Comparison of the surprising metal-ion-binding properties of 5- and 6-uracilmethylphosphonate (5Umpa2- and 6Umpa2-) in aqueous solution and crystal structures of the dimethyl and di(isopropyl) esters of H2(6Umpa)

5- and 6-Uracilmethylphosphonate (5Umpa(2-) and 6Umpa(2-)) as acyclic nucleotide analogues are in the focus of anticancer and antiviral research. Connected metabolic reactions involve metal ions; therefore, we determined the stability constants of M(Umpa) complexes (M(2+)=Mg(2+), Ca(2+), Mn(2+), Co(2+), Cu(2+), Zn(2+), or Cd(2+)). However, the coordination chemistry of these Umpa species is also of interest in its own right, for example, the phosphonate-coordinated M(2+) interacts with (C4)O to form seven-membered chelates with 5Umpa(2-), thus leading to intramolecular equilibria between open (op) and closed (cl) isomers. No such interaction occurs with 6Umpa(2-). In both M(Umpa) series deprotonation of the uracil residue leads to the formation of M(Umpa-H)(-) complexes at higher pH values. Their stability was evaluated by taking into account the fact that the uracilate residue can bind metal ions to give M(2)(Umpa-H)(+) species. This has led to two further important insights: 1) In M(6Umpa-H)-cl the H(+) is released from (N1)H, giving rise to six-membered chelates (degrees of formation of ca. 90 to 99.9 % with Mn(2+), Co(2+), Cu(2+), Zn(2+), or Cd(2+)). 2) In M(5Umpa-H)$-cl the (N3)H is deprotonated, leading to a higher stability of the seven-membered chelates involving (C4)O (even Mg(2+) and Ca(2+) chelates are formed up to approximately 50 %). In both instances the M(Umpa-H)-op species led to the formation of M(2)(Umpa-H)(+) complexes that have one M(2+) at the phosphonate and one at the (N3)(-) (plus carbonyl) site; this proves that nucleotides can bind metal ions independently at the phosphate and the nucleobase residues. X-ray structural analyses of 6Umpa derivatives show that in diesters the phosphonate group is turned away from the uracil residue, whereas in H(2)(6Umpa) the orientation is such that upon deprotonation in aqueous solution a strong hydrogen bond is formed between (N1)H and PO(3) (2-); replacement of the hydro gen with M(2+) gives the M(6Umpa-H)-cl chelates mentioned.     

Pricing vulnerable European options with stochastic default barriers

CF Lo and KC Ku Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China Email: cho-hoi_hui{at}hkma.gov.hk Received on 31 July 2006. Accepted on 15 March 2007. This paper develops a valuation model of European options incorporatinga stochastic default barrier, which extends a constant defaultbarrier proposed in the Hull–White model. The defaultbarrier is considered as an option writer's liability. Closed-formsolutions of vulnerable European option values based on themodel are derived to study the impact of the stochastic defaultbarriers on option values. The numerical results show that negativecorrelation between the firm values and the stochastic defaultbarriers of option writers gives material reductions in optionvalues where the options are written by firms with leverageratios corresponding to BBB or BB ratings.     

On the existence of conically self-similar free-vortex solutions to the Navier-Stokes equations

In this paper a proof of existence and non-existence of theconically self-similar free-vortex solutions to the Navier-Stokesequations, originally found by Yih et al. (1982, Phys. Fluids.25, 2147-2158), is presented. This proof clearly establishesthat these solutions do not have any kind of singularity atthe symmetry axis. This analysis gives considerably improvedexistence and non-existence bounds and it is shown that thesebounds are close to optimal in the low-swirling limit. Thisapproach links the questions of existence and non-existencefor the swirling case and for the non-swirling case. The proof,which is an extension of techniques developed by Serrin (1972,Phil. Trans. R. Soc. Lond. 271, 325-360), is based on Schauder'sFixed Point Theorem and is, therefore, non-constructive. Therefore,the paper ends with a brief discussion of the question of howto compute the conically self-similar free-vortex solutionsto the Navier-Stokes equations.