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.     

Eroded myelin figures

Myelin figures with unusual surface morphology were observed on contacting Tween85 with water. Myelins, which are normally smooth rodlike forms in other surfactants, are in this system found to be with an irregular, rough surface with vesiclelike structures adhered to the myelin tubes. Besides these, smooth myelin figures were also observed. We term the myelin figures with a rough surface eroded myelin figures. The same myelin could show a coexistence of smooth and rough areas with a sharp boundary between the smooth surface at one end whereas the other end shows a rough texture. The transformation of smooth myelins into eroded forms were observed often whereas the reverse is quite rare. In the later stage, the tip of the eroded myelin figures transforms into tentacles and acts as a source for new myelins and the growth of vesiclelike structures which were expelled into the surrounding medium. The eroded myelin figures are stable for a longer period in comparison to simple, smooth rodlike forms. By studying the myelin growth at different temperatures, it was found that eroded myelin figures were stable in the temperature range of 22-42 degrees C and at > 42 degrees C only smooth myelin figures were observed.     

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.     

Micro-Raman investigations of myelins in aerosol-OT/water system

Surfactant outgrowth during dissolution as myelin figures, which happens on contact with water, is of prime importance in emulsification and detergency. Micro-Raman investigation of different lyotropic phases formed during dissolution of aerosol-OT (bis 2-ethylhexyl sulfosuccinate) in water during myelin formation reveals the flexible arrangement of the surfactant bilayers in myelin. The conformation around CC-CS bond and the hydrocarbon chains of aerosol-OT in the different liquid crystalline phases were identified from the fingerprints of CC-CS stretching, C-C stretching, C-H bending, and stretching frequencies. Existence of mixture of trans and gauche conformations around CC-CS bond and that of the hydrocarbon chains in myelin supports the fluid nature of bilayers by which it is made. Similar conformations of hydrocarbon chains in lamellar phase and in myelin support the concept of myelins being rolled up lamella. The observations are in line with the disorderness of the hydrocarbon chains in the bilayers of phospholipids that has been reported earlier. From the C-C stretching frequencies at the root of myelins, the kinked structure of the hydrocarbon chain is identified, and loose packing of molecules which would facilitate water transport across membranes is evident.     

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.