Dissipative N-point-vortex Models in the Plane

A method is presented for constructing point vortex models in the plane that dissipate the Hamiltonian function at any prescribed rate and yet conserve the level sets of the invariants of the Hamiltonian model arising from the SE (2) symmetries. The method is purely geometric in that it uses the level sets of the Hamiltonian and the invariants to construct the dissipative field and is based on elementary classical geometry in ℝ³. Extension to higher-dimensional spaces, such as the point vortex phase space, is done using exterior algebra. The method is in fact general enough to apply to any smooth finite-dimensional system with conserved quantities, and, for certain special cases, the dissipative vector field constructed can be associated with an appropriately defined double Nambu–Poisson bracket. The most interesting feature of this method is that it allows for an infinite sequence of such dissipative vector fields to be constructed by repeated application of a symmetric linear operator (matrix) at each point of the intersection of the level sets.     

A facile synthesis of dihydrobenzofuranols by photocyclization of (2‐alkoxy‐5‐methyl‐phenyl)(aryl) methanone and ethyl 2‐aroyl‐4‐methylphenyloxyacetates

Irradiation of 2‐alkoxy substituted benzophenones 2a–f and ethyl 2‐aroyl‐4‐methylphenyloxyacetates 2g–i in benzene and in acetonitrile underwent photocyclization to substituted dihydrobenzofuranols 3a–i with 3a–c in very less yield being racemate and 3d–i in good yield being mixture of cis‐trans isomers showing high stereoselectivity in benzene and decreased stereoselectivity in acetonitrile. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:212–217, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20111     

Microwave-assisted synthesis of 2-amino and 2-azetidinonyl 5-(2-benzoyl-phenoxymethyl) 1,3,4-oxadiazoles

A simple high yielding method for the integration of heterocyclic rings viz. 1,3,4-oxadiazole and azetidin-2-one at the benzophenone nucleus has been developed starting from substituted 2-hydroxybenzophenones, and by using mild conditions, wet solid surface, and microwave irradiation. A comparison of this microwave-accelerated reaction with conventional heating condition is also illustrated. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 15:37–42, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10210     

Binary Mixtures of n‐C36H74 with Certain Shorter Chain n‐Alkanes: Powder XRD Investigations

Powder XRD investigations on hexatriacontane hydrocarbon, forming binary mixtures with octadecane, hexadecane, decane and decanol were made and the results were interpreted in terms of additive (impurity) effect, phase changes, strength of phases and phase separation. Possibility of the occurrence of super lattices in these systems is considered.