Affine Hecke algebras and the Schubert calculus

Using a combinatorial approach that avoids geometry, this paper studies the structure of K_T(G/B), the T-equivariant K-theory of the generalized flag variety G/B. This ring has a natural basis (the double Grothendieck polynomials), where is the structure sheaf of the Schubert variety X_w. For rank two cases we compute the corresponding structure constants of the ring K_T(G/B) and, based on this data, make a positivity conjecture for general G which generalizes the theorems of M. Brion (for K(G/B)) and W. Graham (for H_T^*(G/B)). Let [X^λ]K_T(G/B) be the class of the homogeneous line bundle on G/B corresponding to the character of T indexed by λ. For general G we prove “Pieri–Chevalley formulas” for the products , , , and , where λ is dominant. By using the Chern character and comparing lowest degree terms the products which are computed in this paper also give results for the Grothendieck polynomials, double Schubert polynomials, and ordinary Schubert polynomials in, respectively K(G/B), H_T^*(G/B) and H^*(G/B).     

Nonnegative curvature and cobordism type

We show that in each dimension n = 4k, k≥ 2, there exist infinite sequences of closed simply connected Riemannian n-manifolds with nonnegative sectional curvature and mutually distinct oriented cobordism type. W. Tuschmann’s research was supported in part by a DFG Heisenberg Fellowship.     

Photonic crystals--a step towards integrated circuits for photonics.

The field of photonic crystals has, over the past few years, received dramatically increased attention. Photonic crystals are artificially engineered structures that exhibit a periodic variation in one, two, or three dimensions of the dielectric constant, with a period of the order of the pertinent light wavelength. Such structures in three dimensions should exhibit properties similar to solid-state electronic crystals, such as bandgaps, in other words wavelength regions where light cannot propagate in any direction. By introducing defects into the periodic arrangement, the photonic crystals exhibit properties analogous to those of solid-state crystals. The basic feature of a photonic bandgap was indeed experimentally demonstrated in the beginning of the 1990s, and sparked a large interest in, and in many ways revitalized, photonics research. There are several reasons for this attention. One is that photonic crystals, in their own right, offer a proliferation of challenging research tasks, involving a multitude of disciplines, such as electromagnetic theory, nanofabrication, semi-conductor technology, materials science, biotechnology, to name a few. Another reason is given by the somewhat more down-to-earth expectations that photonics crystals will create unique opportunities for novel devices and applications, and contribute to solving some of the issues that have plagued photonics such as large physical sizes, comparatively low functionality, and high costs. Herein, we will treat some basics of photonic crystal structures and discuss the state-of-the-art in fabrication as well give some examples of devices with unique properties, due to the use of photonic crystals. We will also point out some of the problems that still remain to be solved, and give a view on where photonic crystals currently stand.     

Dimension Theory and Nonstable K 1

This article provides an introduction to A. Bak's theory of group-valued functors on categories with structure and dimension and applies this theory to the algebraic K-theory functors nonstable K ₁ and K ₂.     

Photocatalytic polypyrrole-TiO2-nanoparticles composite thin film generated at the air-water interface

Herein, we report a new method of generation of TiO(2) nanoparticles (NPs) incorporated thin films of polypyrrole (PPy) at the air-water interface. Aqueous TiO(2) NPs when treated with H(2)O(2) and left in a chamber of pyrrole vapor resulted in the formation of a film at the interface, in addition to bulk precipitate. Spectroscopic, X-ray diffraction, and electron microscopic measurements establish the formation of a thin film of PPy with the incorporation of TiO(2) NPs. The TiO(2)-containing PPy films when transferred onto glass substrates were able to photo catalyze the decomposition of aqueous organic dyes: methyl orange and methylene blue. Further, these films could also photo catalyze the oxidation of iodide to triiodide ions in aqueous potassium iodide solution. We find that the PPy-TiO(2) composite films catalyze the reactions in the presence of light more efficiently than a suspension of TiO(2) NPs.     

On the photometric determination of trivalent rhodium with eriochromecyanine RC

Summary Eriochromecyanine RC has been used as chromogenic reagent for the photometric determination of rhodium(III) on a micro scale. A coloured Rh(III)-ECRC chelate with _max 530 nm at pH 4.0 (25°C) is formed. A detailed study has been made concerning to characteristics, composition and stability of the chelate. Standard deviation was ±1.17%.

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Über die photometrische Bestimmung von dreiwertigem Rhodium mit Eriochromcyanin RC

Zusammenfassung Ergebnisse einer Untersuchung über die Zusammensetzung und Stabilität des Komplexes werden mitgeteilt. Das Absorptionsmaximum liegt bei 530 nm (pH 4,0; 25°C). Bestimmungen konnten mit einer Standardabweichung von ±1,17% durchgeführt werden.

     

Binding studies of sodium dodecyl benzene sulphonate with poly(N-vinyl-2-pyrrolidone)

The binding of sodium dodecyl benzene sulphonate (SDBS) with poly(N-vinyl-2-pyrrolidone) (PVP) has been investigated at 303.15 and 313.15 K using equilibrium dialysis, surface tension, viscosity, ultrasound velocity and ultrasound absorption techniques. From each of these studies four distinct regions of SDBS-PVP interactions were observed. Interaction of SDBS with PVP was found to involve the binding of surfactant dimers with the polymer molecule followed by usual micellization. The binding data has been analyzed in terms of various models of polymer-surfactant interaction.     

Heterocyclic inflammation inhibitors

Non steroidal anti-inflammatory drugs are the most widely used medicines for relief of pain. These drugs have some side effects, particularly toxicity in the gastrointestinal tract and kidneys. Various approaches have been used for obtaining safer anti-inflammatory drugs. In this review we have summarized the recent developments in the following areas; (i) mode of action of NSAIDs (ii) Role of COX-1 & COX-2 in inflammation, (iii) Different approaches used to improve gastric tolerance i.e. chemical manipulation, formulation & co-administration, development of non specific (COX-1 & COX-2 inhibitors) and specific (COX-2 inhibitors) inflammation inhibitors, and development of inflammation inhibitors having a mode of action other than COX-1 & COX-2 inhibition. We have also focused on the safety of COX-2 inhibitors and the synthesis of heterocyclic compounds and their role as inflammation inhibitors.     

Simulation of the Adhesion of Particles to Surfaces

The removal of micrometer and submicrometer particles from dielectric and metal films represents a challenge in postchemical mechanical polishing cleaning. Proper modeling of the adhesive force between contaminant particles and these films is needed to develop optimal solutions to postchemical mechanical polishing cleaning. We have previously developed and experimentally validated a model to describe the adhesion between spherical particles and thin films. This simulation expands previous models to characterize the adhesive interaction between asymmetrical particles, characteristic of a polishing slurry, and various films. Our simulation accounts for the contact area between particles and substrates, as well as the morphology of the surfaces. Previous models fail to accurately describe the contact of asymmetrical particles interacting with surfaces. By properly accounting for nonideal and geometry and morphology, the simulation predicts a more accurate adhesive force than predictions based upon an ideal van der Waals model. The simulation is compared to experimental data taken for both semi-ideal particle-substrate systems (polystyrene latex spheres in contact with silicon films) and asymmetrical systems (alumina particles in contact with various films). Copyright 2001 Academic Press.