Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

Controllability of linear systems,differential geometry curves in grassmannians and generalized grassmannians,and riccati equations

We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators e^t B. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in ⁿ. We then view (t)=Im(e^t B) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(ⁿ). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(ⁿ), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit.     

Direct detection of the biradicals generated in the Norrish type II reaction

The biradicals generated in the Norrish type II reaction from the triplet manifold have been observed using laser flash photolysis techniques. The spectra and extinction coefficients closely resemble those of typical ketyl radicals. Typical lifetimes are in the 40–100 ns range depending on the solvent. Their interaction with oxygen is essentially diffusion controlled.     

Isotope dynamic mixing and vibronic structure

Existing theories which deal with the isotope dependence of vibronic structure have neglected the isotope dependence of vibration dynamics. The latter dependence (isotope dynamic mixing) is an adiabatic correction to vibronic structure theory. A theory of vibronic structure, which includes isotope dynamic mixing, is developed. The results of model calculations are presented.     

Application of parallel processing techniques to improving the efficiency of MM2 molecular mechanics calculations

The application of parallel processing techniques to molecular mechanics calculations is evaluated. Using the standard molecular mechanics package, MM2, four different parallel versions of the program are implemented in a four-processor computing environment. A set of 529 test structures is used to compare the efficiency of the parallel versions of MM2 to a standard serial version of the program. Statistics describing execution times and program execution cycles are gathered and analyzed. The effects of parallel processing overhead and computer system load are explored, and the practical utility of parallel processing in molecular mechanics is estimated. The results of these parallelization experiments indicate that for geometry optimizations requiring significant amounts of computing time an improvement in program execution speed approaching 50% is realizable. © 1993 John Wiley & Sons, Inc.     

The temperature dependence of coherent two-photon processes in naphthalene in the strong exciton-photon coupling regime

Temperature-dependent intensity data for two-photon excitation and second harmonic generation signals phase matched onto the polariton branches of the single a-exciton of naphthalene are presented. The data are shown be in quantitative agreement with the polariton fusion model which accounts for strong exciton-photon coupling. In this model the polariton scattering frequency and group velocity determine the branching ratios for the above signals.     

An explicit description of the fundamental unitary for SU(2) q

In this paper we study the Cauchy problem for the generalized equation of finite-depth fluids