Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.     

Statistical inference and quantum mechanical measurement

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument.     

Phosphoramidites as Synthons for Polynucleotide Synthesis

Abstract

Methods for the rapid synthesis of DNA and RNA are described. The procedures involve using nucleoside phosphoramidites as synthons and silica as a polymeric support. Additionally, a novel reaction involving nucleoside O-alkyl methylphosphonothioates is described.     

Application and modification of the POD method and the POD-DEIM for model reduction in porous-media simulations

Researchers with a continuum-mechanical background typically use a multi-phasic and multi-component modelling approach for materials with a saturated porous microstructure. Therefore, the mechanical behaviour is considered in a continuum-mechanical manner and solved using the finite-element method (FEM). The developed models need to be complex enough to capture the relevant properties of the considered materials, what often results in expensive simulations with a very large number of degrees of freedom (DOF). The aim of the present contribution is to reduce the computing time of these simulations through model-reduction methods, while the accuracy of the solution needs to be maintained. Therefore, the method of proper-orthogonal decomposition (POD) for linear problems and the discrete-empirical-interpolation method (DEIM) in combination with the POD method (POD-DEIM) for nonlinear problems are investigated. Using the POD method, a given data set is approximated with a low-dimensional subspace. To generate this data set, the vector of unknowns of the FE simulation is stored in a pre-computation in the full (unreduced) system in each time-step (so-called “snapshots” of the system). Dealing with porous-media problems, the primary variables are the solid displacement, the pore pressure and, depending on the particular problem, other primary variables. Following this, the primary variables have entries with very huge differences in their absolute values. As a result, non-negligible rounding errors may occur when applying the POD method. To overcome this problems, modifications of the classical POD method need to be performed for such problems. The present contribution discusses this issue and presents results for the reduced simulations of porous media. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

The system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) is tested to determine the saddle points of the potential energy surface of some molecules. The method has been proposed earlier [E and Zhou in Nonlinearity 24:1831 (2011)]. We additionally use the metric of curvilinear internal coordinates. By a number of examples, we explain the possibilities of a GAD curve; it can find the transition state of interest by a gentlest ascent, directly or indirectly, or not. A GAD curve can be a model of a reaction path, if it does not contain a turning point for the energy. We further discuss generalized GAD formulas for the search of saddle points of a higher index. We calculate diverse examples.     

A Strategy for the Preparation of Thioantimonates Based on the Concept of Weak Acids and Corresponding Strong Bases

By following a new synthetic approach, which is based on the in situ formation of a basic medium by the reaction between the strong base Sb(V)S₄^3? and the weak acid H₂O, it was possible to prepare three layered thioantimonate(III) compounds of composition [TM(2,2′‐bipyridine)₃][Sb₆S₁₀] (TM=Ni, Fe) and [Ni(4,4′‐dimethyl‐2,2′‐bipyridine)₃][Sb₆S₁₀] under hydrothermal conditions featuring two different thioantimonate(III) network topologies. The antimony source, Na₃SbS₄ ? 9 H₂O, undergoes several decomposition reactions and produces the Sb^IIIS₃ species, which condenses to generate the layered anion. The application of transition‐metal complexes avoids crystallization of dense phases. The reactions are very fast compared to conventional hydrothermal/solvothermal syntheses and are much less sensitive to changes of the reaction parameters.     

Origin and Use of Hydroxyl Group Tolerance in Cationic Molybdenum Imido Alkylidene N-Heterocyclic Carbene Catalysts

The origin of hydroxyl group tolerance in neutral and especially cationic molybdenum imido alkylidene N-heterocyclic carbene (NHC) complexes has been investigated. A wide range of catalysts was prepared and tested. Most cationic complexes can be handled in air without difficulty and display an unprecedented stability towards water and alcohols. NHC complexes were successfully used with substrates containing the hydroxyl functionality in acyclic diene metathesis polymerization, homo-, cross and ring-opening cross metathesis reactions. The catalysts remain active even in 2-PrOH and are applicable in ring-opening metathesis polymerization and alkene homometathesis using alcohols as solvent. The use of weakly basic bidentate, hemilabile anionic ligands such as triflate or pentafluorobenzoate and weakly basic aromatic imido ligands in combination with a sterically demanding 1,3-dimesitylimidazol-2-ylidene NHC ligand was found essential for reactive and yet robust catalysts.