Sound propagation in metallic glasses—a new look at the tunneling model

A variety of amorphous metals exhibit a characteristic behavior in their acoustic properties at low frequencies which differs from the predictions of the standard tunneling model. We point out that a lower cut-off _min for the tunnel matrix element, which is needed for consistency of the tunneling model, leads to an upper bound on relaxation times induced by the conduction electrons. We derive explicit expressions for the velocity shift and internal friction for the normalconducting and superconducting case. It is shown that a maximum relaxation time plays an essential role at audio frequencies. The corresponding change of the acoustic properties is in qualitative agreement with vibrating reed experiments.     

Perspectivities of odd order and chevalley groups

LetP be a projective plane and X a finite group of Lie-type in Aut(P). Suppose Aut(P) is a perspectivity of odd prime order inducing a nontrivial automorphism on X. We show that in most cases X must contain involutory perspectivities.     

Bordismus verzweigter Überlagerungen von Niedrigdimensionalen Sphären

The concept of bordism between branched coverings is a generalization of the concept of regular homotopy between such maps as given in [3].The main result of this article states that for n=2,3 any two branched coverings of the n-sphere with a finite and equal number of sheets are bordant.

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Diese Arbeit entstand während eines Aufenthaltes des Autors am Sonderforschungsbereich Theoretische Mathematik der Universität Bonn.     

Materials Surgery – Reactivity Differences of Organic Groups in Hybrids

Synergistic properties in hybrid materials can emerge if the inorganic matrix has an electronic influence on the organic constituents and vice versa. This paper describes the drastic effect of SiO₂ in periodically ordered mesoporous organosilica materials (PMOs) on ethylene groups. A sophisticated, in situ solid‐state NMR spectroscopy study showed that the ozonolysis of ethylene groups follows an entirely different mechanism than is normal for organic, molecular groups. Ultimately, this leads to the topotactic transformation of the PMO material. Only if silicon is not in the alpha position to the double bond does it became possible to establish a new method to functionalize PMOs materials: the targeted scission of the ethylene group and the creation of functionalized pockets inside the pore walls of the mesoporous solid.     

COOH-terminated SAMs on gold fabricated from an azobenzene derivative with a 1,2-dithiolane headgroup

Well-defined and homogeneous, contamination-free self-assembled monolayers (SAMs) were fabricated by the chemisorption of lip-NH-p-C₆H₄-NN-p-C₆H₄-COOH (lip = α-lipoyl) onto gold. This adsorbate species is composed of a 1,2-dithiolane-based headgroup, an azobenzene-based (and hence photochromic) spacer unit and a carboxylic acid functional group. The SAM constituents are covalently attached to the substrate by the bidentate thiolate anchor groups and exhibit a strongly tilted binding configuration.     

Uniform asymptotic regularity for Mann iterates

In Numer. Funct. Anal. Optim. 22 (2001) 641-656, we obtained an effective quantitative analysis of a theorem due to Borwein, Reich, and Shafrir on the asymptotic behavior of general Krasnoselski-Mann iterations for nonexpansive self-mappings of convex sets C in arbitrary normed spaces. We used this result to obtain a new strong uniform version of Ishikawa's theorem for bounded C. In this paper we give a qualitative improvement of our result in the unbounded case and prove the uniformity result for the bounded case under the weaker assumption that C contains a point x whose Krasnoselski-Mann iteration (x_k) is bounded. We also consider more general iterations for which asymptotic regularity is known only for uniformly convex spaces (Groetsch). We give uniform effective bounds for (an extension of) Groetsch's theorem which generalize previous results by Kirk, Martinez-Yanez, and the author.     

Embedded resistors and capacitors for organic-based SOP

System-on-package (SOP) architectures take advantage of compact, high-performance designs to place the maximum amount of functionality on a subsystem that can then be mounted on a lower-cost, lower density interconnect board. Embedding passive components is a key technology in achieving these goals since this enables smaller SOP substrate footprints or, equivalently, higher functional density, along with better power distribution, increased design flexibility and improved reliability. The resulting footprint areas of integrating capacitors will have more of an effect on the layer count of SOP assemblies than will integrating resistors due to the rather low specific capacitances of most embeddable dielectrics, but the situation is improving steadily. It may be necessary to use two different dielectric materials to cover the entire required range. The inherently lower parasitic inductance of embedded capacitors makes them much more useful in decoupling than surface mount capacitors, enabling more robust power distribution and decreased power/ground noise. The key to this performance enhancement in large boards is the use of a thin dielectric to decrease the inductance but, for the smaller SOP substrates, the dielectric constant must also be high to provide sufficient decoupling capacitance in the reduced area.