Showing papers by "Tata Institute of Fundamental Research published in 1989"

Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques.

Abstract: Soient X une courbe algebrique projective lisse de genre g ≥ 2 sur ℂ, r, d des entiers, avec r ≥ 2. On note U(r,d) la variete de modules des fibres algebriques semi-stables sur X de rang r et de degre d, Us(r,d) l’ouvert de U(r,d) correspondant aux fibres stables. On sait que U(r,d) est une variete algebrique projective irreductible et normale. Si r et d ne sont pas premiers entre eux, U(r,d) n’est pas lisse, sauf dans une exception : le cas ou g = 2, r = 2, et d est pair. On supposera dans cet article qu’on n’est pas dans ce cas, On a alors codimU(r,d)(U(r,d)\Us(r,d)) ≥ 2, et U(r,d)\Us(r,d) est le lieu des points singuliers de U(r,d). Si L est un fibre en droites de degre d sur X, on note U(r,L) la sous-variete fermee de U(r,d) correspondant aux fibres vectoriels de determinant isomorphe a L. On etudie dans cet article les groupes de Picard Pic(U(r,d)) et Pic(U(r,L)). On montre d’abord que les varietes U(r,d) et U(r,L) sont localement factorielles. On calcule ensuite Pic(U(r,d)) et Pic(U(r,L)), qui sont decrits au moyen des diviseurs thetas generalises.

Exactly solved model of self-organized critical phenomena.

Abstract: We define a variant of the model of Bak, Tang, and Wiesenfeld of self-organized critial behavior by introducing a preferred direction. We characterize the critical state and, by establishing equivalence to a voter model, determine the critical exponents exactly in arbitrary dimension d. The upper critical dimension for this model is three. In two dimensions the model is equivalent to an earlier solved special case of directed percolation.

Gravitational Collapse and Spacetime Singularities

Abstract: Physical phenomena in astrophysics and cosmology involve gravitational collapse in a fundamental way. The final fate of a massive star when it collapses under its own gravity at the end of its life cycle is one of the most important questions in gravitation theory and relativistic astrophysics, and is the foundation of black hole physics. General relativity predicts that continual gravitational collapse gives rise to a space-time singularity. Quantum gravity may take over in such regimes to resolve the classical space-time singularity. This book investigates these issues, and shows how the visible ultra-dense regions arise naturally and generically as an outcome of dynamical gravitational collapse. It will be of interest to graduate students and academic researchers in gravitation physics, fundamental physics, astrophysics, and cosmology. It includes a detailed review of research into gravitational collapse, and several examples of collapse models are investigated in detail.

An epidemiologic assessment of cancer risk in oral precancerous lesions in India with special reference to nodular leukoplakia.

Abstract: A cohort of 12,212 tobacco users was followed up annually to assess malignant potential of oral precancerous lesions in the Ernakulam district in Kerala, India. A total of 19 new oral cancers were diagnosed over a period of 8 years, and 15 (79%) of these arose from some preexisting precancerous lesion or condition. Nodular leukoplakia showed highest rate of malignant transformation (16% per year) as six of 13 nodular leukoplakia underwent malignant transformation over a mean follow-up period of 2.8 years. The relative risk (3243.2) compared with individuals with tobacco habits but without any precancerous oral lesion was also the highest for nodular leukoplakia. In addition, nodular leukoplakia was associated with submucous fibrosis in two patients, which progressed to oral cancer and was the clinical diagnosis for four lesions that turned out to be malignant on histopathologic examination. Nodular appearance was noted in two other precursor lesions as well. Thus, 14 of 19 oral cancers (74%) were either preceded by nodular leukoplakia and with lesions showing a distinct nodular appearance, or had the clinical appearance of nodular leukoplakia.

Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups

Abstract: Supported by the National Science Foundation during 1986–1988 at the Mathematical Sciences Research Institute, Berkeley, and at the Institute for Advanced Study, Princeton.

Quantization of the liouville mode and string theory

Abstract: We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

Standing shocks in isothermal rotating winds and accretion

Abstract: Les proprietes des ondes de choc stationnaires sont etudiees dans les vents et accretions isothermes en rotation au voisinage d'objets compacts (etoile a neutrons ou trous noirs). L'ecoulement est suppose non dissipatif excepte au niveau des chocs. On montre que pour un ensemble donne de parametres initiaux, l'onde de choc peut etre localisee a l'une des quatre positions. Une analyse de stabilite locale est effectuee pour montrer que dans une certaine etendue des parametres, les ondes de choc sont stables pour certaines localisations

Analysis of preflow push algorithms for maximum network flow

Abstract: We study the class of preflow push algorithms recently introduced by Goldberg and Tarjan for solving the maximum network flow problem on a weighted digraph G(V,E). We improve Goldberg and Tarjanis O(n3) time bound for the maximum distance preflow push algorithm to O(n2√m) and show that this bound is tight by constructing a parametrized worst case network. We then develop the maximal excess preflow push algorithm and show that it achieves a bound of O(n2√m) pushes. Based on this we develop a maximum network flow algorithm for the synchronous distributed model of computation that uses at most O(n2√m) messages and O(n2) time, thereby improving upon the best previously known algorithms for this model.

Decoherence in the density matrix describing quantum three-geometries and the emergence of classical spacetime.

Abstract: We construct the quantum gravitational density matrix \ensuremath{\rho}(${g}_{\ensuremath{\alpha}\ensuremath{\beta}}$,${g}_{\ensuremath{\alpha}\ensuremath{\beta}}^{\mathcal{'}}$) for compact three-geometries by integrating out a set of unobserved matter degrees of freedom from a solution to the Wheeler-DeWitt equation \ensuremath{\Psi}[${g}_{\ensuremath{\alpha}\ensuremath{\beta}}$,${q}_{k(\mathrm{matter})]}$. In the adiabatic approximation, \ensuremath{\rho} can be expressed as exp(-${l}^{2}$) where ${l}^{2}$(${g}_{\ensuremath{\alpha}\ensuremath{\beta}}$,${g}_{\ensuremath{\alpha}\ensuremath{\beta}}^{\mathcal{'}}$) is a specific ``distance'' measure in the space of three-geometries. This measure depends on the volumes of the three-geometries and the eigenvalues of the Laplacian constructed from the three-metrics. The three-geometries which are ``close together'' (${l}^{2}$\ensuremath{\ll}1) interfere quantum mechanically; those which are ``far apart'' (${l}^{2}$\ensuremath{\gg}1) are suppressed exponentially and hence contribute decoherently to \ensuremath{\rho}. Such a suppression of ``off-diagonal'' elements in the density matrix signals classical behavior of the system. In particular, three-geometries which have the same intrinsic metric but differ in size contribute decoherently to the density matrix. This analysis provides a possible interpretation for the semiclassical limit of the wave function of the Universe.

Effect of ordering the codebook on the efficiency of the partial distance search algorithm for vector quantization

Abstract: Recently, C.D. Bei and R.M. Gray (1985) used a partial distance search algorithm that reduces the computational complexity of the minimum distortion encoding for vector quantization. The effect of ordering the codevectors on the computational complexity of the algorithm is studied. It is shown that the computational complexity of this algorithm can be reduced further by ordering the codevectors according to the sizes of their corresponding clusters. >

CeRhIn: A new mixed-valent cerium compound.

Abstract: A new ternary equiatomic compound, CeRhIn, has been synthesized which is found to crystallize in the hexagonal ${\mathrm{Fe}}_{2}$P structure. The unit-cell volume of this compound deviates from that expected on the basis of lanthanide contraction, indicating the nontrivalent state of the Ce ions in this compound. The magnetic susceptibility of CeRhIn shows a broad maximum at about 150 K. Such a maximum is a characteristic feature of the mixed-valent cerium compounds. The resistivity of CeRhIn due to magnetic scattering also shows a broad maximum at about 140 K. Thus from lattice volume, susceptibility, and resistivity measurements, it is concluded that cerium ions are in a mixed-valent state in CeRhIn.

Fay's trisecant identity and conformal field theory

Abstract: We study the correlation functions of a system of free chiral fermions on a compact Riemann surface using techniques of algebraic geometry. Fay's trisecant identity arises as a consequence of the proof of the uniqueness of correlation functions.

Binding of thiocyanate to lactoperoxidase: 1H and 15N nuclear magnetic resonance studies.

Abstract: The binding of thiocyanate to lactoperoxidase (LPO) has been investigated by 1H and 15N NMR spectroscopy. 1H NMR of LPO shows that the major broad heme methyl proton resonance at about 61 ppm is shifted upfield by addition of the thiocyanate, indicating binding of the thiocyanate to the enzyme. The pH dependence of line width of 15N resonance of SC15N- in the presence of the enzyme has revealed that the binding of the thiocyanate to the enzyme is facilitated by protonation of an ionizable group (with pKa of 6.4), which is presumably distal histidine. Dissociation constants (KD) of SC15N-/LPO, SC15N-/LPO/I-, and SC15N-/LPO/CN- equilibria have been determined by 15N T1 measurements and found to be 90 +/- 5, 173 +/- 20, and 83 +/- 6 mM, respectively. On the basis of these values of KD, it is suggested that the iodide ion inhibits the binding of the thiocyanate but cyanide ion does not. The thiocyanate is shown to bind at the same site of LPO as iodide does, but the binding is considerably weaker and is away from the ferric ion. The distance of 15N of the bound thiocyanate ion from the iron is determined to be 7.2 +/- 0.2 Amore » from the 15N T1 measurements.« less

Mechanisms of water transport by epithelial cells.

Abstract: Isosmotic transport of fluid across epithelial cell layers occurs by intraepithelial mechanisms that are not fully understood. Newer methods of measuring water flows across epithelia with higher resolution should now permit some key issues regarding solute-linked water transport to be clarified. Unstirred-layer effects are not likely to be serious sources of error in these measurements with judicious choice of experimental conditions. Progress in ultrastructural stereology has shown that in the proximal tubule most of the transporting membrane is located in the basal aspects of cells, making models based on a hyperosmolar lateral compartment less relevant. The current models of simple transcellular osmosis, though appealing for this simplicity, fail to account for some major experimental findings. Experimental design and methodological limitations have not yet achieved rigorous testing of whether or not epithelia can produce a perfectly isosmotic absorbate without any transepithelial driving forces. A better understanding of the mechanism of translocation of water through the lipid bilayer, the plasma membrane proteins, and special membrane structures like the tight junctions would significantly contribute to our knowledge of the mechanisms and intraepithelial routes by which water is transported by epithelia.

Cycles on the generic abelian threefold

Abstract: H Clemens and C Schoen gave examples of three-folds where the group of codimension two cycles modulo algebraic equivalence has infinite rank. This paper provides yet another example of the same phenomenon.

Parabolic vector bundles on curves

Abstract: Seshadri introduced the notion of parabolic structures on vector bundles [4] and later constructed a moduli space for semistable parabolic vector bundles on curves [2]. In this small note we describe a different construction of the moduli space generalising the method of Gieseker [1]. This has some advantages. This construction is much simpler and shorter than in [2]. It avoids the use of unitary bundles and hence is applicable in positive characteristics. One does not need the introduction and comparison of different parabolic structures. Moreover, some computations which have to be repeated here (proposition 2) become simpler in this method. The generalisation to parabolic principal bundles will be considered in a subsequent paper. I would like to thank M. S. Narasimhan and A. Ramanathan for helpful discussions.

Heat capacity, magnetic susceptibility, and electric resistivity of the equiatomic ternary compound CePdSn

Abstract: Results of low-temperature heat-capacity measurements (2--20 K) on CePdSn and of magnetic-susceptibility and electrical resistivity measurements (4.2--300 K) on CePdSn, GdPdSn, and DyPdSn are presented. These compounds are found to order antiferromagnetically with Neel temperatures (/ital T//sub /ital N//) of 7.5, 14.5, and 11.4 K for Ce, Gd, and Dy compounds, respectively. The Neel temperature of CePdSn is anomalously large compared with that expected on the basis of de Gennes scaling from the /ital T//sub /ital N// of 14.5 K of isostructural GdPdSn, suggesting strong Ce 4/ital f/ conduction-electron hybridization. In the paramagnetic state the susceptibility of CePdSn follows Curie-Weiss behavior between 40 and 300 K with an effective paramagnetic moment close to that of free Ce/sup 3+/ ion, but shows deviation from Curie-Weiss behavior below 40 K. The deviation may be due to the crystalline-electric-field effects. The magnetic entropy of CePdSn shows that the crystal-field-split ground state of Ce/sup 3+/ is a doublet. An analysis of the susceptibility and resistivity results on CePdSn in terms of crystal-field effects is presented.

Dimensional reduction of symmetric higher spin actions i: bosons

Abstract: The dimensional reduction of massless gauge-invariant free Lagrangians for totally symmetric and totally antisymmetric tensors of arbitrary integral spins is carried out for the covariant and light-cone gauges. The structure of the auxiliary fields for the massive Lagrangians so obtained is elucidated.