A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

Radiationless transitions in trivalent lanthanide ions embedded in solids

Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.     

Synthesis of cetyltrimethylammonium tribromide (CTMATB) and its application in the selective oxidation of sulfides to sulfoxides

The bright yellow crystalline cetyltrimethylammonium tribromide (CTMATB) reagent has been synthesized from the reaction of CTMAB and KBr with H₂MoO₄·H₂O, H₂O₂ and H₂SO₄ in the molar ratio 1:2:0.01:4:0.93. CTMATB selectively oxidizes a variety of dialkyl and alkyl aryl sulfides to the corresponding sulfoxides in high yields under mild conditions.     

Barbier coupling in water: SnCl2-mediated and Co(acac)2-catalyzed allylation of carbonyls

Co(acac)₂·2H₂O efficiently catalyzes SnCl₂-mediated Barbier coupling in water between carbonyls, including aromatic, aliphatic and α,β-unsaturated aldehydes, ketones, sugars and allyl bromide to afford the corresponding homoallylic alcohols in high yields. The catalyst was reused for several cycles with consistent activity.     

Influence of optical constants in carbon-based dispersions for enhanced solar evaporation

Journal of Thermal Analysis and Calorimetry - Carbon-based nano- and microfluid dispersions show promise as effective media for solar-assisted desalination. They act as strong solar absorbers in...     

X‐ray photoelectron spectroscopy process optimization for characterization of trace contamination elements for extreme ultraviolet resist outgassing study

X‐ray photoelectron spectroscopy (XPS) is used for elemental identification and quantification in a number of fields, and the optimization of XPS performance can help in making better use of the limited XPS tool availability. In the field of extreme ultraviolet (EUV) lithography, one of the requirements is having a clean vacuum environment to minimize contamination of the EUV optics. EUV resist outgassing is viewed as one of the main issues that could affect the vacuum environment. There is a program underway to measure the relative contamination rates from different resists following the ASML (provider of lithography systems) approved protocols for witness plate testing. One of the key steps is the XPS measurement of residue on the optics after cleaning. The role of XPS in quantification of species that adhere to the ruthenium‐coated silicon witness plate sample is discussed. The various XPS tool parameters like the pass energy and source setting were optimized for our application of witness plate analysis. The statistics of our XPS tool were studied, and combined with the fundamental XPS equations, a simple mathematical model was developed to optimize the number of scans for the various elements of interest in our witness plate study. Using the optimized number of scans, the acquisition time to measure the contaminant elements to a precision better than 0.1 at.% was minimized. The model devised in the paper can be adapted to other XPS measurements requiring different levels of precision. Copyright © 2013 John Wiley & Sons, Ltd.