Über einen Interpolations-Algorithmus und gewisse andere Formeln,die in der Theorie der Interpolation durch rationale Funktionen bestehen

Ohne ZusammenfassungDissertation zur Erlangung des Doktorgrades bei der Naturwissenschaftlichen Fakultät der Johannes Gutenberg-Universität zu Mainz. D 77. Der Verfasser möchte gerne Herrn Prof. Dr.F. L. Bauer für seine Ermutigung in dieser und anderen Unternehmungen herzlich danken.     

Polarized x-ray emission from magnetized neutron stars: signature of strong-field vacuum polarization

In the atmospheric plasma of a strongly magnetized neutron star, vacuum polarization can induce a Mikheyev-Smirnov-Wolfenstein type resonance across which an x-ray photon may (depending on its energy) convert from one mode into the other, with significant changes in opacities and polarizations. We show that this vacuum resonance effect gives rise to a unique energy-dependent polarization signature in the surface emission from neutron stars. The detection of polarized x rays from neutron stars can provide a direct probe of strong-field quantum electrodynamics and constrain the neutron star magnetic field and geometry.     

Thiol esters in organic synthesis. : XI. A facile approach to β-hydroxypropionitriles and acrylonitriles,cyanothiolacetate as masked β-hydroxypropionitrile carbanion

The preparation of β-hydroxypropionitriles and acrylonitriles is facilitated by the use of cyanothiolacetate as a formal equivalent of β-hydroxypropionitrile carbanion.     

On the computation of certain functions of large argument and parameter

The paper deals with the derivation of asymptotic expansions for functions of a certain class. The functions concerned satisfy a differential equation in a variablez and a recursion in a parametern and include most of the classical functions of Mathematical Physics.The particular example which is examined in detail by way of illustration is an essay in how to avoid vast amounts of tedious algebraic manipulation by the adroit use of a flexible programming language.     

Renormalised Steepest Descent in Hilbert Space Converges to a Two-Point Attractor

The result that for quadratic functions the classical steepest descent algorithm in R ^d converges locally to a two-point attractor was proved by Akaike. In this paper this result is proved for bounded quadratic operators in Hilbert space. The asymptotic rate of convergence is shown to depend on the starting point while, as expected, confirming the Kantorovich bounds. The introduction of a relaxation coefficient in the steepest-descent algorithm completely changes its behaviour, which may become chaotic. Different attractors are presented. We show that relaxation allows a significantly improved rate of convergence.     

Microcantilever bend testing and finite element simulations of HIP-ed interface-free bulk Al and Al–Al HIP bonded interfaces

Abstract

We report on the strength of Al–Al interfaces and the effects of chemical segregation and interfacial void formation on bond strength using microcantilever bend testing. Interfaces are synthesised via hot isostatic pressing. Microcantilevers of several nominal dimensions were fabricated via focused ion beam and deformed in a nanoindenter. We find increased cantilever strength as a function of decreasing sample size, with a linear dependence of the yield strength on the inverse square root of the length scale characteristic to the cantilever cross-section. The presence of pores and chemical segregation decreases the yield strength of the material by 17% and the accommodated strain energy by 10–15% for strain values in the 6–12% range.     

The weighted Weiss conjecture and reproducing kernel theses for generalized Hankel operators

The weighted Weiss conjecture states that the system theoretic property of weighted admissibility can be characterized by a resolvent growth condition. For positive weights, it is known that the conjecture is true if the system is governed by a normal operator; however, the conjecture fails if the system operator is the unilateral shift on the Hardy space ${H^2(\mathbb{D})}$ (discrete time) or the right-shift semigroup on ${L^2(\mathbb{R}_+)}$ (continuous time). To contrast and complement these counterexamples, in this paper, positive results are presented characterizing weighted admissibility of linear systems governed by shift operators and shift semigroups. These results are shown to be equivalent to the question of whether certain generalized Hankel operators satisfy a reproducing kernel thesis.     

Rotational spectra and properties of complexes B···ICF3 (B = Kr or CO) and a comparison of the efficacy of ICl and ICF3 as iodine donors in halogen bond formation

The ground-state rotational spectra of two weakly bound complexes B···ICF(3) (B = Kr or CO) formed by trifluoroiodomethane have been observed in pulsed jets by using two types of Fourier-transform microwave spectroscopy (chirped-pulse and Fabry-Perot cavity). Both complexes exhibit symmetric-top type spectra, thus indicating that the Kr atom in Kr···ICF(3) and both the C and O atoms in OC···ICF(3) lie along the C(3) axis of ICF(3). The rotational constant B(0), the centrifugal distortion constants D(J) and D(JK), and the iodine nuclear quadrupole coupling constant χ(aa)(I) were determined for each of the isotopologues (84)Kr···ICF(3), (86)Kr···ICF(3), (16)O(12)C···ICF(3), (16)O(13)C···ICF(3), and (18)O(12)C···ICF(3). Interpretation of the spectroscopic constants reveals that the carbon atom of CO is adjacent to I and participates in the weak bond in OC···ICF(3). Simple models based on unperturbed component geometries lead to the distances r(Kr···I) = 3.830(1) ? and r(C···I) = 3.428(1) ? in Kr···ICF(3) and OC···ICF(3), respectively, and to the quadratic force constants for stretching of the weak bond k(σ) = 2.80 N m(-1) and 3.96 N m(-1), respectively. The distances r(Z···I) (Z is the acceptor atom in B), the k(σ) values, and the angular geometries of the pair of complexes B···ICF(3) and B···ICl for a given B are compared when B = Kr, CO, H(2)O, H(2)S, or NH(3). The comparison reveals that the iodine bond in B···ICF(3) is systematically longer and weaker than that of B···ICl, while the angular geometry of the B···I moiety is isomorphic in B···ICF(3) and B···ICl for a given B. It is concluded that -CF(3) is less effective than -Cl as an electron-withdrawing group when attached to an I atom and that the angular geometries of the B···ICF(3) can be predicted by means of a simple rule that holds for many hydrogen- and halogen-bonded complexes.