The continuing search for Wieferich primes

A prime satisfying the congruence

is called a Wieferich prime. Although the number of Wieferich primes is believed to be infinite, the only ones that have been discovered so far are and . This paper describes a search for further solutions. The search was conducted via a large scale Internet based computation. The result that there are no new Wieferich primes less than is reported.

     

On free,projective, and strongly flat acts

Archiv der Mathematik -     

Endomorphism monoids of free acts and O-wreath products of monoids

Monoids and acts which may have zero elements are considered. In Section 1 we construct a O-wreath product of monoids. In 2 we prove the theorem that the endomorphism monoid of a free act over a monoid with zero can be represented as a O-wreath product. Considering monoids with tero we are interested in their annihilator properties. In 3 we give necessary and sufficient conditions for a O-wreath product of monoids to be a right (left) Baer (Rickart) monoid. In 4 we obtain as a consequence corresponding conditions for the endomorphism monoid of a free act over a monoid with zero.     

Observation of megagauss-field topology changes due to magnetic reconnection in laser-produced plasmas

The spatial structure and temporal evolution of megagauss magnetic fields generated by interactions of up to 4 laser beams with matter were studied with an innovative, time-gated proton radiography method that produces images of unprecedented clarity because it uses an isotropic, truly monoenergetic back-lighter (14.7-MeV protons from D3He nuclear fusion reactions). Quantitative field maps reveal precisely and directly, for the first time, changes in the magnetic topology due to reconnection in a high-energy-density plasma (n(e) approximately 10(20)-10(22) cm(-3), T(e) approximately 1 keV).     

Knipholone and related 4-phenylanthraquinones: structurally, pharmacologically, and biosynthetically remarkable natural products

This review gives the first comprehensive overview of the rapidly emerging young class of 4-phenylanthraquinones isolated from the three genera Bulbine, Bulbinella, and Kniphofia, all from the plant family Aphodelaceae: their occurrence, structural elucidation (with particular emphasis on the phenomenon of axial chirality), partial and total synthesis, their pharmacological (i.a., antimalarial and antitumoral) activities, and their biosynthetic origin (from acetate units). Particular emphasis is given to the stereostructure of knipholone, the most abundant of these naturally occurring phenylanthraquinones. The most recent highlight is the discovery of the first dimeric representatives, named joziknipholones, involving interesting phenomena of--partially or fully restricted--rotation at the sp2-sp2 and sp2-sp3 axes.     

Measuring E and B fields in laser-produced plasmas with monoenergetic proton radiography

Electromagnetic (E/B) fields generated by the interaction with plasmas of long-pulse, low-intensity laser beams relevant to inertial confinement fusion have been measured for the first time using novel monoenergetic proton radiography methods. High-resolution, time-gated radiography images of a plastic foil driven by a 10(14) W/cm(2) laser implied B fields of approximately 0.5 MG and E fields of approximately 1.5 x 10(8) V/m. Simulations of these experiments with LASNEX+LSP have been performed and are in overall (though not exact) agreement with the data both for field strengths and for spatial distributions; this is the first direct experimental test of the laser-generated B-field package in LASNEX. The experiments also demonstrated that laser phase plates substantially reduce medium-scale chaotic field structure.     

Lattice parameter variation in inp related to the dopant element and doping level

The variation of the lattice constant was determined across (001) InP wafers from 〈111〉 grown LEC INP: S and InP: Sn + Ga + As monocrystals. The variation correlates to the free carrier distribution. The enrichment of dopants results in lattice spacing in the crystal core (especially for InP: Sn + Ga + As), which occupy a larger region as dopant enrichment do.     

Failure Distribution on Semiconductor Wafers

Investigation of the distribution of dislocations intersecting the free surface of (1, 0, 0), Si-doped Bridgman-grown GaAs wafers. The defect densities were determined by using molten KOH as the defect-revealing etch. Their distribution can well be described by the compound Poisson-gamma distribution. The corresponding formula for the chip-yield is derived and it is shown, under which conditions it goes over into that for the simple Poisson distribution. Further, it is shown how the finite dimension of failures can be taken into account.