Exact interior solutions in 2+1-dimensional spacetime

An exact formulation of two-dimensional chiral hydrodynamics with diffeomorphism and conformal anomalies is provided. The constitutive relation involving the stress tensor is computed. It reveals a one parameter class of solutions which is a new result. For a particular value of this parameter, the results found in the gradient expansion scheme are reproduced. Moreover, the constitutive relation is analogous to the corresponding relation for an ideal fluid, appropriately modified to include the chirality property, which has also been derived here.     

Ceric Ammonium Nitrate Catalysed Protection of Alcohols by 3, 4-Dihydro-2H-pyran

Hydroxyl compounds readily add to dihydropyran in presence of a catalytic amount of ceric ammonium nitrate to give high yield of tetrahydropyranyl ethers.     

1-Soliton solution of the coupled KdV equation and Gear–Grimshaw model

This paper carries out the integration of the coupled KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The domain restrictions of the coefficients of nonlinear and dispersion terms fall out. The results are then supplemented by numerical simulations.     

Asymmetric synthesis of (4S,5S)-2-oxo-4-phenyloxazolidine-5-carboxylic acid using a 1,2-addition of PhMgBr to an N-sulfinimine derived from (R)-glyceraldehyde acetonide and (S)-t-BSA

We report an asymmetric synthesis of (4S,5S)-2-oxo-4-phenyloxazolidine-5-carboxylic acid via stereoselective addition of phenylmagnesium bromide (PhMgBr) to an N-sulfinimine derived from (R)-glyceraldehyde acetonide. (S)- and (R)-Glyceraldehyde acetonides, important chiral synthons in synthetic organic chemistry, are prepared from the corresponding epichlorohydrin using an identical synthetic methodology.     

Differential operators on a polarized abelian variety

Let be an ample line bundle over a complex abelian variety . We show that the space of all global sections over of and are both of dimension one. Using this it is shown that the moduli space of rank one holomorphic connections on a compact Riemann surface does not admit any nonconstant algebraic function. On the other hand, is biholomorphic to the moduli space of characters of , which is an affine variety. So is algebraically distinct from the character variety if is of genus at least one.

     

Projective Structure,Symplectic Connection and Quantization

Let X be a connected Riemann surface equipped with a projective structure . Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using , this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using , a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed.     

Topical issue on Geometry, Integrability and Nonlinearity in Condensed Matter Physics

Recent developments in the study of nonlinear phenomena have led to the realization that a combination of the concepts of integrability, geometry and topology provides a new powerful framework for describing a great variety of physical systems. It was therefore felt that the compilation of a special issue comprising articles on the interdiseiplinary topic of Geometry, Integrability and Nonlinearity in Condensed Matter Physics, would indeed be timely. The enthusiastic response and support that we received from the active researchers in this subject, when we organized an International Conference on the above topic from July 15 to July 20, 2001, in Bansko, Bulgaria, provided a further motivation for undertaking this task. As the topic is interdisciplinary in nature, the articles in this volume contain new results on a wide range of subjects. These include among others, integrable equations and the interplay between geometry and nonlinearity, the role of optical solitons in communication. (and, possibly, computation), common nonlinear and geometrical aspects of condensed matter, field theory, and so on. The increasingly important role played by geometry and topology in diverse areas such as the quantum Hall effect, localization, deformation and elasticity, quasiparticle kinetics and dynamics, spin systems, membranes, is highlighted in some of the articles. There are papers in which essential links of nonlinearity to differential geometry are identified and many elegant mathematical methods are presented. Some other articles focus on how the mathematical tools of geometry and nonlinear analysis can be applied to solve certain physical problems. Given the vast range of titles, it was difficult to strictly divide the contributions into distinct categories. Except for the pedagogical introductory article by Rajaraman titled "CP _N Solitons in Quantum Hall Systems", which essentially "sets the stage" for the various themes covered, we have grouped the articles broadly under the following headings: Geometry, integrability and mathematical physics; Solitons: Interaction phenomena, nonlinear optics; Condensed matter physics; Soft condensed matter physics; Quantum phenomena. We gratefully acknowledge the support from Los Alamos National Lab, USA; Université de Cergy-Pontoise, France; The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and the Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, in putting this special volume together. We believe that the cross-fertilization and synergy of a host of ideas in seemingly disparate fields of physics would lead to the natural emergence of new paradigms, which in turn could pave the way for collaborative research to arrive at new solutions of complex nonlinear problems. It is our hope that this topical issue will be useful in providing an impetus for achieving this broad objective. Radha Balakrishnan, Chennai, India Rossen Dandoloff, Cergy-Pontoise, France Vladimir Gerdjikov, Sofia, Bulgaria Dimitar Pushkarov, Sofia, Bulgaria Avadh Saxena, Los Alamos, USA     

Einstein<Emphasis Type="Italic">A</Emphasis>-coefficients for rotational transitions in the ring-chain isomer of C<Subscript>5</Subscript>H<Subscript>2</Subscript>

Laboratory formation of four isomers of C⁵H² molecule is reported and detection of the ring-chain isomer (isomer 1) of C₅H₂ in cosmic objects has been suggested. For identification of a molecule in cosmic objects, one of the required input data is EinsteinA-coefficients (radiative transition probabilities) for the molecule. Here, we report EinsteinA-coefficients for electric dipole transitions in the ring-chain isomer of C₅H₂ among the rotational levels of the ground electronic and ground vibrational states up to 21 cm⁻¹.     

A modified volumetric method for the estimation of streptomycin sulphate in pharmaceuticals

Summary A volumetric method for the estimation of streptomycin sulphate in pharmaceuticals is based on the quantitative discharge of the violet colour of the maltol-iron complex, produced when streptomycin is hydrolysed in alkaline medium and treated with ferric chloride, by potassium permanganate. It is simple, accurate and other antibiotics such as dihydrostreptomycin, sodium salt of benzyl penicillin, chloramphenicol do not interfere. Procain penicillin has to be separated by extractio with chloroform.

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Zusammenfassung Die beschriebene volumetrische Streptomycinbestimmung in Arzneimitteln beruht auf dem Abbau des Streptomycins in alkalischer Lösung zu Maltol, Bildung des Maltol-Eisen(III)-Komplexes und Titration mit Permanganat bis zur Entfärbung. Das Verfahren ist einfach auszuführen und gibt Werte von befriedigender Genauigkeit. Dihydrostreptomycin, Chloramphenicol sowie das Natriumsalz des Benzylpenicillins stören nicht. Procain-Penicillin muß vorher durch Extraktion mit Chloroform abgetrennt werden.