Riemann-Cartan-Weyl geometries, quantum diffusions and the equivalence of the free maxwell and Dirac-Hestenes equations

We introduce the Riemann-Cartan-Weyl (RCW) space-time geometries of quantum mechanics with the most general trace-torsion non-exact Weyl 1-form, and characterize it in the Clifford bundle. Two electromagnetic potentials appear in the Weyl form, one having a zero field and the other one being the codifferential of a 2-form. We give the derivation of the non-linear equation for the wave function producing the exact Weyl one-form, which also defines the amplitude of a Dirac-Hestenes spinor operator field (DHSOF). We prove an equivalence between the free Maxwell equation for an extremal electromagnetic field and the Dirac-Hestenes equation for a DHSOF on a Riemann-Cartan-Weyl manifold, associating the electromagnetic potentials of the Weyl one-form with the internal electromagnetic potentials derived from the rotational dependance of a DHSOF. We show that this association produces a breaking of detailed balance in the spin plane. We discuss the relations with stochastic electrodynamics and the Navier-Stokes equation.     

Riemann-Cartan-Weyl quantum geometry,I: Laplacians and supersymmetric systems

In this first article of a series dealing with the geometry of quantum mechanics, we introduce the Riemann-Cartan-Weyl (RCW) geometries of quantum mechanics for spin-0 systems as well as for systems of nonzero spin. The central structure is given by a family of Laplacian (or D'Alembertian) operators on forms of arbitrary degree associated to the RCW geometries. We show that they are conformally equivalent with the Laplacian operators introduced by Witten in topological quantum field theories. We show that the Laplacian RCW operators yield a supersymmetric system, in the sense of Witten, and study the relation between the RCW geometries and the symplectic structure of loop space. The RCW family of Laplacians are the infinitesimal generators of diffusion processes on nondegenerate space-times of systems of arbitrary spin.     

Two-dimensional problem of diffraction by dielectric cylinder of arbitrary cross-section in plane-layered medium. TheE-polarization case

An algorithm is developed for numerical solution of the two-dimensional problem of scattering of an E-polarized field by a dielectric cylinder in a plane-layered medium. Plane-wave scattering by a cylinder imbedded in a homogeneous dielectric layer with rectangular and rhombic cross-sections is studied.     

Study of wind characteristics at heights of 200 to 800 meters using a decimeter sodar

The results of the experiment carried out in July–August 1997 using a two-position sodar are reported. Different types of intensity and spectrum variations of scattered acoustic signals have been obtained. The possibilities of using the sodar for the study of atmospheric turbulence and search of signals caused by “Fresnel” scattering from “plane” irregularities are discussed. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 7, pp. 841–848, July, 1998.     

The Linear Kerr Effect

Russian Physics Journal -     

Measurement of energy of medium-mass and heavy cosmic-ray nuclei by a specific energy deposition at the maximum of hadron showers in dense matter

The possibility of measuring the energy of cosmic-ray nuclei (for energies higher than 1 TeV) by means of recording the greatest specific energy deposition in hadron showers generated in dense matter is investigated. This method makes it possible to improve the accuracy of energy measurements by thin calorimeters in studying high-energy cosmic rays at high altitudes. Attainable accuracies in measuring energy are considered for the cases of light and heavy nuclei. The results of a relevant simulation are compared with data from the Kosmos-1713 satellite-borne experiment.     

A note on the equal division kernel and the α‐power model

The equal division kernel and the α‐power solution are two recently proposed theories of coalition formation in n‐person characteristic function games with sidepayments. A closed form solution for payoff disbursement is derived from the α‐power model for n‐person games with only 1, n‐1, and n‐person permissible coalitions and no weak players. It is shown that for this class of games, which are frequently employed to experimentally test theories of coalition formation, the equal division kernel is a special case of the α‐power model with α = 1/2.     

The missing link in teachers’ knowledge about common fractions division

The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers’ knowledge concerning this issue. Nine teachers who study towards a M.Ed. degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers’ pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using constructivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply – multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.     

Superior biolubricant from a species of red microalga

The rheological properties of the sulfated polysaccharide of the red microalga Porphyridium sp., a heteropolymer with a molecular weight of 3-5 x 10(6) Da, indicated that this material might be an excellent candidate for lubrication applications: the viscosity of the polysaccharide is stable over a range of temperatures, pH values, and salinities. In this study, various rheological and lubricant properties of the polysaccharide were evaluated in comparison with those of a widely used biolubricant, hyaluronic acid. The viscosity of the Porphyridium sp. polysaccharide remained essentially unchanged in a temperature range of 25-70 degrees C. In tribology tests on a ball-on-flat ceramic pair, the values for the friction coefficient and wear rate for the pair lubricated with polysaccharide were remarkably lower than those for hyaluronic acid, especially at high loads. In a test on a steel ring/ultrahigh-molecular-weight polyethylene (UHMWPE) block pair, the wear tracks on the surface of the UHMWPE were more pronounced for hyaluronic acid than for the polysaccharide. Atomic force microscopy showed that the polysaccharide was effectively adsorbed onto mica surfaces, forming ultrathin coating layers in the nanometer range. As is required for biolubricant applications, the polysaccharide was not degraded by hyaluronidase. The stability of the Porphyridium sp. polysaccharide to heat and to hyaluronidase combined with its ability to reduce friction and wear indicate its potential as an advantageous biolubricant.