM images show that as-deposited samples with 0.4 at.% concentration of terbium (anatase structure) have bigger crystallites as compared to 2% and 2.6 at.% of Tb (rutile structure). The additional annealing at 1070 K results in a mixed anatase (77%) and rutile (23%) structure.