Magnetic calorimeter for registration of small energy release

A scheme of magnetic calorimeter for registration of rare events characterized by small energy release (cosmic rays, WIMPs, solitary X-ray quanta) is proposed. The calorimeter is brought to operation by adiabatic demagnetization, and its magnetic response is measured by a quantum interferometer (SQUID, A. Barone and G. Paterno, Physics and applications of Josephson Effect). Special consideration is given to the specific features of calorimeter operation in the ferromagnetic transition region. The trigger registration of ultrasmall energy release by a ferromagnetic system in the metastable state is described.     

Raman spectroscopy study of REH3 under pressure

The Raman spectroscopic studies of two rare earth trihydrides: Y H₃, HoH₃, have been performed in the pressure range from ambient up to 16 GPa and 25 GPa respectively. For the first time samples of REH₃ in the form of powder have been studied by Raman spectroscopy using the Diamond Anvil Cell (DAC) technique. A rapid decrease of Raman activity has been observed for the hydrides under pressure values in the vicinity of structural phase transition. Metallization as a possible reason for the observed dramatic change of the REH₃ Raman activity has been discussed.     

Positive Schatten(-Herz) Class Toeplitz Operators on the Half-space

On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided to show that various results are sharp. This research was supported by KOSEF(R01-2003-000-10243-0).     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

g-Natural Contact Metrics on Unit Tangent Sphere Bundles

We construct a three-parameter family of contact metric structures on the unit tangent sphere bundle T ₁ M of a Riemannian manifold M and we study some of their special properties related to the Levi-Civita connection. More precisely, we give the necessary and sufficient conditions for a constructed contact metric structure to be K-contact, Sasakian, to satisfy some variational conditions or to define a strongly pseudo-convex CR-structure. The obtained results generalize classical theorems on the standard contact metric structure of T ₁ M.     

Some Decidability and Undecidability Results on Green's Relations for Automatic Monoids

We consider the problem of deciding Green's relations for various types of finitely presented automatic monoids. We establish some decidability as well as some undecidability results.     

Factorisation des polynômes de Poncelet

La condition pour qu’il existe des n-gones de Poncelet, inscrits dans un cercle, et circonscrits à un autre cercle, est polynomiale en les paramètres définissant ces deux cercles. Nous décomposons ces polynômes “de Poncelet” en facteurs irréductibles que nous interprétons géométriquement.     

Nash Equilibria in Noncooperative Predator-Prey Games

A noncooperative game governed by a distributed-parameter predator-prey system is considered, assuming that two players control initial conditions for predator and prey, respectively. Existence of a Nash equilibrium is shown under the condition that the desired population profiles and the environmental carrying capacity for the prey are sufficiently small. A conceptual approximation algorithm is proposed and analyzed. Finally, numerical simulations are performed, too.     

Case study: problem formulation and solution for a real-world sports scheduling problem

This case study paper describes a problem faced every year by the Devon Cricket League in England. Every league match requires two officiating umpires. There are various preferences relating to the deployment of umpires that fall short of being definite constraints. The requirement was to produce a computer system that would allocate umpires in a satisfactory manner without the need for human interaction, since the users of the system will be unqualified amateurs. This necessitated the construction of a very complex objective function, using imprecise and ill-defined information. The biggest challenge was thus one of problem formulation; the solution technique was relatively straightforward. The system has been put into successful use and it is expected that its use will continue indefinitely. The work raises ethical issues regarding work done for customers who are inexperienced amateurs.