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).     

Study of solar features causing GMSs with 250γ<<Emphasis Type="Italic">H</Emphasis><400γ

The effect of solar features on geospheric conditions leading to geomagnetic storms (GMSs) with planetary index,A ^P ≥ 20 and the range of horizontal component of the Earth’s magnetic fieldH such that 250γ <H < 400γ has been investigated using interplanetary magnetic field (IMF), solar wind plasma (SWP) and solar geophysical data (SGD) during the period 1978–99. Statistically, it is observed that maximum number of GMSs have occurred during the maximum solar activity years of 21st and 22nd solar cycles. A peculiar result has been observed during the years 1982, 1994 when sunspot numbers (SSNs) decrease very rapidly while numbers of GMSs increase. No distinct association between yearly occurrence of disturbed days and SSNs is observed. Maximum number of disturbed days have occurred during spring and rainy seasons showing a seasonal variation of disturbed days. No significant correlation between magnitude (intensity) of GMSs and importance ofH _α , X-ray solar flares has been observed. Maximum number of GMSs is associated with solar flares of lower importance, i.e., SF during the period 1978-93.H _α , X-ray solar flares occurred within lower helio-latitudes, i.e., (0–30)°N to (0–30)°S are associated with GMSs. NoH _α , X-ray solar flares have occurred beyond 40°N or 40°S in association with GMSs. In helio-latitude range (10–40)°N to (10–40)°S, the 89.5% concentration of active prominences and disappearing filaments (APDFs) are associated with GMSs. Maximum number of GMSs are associated with solar flares. Coronal mass ejections (CMEs) are related with eruptive prominences, solar flares, type IV radio burst and they occur at low helio-latitude. It is observed that CMEs related GMS events are not always associated with high speed solar wind streams (HSSWSs). In many individual events, the travel time between the explosion on the Sun and maximum activity lies between 58 and 118 h causing GMSs at the Earth.     

Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

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.     

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.