Singular integrals with rough kernels along real-analytic submanifolds in

mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in .

     

A functional model for polynomially posinormal operators

In this paper we introduce a class of operators naturally extending the classes of hyponormal and posinormal operators. For this class we construct a generating family of eigendistributions, unitary invariants and a functional model.     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

Reply to comments on "Radiative transfer over small distances from a heated metal"

Some previous works showed that radiative transfer between two closely spaced, lossy media diverges as 1/L(2), where L is the spacing between the two media. This divergent power transfer clearly violates energy conservation. The explanation for this unphysical result is that too many optical modes were counted in those previous works, and many of those modes are physically unattainable. Moreover, many physically significant optical modes were not counted in the previous works.     

Jordan Superalgebras Defined by Brackets

Jordan superalgebras defined by brackets on associative commutativesuperalgebras are studied. It is proved that any such superalgebrais imbedded into a superalgebra defined by Poisson brackets.In particular, all Jordan superalgebras of brackets are i-special.The speciality of these superalgebras is also examined, andit is proved, in particular, that the Cheng–Kac superalgebrais special.     

Rapid In-Situ Effective Dose Equivalent Measurement Using the Superheated-Liquid-Droplet Technique

This study performs a rapid in-situ effective dose equivalent evaluation using SLD. The effective dose equivalent recommended by ICRP-26 allows the direct calculation of the primary personnel limiting quantity by measuring the dose equivalent in various internal organs or tissues. Therefore, an indigenous multislab phantom coupled with the SLD multicounting system is set up to evaluate the effective dose equivalent, H _E . Moreover, MCNP computational results are also compared. Comparisons indicate that underestimation of practical evaluations (within –15%) may be largely attributed to the insensitive nature of SLD in measuring the -ray induced dose.     

On the structure of weight modules

Given any simple Lie superalgebra , we investigate the structure of an arbitrary simple weight -module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuperalgebra. Then we classify the cuspidal Levi subsuperalgebras of all simple classical Lie superalgebras and of the Lie superalgebra W. Most of them are simply Levi subalgebras of , in which case the classification of all finite cuspidal representations has recently been carried out by one of us (Mathieu). Our results reduce the classification of the finite simple weight modules over all classical simple Lie superalgebras to classifying the finite cuspidal modules over certain Lie superalgebras which we list explicitly.

     

Reorientation of anisotropy in a square well quantum hall sample

We have measured magnetotransport at half-filled high Landau levels in a quantum well with two occupied electric subbands. We find resistivities that are isotropic in perpendicular magnetic field but become strongly anisotropic at nu = 9/2 and 11/2 on tilting the field. The anisotropy appears at an in-plane field, B(ip) approximately 2.5 T, with the easy-current direction parallel to B(ip) but rotates by 90 degrees at B(ip) approximately 10 T and points now in the same direction as in single-subband samples. This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model.     

Scaling of the conductivity spectra in ionic glasses: dependence on the structure

A scaling approach in the conductivity formalism is applied to lithium tellurite glasses of different compositions. We observe that the hopping frequency can be used as the scaling frequency in the absence of well-defined dielectric loss peaks, and a universality of the scaling of the conductivity can be obtained for compositions with a similar structure. Further, the reasons behind the inapplicability of the scaling approach reported recently are elucidated in terms of structure of the glasses.     

Use of the organic crystal DAST for terahertz beam applications

We report the use of the organic crystal DAST as a freely propagating electromagnetic-wave sensor at terahertz (THz) frequency. We also report the result of using a DAST crystal as a mid-IR THz emitter. Compared with the optical rectification from our best ZnTe emitter, that obtained by use of DAST demonstrates a sixfold enhancement of radiation at 7-20 THz.