Copper(II) and lead(II) complexes of 4,4′-bipyridine-<Emphasis Type="Italic">N,N</Emphasis>′-dioxide

Cu(II) and Pb(II) complexes of 4,4′-bipyridine-N,N′-dioxide have been prepared using a solvent-layering system. [Cu₂Cl₄(bpdo)₃(H₂O)₂] . 2(CH₃)₂SO (1) crystallises in P-1, a=8.731(2), b=8.943(2), c=14.408(3) ?, α=102.85(3), β=97.49(3), γ=109.77(3)°. The Cu(II) complex is a z-shaped discrete molecule with a DMSO molecule hydrogen bonded to the host through coordinated water molecule. Crystallisation of PbCl₂, PbBr₂ and PbI₂ with bpdo afforded isostructural 2D coordination polymers. [PbCl₂(bpdo)]_n is monoclinic, C2/c with a=16.3274(7), b=4.0708(1), c=18.6146(8) ?, β=93.73(1)°; [PbBr₂(bpdo)]_n is monoclinic, C2/c with a=16.403(3), b=4.2412(8), c=18.846(4) ?, β=92.59(3)° and [PbI₂(bpdo)]_n is monoclinic, C2/c with a=16.438(3), b=4.538(1), c=18.973(4) ?, β=91.04(3)°. The adjacent metal centres of these polymers are bridged by coordinated Cl⁻, Br⁻ or I⁻ anions as well as by bpdo ligands. These polymers possess no conventional hydrogen bonds.     

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Some new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.     

Comparison of symmetry and homotopy solutions for nonlinear heat transfer systems

This study deals with the analytic solutions for the two nonlinear problems arising in heat transfer. These problems are due to (i) temperature distribution in lumped system of combined convection–radiation and (ii) temperature distribution in a uniformly thick rectangular fin radiation to free space. Large symmetry algebras are obtained for the nonlinear ordinary differential equations (ODEs) describing the heat transfer. We use method of canonical variables to either linearize or transform the governing equations to integrable forms. Exact solutions are constructed. Finally, a comparison is given between the homotopy and symmetry solutions.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.