Crystal and molecular structure of tetrapyridyl-copper(II)-bis-nitrato-bis-pyridine

The crystal and molecular structure of a pyridine complex of anhydrous copper(II)nitrate is described. The structure has been solved by vector search methods and refined by least-squares methods to R₁=0.049 [I>2(I)]. The complex lies on a twofold axis parallel toa, and two solvent pyridine molecules lie on twofold axes parallel toc. The copper atom is coordinated by four pyridyl groups and two monodentate NO₃ groups. Crystal data: C₃₀H₃₀N₈O₆Cu, orthorhombic, space group Pnna(52),a=14.446(7),b=12.154(5),c=16.881(4) Å,V=2964(2) ų,Z=4.     

Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations

For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch condition which are sufficient for the validity of the coercivity condition. Using the implicit Euler-discretization we approximate the optimal control problem and analyze the convergence of solutions of the local minimum principle for the discretized optimal control problem by applying the general convergence framework of Stetter, which requires the discretization method to be continuous, consistent, and stable.

     

Eisenuntersuchungen

Ohne Zusammenfassung     

Die Flammpunktsbestimmung der Mineralschmier?le

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Die Unterscheidung von Harz?l und Mineral?l

Ohne Zusammenfassung     

On the geometry of master-slave synchronization

In 1990, Pecora and Carroll reported the observation that one can synchronize the orbits of two identical dynamical systems, which may be chaotic, by feeding state variables of one of them to the other one with no feedback, a phenomenon often called master-slave synchronization. We report here some results on the theory of master-slave synchronization for maps and flows, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master-slave synchronization by Tresser, Worfolk, and Bass. Our results are variations on the theme that projection often can compensate for expansion.(c) 2002 American Institute of Physics.