Photochemical reduction of transition metal substituted heteropoly anions in nonpolar solutions

Photochromism of [SiW11O39Ni(X)]6- as a tetraheptylammonium salt in various solvents under broadband UV light is observed in the presence of alcohols. The reaction proceeds faster with benzyl alcohol than with ethanol. Benzaldehyde is identified as the oxidized product of benzyl alcohol. Photochemistry is a reliable means to produce stable reduced transition metal substituted heteropoly tungstates in nonpolar media, where they hold promise as multielectron reduction catalysts. Preliminary reactivity toward CO2 reduction is demonstrated.     

How Points Escape to Infinity Under Exponential Maps

We investigate the finer fractal structure of the set of pointsescaping to infinity under iteration of an arbitrary exponentialmap. Providing exact formulas, we show how sensitively the Hausdorffdimension depends on the rate of growth of canonical Devaney–Krychcodes.     

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.     

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.     

The Properties of Cu Ions in Zeolites CuY Studied by IR Spectroscopy

The properties of both Cu²⁺ and Cu⁺ ions in zeolite CuY were followed with NO and CO as probe molecules. Cu²⁺ was found to be located in S_II, S_II*, and S_III sites, whereas Cu⁺ was found in S_II and S_II* sites. The fine analysis of the spectra of Cu²⁺-NO and Cu⁺-CO adducts suggests that both in S_II and in S_II* sites two kinds of Cu cations exist. They differ in the positive charge, which may be related to the varying numbers of AlO₄⁻ in close proximity. The experiments of NO and CO adsorption and desorption evidenced that both Cu²⁺ and Cu⁺ sites of highest positive charge bind probe molecules most strongly but activate them to a lesser extent than the Cu sites of lowest positive charge. The experiments of reduction with hydrogen evidenced that the Cu ions of higher positive charge are first reduced by hydrogen. On the other hand, Cu sites of the lowest positive charge are first oxidized by oxygen. The experiments with CuNaY zeolites of various Cu contents suggest that the first introduced Cu (at low Cu contents) created Cu⁺, which was the most neutralized by framework oxygens. Such Cu cations are the most stabilized by framework oxygens.