A new method for solving Pareto eigenvalue complementarity problems

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNM_min and SNM_FB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201–213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125–137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.     

Multifrequency EPR and redox reactivity investigations of a bis(mu-thiolato)-dicopper(II,II) complex

From a new tripodal ligand [N2SS'H] with mixed N, S(thioether), and S(thiolate) donor set, the corresponding bis(mu-thiolato)dicopper(II) complex has been prepared and characterized. X-ray crystallographic analysis of the complex [Cu2(N2SS')2](ClO4)2.C4H10O (1) demonstrates that the two five-coordinated Cu atoms are bridged by two thiolates leading to a nearly planar Cu2S2 core with a Cu1...Cu1* distance of 3.418(8) A and a large bridging angle Cu1S1Cu1* of 94.92 degrees. X-band (10 GHz), Q-band (34 GHz), and F-Band (115 GHz) EPR spectra of 1 are consistent with a weakly coupled dicopper(II,II) center attributed to an S = 1 state. Simulations for the three frequencies are obtained with a unique set of electronic parameters. The mean values of the spin Hamiltonian parameters for 1 are D = 0.210(3) cm(-1), E = 0.0295(5) cm(-1), |E/D| = 0.140, gx = 2.030(2), gy = 2.032(2), gz = 2.128(2). The electrochemical one-electron reduction of 1 generates the mixed-valent CuIICuI species. EPR and UV-vis spectra are consistent with a type I localized mixed-valent species, while dinuclear CuA centers of native cytochrome c oxidase (CcO)1-3 or nitrous oxide reductase (N2OR)4 have a delocalized CuIICuI mixed-valent state. After reoxidation of the CuIICuI species, the initial complex 1 is regenerated through a reversible interconversion process.     

Synthesis and molecular structures of some new titanium(IV) aryloxides.

The coordination chemistry of model phenolic ligands (pyrocatechol, salicylic acid, and 2,2'-biphenol) that are able to form respectively five-, six-, or seven-membered rings with titanium(IV) alkoxides is investigated. With pyrocatechol, a polynuclear complex containing 10 Ti atoms was characterized with a not very common doubly bridging mu3-(O,O,O',O') coordination mode. With salicylic acid, a monomeric tris(chelate) complex was obtained. With 2,2'-biphenol, a polynuclear complex containing six Ti atoms was obtained showing both mu2-(O,O') and mu2-(O,O,O') coordination modes for the ligands. Intermolecular interactions in the solid state for these three new compounds are also quantitatively discussed using the partial charge model.