The Livsic Cocycle Equation for Compact Lie Group Extensions of Hyperbolic Systems

In this article we extend well-known results of Livsic on theregularity of measurable solutions to the cocycle equation.Livsic proved a regularity result for real valued cocycles,but for compact Lie group valued cocycles his result was restrictedto coboundaries (that is, trivial or constant cocycles). Inthis article we prove the complete result. We present several useful applications of these results.     

Remark on the size of a Riemann surface

Research partially supported by the National Science Foundation.     

A branching process model for sand avalanches

An analytically solvable model for sand avalanches of noninteracting grains of sand, based on the Chapman-Kolmogorov equations, is presented. For a single avalanche, distributions of lifetimes, sizes of overflows and avalanches, and correlation functions are calculated. Some of these are exponentials, some are power laws. Spatially homogeneous distributions of avalanches are also studied. Computer simulations of avalanches of interacting grains of sand are compared to the solutions to the Chapman-Kolmogorov equations. We find that within the range of parameters explored in the simulation, the approximation of noninteracting grains of sand is a good one.     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

An improved synthesis of isonitrosoacetanilides

A novel two-step synthesis of isonitrosoacetanilides [2-(hydroxyimino)-N-phenylacetamides] has been developed, involving the initial acylation of aniline derivatives with 2,2-diacetoxyacetyl chloride, followed by reaction with hydroxylamine hydrochloride. The method works equally well with a variety of different aniline derivatives, including those with poor aqueous solubility and those containing electron rich ortho-substituents, neither of which react well under traditional conditions.     

Ammonium violurate: a compact structure with extensive hydrogen bonding in three dimensions

The title compound [systematic name: ammonium pyrimidine‐2,4‐5,6(1H,3H)‐tetrone 5‐oximate], NH₄⁺·C₄H₂N₃O₄⁻, crystallizes from water in the triclinic space group P and is ismorphous with a known rubidium complex [Gillier (1965). Bull. Soc. Chim. Fr. pp. 2373–2384]. The principal feature of the structure is hydrogen bonding; each ammonium H atom acts as a bifurcated donor and three of the four violurate O atoms are bifurcated acceptors, with the fourth acting as a trifurcated acceptor. The pattern of hydrogen bonding around the cation is very similar to the rubidium coordination environment in the related structure. The violurate anions pack as hydrogen‐bonded crinkled tapes, which are linked and separated by the ammonium cations to give a compact three‐dimensional structure.     

NMR AND DFT STUDY OF Co-C BOND ACTIVATION MECHANISM IN VITAMIN B_(12) COMPOUNDS

This report focuses on a theoretical study of the cobalt-cabon bond activation mechanism in Vitamin B12, its co enzyme complexes, and model compounds such as cobalamins (Cbl), cobaloximes and cobalt porphyrins. In particular, emphasis is placed on the nucleotide loop and its role in the base on and base off mechanism.     

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M_t/M_t/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.     

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level.