Showing papers by "Tata Institute of Fundamental Research published in 1982"

Semistable sheaves on projective varieties and their restriction to curves

Abstract: Let X be a nonsingular projective variety of dimension n over an algebraically closed field k. Let H be a very ample line bundle on X. If V is a torsion free coherent sheaf on X we define deg V to be cl(V), c~(H)"~ and/~(V) = deg V/rk V. We call V sernistable (resp. stable) if for all proper subsheaves W of V we have #(W) < #(V) [resp. #(W) < #(V)] (cf. [7, 14]). In this paper we prove that if V is semistable on X then its restriction to a general complete intersection curve of sufficiently high degree is semistable (Theorem 6.1). To give an idea of the proof assume X is a surface and V a vector bundle of rank 2. The restriction of V to a general curve C" of degree m is not semistable if and only if it is not semistable on the generic curve Ym defined over the function field of IPH~ H"). Let/S," be the line bundle on Y,, contradicting the semistability of VI Y,, (cf. Sects. 4.1 and 4.2). First we show that L,, extends uniquely to a line bundle L m on X (Proposition 2.1). If we can get L" as a subbundle of V we are through, for then L" would contradict the semistability of V. So we would like the restriction map H~ Hom(Lm, V))~H~ Hom(L m, V)) to be surjective. Now for fixed L it follows from the lemma of Enriques-Severi (Proposition 3.2; [6, Corollary 7.8]) that H~ Horn(L, V))~H~ Horn(L, V)) is surjective for large m. Therefore it is enough if the L" remain the same line bundle L for infinitely many m. To prove that L,, = L we construct a degenerating family of curves D f ~S, X x S 3 D p ~X, such that the generic fibre is a curve Ct"+ 1) of degree 2 "+ 1 and the special fibre is a reduced curve with two nonsingular components CI") of degree 2" (cf. Sect. 5). Let (m) denote 2". Extending the subbundle Lt,,+~)[Ct"+~) to a subsheaf of p*(V) on D and restricting the extension to CI") gives a lower bound for the maximal degree of a line subbundle of V[CIm ) in terms of that for V[Ctm+I ) (Proposition 4.3). This implies that degL,, is bounded (Lemma 6.5.1) so that for an infinite subsequence of m, degL,, is constant. If degLtm + r)= degLt,,) by refining the above argument with the degenerating family one can prove that Lt"+,)[ CI")

Equivalence of the Two-Dimensional Directed-Site Animal Problem to Baxter's Hard-Square Lattice-Gas Model

Abstract: The directed-site animal problem on the square and triangular lattices is shown to be equivalent to Baxter's hard-square lattice-gas model with anisotropic next-nearest-neighbor interactions at a disorder point. The exact solution of the latter is used to determine the animal numbers as functions of their size in the two cases. Expressions in closed form are proposed for the number of animals on an infinite strip in terms of width and animal size, and for the average transverse extent of animals of a given size.

Generalized coherent states and the uncertainty principle

Abstract: We derive from a dynamical symmetry property that the linear and nonlinear Schr\"odinger equations with harmonic potential possess an infinite string of shape-preserving coherent wave-packet states with classical motion. Unlike the Schr\"odinger state with $\ensuremath{\Delta}x\ensuremath{\Delta}p=\frac{\ensuremath{\hbar}}{2}$, the uncertainty product can be arbitrarily large for these states showing that classical motion is not necessarily linked with minimum uncertainty. We obtain a generalization of Sudarshan's diagonal coherent-state representation in terms of these states.

Pentose phosphate pathway mutants of yeast.

Abstract: A glucose-negative mutant of Saccharomyces cerevisiae lacking 6-phosphogluconate dehydrogenase, the second enzyme of the pentose phosphate pathway, has been obtained by inositol starvation. Suppression of this mutant for growth on glucose takes place by the loss of glucose 6-phosphate dehydrogenase. A lesion in the latter enzyme alone leaves growth paractically unaffected. The mutations define the respective structural genes.

Relativistic Beaming in the Central Components of Double Radio Quasars

Abstract: Using a large sample of 78 well-observed double quasars, we have investigated several consequences of the relativistic beaming model. In this model the ratio of the strengths of the central component and outer lobes of a double source depends on whether the jet axis lies close to or away from the line of sight, If this is the actual situation, the fraction of emission from the core,f c, may be used as a statistical measure of the orientation of the source and should be correlated with other source parameters which also depend on the inclination of the jet axis to the line of sight.

On Ergodic quasi-invariant measures of group automorphism

Abstract: We study the dynamics of projective transformations and apply it to (i) prove that the isotropy subgroups of probability measures on algebraic homogeneous spaces are algebraic and to (ii) study the class of ergodic quasi-invariant measures of automorphisms of non-compact Lie groups. It is shown that their support is always a proper subset and that under certain conditions on the Lie group the induced homeomorphism of the support is topologically equivalent to a translation of a compact group.

On uniformly distributed orbits of certain horocycle flows

Abstract: G = SL (2,R), Γ=SL(2,Z), u 1 = ( 1 0 l 1 )(where t e R) and let μ be the G-invariant probability measure on G/Gamma. We show that if x is a non-periodic point of the flow given by the (u t )-action on G/Gamma then the (u t )-orbit of x is uniformly distributed with respect to μ ; that is, if Ω is an open subset whose boundary has zero measure, and l is the Lebesque measure on R then, as T→∞T -1 {0≤t≤ T\u t xeΩ} , converges to μ (Ω).

Temperature-sensitive paralytic mutations on the second and third chromosomes of Drosophila melanogaster

Abstract: Seven temperature-sensitive paralytic mutants were recovered from 4544 lines of ethylmethanesulphonate (EMS) treated autosomes in Drosophila melanogaster. These mutants have been designated temperature-induced paralytic (tip). The tip mutations belong to six different genes; four of these, tip-A, Tip-B, tip-C and tip-D are on the second chromosome while tip-E and tip-F are on the third chromosome. This paper describes the paralysing behaviour and genetic localization of the tip mutants.

Surface-enhanced second-harmonic generation at a metallic grating

Abstract: The theory of surface-enhanced second-harmonic generation at a metallic grating is developed. Using the form of the nonlinear source polarization given by Bloembergen et al. [Phys. Rev. 174, 813 (1968)], we solve Maxwell's equations to obtain the fields at the second-harmonic frequency. The calculations are done up to second order in the surface-roughness parameter. These perturbation expressions are used to evaluate numerically the second-harmonic intensity, in various directions, produced by a plane wave incident on a metallic grating. The resonant enhancement in the second-harmonic intensity due to surface-plasmon excitation at fundamental frequency $\ensuremath{\omega}$ is discussed and the results compared with some recent experimental observations. The second-harmonic fields are also shown to get enhancement due to excitation of surface plasmons at $2\ensuremath{\omega}$; these, however, correspond to local-field enhancements at $2\ensuremath{\omega}$ and are evanescent in nature.

Fibres de ’t Hooft Speciaux et Applications

Abstract: On s’interesse aux fibres vectoriels algebriques de rang deux sur un espace projectif de dimension deux ou trois sur un corps de base algebriquement clos.

A modification over Sakoe and Chiba's dynamic time warping algorithm for isolated word recognition

Abstract: A modification over Sakoe and Chiba's dynamic time warping algorithm for isolated word recognition is proposed. It is shown that this modified algorithm works better without any slope constraint. Also, this algorithm not only consumes less computation time but also improves the word recognition accuracy.

General covariance, Accelerated frames and the particle concept

Abstract: The definition of particle states in various accelerated frames is considered It is shown that in any realistically accelerated system, quantum field theory can be formulated without any ambiguity We further show that the definition of a particle based on Green's function techniques does not always agree with the definition based on explicit quantization We analyse the standard accelerated detector results from this point of view and show that the uncertainty principle imposes a rigorous bound on these detection processes

Intermediate spin iron(III) complexes of N4,N4-disubtituted 2-acetylpyridine thiosemicarbazone

Abstract: Magnetic susceptibility and Mossbauer spectroscopy measurements have been carried out on [FeIII(SAm)Cl2], and indicate an intermediate spin state for the ferric ion. The temperature-independent magnetic moment of (4.17±0.05) μB, the quadrupole splitting=4.09 mm s−1 and isomer shift=0.133 mm s−1 are in agreement with such formulation. These studies, together with infrared data, are used to suggest a possible structure of the complex.

Does the standard hot-big-bang model explain the primordial abundances of helium and deuterium

Abstract: It is shown that according to the standard hot-big-bang nucleosynthesis calculations, no single value of the ratio eta of baryon to the photon number density can explain the right abundances of both /sup 4/He and /sup 2/D. A slight neutrino degeneracy, however, provides a testable solution for eta which is in conformity with the current estimate of the baryonic component of the density parameter (..cap omega../sub N/)/sub 0/ of the Universe.

Overstability of acoustic modes and the solar five-minute oscillations

Abstract: The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the κ-mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.

Quantum conformal fluctuations in a singular space-time

Abstract: The cosmological solutions of Einstein's general relativistic equations lead inevitably to space–time singularities1. However, general relativity is only an approximation to a fully quantized theory of gravity and we need to consider whether singularity persists in the quantum domain. Although a full quantum theory of gravity has not yet been developed, we show here that the above question can be tackled in a simplified model where only the conformal degree of freedom is quantized. Previous applications of this technique had shown that in specific cases the quantum conformai fluctuations (QCF) from the classical solutions diverge at the classical singularity, thus rendering the classical solution physically meaningless2,3. Recently one of us (J.V.N. ref. 4) has generalized this result to cover all dust cosmologies. Here we show that this conclusion is applicable to even more general types of cosmological singularities.