Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

A method of computing the gradient and the Hessian of the quality criterion in parametric optimization of continuous-discrete stochastic systems

We propose an effective method of numerical determination of the gradient vector and the Hessian matrix of a quadratic quality criterion in parametric optimization of continuous-discrete stochastic dynamic control systems based on the application of adjoint equations. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 20–25.     

Temperature Dependence of InSb Reflectivity in the Far Infrared: Determination of the Electron Effective Mass

We measured the dependence of the reflectivity of InSb crystals upon temperature in the submillimeter region using monochromatic radiation from an optically pumped far infrared (FIR) laser. The measures allowed us to determine the value of the electron effective mass at low temperatures with radiations of different frequencies. Our measurements extend the results obtained recently on pure crystals with magneto-optical methods to the low temperatures region where only old measures were available.     

Exciton states in In x Ga1−x As/GaAs double quantum wells: Normalized reflection spectra

Il Nuovo Cimento D - Normalized reflection spectra in GaInAs/GaAs quantum wells are shown for two sets of samples with different alloy concentration (x=9% and 18.5%) and well thickness ranging from...     

Toughening of epoxies via craze-like damage

The fracture behavior of a core-shell rubber (CSR) modified epoxy is investigated using both fracture mechanics and microscopy tools. The CSR-modified epoxy is found to be toughened via numerous line-array cavitations of the CSR particles, followed by plastic flow of the epoxy matrix. The toughening effect via the above craze-like damage process is found to be as effective as that of the well-known widespread rubber cavitation/matrix shear yielding mechanisms. The conditions for triggering the craze-like damage appear to be both stress state and rubber concentration dependent. The type of rubber tougheners utilized also plays a critical role in triggering this rather unusual craze-like damage in epoxy systems. © 1993 John Wiley & Sons, Inc.     

Dependence of an equilibrium state of a two-phase medium on surface tension coefficient and on temperature

An existence theorem for the variational problem for the two-phase medium energy functional is proved. Dependence of the solution on the surface tension coefficient and on the temperature is investigated. Bibliography: 7 titles. Dedicated to V. A. Solonnikov on his sixtieth anniversary Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 131–150. Translated by S. Yu. Pilyugin.     

Using completely implicit methods to solve the direct problem of nozzle theory

An iterative method from the class of completely implicit methods (CIM) is proposed for solving the equation of the velocity potential of elliptical-hyperbolic type. The advantage of the proposed method compared to other CIM schemes is demonstrated in application to mixed perfect gas flows in a nozzle of a given shape. Accuracy issues, rate of convergence, and various techniques of ensuring stability in the hyperbolic region are discussed. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 39–51.     

Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators

This paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.