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.     

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.

     

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.

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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.

     

Biligand metal chelates of 1,10-phenanthroline and several salicyclic acid derivatives in solution

Summary Mixed ligand complexes of copper(II), zinc(II), nickel(II) and cobalt(II) ions involving 1,10-phenanthroline (phen) as primary and 3,5-dinitrosalicylic acid (dnsa), 5-nitrosalicylic acid (nsa), 5-chlorosalicylic acid (csa) and 3,5-dibromosalicylic acid (dbsa) as secondary ligands in solution have been investigated potentiometrically [25°, µ = 0.1 M [NaClO₄], medium 50% v: v aqueous ethanol]. The stability order of mixed ligand complexes with respect to the metal ions obeys the natural order: cobalt(II) < nickel(II) < copper(II) > zinc(II). The stabilities of the heterometal chelates have been compared with the corresponding homometal chelates of the secondary ligands and have been interpreted in terms of metal-ligand effects and coulombic interactions between various ligand anion species present.     

Molybdenum complexes of bioinorganic interest. New dioxomolybdenum(VI) complexes of schiff bases derived from salicylaldehydes and salicylhydrazide

Summary New dioxomolybdenum(VI) complexes MoO₂L · H₂O (LH₂=Schiff base) derived from Salicylhydrazide and salicylaldehyde, 5-chloro-, 5-bromo-, 5-nitro-, 3-methoxy, 3-ethoxy-, 3,5-dichlorosalicylaldehyde and 2-hydroxy-1-naphthaldehyde have been synthesized and characterized, together with the MoO₂L · THF adducts. The complexes are monomers, nonelectrolytes and diamagnetic, and contain acis O=Mo=O     

Ring size effects. III. Carbonium ion stability as a factor in the course of the pinacol rearrangement

The formation of the initial carbonium ion in the pinacol rearrangement will be the major factor in determining product composition when the reaction is carried out at 0°C with concentrated sulfuric acid.     

Anomalies in the asymmetric hydroboration of olefins with the 11 adduct of (+)-α-pinene and BH3 · THF

The hydroboration of cis-2-butene and cis-3-hexene with pure diisopinocampheylborane (IPC₂BH) and monoisopinocampheylborane (IPCBH₂), both prepared from (+)-α-pinene, were studied. In contrast to IPC₂BH, which yielded R-(?)-2-butanol and R-(?)-3-hexanol in 98.4 and 94.5% optical purities, IPCBH₂ yielded S-(+)-2-butanol and S-(+)-3-hexanol in 23.6 and 19.7% optical purifies respectively. PMR examination of the methanolyzed products were utilized to establish the species present in the freshly prepared and aged $\text{1}\text{1}$ adduct from (+)-α-pinene and BH₃ · THF. The results confirm the interpretation previously advanced for the major differences realized in asymmetric hydroboration with the fresh and aged $\text{1}\text{1}$ adducts.