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

Semi-supervised and Active-learning Scenarios: Efficient Acoustic Model Refinement for a Low Resource Indian Language

We address the problem of efficient acoustic-model refinement (continuous retraining) using semi-supervised and active learning for a low resource Indian language, wherein the low resource constraints are having i) a small labeled corpus from which to train a baseline `seed' acoustic model and ii) a large training corpus without orthographic labeling or from which to perform a data selection for manual labeling at low costs. The proposed semi-supervised learning decodes the unlabeled large training corpus using the seed model and through various protocols, selects the decoded utterances with high reliability using confidence levels (that correlate to the WER of the decoded utterances) and iterative bootstrapping. The proposed active learning protocol uses confidence level based metric to select the decoded utterances from the large unlabeled corpus for further labeling. The semi-supervised learning protocols can offer a WER reduction, from a poorly trained seed model, by as much as 50% of the best WER-reduction realizable from the seed model's WER, if the large corpus were labeled and used for acoustic-model training. The active learning protocols allow that only 60% of the entire training corpus be manually labeled, to reach the same performance as the entire data

Growth Stress Induced Tunability of Dielectric Constant in Thin Films

It is demonstrated here that growth stress has a substantial effect on the dielectric constant of zirconia thin films. The correct combination of parameters - phase, texture and stress - is shown to yield films with high dielectric constant and best reported equivalent oxide thickness of 0.8 nm. The stress effect on dielectric constant is twofold, firstly, by the effect on phase transitions and secondly by the effect on interatomic distances. We discuss and explain the physical mechanisms involved in the interplay between the stress, phase changes and the dielectric constant in detail.Comment: 11 pages, 5 figure

RSK bases and Kazhdan-Lusztig cells

From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra. Applications to invariant theory, over various base rings, of the general linear group and representation theory of the symmetric group are discussed.Comment: 31 pages, latex; version 2 differs substantially in exposition from version 1; for version 3: added important references, corrected typos, added comments suggested by referee, results unchange

Inverse beta decay reaction in 232^{232}Th and 233^{233}U fission antineutrino flux

Energy spectra of antineutrinos coming from $^{232}$Th and $^{233}$U neutron-induced fission are calculated, relevant inverse beta decay $\bar{{\nu}_e}+p \to n + e^{+}$ positron spectra and total cross sections are found. This study is stimulated by a hypothesis that a self-sustained nuclear chain reaction is burning at the center of the Earth ("Georeactor"). The Georeactor, according to the author of this idea, provides energy necessary to sustain the Earth's magnetic field. The Georeactor's nuclear fuel is $^{235}$U and, probably, $^{232}$Th and $^{233}$U. Results of present study may appear to be useful in future experiments aimed to test the Georector hypothesis and to estimate its fuel components as a part of developments in geophysics and astrophysics based on observations of low energy antineutrinos in Nature.Comment: 6 pages in LaTeX and 2 ps figures. Submitted to Physics of Atomic Nucle

Urticaria - some observations

Urticaria has been known from antiquity. The disorder was known to the Arabs as essera and it has found a place in the writings of Cesius (circa 30 BC–45 AD). Although the condition was recognised as an entity, its cause was a mystery to the physicians of those times. It was initially thought to be a manifestation of idiosyncrasy and later believed to be a form of neuroses. However, now the pathophysiological basis of urticaria is well understood. The development of antihistamine group of drugs, paved the way for the management of urticaria

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

Unique Factorization For Tensor Products of Parabolic Verma Modules

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra with Cartan subalgebra $\mathfrak{h}$. We prove a unique factorization property for tensor products of parabolic Verma modules. More generally, we prove unique factorization for products of characters of parabolic Verma modules when restricted to certain subalgebras of $\mathfrak{h}$. These include fixed point subalgebras of $\mathfrak{h}$ under subgroups of diagram automorphisms of $\mathfrak{g}$ and twisted graph automorphisms in the affine case.Comment: 20 page

Current Status of Radioisotope Applications in Defence

Reviews the current status of radioisotope applications in Defence- R&D Establishments, Defence Inspectorates, Ordnance Factories, Public Sector Undertakings under the Defence Ministry, Army, Navy and Air Force Establishments and Military Hospitals. It also lists the users of film badge service in Defence. Training programmes in radioisotope applications in Defence conducted by DRDO organisations have also been highlighted