Catalytic Reduction of Hydrazine to Ammonia with MoFe(3)S(4)-Polycarboxylate Clusters. Possible Relevance Regarding the Function of the Molybdenum-Coordinated Homocitrate in Nitrogenase

The catalytic function of the previously synthesized and characterized [(L)MoFe(3)S(4)Cl(3)](2)(-)(,3)(-) clusters (L = tetrachlorocatecholate, citrate, citramalate, methyliminodiacetate, nitrilotriacetate, thiodiglycolate) and of the [MoFe(3)S(4)Cl(3)(thiolactate)](2)(4)(-) and [(MoFe(3)S(4)Cl(4))(2)(&mgr;-oxalate)](4)(-) clusters in the reduction of N(2)H(4) to NH(3) is reported. In the catalytic reduction, which is carried out at ambient temperature and pressure, cobaltocene and 2,6-lutidinium chloride are supplied externally as electron and proton sources, respectively. In experiments where the N(2)H(4) to the [(L)MoFe(3)S(4)Cl(3)](n)()(-) catalyst ratio is 100:1, and over a period of 30 min, the reduction proceeds to 92% completion for L = citrate, 66% completion for L = citramalate, and 34% completion for L = tetrachlorocatecholate. The [Fe(4)S(4)Cl(4)](2)(-) cluster is totally inactive and gives only background ammonia measurements. Inhibition studies with PEt(3) and CO as inhibitors show a dramatic decrease in the catalytic efficiency. These results are consistent with results obtained previously in our laboratory and strongly suggest that N(2)H(4) activation and reduction occur at the Mo site of the [(L)MoFe(3)S(4)Cl(3)](2)(-)(, 3)(-) clusters. A possible pathway for the N(2)H(4) reduction on a single metal site (Mo) and a possible role for the carboxylate ligand are proposed. The possibility that the Mo-bound polycarboxylate ligand acts as a proton delivery "shuttle" during hydrazine reduction is considered.     

Global approximation to arbitrary cost functions: A Bayesian approach with application to US banking

This paper proposes and estimates a globally flexible functional form for the cost function, which we call Neural Cost Function (NCF). The proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates. The functional form can be estimated easily using Markov Chain Monte Carlo (MCMC) techniques or standard iterative SURE. We use a large panel of U.S. banks to illustrate our approach. The results are consistent with previous knowledge about the sector and in accordance with mathematical production theory.     

Density symmetries for a class of 2-D diffusions with applications to finance

We study densities of two-dimensional diffusion processes with one non-negative component. For such diffusions, the density may explode at the boundary, thus making a precise specification of the boundary condition in the corresponding forward Kolmogorov equation problematic. We overcome this by extending a classical symmetry result for densities of one-dimensional diffusions to our case, thereby reducing the study of forward equations with exploding boundary data to the study of a related backward equation with non-exploding boundary data. We also discuss applications of this symmetry for option pricing in stochastic volatility models and in stochastic short rate models.     

On properties of random dissections and triangulations

In this work we study properties of random graphs that are drawn uniformly at random from the class consisting of biconnected outerplanar graphs, or equivalently dissections of large convex polygons. We obtain very sharp concentration results for the number of vertices of any given degree, and for the number of induced copies of a given fixed graph. Our method gives similar results for random graphs from the class of triangulations of convex polygons.     

Measurable events indexed by products of trees

A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b ≥ 2, called the branching number of T, such that every t ∈ T has exactly b immediate successors. A vector homogeneous tree T is a finite sequence (T ₁,...,T _d ) of homogeneous trees and its level product ?T is the subset of the Cartesian product T ₁×...×T _d consisting of all finite sequences (t ₁,...,t _d ) of nodes having common length. We study the behavior of measurable events in probability spaces indexed by the level product ?T of a vector homogeneous tree T. We show that, by refining the index set to the level product ?S of a vector strong subtree S of T, such families of events become highly correlated. An analogue of Lebesgue’s density Theorem is also established which can be considered as the “probabilistic” version of the density Halpern-Läuchli Theorem.     

Large Deviations Principle for a Large Class of?One-Dimensional Markov Processes

We study the large deviations principle for one-dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process X _t in ? that is continuous with probability one, under some minimal regularity conditions, is governed by a generalized elliptic operator D _v D _u , where v and u are two strictly increasing functions, v is right-continuous and u is continuous. In this paper, we study large deviations principle for Markov processes whose infinitesimal generator is ??D _v D _u where 0<???1. This result generalizes the classical large deviations results for a large class of one-dimensional ??classical?? stochastic processes. Moreover, we consider reaction-diffusion equations governed by a generalized operator D _v D _u . We apply our results to the problem of wavefront propagation for these type of reaction-diffusion equations.