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.     

Analytical study of the performance of minSIS solar cells with a back surface field

The effect of a Back Surface Field (BSF) on the performance of a minority-carrier transparent Semiconductor-Insulator-Semiconductor (minSIS) solar cell has been studied. An analytical one-dimensional model has been developed for the calculation of transport characteristics of minSIS solar cells. Short-circuit current, open-circuit voltage, fill factor and efficiency are then calculated for a sputtered Indium-Tin-Oxide (ITO)-SiO₂-pSi-p ⁺Si solar cell under AM1 illumination for different values ofpSi- andp ⁺ Si-layer thicknesses. It is found that for a large base thickness, the effect of BSF is not significant; however, for a small thickness all the quantities increase with BSF.     

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.     

Synthesis and characterization of SPE membrane based on sulfonated FEP‐g‐acrylic acid by radiation induced graft copolymerization for PEM fuel cell

A Novel solid polymer electrolyte (SPE) membrane containing both ? COOH and ? SO₃H group has been prepared by simultaneous method of radiation grafting of acrylic acid onto FEP followed by sulfonation. The presence of weakly acidic acrylic acid controls the swelling in water while ? SO₃H group provides conductivity due to its strongly ionic characteristic. FEP‐g‐acrylic acid and its sulfonated derivatives were characterized by their properties. While the mechanical properties decreased, other properties such as ion exchange capacity (IEC), water uptake and ionic conductivity increased with increase in graft content. These properties further changed on sulfonation. Acrylic acid being weakly acidic in nature, conductivity values of the grafted membrane were quite low. However, introduction of strong ? SO₃H group resulted in conductivity closer to Nafion 117. Few sulfonated membranes have been tested with respect to H₂/O₂ fuel cell performance. Short‐term fuel cell test for 100 hr gave a stable performance. These membranes are less expensive compared to Nafion. Copyright © 2004 John Wiley & Sons, Ltd.