Radon–Nikodým indexes and measures of weak noncompactness

The aim of this paper is to present a quantitative version of the Radon–Nikodým property and some other results related to it. This approach gives an extra insight to the classical results. We introduce two indexes: an index of representability of measures and an index of dentability. We review classic results in order to obtain relationships between these and other indexes.     

On the γ-filtration of oriented cohomology of complete spin-flags

We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the γ-filtration. Moreover, if the formal group law determined by the oriented cohomology theory is congruent to the additive formal group law modulo 2, then at degree 2 and 3, we show that the γ-filtration of complete spin-flags is torsion free.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Impedance spectroscopy and conductometric biosensing for probing catalase reaction with cyanide as ligand and inhibitor

In this work, a new biosensor was prepared through immobilization of bovine liver catalase in a photoreticulated poly (vinyl alcohol) membrane at the surface of a conductometric transducer. This biosensor was used to study the kinetics of catalase–H₂0₂ reaction and its inhibition by cyanide. Immobilized catalase exhibited a Michaelis–Menten behaviour at low H₂0₂ concentrations (< 100 mM) with apparent constant K_M^app = 84 ± 3 mM and maximal initial velocity V_M^app = 13.4 μS min^? 1. Inhibition by cyanide was found to be non-competitive and inhibition binding constant K_i was 13.9 ± 0.3 μM. The decrease of the biosensor response by increasing cyanide concentration was linear up to 50 μM, with a cyanide detection limit of 6 μM. In parallel, electrochemical characteristics of the catalase/PVA biomembrane and its interaction with cyanide were studied by cyclic voltammetry and impedance spectroscopy. Addition of the biomembrane onto the gold electrodes induced a significant increase of the interfacial polarization resistance R_P. On the contrary, cyanide binding resulted in a decrease of Rp proportional to KCN concentration in the 4 to 50 μM range. Inhibition coefficient I₅₀ calculated by this powerful label-free and substrate-free technique (24.3 μM) was in good agreement with that determined from the substrate-dependent conductometric biosensor (24.9 μM).     

两种形貌纳米Fe2O3对TKX-50热分解的催化性能研究

Energy components used in solid rocket propellants are beneficial for improving the energy performance, and their thermal decomposition characteristics significantly affect the combustion properties of the propellants. As a kind of energetic material with both high energy and low sensitivity (impact and friction), 5, 5'-bistetrazole-1, 1'-diolate (TKX-50) can effectively improve the energy and safety characteristics of solid propellants. Burning catalyst is another important component of solid propellants, which can significantly improve the burning rate of the propellant and reduce the pressure exponent. Among various burning catalysts, nanoscale transition metal oxides can promote the thermal decomposition of the energetic component, thus enhancing the combustion properties of the solid propellant. However, the catalytic effects of nanoscale transition metal oxides with different morphologies on the thermal decomposition of TKX-50 have rarely been studied. Based on the excellent catalytic activity of Fe₂O₃ for TKX-50 thermal decomposition, nano-Fe₂O₃ particles with spherical and tubular microstructures were used for TKX-50 thermal decomposition. The Fe₂O₃ nanoparticles were successfully fabricated via the solvothermal method and characterized by scanning electron microscope (SEM), transmission electron microscope (TEM), X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), and X-ray photoelectron spectroscopy (XPS) analyses. The XRD, FT-IR, and XPS results confirmed the successful fabrication of spherical and tubular Fe₂O₃ samples. The SEM and TEM images showed that the spherical Fe₂O₃ samples are composed of agglomerated Fe₂O₃ nanoparticles with an average particle size of 110 nm. In addition, the average diameter and length of hollow tubular Fe₂O₃ nanoparticles are 120 nm and 200 nm, respectively. The catalytic activities of spherical and tubular Fe₂O₃ for TKX-50 decomposition were studied by thermogravimetric analysis (TG) and differential scanning calorimetry (DSC) methods. The DSC and TG-DTG curves showed that both tubular and spherical Fe₂O₃ could effectively promote TKX-50 thermal decomposition. The first thermal decomposition peak temperature (T_FDP) of TKX-50 was reduced by 36.5 K and 26.3 K in the presence of tubular and spherical Fe₂O₃, respectively, at 10 K·min⁻¹. The activation energy (E_a) of TKX-50, determined by the iso-conversional method, was significantly reduced in the presence of both tubular and spherical Fe₂O₃. The results indicated that the microstructure of the catalyst has a significant effect on its catalytic performance for TKX-50 thermal decomposition, and that tubular Fe₂O₃ with hollow microstructure possesses better catalytic activity than spherical Fe₂O₃. The excellent catalytic activity of tubular Fe₂O₃ can be attributed to the hollow microstructure, which has more active sites for TKX-50 thermal decomposition.     

A Reilly inequality for the first Steklov eigenvalue

Let M be a compact submanifold with boundary of a Euclidean space or a Sphere. In this paper, we derive an upper bound for the first non-zero eigenvalue p₁ of Steklov problem on M in terms of the r-th mean curvatures of its boundary ∂M. The upper bound obtained is sharp.     

Failure of n‐uniqueness: a family of examples

In this paper, the connections between model theory and the theory of infinite permutation groups (see 11 ) are used to study the n‐existence and the n‐uniqueness for n‐amalgamation problems of stable theories. We show that, for any n ? 2, there exists a stable theory having (k + 1)‐existence and k‐uniqueness, for every k ? n, but has neither (n + 2)‐existence nor (n + 1)‐uniqueness. In particular, this generalizes the example, for n = 2, due to Hrushovski given in 3 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Multiplication operators on the Bergman space via analytic continuation

In this paper, using the group-like property of local inverses of a finite Blaschke product ?, we will show that the largest C^?-algebra in the commutant of the multiplication operator M? by ? on the Bergman space is finite dimensional, and its dimension equals the number of connected components of the Riemann surface of ?−1°? over the unit disk. If the order of the Blaschke product ? is less than or equal to eight, then every C^?-algebra contained in the commutant of M? is abelian and hence the number of minimal reducing subspaces of M? equals the number of connected components of the Riemann surface of ?−1°? over the unit disk.