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.     

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

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.     

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).