Combinatorial Chemistry for Ligand Development in Catalysis: Synthesis and Catalysis Screening of Peptidosulfonamide Tweezers on the Solid Phase

On the basis of a pyrrolidine tweezer 1, a library of peptidosulfonamide tweezers (15a-e, 16a-e) was synthesized on the solid phase. This library was screened in a simultaneous substrate screening procedure for the ability to enantioselectively catalyze the Ti(O-i-Pr)(4)-mediated addition of diethylzinc to aldehydes. One of the best solid-phase tweezer catalyst (i.e., 16d, giving an ee of 32% in solid-phase catalysis) was resynthesized in solution (compounds 20 and 21). The now homogeneous solution-phase catalysis showed even better enantioselectivity (i.e., up to 66%).     

Lipschitz Kernel of a Closed Set-Valued Map

This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the -Lipschitz kernel of a given set-valued map as the largest -Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps.     

Gamma-ray spectroscopy with relativistic exotic heavy-ions

Feasibility of gamma-ray spectroscopy at relativistic energies with exotic heavy-ions and new generation of germanium detectors (segmented Clover) is discussed. An experiment with such detector array and radioactive is discussed.     

Zur Theorie der Gammafunction

Ohne Zusammenfassung Vergl. meine Abhandlung:Om en ny klass af transcendenta functioner, hvilka ?ro n?ra besl?gtade med gammafunktionen, Acta soc. scient. Fennic?, Tom. XIV, XV; 1885, 1886.     

New families of hypohamiltonian graphs

We construct three new infinite families of hypohamiltonian graphs having respectively 3k+1 vertices (k?3), 3k vertices (k?5) and 5k vertices (k?4); in particular, we exhibit a hypohamiltonian graph of order 19 and a cubic hypohamiltonian graph of order 20, the existence of which was still in doubt. Using these families, we get a lower bound for the number of non-isomorphic hypohamiltonian graphs of order 3k and 5k. We also give an example of an infinite graph G having no two-way infinite hamiltonian path, but in which every vertex-deleted subgraph G - x has such a path.     

Theory of carbon monoxide chemisorption on transition metals

An Anderson formalism including overlap is used to treat the chemisorption of carbon monoxide on the transition metals Cu, Ni and Pd. According to the generally accepted scheme only coupling of the 2π¹- and 5σ-orbitals of CO to the metallic d-states is regarded. The wave functions of the metal surface are approximated by a linear combination of atomic d-orbitals, which are oriented in such a manner that maximum overlap with the 2π¹-orbital of CO is achieved. The error involved in this procedure is absorbed into the only adjustable parameter B. Predictions are made for the electronic structure, i.e. the chemisorption levels and occupation numbers. Comparison with results of photoelectron spectroscopy, energy loss spectroscopy and infrared experiments is encouraging. The variation of adsorption energy with geometric location, crystallographic orientation and nature of the substrate metal is extensively treated and compared with experiment. It was possible for example to predict correctly the structure models derived from LEED data and the changes in adsorption energy associated with structural modifications due to varying coverage.     

An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

Theory of decoherence at solid surfaces

Decoherence processes at solid surfaces are observed at all time scales. The most common surface processes are classified according to the presently common view on decoherence theory. Prominent examples of decoherent surface processes are electronic relaxation and deexcitation, vibrational relaxation, diffusion, inelastic scattering, sticking, STM-induced chemical reactions and desorption, localization of adsorbates. Various mechanisms, suggested at the present state of the art of decoherence theory, are investigated for their ability of providing the understanding of decoherence at solid surfaces. In some cases environmental decoherence by coupling to phonons and electron-hole pairs in the surface is a viable mechanism. Some new ideas are introduced, which have not been discussed in the framework of decoherence theory so far.