Ši’lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems

This paper studies the generalized Lorenz canonical form of dynamical systems introduced by elikovský and Chen [International Journal of Bifurcation and Chaos 12(8), 2002, 1789]. It proves the existence of a heteroclinic orbit of the canonical form and the convergence of the corresponding series expansion. The ilnikov criterion along with some technical conditions guarantee that the canonical form has Smale horseshoes and horseshoe chaos. As a consequence, it also proves that both the classical Lorenz system and the Chen system have ilnikov chaos. When the system is changed into another ordinary differential equation through a nonsingular one-parameter linear transformation, the exact range of existence of ilnikov chaos with respect to the parameter can be specified. Numerical simulation verifies the theoretical results and analysis.     

Classification of repeated measurements data using tree-based ensemble methods

In many medical applications, longitudinal data sets are available. Longitudinal data, as well as observations from paired organs, show a dependency structure which should be respected in the evaluation. Adler et al. (Comput Stat Data Anal 53(3):718–729, 2009) proposed various bootstrapping strategies for ensemble methods based on classification trees for two measurements of paired organs. These strategies have shown to improve the classification performance compared to the traditional approach, where only one observation per subject is used. We extend the methodology to the situation, where an arbitrary number of observations per individual are available and investigate the performance of the proposed methods with bagged classification trees (bagging) and random forests in the situation of longitudinal data. Moreover, we adapt the estimation of classification performance criteria to repeated measurements data. The clinical data set consists of morphological examinations of both eyes of glaucoma patients and healthy controls over a time period of up to 7 years. The performance of our modified classifiers is evaluated by a subject-based leave-one-out bootstrap ROC analysis. Simulation results and results for the glaucoma data set demonstrate that our proposal is an improvement of adhoc strategies and of the use all measurements of each subject or block strategy.     

Repair reactions of pyrimidine-derived radicals by aliphatic thiols

Pyrimidinyl radicals of various structures (Pyr*) were generated in aqueous and alcohol-containing solutions by means of pulse radiolysis to determine the rate constants of their repair reactions by different thiols (RSH = cysteamine, 2-mercaptoethanol, cysteine, and penicillamine): Pyr* + RSH --> PyrH + RS*. C5-OH and C6-OH adduct radicals of the pyrimidines react with thiols with k9 = (1.2-10.0) x 10(6) dm3 mol(-1) s(-1). Similar repair rate constants were found for uracil- and thymine-derived N1-centered radicals, k31 = (1.5-6.1) x 10(6) dm3 mol(-1) s(-1). However, pyrimidine radical anions protonated at their C6 position and C6-uracilyl radicals, with carbonyl groups at their C5 position, react with thiols faster, with k24 = (0.5-7.6) x 10(7) dm3 mol(-1) s(-1) and k14 = (1.4-4.8) x 10(7) dm3 mol(-1) s(-1), respectively. Quantum chemical calculations, at the B3LYP/6-31G(d,p) and self-consistent reaction field polarizable continuum model level point to the combined effects of the energy gap between interacting molecular orbitals, charge distribution within different pyrimidine-derived radicals, and the coefficients of the atomic orbitals as the possible reasons for the differences in the rate constants of repair.     

Vacuum‐UV Irradiation‐Based Formation of Methyl‐Si‐O‐Si Networks from Poly(1,1‐Dimethylsilazane‐co‐1‐methylsilazane)

The vacuum‐UV (VUV)‐induced conversion of commercially available poly(1,1‐dimethylsilazane‐co‐1‐methylsilazane) into methyl‐Si‐O‐Si networks was studied using UV sources at wavelengths around 172, 185, and 222 nm, respectively. Time‐of‐flight secondary ion mass spectroscopy (TOF‐SIMS), X‐ray photo electron spectroscopy (XPS), and Fourier transform infrared (FTIR) measurements, as well as kinetic investigations, were carried out to elucidate the degradation process. First‐order kinetics were found for the photolytically induced decomposition of the Si? NH‐Si network, the subsequent formation of the methyl‐Si‐O‐Si network and the concomitant degradation of the Si? CH₃ bond, which were additionally independent of the photon energy above a threshold of about 5.5 eV (225 nm). The kinetics of these processes were, however, dependent on the dose actually absorbed by the layer and, in the case of Si‐O‐Si formation, additionally on the oxygen concentration. The release of ammonia and methane accompanied the conversion process. Quantum‐chemical calculations on methyl substituted cyclotetrasilazanes as model compounds substantiate the suggested reaction scheme. Layers <100 nm in thickness based on mixtures of poly(1,1‐dimethylsilazane‐co‐1‐methylsilazane) and perhydropolysilazane (PHPS) were coated onto polyethylene terephthalate (PET) foils by a continuous roll to roll process and cured by VUV irradiation by using wavelengths <200 nm and investigated for their O₂ and water vapor‐barrier properties. It was found that the resulting layers displayed oxygen and water vapor transmission rates (OTR and WVTR, respectively) of <1 cm³ m^?2 d^?1 bar^?1 and <4 g m^?2 d^?1, respectively.     

A Posteriori Estimates for Modelling Errors of the Stationary Diffusion Equation with Complicated Coefficients

In this paper, we suggest a new computational strategy for diffusion type problems with coefficients that may sharply change values and have a complicated distribution over the domain. We solve models, which approximate the coefficients, numerically and estimate the corresponding approximation errors by the a posteriori estimates of functional type. We show that the modelling error can be also explicitly calculated. This allows to obtain numerical solutions of complicated diffusion problems by solving much simpler problems that do not require full detailization of the structure of coefficients. Balancing modelling and discretization errors provides an economical way of getting an approximate solution with an a priori given accuracy. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rapidity gap survival in enhanced Pomeron scheme

We apply the phenomenological Reggeon field theory framework to investigate rapidity gap survival (RGS) probability for diffractive dijet production in proton–proton collisions. In particular, we study in some detail rapidity gap suppression due to elastic rescatterings of intermediate partons in the underlying parton cascades, described by enhanced (Pomeron–Pomeron interaction) diagrams. We demonstrate that such contributions play a subdominant role, compared to the usual, so-called “eikonal”, rapidity gap suppression due to elastic rescatterings of constituent partons of the colliding protons. On the other hand, the overall RGS factor proves to be sensitive to color fluctuations in the proton. Hence, experimental data on diffractive dijet production can be used to constrain the respective model approaches.     

Synthesis and catalytic activity of hybrid metal/silicon nanocomposites

In this Letter we demonstrate that hydrogen‐terminated porous silicon (PSi) layers and powders can serve as highly efficient reductive templates for noble metal salts. The reduction results in metal nanoparticle (NP) formation in the pores of PSi. Gold NP formation has been monitored in‐situ by measuring the plasmon resonance response. Pt NPs, formed in the PSi matrix, were investigated by transmission electron microscopy and energy‐dispersive X‐ray analysis. Furthermore, hybrid Pt/PSi nanocomposites exhibit a high catalytic activity for CO oxidation.