Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

X-ray absorption spectra of niobium dichalcogenides and their first-row transition-metal intercalates

X-ra!. K-absorption spectra of niobium in niobium dichalcogenides. namely NbS, and NbSe, and their first-row transition-metal intercalates Mi P 3N bSz (M = Cr. Mn. Fe. Co. Ni) and Ml#,NbSe2 (M = Fe. CO). have been measured together with those in niobium metal. The spectra of these materials are \er? similar to one another. They reflect the transitions to the partially filled niobium d band with some p character. A bariety of x-ray absorption nearedge structures (XASES) associated with the K edges of intercalated atoms are also presented and discussed.

A note on mass transfer in turbulent wall jets

THE PROCESS of mass transfer from saturated porous surfaces virtual origin ; exposed to turbulent air streams finds many practical applitransverse coordinate; cations. In many cases, the air stream will be in the form of a height of nozzle above flat plate--radial wall jet; wall jet over the porous surface. The aerodynamics of both plane and radial wall jets have been investigated in detail and a vast amount of literature is available on the subject [l-3].

Turbulent Wall-Jets in Conical Diffusers

Abstract is not available.

Mathematics, nature and cryptography: Insights from philosophy of information

One influential image that is popular among scientists is the view that mathematics is the language of nature. The present article discusses another possible way to approach the relation between mathematics and nature, which is by using the idea of information and the conceptual vocabulary of cryptography. This approach allows us to understand the possibility that secrets of nature need not be written in mathematics and yet mathematics is necessary as a cryptographic key to unlock these secrets. Various advantages of such a view are described in this article.

Electron energy equation for an atomic radiating plasma

The electron-energy equation for an atomic radiating plasma is considered in this work. Using the atomic model of Bates, Kingston and McWhirter, the radiation loss-term valid for all optical thicknesses is obtained. A study of the energy gained by electrons in inelastic collisions shows that the radiation loss term can be neglected only for rapidly-decaying or fast-growing plasmas. Emission from optically thin plasmas is considered next and an exact expression is given for the total radiation loss in a recombination continuum. A derivation of the Kramers-Unsöld approximation is presented and the error involved in estimating the total emitted recombination radiation by this approximation is shown to be small.

Investigations on the melting and bending modulus of polymer grafted bilayers using dissipative particle dynamics

Understanding the influence of polymer grafted bilayers on the physicomechanical properties of lipid membranes is important while developing liposomal based drug delivery systems. The melting characteristics and bending moduli of polymer grafted bilayers are investigated using dissipative particle dynamics simulations as a function of the amount of grafted polymer and lipid tail length. Simulations are carried out using a modified Andersen barostat, whereby the membrane is maintained in a tensionless state. For lipids made up of four to six tail beads, the transition from the low temperature L-beta phase to the L-alpha phase is lowered only above a grafting fraction of G(f)=0.12 for polymers made up of 20 beads. Below G(f)=0.12 small changes are observed only for the HT4 bilayer. The bending modulus of the bilayers is obtained as a function of G(f) from a Fourier analysis of the height fluctuations. Using the theory developed by Marsh Biochim. Biophys. Acta 1615, 33 (2003)] for polymer grafted membranes, the contributions to the bending modulus due to changes arising from the grafted polymer and bilayer thinning are partitioned. The contributions to the changes in kappa from bilayer thinning were found to lie within 11% for the lipids with four to six tail beads, increasing to 15% for the lipids containing nine tail beads. The changes in the area stretch modulus were also assessed and were found to have a small influence on the overall contribution from membrane thinning. The increase in the area per head group of the lipids was found to be consistent with the scalings predicted by self-consistent mean field results. (C) 2010 American Institute of Physics.

Challenges in Earth sciences: the 21st century

The 21st century poses many challenges for global sustainability. Among them, most importantly, the human race will encounter scarcity of raw materials and conventional energy resources. And, India may have to take the brunt of these problems as it is going to be the most populated region of the world with concomitant increase in energy demand and requirement of other resources. India will be the testing ground for introducing newer ways of green technology and innovative principles of resource management and utilization. With the vagaries of potential climate change gathering clouds in the background, Earth sciences will have a special and predominant role in guiding the society in prioritizing our resource discovery, utilization and their consumption and the upkeep of environment. On the fundamental level, Earth sciences are going through a most exciting phase of development as a born-again science. Technological breakthroughs including the satellite-based observations augur well for gaining new insights into Earth processes. A set of exciting fundamental problems that are globally identified will set the stage for an exhilarating period of new discoveries. Improvements in numerical and computer-based techniques will assist in modelling of Earth processes to unprecedented levels. India will have to take special effort in improving the existing experimentation facilities in the Earth science departments of the country, and also the general level of Earth science education to meet the global standards. This article presents an Earth science vision for the 21st century in an Indian context.

Polymorphism in Opto-Electronic Materials with a Benzothiazole-fluorene Core: A Consequence of High Conformational Flexibility of pi-Conjugated Backbone and Alkyl Side Chains

Fluorene and its derivatives are well-known organic semiconducting materials in the field of opto-electronic devices because of their charge transport properties. Three new organic semiconducting materials, namely, 2,2'-((9,9-butyl-9H-fluorene-2,7-diyl)bis(4,1 phenylene))bisbenzod]thiazole, C4; 2,2'-((octyl-9H-fluorene-2,7-diyl)bis(4,1 phenylene))bisbenzod]thiazole, C8; and 2,2'-((9,9-dodecayl-9H-fluorene-2,7-diyl)bis(4,1 phenylene))bisbenzod]thiazole, C12 with a benzothiazole-fluorene backbone, were synthesized and characterized for their photophysical properties. A phenomenon of concomitant polymorphism has been investigated in the first two derivatives (C4 and C8) and has been analyzed systematically in terms of the packing characteristics involving pi ... pi interactions. The conformational flexibility of the pi-conjugated 2,2'-(fluorene-2,7-diyl)bis(4,1 phenylene)bisbenzod]thiazole backbone coupled with orientational freedom of the terminal alkyl chains were found to be the key factors responsible for these polymorphic modifications. Attempts to grow suitable crystals for single crystal X-ray diffraction of compound C12 were unsuccessful.

Study of local environment of Ag in Ag/CeO2 catalyst by EXAFS

The combustion synthesized Ag/CeO2 catalysts have been characterized by Extended Xray Absorption Fine Structure (EXAFS) spectroscopy at the Ag K-edge. It has been found that Ag+ like species is present in 1% Ag/CeO2 catalyst, whereas mostly Ag metal clusters are found in 3% Ag/CeO2. The analysis of EXAFS spectra indicates that about one oxygen atom is coordinated to Ag central atom at a distance of 2.19 Angstrom in 1% Ag/CeO2 catalyst along with eight coordinated Ag-Ag bond at 2.86 Angstrom. The Ag-O bond is absent in 3% Ag/CeO2. (C) 2002 Elsevier Science Ltd. All rights reserved.

A convenient enantiospecific methodology for (-)-(1R,5S)-1,5-dimethylbicyclo[3.3.0]octa-2,7-dione: A formal total synthesis of (-)-ceratopicanol

An enantiospecific formal total synthesis of (-)-ceratopicanol starting from the readily and abundantly available monoterpene (R)-limonene is described. A combination of Claisen rearrangement-intramolecular diazo-ketone cyclopropanation-regiospecific reductive cyclopropane cleavage reactions are employed for the stereo- and regiospecific generation of the two vicinal ring junction quaternary carbon atoms.

Effect of calcium stoichiometry on the dielectric response of CaCu3Ti4O12 ceramics

CaxCu3Ti4O12 (x=0.90, 0.97, 1.0, 1.1 and 1.15) polycrystalline powders with variation in calcium content were prepared via the oxalate precursor route. The structural, morphological and dielectric properties of the ceramics fabricated using these powders were studied using X-ray diffraction, scanning electron microscope along with energy dispersive X-ray analysis, transmission electron microscopy, electron spin resonance (ESR) spectroscopy and impedance analyzer. The X-ray diffraction patterns obtained for the x = 0.97, 1.0 and 1.1 powdered ceramics could be indexed to a body-centered cubic perovskite related structure associated with the space group Im3. The ESR studies confirmed the absence of oxygen vacancies in the ceramics that were prepared using the oxalate precursor route. The dielectric properties of these suggest that the calcium deficient sample (x = 0.97) has a reduced dielectric loss while retaining the high dielectric constant which is of significant industrial relevance. (C) 2012 Elsevier Ltd. All rights reserved.

AN EXPERIMENTAL STUDY ON EFFERVESCENT ATOMIZATION OF BIO-OIL FUELS

This paper presents the work on detailed characterization of effervescent spray of Jatropha and Pongamia pure plant oils. The spray characteristics of these biofuels are compared with those of diesel. Both macroscopic and microscopic spray characteristics at different injection pressures and gas-to-liquid ratio (GLR) have been studied. The particle/droplet imaging analysis (PDIA) technique along with direct imaging methods are used for the purpose of spray characterization. Due to their higher viscosity, pure plant oils showed poor atomization compared to diesel and a blend of diesel and pure plant oil at a given GLR. Pure plant oil sprays showed a lower spray cone angle when compared to diesel and blends at lower GLRs. However, the difference is not significant at higher GLRs. Droplet size measurements at 100 mm downstream of the exit orifice showed reduction in Sauter mean diameter (SMD) diameter with increase in GLR. A radial variation in the SMD is observed for the blend and pure plant oils. Pure oils showed a larger variation when compared to the blend. Spray unsteadiness has been characterized based on the image-to-image variation in the mean droplet diameter and fluctuations in the spray cone angle. Results showed that pure plant oil sprays are more unsteady at lower GLRs when compared to diesel and blend. A critical GLR is identified at which the spray becomes steady. The three regimes of spray operation, namely ``steady spray,'' ``pulsating spray,'' and ``spray and unbroken liquid jet'' are identified in the injection pressure-GLR parameter space for these pure plant oils. Two-phase flow imaging inside the exit orifice shows that for the pure plant oils, the flow is highly transient at low GLRs and the bubbly, slug, and annular two-phase flow regimes are all observed. However, at higher GLRs where the spray is steady, only the annular flow regime is observed.