The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.     

Experimental identification of physical parameters of fluid-filled pipes using acoustical signal processing

A method is formulated for the identification of an unknown physical parameter of a fluid-filled pipe using the measurement of sound speed in the pipe. The method uses a simple formula which provides the relationship between the sound speed and a few physical parameters of the pipe: thickness, diameter, wall material constants and fluid constants. Once the sound speed in the pipe is measured, the simple formula can be used to extract one of the unknown parameters providing the remaining ones are known.The sound speed in the pipe is measured using a 3-transducer array. In order to demonstrate the potential of the technique the results of several measurements obtained in a water-filled steel pipe are presented.The required accuracy of the measurement of sound speed and of the specification of known parameters is analysed. The accuracy depends on the unknown parameter which is to be identified. For example, if the pipe thickness is the unknown parameter, the other parameters have to be known within a very narrow margin of error. On the contrary, if the fluid properties have to be identified the needed accuracy of known parameters gets much lower.     

On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Formation of functional groups on graphite during oxygen plasma treatment

Improved sample wettability was obtained by oxygen plasma functionalization of pyrolytic graphite. The samples were exposed to highly dissociated oxygen plasma with the density of 1 × 10¹⁶ m⁻³, the electron temperature of about 5.5 eV and the density of neutral oxygen atoms of 8 × 10²¹ m⁻³ for 20 s. The surface wettability was measured by a contact angle of water drop. The contact angle dropped from original 112° down to about 1°. The functional groups were detected by XPS analyses. The survey spectrum showed a substantial increase of oxygen concentration on the surface, while high-resolution analyses showed additional oxygen was bonded onto the graphite surface in the form of C-O polar functional group responsible for the increase of the surface energy.     

Growth and characterization of model oxide catalysts

Oxide catalysts are frequently used to convert toxic species to environmentally benign molecules, and to prevent the formation of toxic species in the first place. In this paper, growth and characterization of model oxide systems employed in both approaches is discussed. An example of the former approach is the selective catalytic reduction (SCR) of NO emitted from power plants by NH₃, which employs tungsten and vanadium oxides supported on the anatase polymorph of TiO₂. To model SCR catalysts, epitaxial titanium, vanadium and tungsten oxide films were grown using molecular beam epitaxy and magnetron sputtering. Two different anatase orientations were grown on LaAlO₃ substrates and their interactions with vanadia were characterized. On LaAlO₃ (0 0 1), anatase exposed a (4 × 1) reconstructed (0 0 1) surface. Vanadia lifted the reconstruction and at 1 ML a (1 × 1) surface with mostly V⁵⁺ was observed. Continued V₂O₅ growth led to loss of order, but at high temperatures epitaxial VO₂ could be grown; vanadia behaved similarly on anatase films on LaAlO₃ (1 1 0). Results suggested that the monolayer is pseudomorphic with O adsorption oxidizing the surface V to 5+, since the anatase structure cannot accommodate more bulk oxygen, only a monolayer can be pseudomorphic and have only V⁵⁺. Thus the vanadia monolayer has unique structural and chemical properties that can help explain why vanadia monolayers on TiO₂ are much more active than bulk V₂O₅. For WO₃, a series of added row reconstructions were observed as the epitaxial films were reduced. The effect of these structures on surface chemistry was characterized by studying 1-propanol adsorption. The results indicated that the structure of the WO₃ surface did not alter its catalytic function but had a strong effect on reaction kinetics. As an example of a system where catalysts prevent the formation of toxic species, the reactivity of oxidized Pd surfaces used in CH₄ catalytic combustion were studied. An ordered PdO-like monolayer was found to be less reactive towards CO than adsorbed O on Pd. On the other hand, the PdO layer favored a lower activation energy C₃H₆ oxidation pathway. The results indicated that Pd oxidation reduces the sticking coefficient of reactive species but once molecules adsorb, the oxide surface can reduce the activation energy for subsequent reaction.     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).