Self-avoiding random walk: A Brownian motion model with local time drift

Summary A natural model for a self-avoiding Brownian motion inR ^d, when specialised and simplified tod=1, becomes the stochastic differential equation , where {L(t, x):t0,xR} is the local time process ofX. ThoughX is not Markovian, an analogue of the Ray-Knight theorem holds for {L(,x):xR}, which allows one to prove in many cases of interest that exists almost surely, and to identify the limit.     

Synthesis and characterization of a new isocyanato carborane anion [7-OCN-7-CB10H12]; study on its reactivity toward amino containing compounds

The new isocyanato carborane anion, [7-OCN-7-CB₁₀H₁₂]⁻ was prepared by the reaction of 7-H₃N-7-CB₁₀H₁₂ with triphosgene in the presence of triethylamine. The structure of this compound was established by ¹H, ¹¹B and ¹³C NMR as well as IR spectroscopy. The reactivigty of this compound with a series of organic amines was investigated. The resulting ureas were obtained in good to excellent yields. This approach is suitable for development of compounds for use in tumor selective Boron Neutron Capture Therapy (BNCT).     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.