Chelated fluoroboron cations : synthesis and multinuclear nmr studies

The preparation of chelated difluoroboron cations (DD)BF2+, where DD is a saturated polydentate tertiary-amine or polydentate aromatic ligand, has been systematically studied by using multinuclear solution and solid state nuclear magnetic resonance spectroscopy and fast atom bombardment mass spectrometry. Three new methods of synthesis of (DD)BF2+ cations are reported, and compared with the previous method of reacting a chelating donor with Et20.BF3. The methods most effective for aromatic donors such as 1,1O-phenanthroline are ineffective for saturated polydentate tertiary-amines like N,N,N' ,Nil ,Nil-pentamethyldiethylenetriamine. Polydentate tertiary-amine donors that form 5-membered rings upon bidentate chelation were found to chelate effectively when the BF2 source contained two leaving groups (a heavy halide and a Lewis base such as pyridine =pyr or isoxazole =ISOX), i.e., pyr.BF2X (X = CI or Br), ISOX.BF2X and (pyr)2BF2+. Those that would form 6membered rings upon chelation do not chelate by any of the four methods. Polydentate aromatic ligands chelate effectively when the BF2 source contained a weak Lewis base, e.g., ISOX.BF3, ISOX.BF2X and Et20.BF3. Bidentate chelation by polydentate tertiaryamine and aromatic donors leads to nmr parameters that are significantly different then their (D)2BF2+ relatives (D =monod~ntate t-amines or pyridines). The chelated haloboron cations (DD)BFCI+, and (DD)BFBr+ were generated from D.BFX2 adducts for all ligands that form BF2+ cations above. In addition, the (DD)BCI2+ and (DD)BBr2+ cations were formed from D.BX3 adducts by the chelating aromatic ligands, except for the aromatic ligand 1,8-bis(dimethylamino)naphthalene, which formed only the (DD)BF2+ cation, apparently due to its extreme steric hindrance. Chelation by a donor is a two-step reaction. For polydentate tertiary-amine ligands, the two rates appear to be very dependent on the two possible leaving groups on the central boron atom. The order of increasing ease of displacement for the donors was: pyr < Cl < Br < ISOX. The rate of chelation by polydentate aromatic ligands appears to be dependent on the displacement of the first ligand from the boron. The order of increasing ease of displacement for the donors was: pyr < CI < ISOX ~ Br < Et20.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.