Fast and exact flow measurements with the fast Fourier flow technique

The fast Fourier flow technique offers a convenient way for extremely exact flow measurements. In combination with ECG gating, arterial flow can be studied. The total acquisition time for a single measurement is about 10 s, an ECG-gated cine sequence can be acquired in about 4 min. Fast Fourier flow can, therefore, be easily combined with a conventional imaging examination.     

Asymmetrische katalysen: XXIV. Cross-coupling von 1-phenylethylgrignard und vinylbromid mit Ni-katalysatoren optisch aktiver P/N-liganden

Sixteen new N/N, P/N, and P/P chelate ligands, together with NiCl₂, were used as in-situ catalysts for the enantioselective cross-coupling of I-phenylethylgrignard and vinylbromide. The N/N ligands give no optical yield in the formation of the product 3-phenyl-1-butene. With the P/N and P/P ligands, 31.9% e.e. can be achieved. The control of optical induction by substituents in the skeleton of the P/N ligands is in accord with the results of conformational analyses of stable model complexes.     

Continuous collocation approximations to solutions of first kind Volterra equations

In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.

     

Spline collocation methods for nonlinear Volterra integral equations with unknown delay

In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation.     

On the approximate solution of the abel integral equation with discontinuous solution

The classical Abel integral equation with discontinuous solution is solved numerically by replacing the inhomogeneous termg(x) (known on some finite subsetZ _N of the interval of integration) by a suitable linear familyψ(β, x) of continuous functions. The choice of these functions will be governed by two criteria: they are to reflect the discontinuous behavior of the exact solution of the integral equation, and they are to be such that the problem of finding a best (discrete) Chebyshev approximation tog onZ _N possesses a unique solution.