Edge-Coloring Bipartite Graphs

Given a bipartite graph G with n nodes, m edges, and maximum degree Δ, we find an edge-coloring for G using Δ colors in time T + O(m log Δ), where T is the time needed to find a perfect matching in a k-regular bipartite graph with O(m) edges and k ≤ Δ. Together with best known bounds for T this implies on edge-coloring algorithm which improves on the algorithm of Hopcroft and Cole. Our algorithm can also be used to find a (Δ + 2)-edge-coloring for G in time O(m log Δ). The previous best approximation algorithm with the same time bound needed Δ + log Δ colors.     

An alternative approach to determine the spot-size of a multi-mode laser beam and its application to diode laser beams

An alternative approach is suggested to determine the spot-size of a multi-mode laser beam. It has been shown by simulations that the suggested approach can give the beam quality factor and characteristic radius with less than 5% error. Unlike the power content method, the proposed method is applicable to the beams even with diameter one tenth of the CCD size. The new approach has been applied to a multi-mode diode laser output and it is shown that the ABCD matrix analysis can be used for beam propagation, with the measured parameters of the laser.     

Phonons and their dispersion in poly(S-benzyl-L-cysteine)

Poly(S-benzyl-L -cysteine) (PBLC) is a S-benzyl derivative of the natural amino acid poly(L -cysteine). Its normal modes and their dispersion in antiparallel β-sheet conformation have been obtained within the first Brillouin zone using Wilson's G.F. matrix method, as modified by Higgs for an infinite polymeric chain. The zone center frequencies and the Urey Bradley force field have been obtained by “best fitting” the observed Fourier transform IR (FTIR) absorption bands. The characteristic features of dispersion curves such as crossing, repulsion, and exchange of character are discussed. Predictive values of heat capacity in the temperature range of 50–500 K are reported. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3269–3287, 1999     

Pulse and steady‐state radiolysis studies of some homonuclear copper(II) and heteronuclear copper(II)‐molybdenum(VI) peroxo compounds containing a simple peptide molecule

The reactions of e_aq⁻, OH·, CO₂⁻·, and N₃· radicals with some novel homo nuclear and hetero nuclear peroxo peptide complexes viz: copper peroxo glycylglycine, [Cu(O₂)(H₂L)₂]; molybdenum oxoperoxo glycylglycine, [Mo(O)(O₂)₂(H₂L)₂]; Cu,Mo oxoperoxo glycylglycine [CuMo(O)(O₂)(L)₂] and Cu,Mo, oxo glycylglycine, [CuMo(O)₂(L)₂] (H₂L=glycyl glycine) in aqueous solutions were investigated by pulse radiolysis. Three types of reactions were observed: (1) reduction of Cu(II) to Cu(I) by e_aq⁻ and CO₂⁻·, (2) oxidation of Cu(II) to Cu(III) by N₃⁻·, and (3) formation of a radical on H abstraction from the ligand by OH· radical. Rate constants were reported for formation and decomposition of all intermediates. In case of one electron reduced complexes of hetero atoms, CuMo(O)₂L₂ and CuMo(O)(O₂)L₂, prepared via the reduction of the corresponding complexes by e_aq⁻, formation of a new dimer radical anion complex was observed. It is also noteworthy to mention the possibility of the effect of peroxo ligand on intermediate steps during the formation of Cu clusters. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 159–168, 1999