The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

On the anharmonic vibrations in crystalline silicon

Using a total of 1052 Bragg reflections of silicon, an X-ray investigation has been carried out to deduce the anharmonic thermal parameter beta, apart from the estimation of the harmonic contribution of the thermal vibration at room temperature. Reflections of type h + k + l = 4n, and 4n +/- 1 were used to estimate these parameters using MoKalpha radiation and a Nonius CAD-4 X-ray diffractometer. We obtain B(Si) = 0.451 (0.008) angstrom2 and beta(Si) = 0.279(2.630) eV angstrom-3 with R = 3.12%. The present B and beta values are in very good agreement with the earlier studies.

Intramolecular Reactivity - Keto Participation in the Hydrolysis of N-Methyl-N-(9-Oxobicyclo[3.3.1]Nonan-2-Alpha-YL) Morpholinium Iodide, and A Cannizzaro-Type Reaction of 3-(2-Oxocyclohexyl)Propanal

Mechanistic studies of two intramolecular processes, nucleophilic displacement of N-methylmorpholinium in N-methyl-N-{9-oxobicyclo[3,3,1]nonan-2 alpha-yl}morpholinium iodide, anchimerically assisted by keto carbonyl, and a Cannizzaro-type reaction of 3-(2-oxocyclohexyl)propanal, occurring via axial hydride transfer onto the cyclohexanone, are reported.

Magnetic field-induced metal-insulator transitions in graphite and diluted magnetic semiconductors - Discussion

Two topical subjects related with the effect of magnetic field on electrical conduction and the metal-insulator transition are discussed. The first topic is an electronic phase transition in graphite, which is interpreted as a manifestation of a nestingtype instability inherent to a one-dimensional narrow Landau sub-band. The second topic is spin-dependent tranport in III-V based diluted magnetic semiconductors; in particular, a large negative magnetoresistance observed in the vicinity of metal-nonmetal transition.

Ab initio studies of solvent effect on conformational equilibria and vibrational spectra of dipropionamide

Systematic ab initio molecular orbital studies of the conformational equilibria and vibrational spectra of dipropionamide using the basis sets 6-31g(d) and 6-31++G(d,p) have been carried out. The vibrational spectra of dipropionamide have been satisfactorily interpreted taking into account the agreement between the calculated frequencies, infrared and Raman band intensities and the shifts in the spectra of deuterated molecules with those observed. The previous assignments of most of the vibrational bands are well confirmed, a few bands need reassignment, however. The solvent effects were investigated by self-consistent reaction field theory using dipole and self-consistent isodensity polarized continuum model methods. The introduction of a dielectric medium has only a marginal effect on the conformational equilibria and vibrational spectra. However, the calculated changes in geometry and vibrational spectra on going from the gas phase to the solution phase are in accord with the increasing weight of the dipolar resonance structure in polar solvents. (C) 2002 Elsevier Science B.V. All rights reserved.

First-principles electronic structure of the delafossites ABO(2) (A=Cu, Ag, Au; B=Al, Ga, Sc, In, Y): evolution of d(10)-d(10) interactions

While bonding between d(10) atoms and ions in molecular systems has been well studied, less attention has been paid to interactions between such seemingly closed shell species in extended inorganic solids. In this contribution, we present visualizations of the electronic structures of the delafossites ABO(2) (A = Cu, Ag, Au) with particular emphasis on the nature of d(10)-d(10) interactions in the close packed plane of the coinage metal ion. We find that on going from Cu to Ag to Au, the extent of bonding between A and A increases. However, the structures (in terms of distances) of these compounds are largely determined by the strongly ionic 13,11 0 interaction and for the larger B ions Sc, In and Y, the A atoms are sufficiently well-separated that A-A bonding is almost negligible. We also analyze some interesting differences between Ag and Au, including the larger A-O covalency of the Au. The trends in electronic structure suggest that the Ag and Au compounds are not good candidate transparent conducting oxides. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Microwave heating in multiphase systems: evaluation of series solutions

The 1D electric field and heat-conduction equations are solved for a slab where the dielectric properties vary spatially in the sample. Series solutions to the electric field are obtained for systems where the spatial variation in the dielectric properties can be expressed as polynomials. The series solution is used to obtain electric-field distributions for a binary oil-water system where the dielectric properties are assumed to vary linearly within the sample. Using the finite-element method temperature distributions are computed in a three-phase oil, water and rock system where the dielectric properties vary due to the changing oil saturation in the rock. Temperature distributions predicted using a linear variation in the dielectric properties are compared with those obtained using the exact nonlinear variation.

Transformations of two-dimensional layered zinc phosphates to three-dimensional and one-dimensional structures

Transformations of the layered zinc phosphates of the compositions [C6N4H22](0.5) [Zn-2 (HPO4)(3)], I, [C3N2H12][Zn-2 (HPO4)(3)], II and [C3N2OH12][Zn-2 (HPO4)(3)], III, containing triethylenetetramine, 1,3-diaminopropane, and 1,3-diamino-2-hydroxypropane, respectively, have been investigated under different conditions. On heating in water, I transforms to a one-dimensional (1-D) ladder and a three-dimensional (3-D) structure, while II gives rise to only a two-dimensional (2-D) layered structure. In the transformation reaction of I with zinc acetate, the same ladder and 3-D structures are obtained along with a tubular layer. Under similar conditions II gives a layered structure formed by the joining of two ladder motifs. III, on the other hand, is essentially unreactive when heated with water and zinc acetate, probably because the presence of the hydroxy group in the amine which hydrogen bonds to the framework. In the presence of piperazine, I, II and III give rise to a four-membered, corner-shared linear chain which is likely to be formed via the ladder structure. In addition, 2-D and 3-D structures derived from the 1-D linear chain or ladder structures are also formed. The primary result from the study is that the layers produce 1-D ladders, which then undergo other transformations. It is noteworthy that in the various transformations carried out, most of the products are single-crystalline.

Circuits on cylinders

We consider the computational power of constant width polynomial size cylindrical circuits and non deterministic branching programs. We show that every function computed by a Pi(2) o MOD o AC(0) circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC(0).

Gibbs energy formation of lead titanate

The Gibbs energy of formation of titania-saturated lead titanate has been determined by e.m.f. measurements on the solid state cell;Pt,Ir,Pb + Pb1−xTiO3−x + TiO2(rutile)/CaO-ZrO2/Ni + NiO,Pt in the temperature range 1075–1350 K. The results obtained are significantly different from those reported in the literature based upon vapour pressure measurements, employing Knudsen effusion and transportation techniques, and assuming that the vapor phase consisted entirely of monomeric PbO molecules. A reanalysis of the data obtained in the earlier vapor pressure studies using mass spectrometric measurements on polymeric PbO species in the gas phase, gives Gibbs energies of formation of lead titanate which are in better agreement with those obtained in this study. Earlier electrochemical measurements by Mehrotra et al. and more recent electrochemical measurements by Schmahl et al. both employing CaO-ZrO2 solid electrolytes are in good agreement with the present study. The electro-chemical measurements by Schmahl et al. using PbF 2 solid electrolyte give a slightly more positive Gibbs energy of formation. There was no evidence supporting the formation of compounds other than Pb1−xTiO3−x from yellow PbO and rutile form of TiO2 in the temperature range covered in this study.Résumé L'enthalpie libre de formation du titanate de plomb saturé en oxyde de titane a été déterminée par des mesures de FEM de la pile: Pt,Ir,Pb + Pb1−xTiO3−x + TiO2(rutile)/CaO-ZrO2/Ni + NiO,Pt dans le domaine de températures 1075–1350 K. Les résultats obtenus, different appréciablement de ceux publiés, déterminés par mesures de tensions de vapeur (techniques de transport et d'effusion de Knudsen) en supposant que la phase gazeuse etait uniquement constituée de molécules monomériques de PbO. Une réanalyse des résultats de la littérature, à partir de mesures par spectrométrie de masse sur les polymères de PbO gazeux, donne des enthalpies libres de formation du titanate de plomb se rapprochant de celles obtenues dans cette étude. Les mesures de Mehrotra et al. et plus récemment de Schmahl et al. utilisant toutes deux l'électrolyte CaO-ZrO2 concordent bien avec celles de la présente étude. Les mesures de Schmahl et al., à l'aide de l' électrolyte solide PbF2, donnent une enthalpie de formation légèrement plus positive. Pour la gammede températures étudiée, rien ne permet de supposer que des composés autres que Pb1−x TiO3−x puissent se former à partir du PbO Gaune) et du rutile (TiO2).

Validation of Decision Tables Used in Process Control

Process control rules may be specified using decision tables. Such a specification is superior when logical decisions to be taken in control dominate. In this paper we give a method of detecting redundancies, incompleteness, and contradictions in such specifications. Using such a technique thus ensures the validity of the specifications.

Null Dereference Verification via Over-approximated Weakest Pre-conditions Analysis

Null dereferences are a bane of programming in languages such as Java. In this paper we propose a sound, demand-driven, inter-procedurally context-sensitive dataflow analysis technique to verify a given dereference as safe or potentially unsafe. Our analysis uses an abstract lattice of formulas to find a pre-condition at the entry of the program such that a null-dereference can occur only if the initial state of the program satisfies this pre-condition. We use a simplified domain of formulas, abstracting out integer arithmetic, as well as unbounded access paths due to recursive data structures. For the sake of precision we model aliasing relationships explicitly in our abstract lattice, enable strong updates, and use a limited notion of path sensitivity. For the sake of scalability we prune formulas continually as they get propagated, reducing to true conjuncts that are less likely to be useful in validating or invalidating the formula. We have implemented our approach, and present an evaluation of it on a set of ten real Java programs. Our results show that the set of design features we have incorporated enable the analysis to (a) explore long, inter-procedural paths to verify each dereference, with (b) reasonable accuracy, and (c) very quick response time per dereference, making it suitable for use in desktop development environments.

One step synthesis of monoclinic VO2 (B) bundles of nanorods: Cathode for Li ion battery

One of the metastable phases of vanadium dioxide, VO2(B) bundles of nanorods and microspheres have been synthesized through a simple hydrothermal method by dispersing V2O5 in aqueous quinol. The obtained products were characterized by X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM) and electrochemical discharge-charge test for lithium battery. It was found that the morphologies of the obtained VO2(B) can be tuned by manipulating the relative amount of quinol. The electrochemical test found that the bundles of nanorods exhibit an initial discharge capacity of 171 mAh g(-1) and its almost stabilized capacity was reached to 108 mAh g(-1) after 47 cycles at a current density of 0.1 mA g(-1). The formation mechanism of the VO2(B) bundles of nanorods and microspheres was also discussed. (C) 2012 Elsevier Inc. All rights reserved.