On the compactness of isometry groups in complex analysis

We prove that the group of continuous isometries for the Kobayashi or Caratheodory metrics of a strongly convex domain in C-n is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a continuous isometry between a strongly convex domain and the ball has to be biholomorphic or anti-biholomorphic. Combining this with a metric version of Pinchuk's rescaling technique gives the main result.

Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.

Belief Propagation Based Decoding of Large Non-Orthogonal STBCs

In this paper,we present a belief propagation (BP) based algorithm for decoding non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approachinvolves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode non-orthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BP-based decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves near-capacity turbo coded BER performance; for e.g., with BP decoding of 24 x 24 STBC from CDA using BPSK (i.e.,n576 real dimensions) and rate-1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved.

High-Rate,2-Group ML-Decodable STBCs for 2(m) Transmit Antennas

A Space-Time Block Code (STBC) in K-variables is said to be g-Group ML-Decodable (GMLD) if its Maximum-Likelihood (ML) decoding metric can be written as a sum of g independent terms, with each term being a function of a subset of the K variables. In this paper, a construction method to obtain high-rate, 2-GMLD STBCs for 2(m) transmit antennas, m > 1, is presented. The rate of the STBC obtained for 2(m) transmit antennas is 2(m-2) + 1/2(m), complex symbols per channel use. The design method is illustrated for the case of 4 and 8 transmit antennas. The code obtained for 4 transmit antennas is equivalent to the rate-5/4 Quasi-Orthogonal design (QOD) proposed by Yuen, Guan and Tjung.

Novel phase-transition behavior in an aqueous electrolyte solution

We have investigated the near-critical behavior of the susceptibility of a ternary liquid mixture of 3-methylpyridine. water, and sodium bromide as a function of the salt concentration. The susceptibility was determined from light-scattering measurements performed at a scattering angle of 90 degrees in the one-phase region near the locus of lower consolute points. A sharp crossover from asymptotic Ising behavior to mean-field behavior has been observed at concentrations ranging from 8 to 16.5 mass% NaBr. The range of asymptotic Ising behavior shrinks with increasing salt concentration and vanishes at a NaBr concentration of about 17 mass%. where complete mean-field-like behavior of the susceptibility is observed. A simultaneous pronounced increase in the background scattering at concentrations above 15 mass%, as well as a dip in the critical locus at 17 mass % NaBr, suggests that this phenomenon can be interpreted as mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of the molecules and ions. An analogy with tri critical behavior observed in polymer solutions as well as the possibility of a charge-density-wave phase is also discussed. In addition, we, have observed a third soap-like phase an the liquid-liquid interface in several binary and ternary liquid mixtures.

Studies on hypomethylation of liver DNA during early stages of chemical carcinogenesis in rat liver

Our finding that the inhibitors of DNA methylation, 5-azacytidine, 5-azadeoxycytidine or adenosine dialdehyde, given after a carcinogen all potentiated initiation suggested that hypomethylation of DNA during repair synthesis of DNA might play a role in the initiation of the carcinogenic process. To examine this aspect further, we have asked the question, do the nodules which develop from initiated cells after promotion with 1% orotic acid exhibit an altered methylation pattern in their DNA? The methylation status of the DNA from nodules has been examined using the restriction endonucleases HpaII/MspI and HhaI which distinguish between methylated and unmethylated cytosines in their nucleotide recognition DNA 5'-CCGG and 5'-GCGC respectively. The proto-oncogenes, c-myc, c-fos and c-Ha-ras, in the DNA were primarily studied in this investigation because of their possible involvement in cell proliferation and/or in cell transformation and tumorigenesis. The results indicate that in the nodule DNA, c-myc and c-fos are hypomethylated in the sequence of CCGG while the c-Ha-ras shows hypomethylation in the alternating GCGC sequence. This methylation pattern seen in the nodule DNA is not found in the DNA of the non-nodular surrounding liver or liver tissue after exposure to promoter or carcinogen alone. It is also not found in the DNA of regenerating liver. It is particularly significant that the methylation patterns in the c-myc and c-Ha-ras regions are similar to those found in several cancer tissues. The results suggest that this methylation pattern is acquired early in the carcinogenic process and raises the question whether it has any bearing on the process.

A survey of wind engineering studies in India

In this paper, the work that has been done in several laboratories and academic institutions in India in the area of wind engineering in the past 20–30 years has been reviewed. Studies on extreme and mean hourly winds, philosophies adopted in model studies in wind tunnels and some of the important results that have been obtained are described. Suggestions for future studies are indicated.

Temporal associations in fig-wasp-ant interactions: diel and phenological patterns

In a complex multitrophic plant-animal interaction system in which there are direct and indirect interactions between species, comprehending the dynamics of these multiple partners is very important for an understanding of how the system is structured. We investigated the plant Ficus racemosa L. (Moraceae) and its community of obligatory mutualistic and parasitic fig wasps (Hymenoptera: Chalcidoidea) that develop within the fig inflorescence or syconium, as well as their interaction with opportunistic ants. We focused on temporal resource partitioning among members of the fig wasp community over the development cycle of the fig syconia during which wasp oviposition and development occur and we studied the activity rhythm of the ants associated with this community. We found that the seven members of the wasp community partitioned their oviposition across fig syconium development phenology and showed interspecific variation in activity across the day-night cycle. The wasps presented a distinct sequence in their arrival at fig syconia for oviposition, with the parasitoid wasps following the galling wasps. Although fig wasps are known to be largely diurnal, we documented night oviposition in several fig wasp species for the first time. Ant activity on the fig syconia was correlated with wasp activity and was dependent on whether the ants were predatory or trophobiont-tending species; only numbers of predatory ants increased during peak arrivals of the wasps.

A novel supersecondary structure in globular proteins comprising the collagen-like helix and ?-turn

A structure consisting of the polyproline-II or collagen-like helix immediately succeeded by a ?-turn is seen in several synthetic peptides and has been suggested to be the conformational requirement for proline hydroxylation in nascent procollagen. Using a simple algorithm for detecting secondary structures, we have analysed crystal structure data on 40 globular proteins and have found eight examples of the collagen-helix + ?-turn supersecondary structure in 15 proteins that contain the collagen-like helical segments.

Signaling different pathways of cell death: Abrin induced programmed necrosis in U266B1 cells

Abrin is a type II ribosome-inactivating protein comprising of two subunits, A and B. Of the two, the A-subunit harbours the RNA-N-glycosidase activity and the B subunit is a galactose specific lectin that enables the entry of the protein inside the cell. Abrin inhibits protein synthesis and has been reported to induce apoptosis in several cell types. Based on these observations abrin is considered to have potential for the construction of immunotoxin in cell targeted therapy. Preliminary data from our laboratory however showed that although abrin inhibited the protein synthesis in all cell types, the mode of cell death varied. The aim of the present study was therefore to understand different death pathways induced by abrin in different cells. We used the human B cell line, U266B1 and compared it with the earlier studied T cell line Jurkat, for abrin-mediated inhibition of protein translation as well as cell death. While abrin triggered programmed apoptosis in Jurkat cells in a caspase-dependent manner, it induced programmed necrosis in U266B1 cells in a caspase-independent manner, even when there was reactive oxygen species production and loss of mitochondrial membrane potential. The data revealed that abrin-mediated necrosis involves lysosomal membrane permeabilization and release of cathepsins from the lysosomes. Importantly, the choice of abrin-mediated death pathway in the cells appears to depend on which of the two events occurs first: lysosomal membrane permeabilization or loss of mitochondrial membrane potential that decides cell death by necrosis or apoptosis. (C) 2010 Elsevier Ltd. All rights reserved.

Chemical Shift of the X-Ray K-Absorption Edge of Cu in Some of Its Compounds, Complexes and Superconductors

Chemical shifts, ΔE, of the X-ray K-absorption edge in several compounds, complexes of copper including its superconducting oxides possessing formal oxidation states +1 and +2 have been measured. It has been shown that the chemical shift is primarily governed by the effective ionic charge on the absorbing ion and the nature of the atoms in the first coordination shell around the absorbing ion. The relation between the chemical shift, ΔE , and the effective charge q on the absorbing ion is found to be ΔE=Aq+Bq2+Cq3+Dq4 (A, B, C and D are constants). The effects of electronegativity, atomic number, oxidation state, crystal structure, the valence d-orbital electrons, etc. on the X-ray absorption chemical shift have been discussed. ©1990 The Physical Society of Japan

Quantum Properties in Transport Through Nanoscopic Rings:Charge-Spin Separation and Interference Effects

Many of the most intriguing quantum effects are observed or could be measured in transport experiments through nanoscopic systems such as quantum dots, wires and rings formed by large molecules or arrays of quantum dots. In particular, the separation of charge and spin degrees of freedom and interference effects have important consequences in the conductivity through these systems. Charge-spin separation was predicted theoretically in one-dimensional strongly inter-acting systems (Luttinger liquids) and, although observed indirectly in several materials formed by chains of correlated electrons, it still lacks direct observation. We present results on transport properties through Aharonov-Bohmrings (pierced by a magnetic flux) with one or more channels represented by paradigmatic strongly-correlated models. For a wide range of parameters we observe characteristic dips in the conductance as a function of magnetic flux which are a signature of spin and charge separation. Interference effects could also be controlled in certain molecules and interesting properties could be observed. We analyze transport properties of conjugated molecules, benzene in particular, and find that the conductance depends on the lead configuration. In molecules with translational symmetry, the conductance can be controlled by breaking or restoring this symmetry, e.g. by the application of a local external potential. These results open the possibility of observing these peculiar physical properties in anisotropic ladder systems and in real nanoscopic and molecular devices.

Exact free-surface flows for shallow-water equations .1. - the incompressible case

A comprehensive exact treatment of free surface flows governed by shallow water equations (in sigma variables) is given. Several new families of exact solutions of the governing PDEs are found and are shown to embed the well-known self-similar or traveling wave solutions which themselves are governed by reduced ODEs. The classes of solutions found here are explicit in contrast to those found earlier in an implicit form. The height of the free surface for each family of solutions is found explicitly. For the traveling or simple wave, the free surface is governed by a nonlinear wave equation, but is arbitrary otherwise. For other types of solutions, the height of the free surface is constant either on lines of constant acceleration or on lines of constant speed; in another case, the free surface is a horizontal plane while the flow underneath is a sine wave. The existence of simple waves on shear flows is analytically proved. The interaction of large amplitude progressive waves with shear flow is also studied.

Glasslike elastic properties in the omega-beta alloys

We have measured the internal friction and speed of sound in several polycrystalline alloys, using compound torsional oscillators at frequencies between 60 kHz and 100 kHz and temperatures between 50 mK and 100 K. By combining these data with existing elastic and thermal data on similar alloys, we find that those alloys which can undergo diffusionsless phase transitions, such as Ti:Nb, Ti:V, or Zr:Nb in certain ranges of composition have glasslike excitations, since they have elastic properties which agree in magnitude and temperature dependence with those of amorphous solids. By contrast, crystalline continuous solution alloys, such as Nb:Ta, or alloys with diffusive phase transitions, such as high-pressure quenched Al94Si6, have the same elastic properties as are known for crystals.