The reference wave solution for a two-frequency wave propagating in a random medium

In this work a new reference wave method for solving parabolic-type equations is proposed. The performance of the method is demonstrated by applying it to the equation governing the propagation of the two-frequency mutual coherence function in a random medium. An analytic solution is presented for arbitrary correlation properties of the medium. It is shown that when approximating the transverse structure function of the medium by a quadratic form, the solution reduces to the exact result derived previously. Extensions to more general types of media are considered.     

High-frequency magnetoimpedance in nanocomposites

The transmission of millimeter-range electromagnetic waves (30–50 GHz) through a magnetic nanocomposite thin film exhibiting tunnel magnetoresistance (TMR) is calculated. The relative change of transmission coefficient in an applied magnetic field due to the magnetorefractive effect is approximately linear with TMR and strongly depends on nanocomposite resistivity and film thickness. The obtained results are in a good agreement with experiment.     

Heat polynomial analogues for equations with higher order time derivatives

We generalize the heat polynomials for the heat equation to more general partial differential equations, of higher order with respect to both the time variable and the space variables. Whereas the heat equation requires only one family of polynomials, for an equation of the ?th order with respect to time we introduce ? families of polynomials. These families correspond to the ? initial conditions specified by the Cauchy problem.     

Many body effects and internal transitions of confined excitons in GaAs and CdTe quantum wells

Many body effects contribute significantly to the energy states of electron-hole pairs confined in quantum wells in the presence of excess electrons. We present results of optically detected resonance spectroscopy of the internal transitions of photo-excited electron-hole pairs in the presence of excess electrons for GaAs QWs and CdTe QWs. Compared to the case of isolated negatively charged excitons, excess electrons produce a large blue shift of the internal transitions in modulation-doped GaAs quantum wells (QWs) for filling factor <2, and similar effects are found in CdTe QWs. For filling factor >2 no internal transitions are observed. These measurements demonstrate the strong effects of electron-electron correlations on the internal transitions of charged excitons in these quasi-2D systems and the importance of magnetic translation invariance. In the presence of excess electrons, the observed internal transitions are those of a magnetoplasmon bound to a mobile valence band hole.     

The convex hull property and topology of hypersurfaces with nonnegative curvature

We prove that, in Euclidean space, any nonnegatively curved, compact, smoothly immersed hypersurface lies outside the convex hull of its boundary, provided the boundary satisfies certain required conditions. This gives a convex hull property, dual to the classical one for surfaces with nonpositive curvature. A version of this result in the nonsmooth category is obtained as well. We show that our boundary conditions determine the topology of the surface up to at most two choices. The proof is based on uniform estimates for radii of convexity of these surfaces under a clipping procedure, a noncollapsing convergence theorem, and a gluing procedure.     

Annealing behavior of gel‐spun polyethylene fibers at temperatures lower than needed for significant shrinkage

The annealing at 373 K of ultrastrong, gel‐spun polyethylene (PE) has been studied. At this temperature, the fibers show no significant shrinkage. Still, a significant decrease in the mechanical properties is observed. The fibers have been analyzed with differential scanning calorimetry (DSC), temperature‐modulated differential scanning calorimetry (TMDSC), atomic force microscopy (AFM), and small‐angle X‐ray scattering (SAXS). During the annealing, the glass transition of the intermediate phase is exceeded, as shown by DSC. When split for structure analysis by AFM, the annealed fibers undergo plastic deformation around the base fibrils instead of brittle fracture. The quasi‐isothermal TMDSC experiments are compared to the minor structural changes seen with SAXS and AFM. The loss of performance of the PE fibers at 373 K is suggested to be caused by the oriented intermediate phase, and not by major changes in the structure or morphology. The overall metastable, semicrystalline structure is shown by TMDSC to posses local regions that can melt reversibly. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 403–417, 2003     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.