1.3 µm vertical microcavities with InAs/InGaAs quantum dots and devices based on them

Various structures with optical microcavities and active layers based on InGaAs/GaAs quantum dots MBE-grown on GaAs substrates were studied theoretically and experimentally. LEDs for the 1.3 μm spectral range with narrow spectral characteristics and low light beam divergence were fabricated. Vertical lasing at 1.3 μm was obtained in a structure with oxidized AlO/GaAs mirrors under injection pumping. __________ Translated from Fizika i Tekhnika Poluprovodnikov, Vol. 35, No. 7, 2001, pp. 889–895. Original Russian Text Copyright ? 2001 by Sakharov, Krestnikov, Maleev, Kovsh, Zhukov, Tsatsul’nikov, Ustinov, Ledentsov, Bimberg, Lott, Alferov.     

Weak curvature conditions and functional inequalities

We give sufficient conditions for a measured length space (X,d,ν) to admit local and global Poincaré inequalities, along with a Sobolev inequality. We first introduce a condition DM on (X,d,ν), defined in terms of transport of measures. We show that DM, together with a doubling condition on ν, implies a scale-invariant local Poincaré inequality. We show that if (X,d,ν) has nonnegative N-Ricci curvature and has unique minimizing geodesics between almost all pairs of points then it satisfies DM, with constant N². The condition DM is preserved by measured Gromov-Hausdorff limits. We then prove a Sobolev inequality for measured length spaces with N-Ricci curvature bounded below by K>0. Finally we derive a sharp global Poincaré inequality.     

Remark about scalar curvature and Riemannian submersions

We consider modified scalar curvature functions for Riemannian manifolds equipped with smooth measures. Given a Riemannian submersion whose fiber transport is measure-preserving up to constants, we show that the modified scalar curvature of the base is bounded below in terms of the scalar curvatures of the total space and fibers. We give an application concerning scalar curvatures of smooth limit spaces arising in bounded curvature collapses.

     

Some Geometric Calculations on Wasserstein Space

We compute the Riemannian connection and curvature for the Wasserstein space of a smooth compact Riemannian manifold. This research was partially supported by NSF grant DMS-0604829.     

Second hyperpolarizability of ethynyl-linked azobenzene molecular wires

A series of oligomers consisting of ethynyl-linked azobenzene units was prepared using Pd-catalyzed cross coupling. The linear and nonlinear optical properties of the oligomers were investigated. The molecular second hyperpolarizability, gamma, followed the power law gamma proportional, variant n(2.12+/-0.05) (n is the number of repeat units) for unusually large molecular lengths exceeding 360 conjugated bonds (>49 nm). The exceptional exciton delocalization length is attributed to the rigidity of the conjugated backbone.     

Naphtho[2,3-d]-2-selena-l,3-diazole as a reagent for the determination of macro to submicro quantities of palladium

Five analytical procedures, gravimetric, spectrophotometric, radiometric, fluorometric and atomic-absorption, have been developed for the determination of macro to submicro amounts of palladium. The methods are based on the reaction of PdCl(2), with naphtho[2,3-d]-2-selena-l,3-diazole. Analytical conditions such as the reaction time, concentration ranges, effect of pH and of 68 foreign ions, and solvent extraction were studied. Information relating to the structure and formula of palladium-piazselenol reaction products is included.     

Supersymmetric path integrals

The supersymmetric path integral is constructed for quantum mechanical models on flat space as a supersymmetric extension of the Wiener integral. It is then pushed forward to a compact Riemannian manifold by means of a Malliavin-type construction. The relation to index theory is discussed.Research supported by an NSF postdoctoral fellowship     

Theoretical and experimental approach to spectrofluorometric extractive titrations

Spectrofluorometric extractive titration (SFET) is a sensitive method for determining trace amounts of certain metals. This technique combines titration, extraction and fluorometry and is more sensitive than any of these individual techniques. A theoretical treatment is derived and is compared favorably to an experimental procedure using Ga(III) and Al(III) as metals being titrated by 8-hydroxyquinoline(oxine). A sensitivity value for the experimental SFET is derived and calculated for the Ga(III) and Al(III)-oxine systems.     

Remark about the spectrum of the -form Laplacian under a collapse with curvature bounded below

We give a lower bound on the number of small positive eigenvalues of the -form Laplacian in a certain type of collapse with curvature bounded below.