Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering

We prove local uniqueness for the inverse problem in obstacle scattering at a fixed energy and fixed incident angle.

     

PNA: Synthetic Polyamide Nucleic Acids with Unusual Binding Properties

The astonishing discovery that peptide nucleic acids (PNAs, B=nucleobase), in spite of their drastic structural difference to natural DNA, are better nucleic acid mimetics than many other oligonucleotides has resulted in an explosion of research into this class of compounds. The synthesis, physical properties, and biological interactions of PNAs as well as their chimeras with DNA and RNA are summarized here.     

Processing and Photostability of Pyrromethene 567 Polycerams

Polyceram materials are attractive hosts for laser dyes because they can have high optical transparencies, high laser damage thresholds, and the ability to tailor optical properties by varying the composition and synthetic routes. Pyrromethene 567 has been successfully incorporated within silica: polydimethylsiloxane (PDMS) Polycerams to obtain polishable, crack-free, transparent monoliths using the sol-gel process. Fluorescence photostability was measured by pumping with aQ-switched, frequency doubled Nd: YAG laser (532 nm) at a pulse rate of 10 Hz. Fluorescence intensity dropped to 50% after approximately 50,000 pulses at a fluence of 0.10 J/cm². UV degradation studies were performed on Polycerams with different polymer contents, and the absorption photostability is related to the solubility and type of caging of the dye.     

Some remarks on reflection positivity

The requirement of reflection positivity is investigated and its general applicability to different physical theories is pointed out. Its role is illustrated on an example from electrostatics and on several simple examples of field theories. Then, after presenting an abstract construction of the concept, the role of reflection positivity in classical lattice systems is discussed.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.For valuable discussions I should like to thank J.Löffenholz.     

Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory

We show that the Wigner-Yanase-Dyson-Lieb concavity is a general property of an interpolation theory which works between pairs of (hilbertian) seminorms. As an application, the theory extends the relevant work of Lieb and Araki to positive linear forms of arbitrary *-algebras. In this context a relative entropy is defined for every pair of positive linear forms of a *-algebra with identity. For this generalized relative entropy its joint convexity and its decreasing under identity-preserving completely positive maps is proved.     

Glycosylidene Carbenes. Part 20. Synthesis of deprotected,spiro-linked C-glycosides of C60

Mannosylidenation of buckminsterfullerene (C₆₀; 1 ) with the 2,3-di-O-benzyl-4,6-O-benzylidene-protected diazirine 7 and the 2,3:4,6-di-O-isopropylidene-protected diazirine 8 leads to the spiro-linked C -glycosides 6 and 10 in 44 and 31% yield, respectively (Scheme). The diazirine 8 was prepared in five steps from 2,3:4,6-di-O-iso-propylidene-α-D -mannopyranose ( 11 ) via the oximes 12 , the (Z)-hydroximolactone 13 , the mesylate 14 , and the diaziridines 15 . Deprotection of the mannosylidenated fullerenes 6 and 10 under acidic conditions gave the partially deprotected diol 9 (97%) and the unprotected mannosylidenated fullerene 16 (73%), respectively. The mannosylidene-fullerenes 6, 9, 10 , and 16 possess a 6–6 ring-bridged σ-homoaromatic structure.     

Viscosity of liquid albite,a network material

The viscosity of liquid albite (NaAlSi₃O₈) has been determined over the temperature range 800–1000°C. The results are combined with data obtained at higher temperatures to obtain the overall log η versus $\text{1}\text{T}$ relation. The relation indicates Arrhenian behavior, with an apparent activation energy of ～95 kcal mol^?1. By comparing the viscous flow behavior of albite with that of the other materials, including SiO₂, GeO₂ and B₂O₃, it is suggested that liquid albite is a random network of SiO₄ and AlO₄ tetrahedra.