Equivariant K-theory of compactifications of algebraic groups

In this paper we describe the G × G-equivariant K-ring of X, where X is a regular compactification of a connected complex reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint type, and X its wonderful compactification, we describe its ordinary K-ring K(X). More precisely, we prove that K(X) is a free module over K(G/B) of rank the cardinality of the Weyl group. We further give an explicit basis of K(X) over K(G/B), and also determine the structure constants with respect to this basis.     

Non-classicality of photon added coherent and thermal radiations

Production and analysis of non-Gaussian radiation fields has evinced a lot of attention recently. Simplest way of generating such non-Gaussians is through adding (subtracting) photons to Gaussian fields. Interestingly, when photons are added to classical Gaussian fields, the resulting states exhibit non-classicality. Two important classical Gaussian radiation fields are coherent and thermal states. Here, we study the non-classical features of such states when photons are added to them. Non-classicality of these states shows up in the negativity of the Wigner function. We also work out the entanglement potential, a recently proposed measure of non-classicality for these states. Our analysis reveals that photon added coherent states are non-classical for all seed beam intensities; their non-classicality increases with the addition of more number of photons. Thermal state exhibits non-classicality at all temperatures, when a photon is added; lower the temperature, higher is their non-classicality.     

Synthesis,characterization, and evaluation of antimicrobial activities of a new class of macrocyclic phosphonates

A series of a new class of phosphorus analogue macrocycles was accomplished by condensation of N‐substituted‐[bis(3,5‐dimethyl‐2‐hydroxybenzyl)]‐amines with various phosphorus dichlorides in dry toluene in the presence of triethylamine at 0–50°C. All the title compounds were evaluated for antimicrobial activity to determine their efficacy and were effective in suppressing the growth of bacteria and fungi. The chemical structures of the title products were characterized by IR, ¹H, ¹³C, ³¹P‐NMR, mass spectral studies, and elemental analysis. J. Heterocyclic Chem., (2011).     

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.     

Spectral, thermal and optical properties of L-tryptophanium picrate: a nonlinear optical single crystal

A new organic nonlinear optical material L-tryptophanium picrate was synthesized. From the powder XRD pattern the various planes of reflections were identified. The grown crystals were subjected to FT-IR and (1)H NMR spectral analyses to confirm the synthesized compound. Thermal properties of the crystals were investigated using thermo gravimetric (TG) and differential thermal analyses (DTA). The second harmonic generation (SHG) efficiency of the title compound was found using the modified experimental setup of Kurtz and Perry.     

Polarization induced water molecule dissociation below the first-order electronic-phase transition temperature

Hydrogen produced from the photocatalytic splitting of water is one of the reliable alternatives to replace the polluting fossil and the radioactive nuclear fuels. Here, we provide unequivocal evidence for the existence of blue- and red-shifting O-H covalent bonds within a single water molecule adsorbed on the MgO surface as a result of asymmetric displacement polarizabilities. The adsorbed H-O-H on MgO gives rise to one weaker H-O bond, while the other O-H covalent bond from the same adsorbed water molecule compensates this effect with a stronger bond. The weaker bond (nearest to the surface), the interlayer tunneling electrons and the silver substrate are shown to be the causes for the smallest dissociative activation energy on the MgO monolayer. The origin that is responsible to initiate the splitting mechanism is proven to be due to the changes in the polarizability of an adsorbed water molecule, which are further supported by the temperature-dependent static dielectric constant measurements for water below the first-order electronic-phase transition temperature.     

Observation of subcellular nanostructure of single neurons with an illumination mode photon scanning tunneling microscope

We report about the observation of microtubules lying underneath the cell membrane of neural process in neurons with a resolution as high as that of an electron microscope by an illumination mode photon scanning tunneling microscope. Nanoapertures used in our observations were fabricated by means of selective chemical etching and metal coating of an optical fiber. The narrowest observed tube has got an average diameter of 26 nm. Comparing this with its nominal value of 25 nm, the difference which is considered as a measure of resolution (δ) is 1 nm implying a resolution comparable to that of an electron microscope in imaging dielectric specimens. This was possible due to the presence of a boundary between the glass and the metal coating and also due to the use of an aperture of almost the same size as that of the microtubule that enhances the detection.     

Intra–intermolecular gel-free cyclopolymerization of nonconjugated diene with peroxodiphosphate/different activators redox pairs

Gel-free cyclopolymerization of N,N′-methylenebisacrylamide has been carried out using potassium peroxodiphosphate (PDP) as initiator in combination with different activators such as mercaptosuccinic acid (MSA) and thioglycollic acid (TGA) in an inert atmosphere at 45 ± 1°C and 40 ± 1°C, respectively. The rate of polymerization was found proportional to the first power of the monomer and activator concentration and the half-power of PDP in both redox systems. A mechanism involving cyclopolymerization in the propagation path has been proposed. © 1993 John Wiley & Sons, Inc.