Measure functions for frames

This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful comparison of frames indexed by the same set. We define the ultrafilter measure function, an explicit frame measure function that we show is contained both algebraically and topologically inside all frame measure functions. We explore additional properties of frame measure functions, showing that they are additive on a large class of supersets—those that come from so called non-expansive frames. We apply our results to the Gabor setting, computing the frame measure function of Gabor frames and establishing a new result about supersets of Gabor frames.     

Catalysis by Ir(III), Rh(III) and Pd(II) metal ions in the oxidation of organic compounds with H2O2

Catalytic activities of three transition metals, as iridium (III) chloride, rhodium (III) chloride and palladium (II) chloride, were compared in the oxidation of six aromatic aldehydes (benzaldehyde, p‐chloro benzaldehyde, p‐nitro benzaldehyde, m‐nitro benzaldehyde, p‐methoxy benzaldehyde and cinnamaldehyde), two hydrocarbons (viz. (anthracene and phenanthrene)) and one aromatic and one cyclic alcohol (cyclohexanol and benzyl alcohol) by 50% H₂O₂. The presence of traces (substrate: catalyst ratio equal to 1:62500 to 1:1961) of the chlorides of iridium(III), rhodium(III) and palladium(II) catalyze these oxidations, resulting in good to excellent yields. It was observed that in most of the cases palladium(II) chloride is the most efficient catalyst. Conditions for the highest and most economical yields were obtained. Deviation from the optimum conditions decreases the yields. Oxidation in aromatic aldehydes is selective at the aldehydeic group only and other groups remain unaffected. This new, simple and economical method, which is environmentally safe, also requires less time. Reactive species of catalysts, existing in the reaction mixture are also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Average local electrostatic potential and the core-valency separation in atoms

The average local electrostatic potential function, V(r)/ ρ(r), is calculated for 87 atoms, Li-Ac, in the ground state using the nonrelativistic average-over-configuration numerical Hartree-Fock density. It is found empirically that in a given atom the shell boundaries are expressed as the successively increasing maxima in V(r)/ ρ(r) and the outermost maximum presents good approximate estimates of the core-valence separation in atoms. The likeness in behavior of V(r)/ ρ(r) at each shell boundary with the maximum hardness principle is discussed. The single-exponent-fit parameters for the electron density in the valency region are provided for all atoms. © 1995 John Wiley & Sons, Inc.     

Aminonaphthalic anhydrides as red-emitting materials: electroluminescence, crystal structure, and photophysical properties

The red and orange emitters (ANA-1-3) consisting of a 4-amino-1,8-naphthalic anhydride group were synthesized. The lowest absorption band of these ANA molecules centered at approximately 450 nm is assigned to be a charge-transfer transition with emission at 514-536 nm in nonpolar solvents such as n-hexane and at approximately 590-640 nm in polar solvents such as THF and CH(2)Cl(2) and in the solid states. Emission lifetimes are measured with time-correlated single photon counting. Shorter lifetimes are observed for the ANA molecules when dissolved in polar solvents compared with those in nonpolar solvents. Strong dipole-dipole interaction of ANA molecules with solvents is indicated. At high concentrations the measured emission lifetimes, generally shortened from self-quenching, are found to remain about the same order of magnitude in ANAs. This implies that the exciton states of aggregates are formed and they exhibit a relatively long lifetime. Crystallographic data of 4-(phenyl antracen-9-yl) (ANA-2) and 4-(phenyl-2-naphthyl) amino-1,8-naphthalic anhydrides (ANA-3) show that the molecules exist as dimeric structures with antiparallel head-to-tail stacking of naphthalic anhydride planes in addition to other pi-pi stacking. The strong dipole-dipole interactions and the pi-pi stacking account for the observed red-shifted emissions of ANAs in the powders. For films prepared from vacuum sublimation, a structure similar to that in the crystal but with less crystalline order is expected based on the emission wavelength. Several electroluminescent devices based on these ANAs are reported here; they emit orange-red light at 602-628 nm with high brightness and steady external quantum efficiency.     

The use of McMurry coupling for the synthesis of indolophanes and cis-stilbenophanes

Treatment of 2 equiv of indole-3-aldehyde with o, m, p-xylyl, 2,5-dimethoxy-p-xylyl dibromides and 4,4′-bis(bromomethyl)-1,1′-biphenyl gave the bisalkylated products, which underwent McMurry coupling with low valent titanium to give indolophanes. Various cis-stilbenophanes with m-terphenyl building blocks were also synthesized by application of the McMurry coupling technique.     

Kinetic and mechanistic studies on the formation of bis(dicarboxylato)carbonatochromate(III) complexes

The reaction of the Cr(xx)₂(H₂O)₂ ⁻ (xx = oxalate, malonate and methylmalonate) complexes with dissolved CO₂ was studied by stopped-flow spectrophotometry in the 7 < pH < 9 range and between 20 to 30°C at an ionic strength of 0.5 mol dm⁻³ (NaCl). Under the experimental conditions the aqua complex ion consists of a pH-dependent mixture of Cr(xx)₂(H₂O)₂ ⁻, Cr(xx)₂(OH) (H₂O)²⁻ and Cr(xx)₂(OH)₂ ³⁻. The monohydroxo and dihydroxo species undergo CO₂ uptake and subsequent intramolecular carbonate ligand chelation independently, at rates which are readily distinguishable and are governed by the uptake rate constants k ₁ and k ₂ and chelation rate constants k ₃ and k ₄, respectively. Only the k ₁ values for oxalato, malonato and methylmalonato complexes could be calculated; k ₁ = 1084 and 1333 and 1650 mol⁻¹ dm³ s⁻¹, respectively. The results obtained were compared with those obtained from other systems that have either cobalt(III), iridium(III) or rhodium(III) as central atoms. This revised version was published online in June 2006 with corrections to the Cover Date.     

HPTLC Method for Quantification of Apigenin in the Dried Root Powder of Gmelina arborea Linn.

JPC – Journal of Planar Chromatography – Modern TLC - A sensitive high-performance thin-layer chromatographic method has been established for quantification of apigenin in dried root...     

Spectrophotometric determination of vanadium with n-benzoyl-o-tolylhydroxylamine

N-Benzoyl-o-tolylhydroxylamine is shown to provide a virtually specific reagent for the spectrophotometric determination of vanadium. The reddish-violet complex formed with the reagent in 4–8 N hydrochloric acid after extraction with chloroform shows absorption maxima at 510 mm, and obeyes Beer's law from 0.5 to 10 μg with an optimum range of 2–10 μg; the percent relative error is 2.7. The sensitivity is 0.0108 μg V/cm². The complex contains the metal and the reagent in a ratio of 1:2 and the dissociation constant is of the order of 10^-9.     

Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation

This paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the “thickness” direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications—both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems.