Weighted Composition Operators between Different Hardy Spaces

Let and be two analytic functions defined on such that. The operator given by is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from a Hardy space H _p into another Hardy space H _q . We apply these results to study composition operators on Hardy spaces of a half-plane. Submitted: November 20, 2001.     

Effect of finite pixel size on optical coupling in QWIPs

We study the optical coupling in quantum well photodetectors, focusing on finite size effects. We introduced a finite-element model of the detector and we show experimentally that the optical coupling efficiency is strongly dependent on the pixel size and that in very small detectors diffraction dominates the grating coupling. A 640 × 512 QWIP focal plane array was characterized to show that the optical response of thinned samples may depend on the substrate thickness noticeably. These results are in much closer agreement with predictions obtained with our model than using standard techniques.     

Spatial-angular Mueller matrices

Arbitrary polarization changing devices are described within paraxial approximation by their action on the spatial angular Stokes parameters associated with the generalized rays of a Wigner formulation of wave optics. This approach leads to the introduction of generalized Mueller matrices being functions of the spatial and angular variables parameterizing generalized rays. We apply this approach to a polarization grating.     

Letter: O(d + 1, d + n + 1)-Invariant Formulation of Stationary Heterotic String Theory

We present a pair of symmetric formulations of the matter sector of the stationary effective action of heterotic string theory that arises after the toroidal compactification of d dimensions. The first formulation is written in terms of a pair of matrix potentials Z ₁ and Z ₂ which exhibits a clear symmetry between them and can be used to generate new families of solutions on the basis of either Z ₁ or Z ₂; the second one is an O(d + 1, d + n + 1)-invariant formulation which is written in terms of a matrix vector W endowed with an O(d + 1, d + n + 1)-invariant scalar product which linearizes the action of the O(d + 1, d + n + 1)symmetry group on the coset space O(d + 1, d + n + 1)/[O(d + 1) × O(d + n + 1)]; this fact opens as well a simple solution-generating technique which can be applied on the basis of known solutions.     

2D thermal/isothermal incompressible viscous flows

2D thermal and isothermal time‐dependent incompressible viscous flows are presented in rectangular domains governed by the Boussinesq approximation and Navier–Stokes equations in the stream function–vorticity formulation. The results are obtained with a simple numerical scheme based on a fixed point iterative process applied to the non‐linear elliptic systems that result after a second‐order time discretization. The iterative process leads to the solution of uncoupled, well‐conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the first time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state flows obtained from the unsteady problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Diboryldiborenes: π‐Conjugated B4 Chains Isoelectronic to the Butadiene Dication

B(sp²)–B(sp³) diborane species based on bis(catecholato)diboron and N‐heterocyclic carbenes (NHCs) underwent catechol/bromide exchange selectively at the sp³‐hybridized boron atom. The reduction of the resulting 1,1‐dibromodiborane adducts led to reductive coupling and isolation of doubly NHC‐stabilized 1,2‐diboryldiborenes. These compounds are the first examples of molecules exhibiting π‐electron delocalization over an all‐boron chain.     

Unsymmetrical,Cyclic Diborenes and Thermal Rearrangement to a Borylborylene

Cyclic diboranes(4) based on a chelating monoanionic benzylphosphine linker were prepared through boron–silicon exchange between arylsilanes and B₂Br₄. Coordination of Lewis bases to the remaining sp² boron atom yielded unsymmetrical sp³‐sp³ diboranes, which were reduced with KC₈ to their corresponding trans‐diborenes. These compounds were studied with a combination of spectroscopic methods, X‐ray diffraction, and DFT calculations. PMe₃‐stabilized diborene 6 was found to undergo thermal rearrangement to gem‐diborene 8 . DFT calculations on 8 reveal a polar boron–boron bond, and indicate that the compound is best described as a borylborylene.