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).     

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.     

Tracing of interference fringes using average gray value and simultaneous row and column scan

An algorithm for computer tracing of interference fringes is reported. The method uses the average gray-level value for thresholding, row and column scans for determining the type of the scan and simultaneous row and column scan for tracing. The proposed method yield good result even for low-contrast and high-noise images. The program for the interferogram tracing was written using MATLAB6.     

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.     

Thermal analysis and thermal expansion studies on high density YBa2−xLaxCu3O7−δ, 0x0.2

The compositions in the YBa_2−xLa_xCu₃O_7−δ (0x0.2) system were prepared by the solid state reaction, employing a novel high-temperature oxygen sintering route. The modified sintering route yields dense slab like microstructures with large grains. The decomposition (incongruent melting) temperature of the YBa₂Cu₃O_7−δ (Y-123) phase was found to shift to higher temperatures with increasing oxygen partial pressure and lanthanum content. Structure remained orthorhombic up to x=0.2 with a decrease in the orthorhombic strain ((b−a)/b). Iodometric titration indicated a systematic increase in the oxygen content with increasing lanthanum content. Thermo-gravimetric studies in various oxygen partial pressures revealed that the oxygen diffusion in to the YBa₂Cu₃O_7−δ (δ>0.5) lattice is an exothermic event and takes place at temperatures not less than 573 K. High-temperature thermal-expansion measurements in air indicated that the nonlinearity in thermal expansion behaviour was reduced by the substitution of lanthanum.     

Iridodials: enantiospecific synthesis and stereochemical assignment of the pheromone for the golden-eyed lacewing, Chrysopa oculata

1R,2S,5R,8R; 1R,2S,5R,8S; 1S,2S,5R,8R; and 1S,2S,5R,8S-Iridodials have been prepared in five steps from 4aS,7S,7aR and 4aS,7S,7aS-nepetalactones, major components of catnip oil. 1R,2S,5R,8R-Iridodial has been identified as a male-produced male-aggregation pheromone for Chrysopa oculata, the first pheromone of any kind identified for lacewings.     

Synthesis of O,O Ethane Bridged Bis-copper(II) Macrocycles. Selective Enzyme Model for Catecholase Activity

New mononuclear and dinuclear complexes [3-hydroxyethyl-1,3,5,8,11pentaazacyclotridecane]copper(II) (1)/nickel(II) (2) perchlorate and O,O ethane bridged bis-copper(II) (3)/nickel(II) (4) macrocycles have been synthesized and characterized by various spectroscopic techniques, viz. i.r., n.m.r., e.p.r., u.v.–vis. and conductance measurements. Spectral data and conductance measurements reveal that all the complexes are consistent with square-planar geometry and are ionic in nature. The catalytic activity of the dinuclear Cu(II) complex (3) in the presence of pyrocatechol was determined spectrometrically by monitoring the increase of the o-benzoquinone characteristic absorption band at 25,000 cm⁻¹ with respect to time in DMF saturated with molecular oxygen. The kinetic parameters V_max (2.8×10⁻³ M s⁻¹) and K_M (1.4×10⁻³ mm) have been determined by Michaelis–Menten method. Electrochemistry of the dinuclear Cu(II) complex has been studied in the presence of molecular oxygen with pyrocatechol and without pyrocatechol at a scan rate of 0.1 V s⁻¹ by cyclic voltammetry. On addition of pyrocatechol, complex shows a shift in E_pc, E_pa and E_1/2 values indicating the oxidation of substrate (pyrocatechol).     

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%.

---

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.

     

Spectrophotometric determination of indium using gallion

Summary The formation of violet coloured chelate of indium with Gallion has been studied. Indium forms only one chelate with Gallion at p_H 4.5 having _max 610 nm. The composition of the complex formed has been determined by various methods and is found to be 11 (MR). The values of stability constant have been calculated by three methods and the average value of logK obtained is 5.6 ± 0.1. A procedure for the spectrophotometric determination of indium has been suggested.

---

Zusammenfassung Die Bildung eines violetten Chelates von Indium mit dem Reagens Gallion wurde studiert. In bildet damit ein einziges Chelat bei p_H=4,5 und _max=610 nm. Die Zusammensetzung des entstandenen Komplexes wurde nach verschiedenen Methoden ermittelt und gleich 11 (MetallReagens) gefunden. Die Stabilitätskonstante wurde nach drei Verfahren berechnet, wobei sich als Mittelwert logK=5,6±0,1 ergab. Eine Arbeitsvorschrift für die spektrophotometrische Bestimmung des In wird vorgeschlagen.