Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

Caratheodory interpolation kernels

Kernels over the unit disk for which a version of Carathéodory interpolation is true are characterized in a simple computationally verifiable manner.     

Sewings of crumpled cubes revisited

This paper sets forth three mismatch properties, strictly ordered in strength, about sewings of crumpled n-cubes. The strongest is a sufficient but not a necessary condition for a sewing to yield Sn, and the weakest, a necessary but not sufficient one. We show that when both crumpled cubes satisfies the Disjoint Disks Property, then the weakest property implies the sewing yields Sn, and we also show that the intermediate property leads to the same conclusion when just one of the crumpled cubes possesses the Disjoint Disks Property. In addition, we develop examples that confirm sharpness of the relevant Disjoint Disks conditions.     

Effects of UV photon irradiation on SiOx (0 < x < 2) structural properties

Thin films of a-SiO_x (0 < x < 2) were prepared by reactive r.f. magnetron sputtering from a polycrystalline-silicon target in an Ar/O₂ gas mixture. The oxygen partial pressure in the deposition chamber was varied so as to obtain films with different values of x. The plasma was monitored, during depositions, by optical emission spectroscopy (OES) system. Energy dispersive X-ray (EDX) measurements and infra-red (IR) spectroscopy were used to study the compositional and structural properties of the deposited layers.Structural modifications of SiO_x thin films have been induced by UV photons’ bombardment (wavelength of 248 nm) using a pulsed laser. IR spectroscopy and X-ray photoemission spectroscopy (XPS) were used to investigate the structural changes as a function of x value and incident energy. SiO_x phase separation by spinodal decomposition was revealed. The IR peak position shifted towards high wavenumber values when the laser energy is increased. Values corresponding to the SiO₂ material (only Si⁴⁺) have been found for laser irradiated samples, independently on the original x value. The phase separation process has a threshold energy that is in agreement with theoretical values calculated for the dissociation energy of the investigated material.For high values of the laser energy, crystalline silicon embedded in oxygen-rich silicon oxide was revealed by Raman spectroscopy.     

Thermoelectric properties of tin clathrates under hydrostatic pressure

We report the temperature dependence of electrical resistance (R) and thermopower (S) of clathrate Cs₈Sn₄₄ under high pressure up to 1.2 GPa. We observe a reversible gap widening, prominent relaxation effect of R, irreversible increase of |S| under high pressure. We also find that the power factor S²σ (σ: electrical conductivity) reaches a maximum at pressure of 0.3 GPa. Comparison of the experimental results with band structure calculations suggests that the intrinsic vacancy in the clathrate structure of Cs₈Sn₄₄ plays an important role in transport properties under high pressure. Measurements on Cs₈Zn₄Sn₄₂, a clathrate which has defects other than vacancies, are compared with Cs₈Sn₄₄. The results indicate that replacing Sn by Zn has similar effect as the intrinsic vacancy on S.     

Finite Groups Acting on Homology 3-Spheres: On a Result of M. Reni

 We give a list including all finite groups G which admit smooth orientation preserving actions on homology 3-spheres (arbitrary actions, i.e. possibly with fixed points; if the action is free then the group G has periodic cohomology and the classification of such groups is well known). The main work in this direction is due to M. Reni. In the present paper, we complete and extend his results for the case of nonsolvable groups G. Received 19 March 2001; in revised form 15 September 2001     

Feasibility Exploration of Laser‐based Techniques for Characterization of a Flashing Jet

Two‐phase flows hold an interest in many areas of science and engineering. In the safety field, one such topic is the accidental release of flammable and toxic pressure‐liquefied gases. In case of such a release, a flashing vapor explosion takes place resulting in a very dense two‐phase cloud. If the released substance is flammable, this cloud can be combustible and can lead to deflagration or detonation. For understanding the source processes of flashing and risk assessment, data related to cloud characteristics (i.e. droplet size, velocity etc.) is needed especially in the near region of the release. Due to the non‐equilibrium nature of the near field regions accurate data measurement is not possible with intrusive techniques. Therefore, laser‐based optical techniques (like Particle Image Velocimetry (PIV), Particle Tracking Velocimetry and Sizing (PTVS), Phase Doppler Anemometry (PDA) etc.) present the only possibility to obtain information for particle diameter and velocity evolution in this harsh environment.