On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions

It is shown that, under certain conditions, orthonormalizingthe positive integer shifts of an exponentially decaying functionon the half line by the Gram-Schmidt process leads to a limitingprofile given by orthonormalizing all their integer shifts onthe whole line. These results derive from properties of Choleskyfactorization of bi-infinite and semi-infinite matrices. Anexample is provided by the negative exponential function andconjectures are given, supported by numerical evidence, forthe Gaussian and Lorentz function.     

Faster proton transfer dynamics of water on SnO2 compared to TiO2

Proton jump processes in the hydration layer on the iso-structural TiO(2) rutile (110) and SnO(2) cassiterite (110) surfaces were studied with density functional theory molecular dynamics. We find that the proton jump rate is more than three times faster on cassiterite compared with rutile. A local analysis based on the correlation between the stretching band of the O-H vibrations and the strength of H-bonds indicates that the faster proton jump activity on cassiterite is produced by a stronger H-bond formation between the surface and the hydration layer above the surface. The origin of the increased H-bond strength on cassiterite is a combined effect of stronger covalent bonding and stronger electrostatic interactions due to differences of its electronic structure. The bridging oxygens form the strongest H-bonds between the surface and the hydration layer. This higher proton jump rate is likely to affect reactivity and catalytic activity on the surface. A better understanding of its origins will enable methods to control these rates.     

Preconditioning trace coupled 3d‐1d systems using fractional Laplacian

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three‐dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well‐defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.     

Zur Bestimmung von Chrom und Vanadin im Stahl

Ohne Zusammenfassung     

Principal minors, Part I: A method for computing all the principal minors of a matrix

An order O(2ⁿ) algorithm for computing all the principal minors of an arbitrary n × n complex matrix is motivated and presented, offering an improvement by a factor of n³ over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a binary order. An implementation of the algorithm in MATLAB® is also given and practical considerations are discussed and treated accordingly.     

Comparison of sub-coulomb stripping and analog resonance results in Zr

The ⁹²Zr(d, p)⁹³Zr reaction, leading to states in ⁹³Zr which are parents of analog states observed in ⁹²Zr(p, p) elastic scattering, has been studied for incident deuteron energies below the Coulomb barrier. For each of the parent states the reduced normalization has been extracted, and these have been compared with the reduced normalizations calculated for the analog resonances on the basis of various analog resonance theories.     

A model study of the laser-induced stabilization of a collision complex

The possibility of stabilizing a collision complex by stimulated emmission with coherent radiation is explored for a model. three-atom system. The lifetimes of several resonance states of this system were obtained previously and are used in a simple two-level model to describe the interaction of radiation with a resonance state and a true bound state. For the case where the energy difference between the two levels is time independent, simple, analytical expressions are used to obtain the time-dependent transition probability. Numerical solutions are obtained for the more realistic case where this energy difference is time dependent. For both cases, a substantial transition probability for stabilization is calculated for moderate laser intensities (e.g. 8.1 kW/cm² for an assumed dipole matrix element of 0.01 D).