A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

A new mode of ring cleavage of 2,3-dihydroxybenzoic acid in Tecoma stans (L.). Partial purification and properties of 2,3-dihydroxybenzoate 2,3-oxygenase.

2,3-Dihydroxybenzoic acid has been shown to be oxidized via the 3-oxoadipate pathway in the leaves of Tecoma stans. The formation of 2-carboxy-cis,cis-muconic acid, a muconolactone, 3-oxoadipic acid and carbon dioxide during its metabolism has been demonstrated using an extract of Tecoma leaves. The first reaction of the pathway, viz., the conversion of 2,3-dihydroxybenzoate to 2-carboxy-cis,cis-muconic acid has been shown to be catalysed by an enzyme designated as 2,3-dihydroxybenzoate 2,3-oxygenase. The enzyme has been partially purified and a few of its properties studied. The enzyme is very labile with a half-life of 3--4 h. It is maximally active with 2,3-dihydroxybenzoate as the substrate and does not exhibit any activity with catechol, 4-methyl catechol, 3,4-dihydroxybenzoic acid, etc. However, 2,3-dihydroxy-p-toluate and 2,3-dihydroxy-p-cumate are also oxidized by the enzyme by about 38% and 28% respectively, compared to 2,3-dihydroxybenzoate. Sulfhydryl reagents inhibit the enzyme reaction and the inhibition can be prevented by preincubation of the enzyme with the substrate. Substrate also affords protection to the enzyme against thermal inactivation. Sulfhydryl compounds strongly inhibit the reaction and the inhibition cannot be prevented by preincubation of the enzyme with its substrates. Data on the effect of metal ions as well as metal chelating agents suggest that copper is the metal cofactor of the enzyme. Evidence is presented which suggests that iron may not be participating in the overall catalytic mechanism.

Measurements of partial discharges-corrections to erroneous counts occurring in a cumulative pulse-counting system

The discharge pulse rates at different magnitude levels are often used as criteria for monitoring the partial-discharge aging of insulation systems. Use of suggested corrections for errors in cumulative probability counting leads to better use of available counters.

Partial Integrated Guidance and Control of Surface-to-Air Interceptors for High Speed Targets

An important limitation of the existing IGC algorithms, is that they do not explicitly exploit the inherent time scale separation that exist in aerospace vehicles between rotational and translational motions and hence can be ineffective. To address this issue, a two-loop partial integrated guidance and control (PIGC) scheme has been proposed in this paper. In this design, the outer loop uses a recently developed, computationally efficient, optimal control formulation named as model predictive static programming. It gives the commanded pitch and yaw rates whereas necessary roll-rate command is generated from a roll-stabilization loop. The inner loop tracks the outer loop commands using the Dynamic inversion philosophy. Uncommonly, Six-Degree of freedom (Six-DOF) model is used directly in both the loops. This intelligent manipulation preserves the inherent time scale separation property between the translational and rotational dynamics, and hence overcomes the deficiency of current IGC designs, while preserving its benefits. Comparative studies of PIGC with one loop IGC and conventional three loop design were carried out for engaging incoming high speed target. Simulation studies demonstrate the usefulness of this method.

Interaction of surfactants with DNA. Role of hydrophobicity and surface charge on intercalation and DNA melting

A probe, 9-(anthrylmethyl)trimethylammonium chloride, 1, was prepared. 1 binds to calf-thymus DNA or Escherichia coli genomic DNA with high affinity, as evidenced from the absorption titration. Strong hypochromism, spectral broadening and red-shifts in the absorption spectra were observed. Half-reciprocal plot constructed from this experiment gave binding constant of 5±0.5×104 M−1 in base molarity. We employed this anthryl probe-DNA complex for studying the effects of addition of various surfactant to DNA. Surfactants of different charge types and chain lengths were used in this study and the effects of surfactant addition to such probe-DNA complex were compared with that of small organic cations or salts. Addition of either salts or cationic surfactants led to structural changes in DNA and under these conditions, the probe from the DNA-bound complex appeared to get released. However, the cationic surfactants could induce such release of the probe from the probe-DNA complex at a much lower concentration than that of the small organic cations or salts. In contrast the anionic surfactants failed to promote any destabilization of such probe-DNA complexes. The effects of additives on the probe-DNA complexes were also examined by using a different technique (fluorescence spectroscopy) using a different probe ethidium bromide. The association complexes formed between the cationic surfactants and the plasmid DNA pTZ19R, were further examined under agarose gel electrophoresis and could not be visualized by ethidium bromide staining presumably due to cationic surfactant-induced condensation of DNA. Most of the DNA from such association complexes can be recovered by extraction of surfactants with phenol-chloroform. Inclusion of surfactants and other additives into the DNA generally enhanced the DNA melting temperatures by a few °C and at high [surfactant], the corresponding melting profiles got broadened.

Role of Arg-401 of cytosolic serine hydroxymethyltransferase in subunit assembly and interaction with the substrate carboxy group.

In an attempt to identify the arginine residue involved in binding of the carboxylate group of serine to mammalian serine hydroxymethyltransferase, a highly conserved Arg-401 was mutated to Ala by site-directed mutagenesis. The mutant enzyme had a characteristic visible absorbance at 425 nm indicative of the presence of bound pyridoxal 5'-phosphate as an internal aldimine with a lysine residue. However, it had only 0.003% of the catalytic activity of the wild-type enzyme. It was also unable to perform reactions with glycine, beta-phenylserine or d-alanine, suggesting that the binding of these substrates to the mutant enzyme was affected. This was also evident from the interaction of amino-oxyacetic acid, which was very slow (8.4x10(-4) s-1 at 50 microM) for the R401A mutant enzyme compared with the wild-type enzyme (44.6 s-1 at 50 microM). In contrast, methoxyamine (which lacks the carboxy group) reacted with the mutant enzyme (1.72 s-1 at 250 microM) more rapidly than the wild-type enzyme (0.2 s-1 at 250 microM). Further, both wild-type and the mutant enzymes were capable of forming unique quinonoid intermediates absorbing at 440 and 464 nm on interaction with thiosemicarbazide, which also does not have a carboxy group. These results implicate Arg-401 in the binding of the substrate carboxy group. In addition, gel-filtration profiles of the apoenzyme and the reconstituted holoenzyme of R401A and the wild-type enzyme showed that the mutant enzyme remained in a tetrameric form even when the cofactor had been removed. However, the wild-type enzyme underwent partial dissociation to a dimer, suggesting that the oligomeric structure was rendered more stable by the mutation of Arg-401. The increased stability of the mutant enzyme was also reflected in the higher apparent melting temperature (Tm) (61 degrees C) than that of the wild-type enzyme (56 degrees C). The addition of serine or serinamide did not change the apparent Tm of R401A mutant enzyme. These results suggest that the mutant enzyme might be in a permanently 'open' form and the increased apparent Tm could be due to enhanced subunit interactions.

In situ cryocrystallization of low melting chloro and bromo substituted anilines

In situ cryocrystallographic Studies of chloro and bromo substituted anilines have been performed to evaluate the role of halogen...halogen interactions and the subsequent formation of supramolecular assemblies in the solid state. Ortho Cl/Br substituted anilines are isostructural and belong to the trigonal P3(1) space group. Halogen...halogen intermolecular contacts along with stronger N-H center dot center dot center dot N hydrogen bonds generate helical motifs along the crystallographic c-axis. (C) 2009 Elsevier B.V. All rights reserved.

Effect of oxygen partial pressure on the growth of zinc micro and nanostructures

Zinc micro and nanostructures were synthesized in vacuum by condensing evaporated zinc on Si substrate at different gas pressures. The morphology of the grown Zn structures was found to be dependent on the oxygen partial pressure. Depending on oxygen partial pressure it varied from two-dimensional microdisks to one-dimensional nanowire. The morphology and structural properties of the grown micro and nanostructures were studied by scanning electron microscopy (SEM) and X-ray diffraction (XRD). Transmission electron microscopy (TEM) studies on the grown Zn nanowires have shown that they exhibit core/shell-like structures, where a thin ZnO layer forms the shell. A possible growth mechanism behind the formation of different micro and nanostructures has been proposed. In addition, we have synthesized ZnO nanocanal-like structures by annealing Zn nanowires in vacuum at 350 °C for 30 min.

Effect of oxygen partial pressure on the structural and optical properties of dc reactive magnetron sputtered molybdenum oxide films

Molybdenum oxide films (MoO3) were deposited on glass and crystalline silicon substrates by sputtering of molybdenum target under various oxygen partial pressures in the range 8 × 10−5–8 × 10−4 mbar and at a fixed substrate temperature of 473 K employing dc magnetron sputtering technique. The influence of oxygen partial pressure on the composition stoichiometry, chemical binding configuration, crystallographic structure and electrical and optical properties was systematically studied. X-ray photoelectron spectra of the films formed at 8 × 10−5 mbar showed the presence of Mo6+ and Mo5+ oxidation states of MoO3 and MoO3−x. The films deposited at oxygen partial pressure of 2 × 10−4 mbar showed Mo6+ oxidation state indicating the films were nearly stoichiometric. It was also confirmed by the Fourier transform infrared spectroscopic studies. X-ray diffraction studies revealed that the films formed at oxygen partial pressure of 2 × 10−4 mbar showed the presence of (0 k 0) reflections indicated the layered structure of α-phase MoO3. The electrical conductivity of the films decreased from 3.6 × 10−5 to 1.6 × 10−6 Ω−1 cm−1, the optical band gap of the films increased from 2.93 to 3.26 eV and the refractive index increased from 2.02 to 2.13 with the increase of oxygen partial pressure from 8 × 10−5 to 8 × 10−4 mbar, respectively.

On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.

Melting of an Anchored Bilayer: Phase Transitions in the Organic-Inorganic Hybrid Pervoskite (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n=11, 13, 15, 17)

The conformation, organization, and phase transitions of alkyl chains in organic-inorganic hybrids based on the double pervoskite-slab lead iodides, (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n = 11, 13, 15, 17) have been investigated by X-ray diffraction, calorimetry, and infrared vibrational spectroscopy. In these hybrid solids, double pervoskite (CH3NH3)Pb2I7 slabs are interleaved with alkyl ammonium chains with the anchored alkyl chains arranged as tilted bilayers and adopting a planar all-trans conformation at room temperature. The (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 compounds exhibit a single reversible phase transition above room temperature with the associated enthalpy change varying linearly with alkyl chain length. This transition corresponds to the melting in two-dimensions of the alkyl chains of the anchored bilayer and is characterized by increased conformational disorder of the methylene units of the chain and loss of tilt angle coherence leading to an increase in the interslab spacing. By monitoring features in the infrared spectra that are characteristic of the global conformation of the alkyl chains, a quantitative relation between conformational disorder and melting of the anchored bilayer is established. It is found that, irrespective of the alkyl chain length, melting occurs when at least 60% of the chains in the anchored bilayer of (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 have one or more gauche defects. This concentration is determined by the underlying lattice to which the alkyl chains are anchored.

Distributed space-time codes for cooperative networks with partial CSI

Design criteria and full-diversity Distributed Space Time Codes (DSTCs) for the two phase transmission based cooperative diversity protocol of Jing-Hassibi and the Generalized Nonorthogonal Amplify and Forward (GNAF) protocol are reported, when the relay nodes are assumed to have knowledge of the phase component of the source to relay channel gains. It is shown that this under this partial channel state information (CSI), several well known space time codes for the colocated MIMO (Multiple Input Multiple Output) channel become amenable for use as DSTCs. In particular, the well known complex orthogonal designs, generalized coordinate interleaved orthogonal designs (GCIODs) and unitary weight single symbol decodable (UW-SSD) codes are shown to satisfy the required design constraints for DSTCs. Exploiting the relaxed code design constraints, we propose DSTCs obtained from Clifford Algebras which have low ML decoding complexity.

Low PAPR STBCs from Complex Partial-Orthogonal Designs (CPODs)

Space-time codes from complex orthogonal designs (CODs) with no zero entries offer low Peak to Average power ratio (PAPR) and avoid the problem of turning off antennas. But CODs for 2(a) antennas with a + 1 complex variables, with no zero entries are not known in the literature for a >= 4. In this paper, a method of obtaining no zero entry (NZE) codes, called Complex Partial-Orthogonal Designs (CPODs), for 2(a+1) antennas whenever a certain type of NZE code exists for 2(a) antennas is presented. This is achieved with slight increase in the ML decoding complexity for regular QAM constellations and no increase for other complex constellations. Since NZE CODs have been constructed recently for 8 antennas our method leads to NZE CPODs for 16 antennas. Moreover, starting from certain NZE CPODs for n antennas, a construction procedure is given to obtain NZE CPODs for 2n antennas. The class of CPODs do not offer full-diversity for all complex constellations. For the NZE CPODs presented in the paper, conditions on the signal sets which will guarantee full-diversity are identified. Simulations results show that bit error performance of our codes under average power constraint is same as that of the CODs and superior to CODs under peak power constraint.

Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film

To gain a better understanding of recent experiments on the turbulence-induced melting of a periodic array of vortices in a thin fluid film, we perform a direct numerical simulation of the two-dimensional Navier-Stokes equations forced such that, at low Reynolds numbers, the steady state of the film is a square lattice of vortices. We find that as we increase the Reynolds number, this lattice undergoes a series of nonequilibrium phase transitions, first to a crystal with a different reciprocal lattice and then to a sequence of crystals that oscillate in time. Initially, the temporal oscillations are periodic; this periodic behaviour becoming more and more complicated with increasing Reynolds number until the film enters a spatially disordered nonequilibrium statistical steady state that is turbulent. We study this sequence of transitions using fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes between vortical and extensional regions in the flow, ideas from nonlinear dynamics, e.g. Poincare maps, and theoretical methods that have been developed to study the melting of an equilibrium crystal or the freezing of a liquid and that lead to a natural set of order parameters for the crystalline phases and spatial autocorrelation functions that characterize short- and long-range order in the turbulent and crystalline phases, respectively.