A proof of Howard's conjecture in homogeneous parallel shear flows—II: Limitations of Fjortoft's necessary instability criterion

The present paper on the linear instability of nonviscous homogeneous parallel shear flows mathematically demonstrates the correctness of Howard's [4] prediction, for a class of velocity distributions specified by a monotone functionU of the altitudey and a single point of inflexion in the domain of flow, by showing not only the existence of a critical wave numberk _c>0 but also deriving an explicit expression for it, beyond which for all wave numbers the manifesting perturbations attain stability. An exciting conclusion to which the above result leads to is that the necessary instability criterion of Fjortoft has the seeds of its own destruction in the entire range of wave numbersk>k _c—a result which is not at all evident either from the criterion itself or from its derivation and has thus remained undiscovered ever since Fjortoft enunciated [3].     

On the principle of exchange of stabilities in the magnetohydrodynamic simple Bénard problem

The present paper establishes a new result which was long sought after in the field of magnetoconvection, namely, the validity of the principle of exchange of stabilities for the magnetohydrodynamic simple Bénard problem in the regime Qσ₁ ? π² where Q is the Chandrasekhar number and σ₁ is the magnetic Prandtl number. This result is applicable for quite general boundary conditions and provides a natural extension of A. Pellew and R. V. Southwell's (Proc. Roy. Soc. London Ser. A176 (1940), 312–343) result for the simple Bénard problem. A corresponding result for rotatory magnetohydrodynamic simple Bénard problem is also given.     

Optical rotatory dispersion of rare earth crystal

The ORD spectrum of optically active single crystal of praseodymium oxydiacetate has been studied in the visible range at 77 K. The results have been compared with those obtained in the cases of transition metal complexes and other RE complexes with optically active ligands, and correlated with the site symmetry of the RE ion in the crystal. The optical activity has been related to the magnetic dipole strengths of the transitions.     

Studies in some new initiator systems for vinyl polymerization. Part I. Molecular halogens or halates as one component

Several new initiating systems involving a molecular halogen, halates, or perhalate as one of the components and a reducing metal salt, ammonia, an amine or an organic compound as the other component, have been introduced for the aqueous (and in a few cases the non-aqueous) polymerization of methyl methacrylate. Some of the resulting polymers have been subjected to endgroup analysis by the application of the ultrasensitive dye techniques recently developed in our laboratory. Reducing metal salt—halogen-initiated polymers are found to incorporate hydroxyl and halogen endgroups, while polymers initiated by amine—halogen systems incorporate hydroxyl and halogen as well as amino endgroups. However, in the ammonia—halogen system polymers incorporate only halogen endgroups. On the basis of the results of the endgroup analysis of the polymers an attempt has been made to explain the probable initiation mechanism with regard to the nature and identity of the initiating species involved in such processes.     

Porphyrins with exocyclic rings. Part 19: Efficient syntheses of phenanthrolinoporphyrins

5-Nitro-1,10-phenanthrolines react with isocyanoacetate esters in the presence of DBU in THF to give excellent yields of the corresponding phenanthrolinopyrroles. These were condensed with acetoxymethylpyrroles using catalytic quantities of p-toluenesulfonic acid in acetic acid to give dipyrrylmethanes, but these structures proved to be poorly suited for porphyrin synthesis due to the electron-withdrawing nature of the fused phenanthroline unit. However, phenanthrolinopyrrole ethyl esters could be converted to the corresponding α-unsubstituted pyrroles with KOH in ethylene glycol at 180-190 °C, and these condensed with 2 equiv of acetoxymethylpyrroles in refluxing acetic acid-isopropyl alcohol to give tripyrranes. In a one pot procedure, tripyrrane di-tert-butyl esters were treated with TFA at room temperature to cleave the protective groups, diluted with dichloromethane, reacted with pyrrole dialdehydes and oxidized to afford phenanthrolinoporphyrins in 52-83% yield. These conditions also allow the synthesis of porphyrins with additional fused acenaphthylene or phenanthrene rings. Although the UV-vis spectra for these porphyrins are unexceptional, the presence of an external coordination site allows many potential applications to be considered. Porphyrins with two phenanthroline units could not be prepared by the ‘3+1’ strategy. Instead, α-unsubstituted phenanthrolinopyrroles were reacted with a bis(dimethylaminomethyl)pyrrole in refluxing acetic acid to give moderate yields of the corresponding opp-diphenanthrolinoporphyrins. In one case, a triphenanthrolinoporphyrin and trace amounts of an adj-diphenanthrolinoporphyrin were formed as by-products.     

Synthesis and properties of lead-free formamidinium bismuth bromide perovskites

In the past few years, Pb-free metal halide perovskites have been recognized as a promising material for various optoelectronic applications because of some of their unique features, such as direct and tunable bandgap, visible light emission, narrow emission spectra, lower toxicity level, and easy solution processability. Recently, several Bi-based perovskite-like single crystals (SCs) and nanocrystals (NCs) were reported, which are mostly suffering from their poor structural stability and lower emission intensity. Here, we report the growth of millimeter-sized formamidinium bismuth bromide (FA₃Bi₂Br₉) perovskite SCs via slow solvent evaporation method. They crystallized into a trigonal crystal structure and exhibit an indirect bandgap of 2.71 eV. These results are supported by the first-principle density-functional theory studies. We have also synthesized nanometer-sized spherical blue-emitting FA₃Bi₂Br₉ NCs by solvent ligand-assisted reprecipitation method and achieved a maximum photoluminescence quantum yield of 22%. We observe that the addition of excess ligands into the FA₃Bi₂Br₉ NCs solution before the purification step significantly improves the optical and colloidal stability of the NCs.