Equivariant Giambelli and determinantal restriction formulas for the Grassmannian

The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in the torus equivariant integral cohomology ring of the Grassmannian. As a corollary, we obtain an equivariant version of the Giambelli formula.Comment: 16 pages, 3 figures, LaTex, uses epsfig and psfrag; for the revised version: title changed; Proof of Theorem 3 changed; 3 references added and 1 deleted; other minor change

High precision laser radar tracking device

This thesis explores a relatively new Solid Silver Thin Film Source technology, for the implementation of a novel High Precision Laser Radar Tracking device. The process which consists of a Ag+-Na+ ion exchange, is designed in two steps. It utilizes an initial electric field-aided ion exchange step for a predeposition, and a subsequent second diffusion step to force the profile latitude necessary for optimization of the device. While the entire project of implementing this device, consists of analyzing, processing, polishing and testing, this thesis covers only the process aspect in detail. The success achieved by obtaining the required Power Coupling Ratio curve on a Simple Coupler, demonstrates a novel integrated optic multimode feed for a Monopulse LIDAR application

On the Mass Eigenstate Composition of the 8B Neutrinos from the Sun

The present data of gallium experiments provide indirectly the only experimental limit on the fraction of $\nu_2$ mass eigenstate for the $^8$B neutrinos from the Sun. However, if to use the experimental data alone, the fraction of $\nu_2$ and, consequently, $sin^2\theta_{sol}$ still is allowed to be varied within a rather broad range. The further experimental efforts are needed to clear this point.Comment: 13 pages, 1 figure, 1 table. Corrected version, published in JCAP04(2007)00

Numerical bifurcation study of superconducting patterns on a square

This paper considers the extreme type-II Ginzburg-Landau equations that model vortex patterns in superconductors. The nonlinear PDEs are solved using Newton's method, and properties of the Jacobian operator are highlighted. Specifically, it is illustrated how the operator can be regularized using an appropriate phase condition. For a two-dimensional square sample, the numerical results are based on a finite-difference discretization with link variables that preserves the gauge invariance. For two exemplary sample sizes, a thorough bifurcation analysis is performed using the strength of the applied magnetic field as a bifurcation parameter and focusing on the symmetries of this system. The analysis gives new insight in the transitions between stable and unstable states, as well as the connections between stable solution branches.Comment: 31 page

Possibility of Recoating of Impurities on Product Kaolin during Froth Flotation - HRTEM-EDS Study

Attempts were made to remove the Fe, Ti minerals from Gujarat kaolin by SC-HGMS and ultraflotation to improve the optical properties. The removal of Fe was higher by SC-HGMS, but that of Ti was almost the same by both techni-ques. The Fe content of the products was relatively low, but the brightness was lower than the expected. A drastic improvement in brightness was observed for the SC-HGMS product compared to the ultra flotation product. One of the probable reasons for the low enhancement in brightness by flotation was thought to be recoating of the impurities on the clay surface during flotation. XPS study conducted on the flotation product ruled out the possibility of such a coating. HRTEM-EDS analyses showed that most of the titania is present in the form of anatase particles of very small size. A part of the Fe forms independent parti-cles of goethite /hematite having nano size. Rest of the Fe is found to be closer to anatase or kaolinite particles either as a part of the structure or nano sized independ-ent particles adhering to the surface and hence is not easily separated. The ultra fine grains of Fe stained ana-tase remaining in the kaolinite surface after flotation is found to have a strong pigment effect. During flotation, high shear energy is given for dispersion and conditioning which is possibly reducing the particle size to sub-micron / nano level. The dissatisfying brightness of the flotation product is attributed to the presence of these fine / colloidal impurities. Fe content in the product samples is relatively low and its influence on brightness is probably smaller than that of the Fe stained anatase. The organic matter and ferriferous smectite identified in the sample even at small percentages may also have a pig-ment effect due to their dark color and colloidal distri-bution

Planar Optical Waveguides Using a Silver-Sodium Ion Exchange

A planar optical waveguide fabrication is reported using a silver-sodium, electric field enhanced, Al thin film masked, ion exchange process. In this study, silver atoms from the thin film replace the sodium ions in soda-lime glass, resulting in a higher index of refraction. It should be noted that soda lime glass was used as a substrate even though it varies in composition, contains metallic impurities and is generally not of optical quality. Problems related with sterling silver and design width are discussed. A better understanding of requirements for coupling light into the waveguide, edge polishing, index profiling, focusing of the source etc, is needed to further analyze this wave guide

Antioxidant Activity in Pulp and Peel of Three Mango Varieties

The aim of the present study was to estimate the content of total polyphenols and flavonoids and to investigate in-vitro antioxidant potential of methanolic extracts of peel and pulp in three Indian mango varieties. Antioxidant activity was assessed using [2,2'-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid)] ABTS+ assay, 2,2-diphenyl-1-picryl-hydrazyl (DPPH) assay, ferric-reducing ability of plasma (FRAP) assay, and phosphomolybdate assay for Total Antioxidant Capacity (TAC). Total phenolic and flavonoid content was also determined, and expressed in gallic acid equivalent (GAE) and quercetin equivalent (QE), respectively. Results of this study indicated that methanolic extracts of mango peel had significantly higher antioxidant activity compared to that of pulp (29.69 and 3.12), irrespective of the method or variety used. Free radical scavenging and antioxidant activity may be attributed to presence of phenolic (24.61mg GAE/g DM in the peel and 2.01mg GAE/g DM in the pulp) and flavonoid compounds (24.95mg QE/g DM in the peel and 16.15mg E/g DM in the pulp). Antioxidant activity determined by ABTS, DPPH and FRAP assays in mango peel was significantly higher than in the mango pulp (24.95 1.96mg TE /g DM, 23.68 versus 4.60mg BHA/g DM and 40.52 versus 2.781mg TE/g DM), respectively. Results for scavenging activity against DPPH were 96.18% for the peel and 23.86% for the pulp, while, free radical scavenging activity results using ABTS+ assay were 99.62% in the peel and 13.46% in the pulp. Our study justifies research in processing of mango peel into useful, functional food ingredients (powders or extracts)