Boundary Value Problems for Systems of Functional Differential Equations

Algorithms for finding an approximate solution of boundary value problems for systems of functional ordinary differential equations are studied. Sufficient conditions for consistency and convergence of these methods are given. In the last section, a construction of methods of arbitrary order is presented.     

Exact mass analysis of DNA fragments

High resolution data for the major ions from the salmon sperm DNA mass spectrum are reported. The presence of two series of ions for each characteristic fragment is shown, the first containing a phosphate moiety and the second having CHNO compositions only.     

Differential-algebraic systems with maxima

The numerical-analytic method is applied to a class of nonlinear differential-algebraic systems with maxima to find a solution assuming that functions (f,g) satisfy the Lipschitz conditions in matrix notation. This solution is given as a limit of corresponding sequences including Seidel's iterations too. Some existence results are also obtained for problems with retardations.     

Optimisation et Calcul d'Erreurs des Equations du Type Karplus

Three methods for obtaining solutions of Karplus-type equations and the calculation of errors are analysed. A geometric interpretation of the problem makes its solution by an iterative method possible.     

A characterization of pairs of subspaces for quantum chemical applications of the Galerkin–Petrov method

A method is proposed for characterizing pairs of finite dimensional subspaces of the Hilbert space. The method might be helpful for the proper selection of coordinate and projective spaces leading to reliable realizations of the Galerkin–Petrov method for use in quantum chemistry. In order to illustrate the method some numerical results are presented.     

Intershell nl4f electron correlation effects

The pair correlation energies for some nl4f pairs of the ground state of the Yb atom are calculated for the first time. The partial wave (PW ) increments to the second-order pair energies are generated using numerical first-order radial pair functions obtained as the solution of two-dimensional differential equations. The analysis of the PW s contributions shows the dominant role of the df, fg, and gh PW s for the 4d4f pair, of the pf and dg PW s for the 4p4f and 5p4f pairs, and of the sf and pg PW s for the 4s4f, 5s4f, and 6s4f pairs. A discussion of the similarities and differences of the structure of the correlation energy found in this paper with those calculated earlier for smaller atoms is given.     

Measurements of heavy-atom isotope effects using 1H NMR spectroscopy

A novel method for measuring heavy-atom KIEs for magnetically active isotopes using (1)H NMR is presented. It takes advantage of the resonance split of the protons coupled with the heavy atom in the (1)H spectrum. The method is validated by the example of the (13)C-KIE on the hydroamination of styrene with aniline, catalyzed by phosphine-ligated palladium triflates.     

13C and 1H NMR of 2,6-diaryl-1-hydroxy piperidin-4-one oximes; substituent effects on cis/trans ratio and conformational equilibria

The reaction of substituted diarylidene acetones with hydroxylamine hydrochloride affords isomeric N-hydroxy diaryl piperidinone oximes as main products. The structures as well as conformational equilibria of these products were established by 1H and 13C NMR spectroscopy and further studied by variable temperature NMR. It was found that the cis/trans ratio of 2,6-substituted piperidine derivatives depended on the position of the substituent on the aromatic ring.     

Differential Inequalities with Initial Time Difference

Some comparison results are obtained for differential inequalities with initial time difference. They are useful to get existence and stability theorems for differential equations.