Spectral problems for pencils of polynomial matrices. Methods and algorithms. V

Methods and algorithms for the solution of spectral problems of singular and regular pencils D(λ, μ)=A(μ)-λB(μ) of polynomial matrices A(μ) and B(μ) are suggested (the separation of continuous and discrete spectra, the computation of points of a discrete spectrum with the corresponding, Jordan chains, the computation of minimal indices and a minimal basis of polynomial solutions, the computation of the determinant of a regular pencil). Bibliography: 13 titles. Translated by V. N. Kublanovskaya Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 26–70     

Thermodynamic and kinetic studies on reversible liquid-phase Diels Alder reaction between maleic anhydride and 2-methyl furan

The liquid phase reaction between maleic anhydride and 1-methyl-furan leads to an exothermic cycloaddition. The reaction enthalpy, the rate constant and the equilibrium constant are evaluated with good precision by a method of analysis using thermal data and a dynamic model based on physical properties. The mathematical models that are presented here in a simple way (first-order system) represent the reaction accurately and are useful for studying other reactions and even industrial processes.     

The excited states of pyrazine: A basis set study

Summary Multiconfigurational second order perturbation theory (CASSCF/CASPT2) has been used to investigate the dependence of computed valence excitation energies and transition moments on the basis sets. Pyrazine has been selected as the test molecule. Atomic normal orbital (ANO) type basis sets are used throughout. Contractions of the structure (4s3p1d/2s) are found to be an optimal compromise between the quality and the size of the calculations and are capable of yielding results virtually identical to more extended basis sets.