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.     

Rapid and efficient removal of Hg(II) from aqueous solution by potassium hexa-titanate: A radiotracer study

The adsorption of mercury(II) on potassium titanate has been studied in chloride media at different pH values, adsorbate concentrations and temperatures. Effect of different ligands and acid concentrations on the uptake was also investigated. Desoprtion studies were also done to check the reversibility of the process. Interestingly a more or less constant and high value of adsorption has been found at different temperatures, pH values and concentrations and a decrease in the uptake with an increase in the bulk acid concentration was observed.     

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.     

Electron impact induced fragmentation of some 1,2,4-triazole derivatives

The mass spectra of eight 1,2,4-triazole derivaties have been recorded and found tao reveal extensive hydrogen and skeletal migrations. The structures of the fragments have been confirmed by deuterium labelling and exact mass measurement. The compounds revealed striking differences in their spectra depending on the nature of the substituents.     

Reactions of aromatic ketones with 3-mercapto-1,2-propanediol. Synthesis of cis- and trans-2-alkyl-2-aryl-(1,3-oxathiolane-5-methanols and 1,3-dioxolane-4-methanethiols)

Aromatic ketones react with 3-mercapto-1,2-propanediol ( 1 ) in refluxing benzene under the catalytic influence of a sulfonic acid and with azeotropic removal of water to yield a mixture comprised predominantly of cis- and trans-2-alkyl-2-aryl-1,3-oxathiolane-5-methanols 7, accompanied by lesser amounts of cis- and trans-2-alkyl-2-aryl-1,3-dioxolane-4-methanethiols 8 (up to 30%). It was discovered that 8 is the kinetic product and is isomerized by 4-toluenesulfonic acid in hot benzene to the thermodynamically more stable 7 . Under these conditions, ortho- and α-substituted aromatic ketones tend to produce more of 8 , which can be attributed to steric hindrance encountered by the thiol as it attacks the ketone. Ketalizations of 1-aryl-2-(1H-imidazol-1-yl)-1- as well as 1-aryl-2-(1,H-1,2,4-triazol-1-yl)-1-ethanones by 1 fail under these conditions, even after 24 hours of reflux in toluene. However, 1-(4-chlorophenyl)-3-(1H-imidazol-1-yl)-1-propanone and 1-(4-bromophenyl)-4-(1H-imidazol-1-yl)-1-butanone are ketalized by 1 as expected. Interestingly, the reaction of 2-bromo-4′-chloroace-tophenone with 1 produces 1-(4-chlorophenyl)-2,8-dioxa-6-thiabicyclo[3.2.1]octane. Characterization of all isomers and separation of some diastereomers is described. Nuclear Overhauser enhancement experiments are utilized to establish the stereochemistry of 1,3-oxathiolanes.     

Synthesis and stereochemical assignment of 7-arylidene and 7-heteroarylidene morphinan-6-ones

A number of (E)-7-arylidenenaltrexones were synthesized by azeotropic distillation of water from a benzene solution of naltrexone and an aromatic aldehyde (benzaldehyde, 4-chloro- and 4-fluorobenzaldehyde, 3-and 4-pyridinecarboxaldehyde and 1-methyl-2-imidazolecarboxaldehyde) using piperidine as a catalyst. In addition, (E)-7-benzylidenenaloxone was prepared by the previously published Claisen-Schmidt condensation using sodium hydroxide in methanol. The stereochemistry of these arylidene derivatives 3–9 was determined to be (E) by means of nuclear Overhauser enhancement experiments. The ¹³C nmr spectra of (E)- 3–9 are recorded in deuteriochloroform and those of the hydrochlorides in deuteriodimethyl sulfoxide.