Synthesis of silylated methylenecyclopropanes

2-Trimethylsilylmethylenecyclopropane (=3) was synthesized by reaction of lithio methylenecyclopropane with TMSCl. The lithium salt of (=3) reacts with some electrophiles by α- or γ-attack depending on the nature of the electrophile. Whereas alkenylbromides $\text{8}$ and $\text{9}$ or alkinylbromide $\text{10}$ give exclusively α-attack, benzaldehyde reacts with γ-alkylation.     

Synthesis of gamma-substituted peptide nucleic acids: a new place to attach fluorophores without affecting DNA binding

Molecular beacon strategies using PNA are currently restricted to fluorophore attachment to the ends of the PNA. We report the synthesis of PNA oligomers wherein fluorophores can be attached to the PNA backbone from novel gamma-lysine PNA monomers. Oligomers incorporating the modified PNA showed comparable thermal stability to the corresponding aegPNA oligomer with DNA. When the modified PNA oligomer was annealed with complementary DNA, the fluorescence intensity increased 4-fold over the unbound PNA. [structure: see text]     

On charge conjugation

The group of automorphisms of the conformal algebra su(2, 2) has four components giving the usual four components of symmetries of space time. Only two of these components extend to symmetries of the conformal superalgebra — the identity component and the component which induces the parity transformation,P, on space time. There is no automorphism of the conformal superalgebra which inducesT or PT on space time. Automorphisms of su(2, 2) which belong to these last two components induce transformations on the conformal superalgebra which reverse the sign of the odd brackets. In this sense conformal supersymmetry prefers CP to CPT. The operator of charge conjugation acting on spinors, as is found in the standard texts, induces conformal inversion and hence a parity transformation on space time, when considered as acting on the odd generators of the conformal superalgebra. Although it commutes with Lorentz transformations, it does not commute with all of su(2, 2). We propose a different operator for charge conjugation. Geometrically it is induced by the Hodge star operator acting on twistor space. Under the known realization of conformal states from the inclusion SU(2, 2) Sp(8) and the metaplectic representations, its action on states is induced by the unique (up to phase) antilinear intertwining operator between the two metaplectic representations. It is consistent with the split orthosymplectic algebras and hence, by the inclusion of the superconformal in the orthosymplectic, with the orthosymplectic algebra.     

Load-absorption by a filament in a fiber-reinforced material

Zusammenfassung Die Arbeit befasst sich mit der statischen Lastübertragung auf eine halbunendliche elastische Faser, die in einer unendlich ausgedehnten elastischen Matrix mit bestimmten mechanischen Eigenschaften eingebettet ist. Im Unendlichen wird für die Matrix ein einachsiger Spannungszustand parallel zur Faser angenommen. Mit Hilfe eines angereicherten Vorgehens lässt sich die gesuchte Faserkraft durch eine Fredholmsche Integralgleichung zweiter Art charakterisieren. Zur Erleichterung der numerischen Lösung der Integralgleichung wird das asymptotische Verhalten der von der Faser aufgenommenen Kraft herangezogen. Eine Reihe quantitativer Resultate zeigt die Vertiefung der Faserkraft und ihre Abhängigkeit von den physikalischen Parametern; ferner wird die Singularität am Faserende diskutiert.

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Dedicated to Professor Ziegler on his sixtieth birthday

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The results communicated in this paper were obtained in the course of an investigation conducted under Contract Nonr-220(58) with the Office of Naval Research in Washington, D.C.     

Double photoexcitation of helium in a strong dc electric field

We report the first experimental measurements of the effect of an applied field on the photoexcitation and autoionization of doubly excited states of helium. Ground-state photoionization spectra have been measured in the region below the He+(N=2) threshold with static electric fields of up to 84.4 kV/cm across the interaction region. The results are compared to the theoretical calculations of Chung et al. [J. Phys. B 34, 165 (2001)]], which are the only calculations available in this regime. Transitions to several states in the N=2, n=6 manifold are assigned, and a wealth of new structure is observed. Our data show that many more series are mixed in by the field than those predicted by theory.     

Large deformations near a tip of an interface-crack between two Neo-Hookean sheets

This paper contains an asymptotic investigation - within the nonlinear theory of elastostatic plane stress - of the deformations and stresses near the tips of a traction-free interface-crack between two dissimilar semi-infinite Neo-Hookean sheets. The results obtained are free of oscillatory singularities of the kind predicted by the linearized theory, which would require the two deformed faces of an interface-crack to overlap in the vicinity of its tips. Instead, the crack is found to open smoothly near its ends, regardless of the specific loading at infinity.     

Steady-state heat conduction in a circular cone

Zusammenfassung Diese Arbeit befasst sich mit der Bestimmung des stationären Temperaturfeldes, das in einem Kreiskegel durch eine unstetige Verteilung der vorgegebenen Oberflächentemperatur hervorgerufen wird. Die Temperatur der Mantelfläche wird oberhalb und unterhalb einer festen Entfernung von der Kegelspitze konstant angenommen. Dieses Problem wird mit Hilfe der Mellin-Transformation streng gelöst. Die so erhaltene Lösung wird in einer später erscheinenden Arbeit auf die Bestimmung der zugehörigen Temperaturspannungen angewendet.

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The results communicated in this paper were obtained in the course of an investigation conducted under Contracts Nonr 562(20) and Nonr 562(25) of Brown University with the Office of Naval Research in Washington, D.C.