Structures of the I-, II- and H-methane clathrates and the ice-methane clathrate phase transition from quantum-chemical modeling with force-field thermal corrections

Methane hydrates with the three clathrate structures I, II, and H are studied by quantum-chemical methods. Hybrid density-functional theory B3LYP computations using periodic boundary conditions are combined with force-field methods for the thermal energy effects to calculate energetic, thermodynamic, and structural properties. The pressure dependencies for the crystal structures, lattice energies, and guest molecule interactions are derived. The quantum-chemical geometry optimizations predict too small cell volumes as compared to experimental data, but by including zero-point energy and thermal energy effects, we find the cell volumes increase and the correct densities are obtained. The phase transition from MH-I to ice Ih and methane was computed and found to occur at about 9.7 MPa.     

Manipulation of atoms and molecules with a low temperature scanning tunneling microscope

Apart from its ability to image surfaces with atomic resolution the scanning tunneling microscope has evolved as a tool to manipulate single atoms and molecules. In this paper we present several examples of atomic manipulation and the formation of nanostructures with this technique. As examples for lateral manipulation, i.e. the sliding of atoms and molecules along the surface, we show CO, C₂H₄ and Pb on a stepped copper surface, the Cu(211). As examples for vertical manipulation, i.e. the transfer of atoms and molecules between the tip and the surface, we discuss Xe and C₃H₆. The design of our low temperature scanning tunneling microscope is shortly described.     

Optimal control of single-server queueing networks

A general single-server queueing network model is considered. It is well-known that an optimal policy is determined by the largest-index policy. There is an index for each given queue and one allocates the server to a queue with largest current index. Using discounted dynamic programming we give a new and short proof of this result and derive some characterizations and bounds of the indices. Moreover, it is shown that an approximate largest-index policy yields an approximately optimal policy. These results lead to efficient methods for computing the indices. In particular, we present a general largest-remaining-index method.     

Markov games with incomplete information

We consider zero-sum Markov games with incomplete information. Here, the second player is never informed about the current state of the underlying Markov chain. The existence of a value and of optimal strategies for both players is shown. In particular, we present finite algorithms for computing optimal strategies for the informed and uninformed player. The algorithms are based on linear programming results.     

Ein Beitrag zur Dynamik des Lichtbogens

Ohne Zusammenfassung     

Importance of the polarization forces in He-metal surface interaction potential

In this paper we describe coupled channel calculation for atom-surface scattering for arbitrary potentials. We study, for the first time, the effect of the polarization-van der Waals forces. It is concluded that these forces are important for defining the repulsive part of the atom-metal surface potential. We study the He-Ni (110) system and present good agreement with experimental data for energies between 20 and 250 meV.     

Die basenkatalysierte Umlagerung von N-Aryl-S,S-dialkylsulfimiden zu o-Alkylthioalkylanilinen

Zusammenfassung Die Umlagerung von N-Aryl-S,S-dimethylsulfimiden in Toluol/Triäthylamin liefert in hohen Ausbeuten o-Methylthiomethylaniline. In Alkohol verläuft die Umlagerung ohne Zusatz von Basen rascher, als Nebenreaktion läuft aber die Spaltung zu dem zugrunde liegenden aromatischen Amin ab. 2,6-Di-substituierte N-Arylsulfimide ergeben durch analoge Umlagerung Cyclohexadienimine. Die Umlagerung von N-Aryl-S,S-dialkylsulfimiden erfolgt langsamer als die der S-Methylderivate; sie führte in einem Fall in hohen Ausbeuten zu einem durch 1,2-Wanderung entstandenen N-Alkylthioalkylprodukt. Die Ergebnisse liefern Aufschlüsse über den Mechanismus von Methylthiomethylierungen von anilinen und Phenolen.

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Methylthiomethylation of anilines and phenols, VII: Basecatalysed rearrangement of N-aryl-S.S-dialkyl sulfimides to o-methylthiomethyl anilines

Rearrangement of N-aryl-S.S-dimethyl sulfimides in toluene/triethyl amine yields high amounts of o-methylthiomethylated anilines. Rearrangement in ethanol without addition of base proceeds faster, but yields also the original aniline as by-product. 2.6-Di-substituted N-aryl sulfimides yielded on analogous rearrangement cyclohexadiene imines. The rearrangement of N-aryl-S.S-dialkyl sulfimides is slower than that of the S-methyl derivatives, and yielded in one case high amounts of N-alkylthioalkyl product formed via 1.2-migration. The results offer some informations on the mechanism of methylthiomethylations of anilines and phenols.

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Herrn Prof. Dr.H. Nowotny gewidmet.

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6. Mitt.:P. Claus, N. Vavra undP. Schilling, Mh. Chem.102, 1072 (1971).     

A Lax equivalence theorem for stochastic differential equations

In this paper, a stochastic mean square version of Lax’s equivalence theorem for Hilbert space valued stochastic differential equations with additive and multiplicative noise is proved. Definitions for consistency, stability, and convergence in mean square of an approximation of a stochastic differential equation are given and it is shown that these notions imply similar results as those known for approximations of deterministic partial differential equations. Examples show that the assumptions made are met by standard approximations.     

On the number of lattice points in a small sphere and a recursive lattice decoding algorithm

Let L be a lattice in ${\mathbb{R}^n}$ . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in ${\mathbb{R}^n}$ . The first method is based on the observation that if the sphere is sufficiently small then the lattice points contained in the sphere give rise to a spherical code with a certain minimum angle. The second method involves Gaussian measures on L in the sense of Banaszczyk (Math Ann 296:625–635, 1993). Examples where the obtained bounds are optimal include some root lattices in small dimensions and the Leech lattice. We also present a natural decoding algorithm for lattices constructed from lattices of smaller dimension, and apply our results on the number of lattice points in a small sphere to conclude on the performance of this algorithm.