On a question of Gross

Using the notion of weighted sharing of sets we prove two uniqueness theorems which improve the results proved by Fang and Qiu [H. Qiu, M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc. 25 (2002) 31-38], Lahiri and Banerjee [I. Lahiri, A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004) 575-584] and Yi and Lin [H.X. Yi, W.C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80 (2004) 136-140] and thus provide an answer to the question of Gross [F. Gross, Factorization of meromorphic functions and some open problems, in: Proc. Conf. Univ. Kentucky, Lexington, KY, 1976, in: Lecture Notes in Math., vol. 599, Springer, Berlin, 1977, pp. 51-69], under a weaker hypothesis.     

A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

DRIFTS study of surface reactivity to NO2 by zinc nanoparticle aggregates and zinc hollow nanofibers

Zinc nanostructures synthesized with different morphologies from the same evaporation/condensation technique are studied with concern to surface reactivity to NO₂ by Diffuse Reflectance Infrared Fourier Transformed Spectroscopy (DRIFTS). Synthesis of nanopowders is obtained, according to previous work, by gas flow thermal evaporation at 540 °C of bulk Zn grains. Two types of Zn powders are obtained and studied in experiments. The first one is collected on the cold walls of the reactor as a deposit produced by thermophoretic effect. It is constituted by grains (∼10 μm) originated by the stratification of smaller aggregates (∼200 nm) and isolated primary particles (∼50 nm) born in the gas flow. The second type of powder is grown from the condensation of Zn chemical vapors within the expansion orifice of the quartz reactor after relatively long time (∼1 h) deposition process. It is constituted mainly by hollow Zn nanofibers with external and internal diameter about 100 and 60 nm. Preliminary characterization of the two types of powders is made by SEM, TEM, XRD. Thereafter, the two types of samples are studied by DRIFTS at variable temperature (VT). Comparison is made between the home-synthesized nanopowders with respect to commercial Zn standard dust. The Zn hollow nanofibers when exposed to NO₂ are found to exhibit dramatic reactivity, which is not observed at all either in the case of clustered aggregate zinc or of commercial Zn dust powders. Results indicate that, at increasing temperature from RT to 300 °C, the hollow nanofibers surface reacts distinctively with adsorbant gas NO₂, with contemporary formation of a progressively growing narrow absorption band at 2500 cm⁻¹ and contemporary depression of a doublet (∼1600-1628 cm⁻¹) band. In order to justify this striking spectral feature, we propose the occurring of a possible polymerization process at nanofibers surface where most probably as a consequence of pre-treatment and exposure to gas NO₂ a very thin film of ZnO is formed. The possible role of huge specific surface of hollow nanofibers as inferred by preliminary SEM, TEM, XRD studies is discussed.     

Nonstatic perfect fluid sphere in higher-dimensional space-time

It is shown that in the case of a spherical nonstatic fluid distribution undergoing shear-free motion the field equations in higher dimensional space-time can be reduced to a single second-order differential equation involving an arbitrary function of the radial co-ordinate. This result extends to higher dimensions a similar one obtained by Wyman and Faulkes earlier for 4D space-time. Solving this differential equation a number of new solutions is found, and the dynamical behaviour of one of the models is briefly discussed. The ansatz is later generalised to include the electromagnetic field as well.     

Analysis of numerical integration in p-version finite element eigenvalue approximation

We study the effect of numerical integration when the p-version of the finite element method is used to approximate the eigenpairs of elliptic partial differential operators. We obtain optimal orders of convergence for approximate eigenvalues and eigenvectors under a certain set of requirements on the quadrature rules employed. This is the same set of conditions that has been shown (in an earlier work) to be sufficient for the optimal approximation of the solutions of the corresponding source problems.     

Synergistic effect of neutral donors on the extraction of zirconium(IV) by salicylaldoxime in dichloromethane

Liquid-liquid extraction of zirconium(IV) was investigated from dilute hydrochloric acid medium by salicyaldoxime (HA) in dichloromethane. The metal was spiked with ⁹⁵Zr and analyzed by its radioactivity. The effects of different donors, like trioctyl phosphine oxide (TOPO), triphenyl phosphine oxide (TPPO), tributyl phosphine oxide (TBPO), tributyl phosphate (TBP), trioctyl amine (TOA) and Amberlite LA-2 were studied. The adduct formation constants for both binary species (metal-ligand) and ternary species (metal-ligand-donor) were also calculated form the distribution data.One of the authors (S.B.) thanks The University of Burdwan for providing senior research fellowship to her. She also wishes to thank Dr. D. Mukherjee and Dr. S. Bhattacharya, B.U. for their valuable suggestions.     

Increased Photosensitivity in HL60 Cells Expressing Wild-Type p53

Loss of p53 function has been correlated with decreased sensitivity to chemotherapy and radiation therapy in a variety of human tumors. Comparable analysis of p53 status with sensitivity to oxidative stress induced by pho-todynamic therapy has not been reported. In the current study we examined photosensitivity in human promye-locytic leukemia HL60 cells exhibiting either wild-type p53, mutated p53 or deleted p53 expression. Experiments were performed using a purpurin, tin ethyl etiopurpurin (SnET2)-, or a porphyrin, Photofrin (PH)-based photo-sensitizer. Total SnET2 accumulation was comparable in all three cell lines. Uptake of PH was highest in cells expressing wild-type p53 but incubation conditions could be adjusted to achieve equivalent cellular PH levels during experiments that analyzed photosensitivity. Survival measurements demonstrated that HL60 cells expressing wild-type p53 were more sensitive to PH- and SnET2-mediated photosensitization, as well as to UVC irradiation, when compared to HL60 cells exhibiting deleted or mutated p53 phenotypes. A rapid apoptotic response was observed following purpurin- and porphyrin-induced photosensitization in all cell lines. Results of this study indicate that photosensitivity is increased in HL60 cells expressing wild-type p53 and that photosensitizer-medi-ated oxidative stress can induce apoptosis through a p53-independent mechanism in HL60 cells .     

Recent results from large electron positron collider

We summarize here the recent results from the four experiments at the large electron positron collider (LEP). These experiments provide precise measurements of theW and Z boson properties and their couplings to leptons and quarks. These measurements, together with measurements of the top quark andW boson masses in the Tevatron collider provide a stringent test of the standard electroweak theory. Searches for Higgs boson and supersymmetric particles have yielded null results so far giving rise to lower bounds in the parameter space.