Probabilistic viscosity algorithm for the scalar conservation law

We derive an algorithm for solving the initial value problem for u_t = ½σ²u_xx + f(u)u_x. The approach is based on the representation of the solution to the above equation in the form of the functional of Brownian motion. For small σ we get the approximation for u_t = f(u)u_x. A comparison with the random choice method is illustrated by the numerical example.     

Method development for the determination of residual fluorotelomer raw materials and perflurooctanoate in fluorotelomer-based products by gas chromatography and liquid chromatography mass spectrometry

The methodology for the determination of perfluorooctanoate (C(7)F(15)COO-, PFO), fluorotelomer alcohols (FTOHs: 6-2, 8-2, and 10-2), perfluorooctyl iodide (PFOI), and 8-2-8 fluorotelomer alcohol ester in complex fluorotelomer-based commercial products has been demonstrated and validated. Sample preparation procedures allowing determination of residual levels of these compounds were developed. The analytes were detected either by LC/MS/MS (PFO), LC/MS (FTOHs), or GC/MS (PFOI, 8-2-8 ester). The methods were validated by investigating the recoveries of analytes spiked at multiple levels to authentic sample matrices. The recoveries generally were between 70 and 130%. The limits of detection were in sub-microg/g range and the limits of quantitation were in the mug/g range. The methods were applied to fluorotelomer-based raw materials and fluorotelomer-based surfactants and polymeric products and represent methods useful for the determination of higher carbon chain length homologs as well.     

Path-Integral Calculations for the First Excited State of Hydrogen Atom

Consider a path-integral which is the solution to a diffusion version of the generalized Schro¨dinger's equation . Here , where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process . For and V replaced by one obtains , which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of by generating a large number of trajectories of an ergodic diffusion process.     

Conversion of arenediazonium tetrafluoroborates into unsymmetrical biaryls using catalysts other than polyethers

In addition to crown ethers and glymes which catalyze the phase transfer Gomberg-Bachmann reaction, quaternary salts, carboxylate anions, and acetonitrile cosolvent are all shown to be effective in this system.