Investigation of multi-layer coatings on cemented carbide cutting tools by analytical electron microscopy

Multi-layer coatings on cemented carbide substrates have been investigated by analytical electron microscopy (AEM). The samples were taken from cross-sections through the coating thus enabling a study of individual layers and interfaces. Various phenomena are shown: (1) tungsten diffusion and graphite inclusions in TiC layers, (2) oxygen impurities in Ti(C, N) coatings and (3) the occurrence of titanium oxinitrides in the interface between the Al₂O₃ and TiN-layers.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

Opticon: An algorithm for the optimal control of nonlinear stochastic models

In this paper we describe the algorithm OPTCON which has been developed for the optimal control of nonlinear stochastic models. It can be applied to obtain approximate numerical solutions of control problems where the objective function is quadratic and the dynamic system is nonlinear. In addition to the usual additive uncertainty, some or all of the parameters of the model may be stochastic variables. The optimal values of the control variables are computed in an iterative fashion: First, the time-invariant nonlinear system is linearized around a reference path and approximated by a time-varying linear system. Second, this new problem is solved by applying Bellman's principle of optimality. The resulting feedback equations are used to project expected optimal state and control variables. These projections then serve as a new reference path, and the two steps are repeated until convergence is reached. The algorithm has been implemented in the statistical programming system GAUSS. We derive some mathematical results needed for the algorithm and give an overview of the structure of OPTCON. Moreover, we report on some tentative applications of OPTCON to two small macroeconometric models for Austria.     

Ein neuer Zugang zu 2,6,6-Trimethylcyclohexa-2,4-dienon aus 4-Oxoisophoron

A New Access to 2,6,6-Trimethylcyclohexa-2,4-dienone from 4-Oxoisophorone 2,6,6-Trimethylcyclohexa-2,4-dienone ( 1 ), a versatile starting material for the preparation of some carotenoids and several natural products, was efficiently (73% yield) prepared from oxoisophorone 3 . After conversion of 3 to the alcohol 4 or the acetate 5 , H₂O was eliminated ( 4→1 ) under acidic distillative conditions, whereas AcOH could be eliminated ( 5→l ) under Pd(O) catalysis.     

A separation property of planar triangulations

Every planar triangulation G has the property that each induced cycle C of length at least 4 in G separates G, but no proper subgraph of C does. This property is trivially shared by all chordal graphs since these contain no such cycles at all. We ask to what extent maximally planar graphs and chordal graphs are unique with this property — or how much larger the class of graphs is that it determines. The answer is given in the form of a characterization of this class in terms of the simplicial decompositions of its elements. The theory of simplicial decompositions appears to be a very interesting, but still largely unexploited, method of characterization in graph theory, which seems tailor-made for problems like the one discussed.     

Conditions for the validity of ATDHF and the local harmonic approach

A short derivation of the local harmonic approach and ATDHF is given which elucidates the formal similirity between them. The conditions for the validity of the approaches are studied. We show first, that they are related to deviation forces within second order RPA which drive the system out of the collective mode, and second, that the local harmonic approach is more restricted than ATDHF.     

Nanosecond time resolution in EPR transient nutation spectroscopy of triplet states

The dynamic behavior of transient EPR nutation signals during the first 100 ns after N₂-laser excitation or molecular triplet states in single crystals has been investigated. The onset of the signal is found to depend on the inhomogeneous width and form of the cw EPR line With phenazine (in fluorene) a time resolution of 15 ns could be demonstrated.     

Expansion of Analytic Functions in Series of Floquet Solutions of First Order Differential Systems

In this paper we study boundary eigenvalue problems for first order systems of ordinary differential equations of the form \[zy'\left( z \right) = \left( {\lambda A_1 \left( z \right) + A_0 \left( z \right)} \right)y\left( z \right),\,\,y\left( {ze^{2\pi i} } \right) = e^{2\pi iv} y\left( z \right)\] for z ? S^log, where S is a ring region around zero, S^log denotes the Riemann surface of the logarithm over S, the coefficient matrix functions A₁(z) and A₀(z) are holomorphic on S, and v is a complex number. The eigenfunctions of this eigenvalue problem are the Floquet solutions of the differential system with v as characteristic exponent. For an open subset S₀ of S, the notion of A₁-convexity of the pair (S₀, S) is introduced. For A₁-convex pairs (S₀, S) it is shown that the expansion into eigenfunctions and associated functions of holomorphic functions on S^log, satisfying the monodromy condition y(ze^2πi) = e^2πivy(z), converges regularly on S^log₀ and is unique. If S is a pointed neighbourhood of 0 and A₁(z) is holomorphic in SU{0}, it is shown that there is a pointed neighbourhood S₀ of 0 such that (S₀, S) is A₁-convex. It follows from the results of this paper that many expansions of analytic functions in terms of special functions can be considered as eigenfunction expansions of this kind.