Convexity of spheres in a manifold without conjugate points

For a non-compact, complete and simply connected manifoldM without conjugate points, we prove that if the determinant of the second fundamental form of the geodesic spheres inM is a radial function, then the geodesic spheres are convex. We also show that ifM is two or three dimensional and without conjugate points, then, at every point there exists a ray with no focal points on it relative to the initial point of the ray. The proofs use a result from the theory of vector bundles combined with the index lemma.     

Low-temperature polymer-assisted synthesis of shape-tunable zinc oxide nanostructures dispersible in both aqueous and non-aqueous media

We report the shape-controlled synthesis of zinc oxide (ZnO) nanostructures by a poly(vinyl methyl ether) (PVME)-assisted alkaline hydrolysis of zinc acetate at low temperature (20 °C). In this method, ZnO nanostructures of various morphologies including dumbbells, lances and triangles have been successfully prepared via a simple variation of different reaction parameters such as polymer concentration, pH of the reaction mixture and precursor concentration. However, without PVME, ZnO of such structurally uniform morphologies were not formed; rather ZnO of a mixture of defined and undefined morphologies were obtained indicating PVME-assisted the growth of such regular shaped ZnO nanostructures. HRTEM analysis of lance- and triangle-shaped samples as well as SAED patterns of all kinds of samples (dumbbell, lance and triangle) revealed that the ZnO nanostrcutures are single crystalline in nature and might form through oriented growth. XRD analysis also revealed the formation of well crystalline ZnO with a hexagonal structure. FTIR spectroscopy and TGA analysis confirmed the adsorption of PVME on the surface of ZnO nanostructures. Being a solvent adaptable polymer, the adsorbed PVME makes these shaped ZnO nanostructures highly dispersible in both polar and non-polar organic solvents including water. The extent of dispersibility in different solvents was studied by spectroscopic and microscopic techniques. Such solvent adoptability of PVME-coated ZnO nanostructures increases its ease of applications in device fabrication as well as in biological systems.     

Free and forced finite amplitude oscillation of a spherical shell of radially isotropic elastic material

A spherical elastic shell with radial transverse isotropy is considered. The periods of finite amplitude radial oscillation of the shell have been obtained in two cases, namely (i) when both the surfaces of the shell are free from traction, and (ii) when the shell boundaries are uniformly loaded in such a way that the pressure difference between inner and outer surfaces is constant with respect to time. It is observed that for free oscillation to take place it is necessary to impose a new restriction on the strain energy function in addition to those already obtained for finite amplitude oscillation of an isotropic elastic shell. In the forced oscillation case however the required conditions are of the same form as in the corresponding case for isotropic media.     

Pyridiniums as potential synthetic substitutes for nitrogen mustards

Dialkylamino-alkyl primary amines 1b and 2b are converted by pyrylium salts into the corresponding pyridinium derivatives. The pyridinium salts act as aminoalkylating agents for representative O-, S-, N-, and C-nucleophiles and are potentially safe substitutes for nitrogen mustards in the reactions.     

A simple synthesis of α, β-unsaturated aldehydes by 1,3-carbonyl transposition through one carbon homologation

α,β-Unsaturated aldehydes are conveniently prepared from ketones through their β-diethoxymethyl derivatives by sodium borohydride reduction followed by acid-catalysed rearrangement of the resulting diacetal carbinols.     

Realizing green phosphorescent light-emitting materials from rhenium(i) pyrazolato diimine complexes

Two neutral pyrazolato diimine rhenium(I) carbonyl complexes with formula [Re(CO)(3)(N-N)(btpz)] where N-N = 2,2'-bipyridine (1) and 1,10-phenanathroline (2), and btpz = 3,5-bis(trifluoromethyl) pyrazolate, were synthesized and characterized by elemental analysis, routine spectroscopic methods, and single-crystal X-ray diffraction study. Ground and excited state properties of these complexes were investigated by steady-state and time-resolved spectroscopies. Complexes 1 and 2 show photoluminescent emission in both solution and solid-state at room temperature, arising from metal to ligand charge-transfer (MLCT) transition with strong overlapping of intraligand pi --> pi transitions. The long-lived excited state lifetimes of complexes 1 and 2, which are on the order of microseconds, indicate the presence of phosphorescent emission. As these complexes hold the potential to serve as phosphors for organic light-emitting diodes (OLEDs), their electroluminescent performances were evaluated by employing them as dopants of various electron transport layer (ETL) or hole transport layer (HTL) hosts. For complex 1, a green electrophosphorescence emission centered at lambda(max) = 530 nm was observed at low turn-on voltage ( approximately 6 V) with luminous power efficiency of 0.72 lm/W, external quantum efficiency of 0.82%, and luminance of 2300 cd/m(2) at a current density of 100 mA/cm(2).     

Quantum analogue of the Kolmogorov–Arnold–Moser transition in different quantum anharmonic oscillators

The results of numerical computations are presented for the Bohmian trajectories of the family of different one‐ and two‐dimensional anharmonic oscillators, which exhibit regular or chaotic motion in both classical and quantum domains, depending on the values of the parameters appearing in the respective Hamiltonians. Quantum signatures of the Kolmogorov–Arnold–Moser (KAM) transition from the regular to chaotic classical dynamics of these oscillators are studied using a quantum theory of motion (QTM) as developed by de Broglie and Bohm. A phase space distance function between two initially close Bohmian trajectories, the associated Kolmogorov–Sinai–Lyapunov (KSL) entropy, the phase space volume, the autocorrelation function, the associated power spectrum, and the nearest‐neighbor spacing distribution, clearly differentiate the quantum analogues of the corresponding regular and chaotic motions in the classical domain. These quantum anharmonic oscillators are known to be useful in several diverse branches of science. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Synthetic applications of 2-chloro-3-formylquinoline

New examples of synthetic applications of 2-chloro-3-formylquinoline, as evident from the novel and facile syntheses of 3-aminoisooxazolo[5,4-b]quinoline (4), 3-hydroxyfuro[2,3-d]theino[2,3-b]quinoline-2-carboxamide (7) and 3-hydroxymethyl-2-(3-formyl)phenylquinoline ( 13 ), have been furnished.