New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

A method for separation of stresses in Two- and three-dimensional photoelasticity

A method for separation of stresses in two and three-dimensional photo elasticity using the harmonisation ofjrst stress invariant along a straight section is deve- ,dped. For two-dimensions, the equations of equilibrium are reformulated in terms ojsum and difference of normal stresses and relations are obtained which can be used for harmonisation of the first invariant of stress along a straight section. A similar procedure is adopted for three-dimensions by making use of the Beltrmi-MicheN equations. The new relations are used in finite d~yerencefo rm to evaluate the sum of normal stresses along straight sections in a three-dimensional body. The method requires photoelastic data along the section as well ~rra djacent sections. This method could be used as an alternative to the shear d@erence method for separation of stresses in photoelasticity. 7he accuracy and reliability of the method is ver$ed by applying the method to problems whose solutions are known.

The Noether-Lefschetz theorem for the divisor class group

Let X be a normal projective threefold over a field of characteristic zero and vertical bar L vertical bar be a base-point free, ample linear system on X. Under suitable hypotheses on (X, vertical bar L vertical bar), we prove that for a very general member Y is an element of vertical bar L vertical bar, the restriction map on divisor class groups Cl(X) -> Cl(Y) is an isomorphism. In particular, we are able to recover the classical Noether-Lefschetz theorem, that a very general hypersurface X subset of P-C(3) of degree >= 4 has Pic(X) congruent to Z.

Microbially induced separation of arsenopyrite and bioremediation of arsenic

This paper discusses the role of the mineral-adapted acidiphilic microorganism. Acidithiobacillus ferrooxidans in the beneficiation of arsenopyrite-containing multisulfides (pyrite and chalcopyrite) and the bioremediation of the resulting arsenical waste water. It was found that adaptation to minerals alters the surface properties of the microorganism. Bacterial adaptation to arsenopyrite and controlled bacterial adhesion to mineral surfaces lead to selectivity in arsenopyrite separation. Bioremoval of arsenic ions (both arsenite and arsenate ions) by Acidithiobacillus ferrooxidans is also discussed.

The incongruous observation of magnetic phase separation in La0.85Sr0.15CoO3 spin glass system

Phase separation (PS) in hole-doped cobaltites (La1-xSrxCoxO3) is drawing renewed interest recently. In particular, the magnetic behavior of La0.85Sr0.15CoO3 has been subjected to a controversial debate for the past several years; while some groups show evidence for magnetic PS, others show spin glass (SG) behavior. Here, an attempt is made to resolve the controversy related to ``PS versus SG'' behavior in this compound. We present the results of a comprehensive investigation of the dc magnetization, ac susceptibility, and the magnetotransport properties of La0.85Sr0.15CoO3 samples. We contemplate that the magnetic PS in La0.85Sr0.15CoO3 is neither intrinsic nor inherent, but it is a consequence of the preparation conditions. It is realized that a low temperature annealed (LTA) sample shows PS whereas the high temperature annealed (HTA) sample shows SG behavior. The Brillouin-like behavior of field cooled dc magnetization and apparently no frequency dependent peak shift in ac susceptibility for the LTA sample characterize it to be of ferromagneticlike whereas a kink in field cooled dc magnetization and a considerable amount (similar to 3 K) of frequency dependent peak shift in the ac susceptibility for the HTA sample characterize it to be of SG state. The magnetotransport properties show that the HTA sample is more semiconducting as compared to the LTA sample. This is interpreted in terms of the presence of isolated as well as coalescing metallic ferromagnetic clusters in the case of LTA sample. The magnetoresistance (MR) at 10 K for the HTA sample exhibits a huge value (similar to 65%) as compared to the LTA sample, and it monotonically decreases with the rise in temperature. Such a high value of MR in the case of HTA sample is strongly believed to be due to the spin dependent part of random potential distribution. Further, the slow decay of remnant magnetization with progress of time and the existence of hysteresis at higher temperatures (up to 200 K) in the case of LTA sample as compared to the HTA sample clearly unveil different magnetic states associated with them.

Separation of Metallic and Semiconducting Single-Walled Carbon Nanotubes Through Fluorous Chemistry

Separation of metallic from semiconducting single-walled carbon nanotubes has been a major challenge for some time and some previous efforts have resulted in partial success. We have accomplished the separation effectively by employing fluorous chemistry wherein the diazonium salt of 4-heptadecafluorooc tylaniline selectively reacts with the metallic nanotubes present in the mixture of nanotubes. The resulting fluoroderivative was extracted in perfluorohexane leaving the semiconducting nanotubes in the aqueous layer. The products have been characterized by both Raman and electronic absorption spectroscopy. The method avoids the cumbersome centrifugation step required by some other procedures.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Localized reversible nanoscale phase separation in Pr0.63Ca0.37MnO3 single crystal using a scanning tunneling microscope tip

We report the destabilization of the charge ordered insulating (COI) state in a localized region of Pr0.63Ca0.37MnO3 single crystal by current injection using a scanning tunneling microscope tip. This leads to controlled phase separation and formation of localized metallic nanoislands in the COI matrix which have been detected by local tunneling conductance mapping. The metallic regions thus created persist even after reducing the injected current to lower values. The original conductance state can be restored by injecting a current of similar magnitude but of opposite polarity. We thus achieve reversible nanoscale phase separation that gives rise to the possibility to "write, read, and erase" nanosized conducting regions in an insulating matrix with high spatial resolution. (c) 2007 American Institute of Physics.

Highly biocompatible and water-dispersible, amine functionalized magnetite nanoparticles, prepared by a low temperature, air-assisted polyol process: a new platform for bio-separation and diagnostics

A low temperature polyol process, based on glycolaldehyde mediated partial reduction of FeCl3 center dot 6H(2)O at 120 degrees C in the presence of sodium acetate as an alkali source and 2,2'-(ethylenedioxy)-bis-(ethylamine) as an electrostatic stabilizer has been used for the gram-scale preparation of biocompatible, water-dispersible, amine functionalized magnetite nanoparticles (MNPs) with an average diameter of 6 +/- 0.75 nm. With a reasonably high magnetization (37.8 e.m.u.) and amine groups on the outer surface of the nanoparticles, we demonstrated the magnetic separation and concentration implications of these ultrasmall particles in immunoassay. MRI studies indicated that these nanoparticles had the desired relaxivity for T-2 contrast enhancement in vivo. In vitro biocompatibility, cell uptake and MR imaging studies established that these nanoparticles were safe in clinical dosages and by virtue of their ultrasmall sizes and positively charged surfaces could be easily internalized by cancer cells. All these positive attributes make these functional nanoparticles a promising platform for further in vitro and in vivo evaluations.

LOX separation studies using cryogenic vortex tube

In-flight collection of air, pre-cooling, liquefaction and separation of liquid oxygen (LOX) are key technologies for futuristic launch vehicles, Vortex tube technology is one of the few potential technologies for this application. Extensive studies have been carried out on straight and conical vortex tubes for developing vortex tube technology for high purity LOX separation. Studies show that 12mm. diameter conical vortex tube with L/D of 10 could achieve LOX purity of similar to 96% with separation efficiency of similar to 14% indicating that it is not possible to obtain both high LOX purity and high separation efficiency simultaneously in a single vortex tube. However, it is possible to achieve both high LOX purity and separation efficiency by staging of vortex tubes. LOX purity of 96% and separation efficiency of similar to 73.5% has been achieved for second stage vortex tube supplied with pre-cooled air having 60% oxygen purity. LOX purity has been further increased to 97% by applying controlled heating power over liquid oxygen flowing discharge surface of the vortex tube.

Microbially-induced separation of chalcopyrite and galena

Cells of Paenibacillus polymyxa and their metabolic products such as bioproteins and exopolysaccharides could be effectively used in the separation of galena from chalcopyrite. While interaction with bacterial cells resulted in significant flocculation of both chalcopyrite and galena, treatment with bioproteins selectively flocculated only chalcopyrite, dispersing galena. Microbially-induced selective flocculation after conditioning with cells, bioproteins or exopolysaccharides resulted in efficient separation of chalcopyrite and galena from their mixtures. Prior interaction with bioproteins facilitated enhanced flotation of galena from chalcopyrite. The role of bacterial cells and bioreagents such as proteins and polysaccharides in mineral beneficiation is demonstrated.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Physicochemical studies on the gelation of hen egg yolk; separation of gelling protein components from yolk plasma

A study of the component(s) in egg yolk responsible for gelation of yolk on freezing and thawing has shown that granule-free yolk plasma, obtained by high-speed centrifugation of yolk, has the capacity to gel. As with the whole yolk, gelation of yolk plasma on freezing and thawing could be inhibited by additives such as sugars, sodium chloride, proteolytic enzymes, and phospholipase-A. Phospholipase-C, which induces gelation of whole yolk at room temperature, has a similar effect on yolk plasma. Yolk plasma has been separated into aggregating (gelling) and soluble fractions by delipidation, using formic acid. Each of these fractions consists of three or four protein components, as observed by gel filtration, ultracentrifugation, and agar electrophoresis. The proteins are glycoproteins and contain bound hexoses, hexosamine, and sialic acid. The gelation of yolk has been attributed to the interactions between protein molecules following disruption of lipid-protein bonds.