Two-dimensional isotropic scattering in a semi-infinite cylindrical medium

Beginning with the integral equation for the source function, the solutions for the source function, flux and intensity at the boundary of a two-dimensional, isotropically scattering cylindrical medium are found. The incident radiation is collimated and normal to the surface of the medium and depends only on the radial coordinate. For a Bessel function boundary condition, separation of variables is used to reduce the source function integral equation to a one-dimensional equation. The resulting integral equation is shown to be the same as that for the two-dimensional planar case. Solutions for other boundary conditions are then shown to be superpositions of the Bessel function solution. Numerical results are presented for a Gaussian distribution of incident radiation which closely models a laser beam. These multiple scattering results are compared to the single scattering approximation. Also, the solution for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function is expressed in terms of the isotropic results.     

Silicon on spinel: The interaction between deposition constituents and the substrate surface

The examination of the growth of silicon on flame fusion and Czochralski spinel prior to complete coverage of the substrate provides information on the chemical interaction between the deposition constituents and the substrate material. The flame fusion spinel appears to be eroded primarily by silicon, while the Czochralski spinel is eroded by both hydrogen and silicon. The hole mobilities in (111) silicon deposited in helium on the Czochralski spinel are similar to the mobilities in (111) silicon deposited in hydrogen on the flame fusion spinel. The semiconducting properties of silicon on the Czochralski spinel are degraded by annealing the substrate in hydrogen, and are unaffected by annealing the substrate in helium. The substrate surface work damage appears to be removed as the result of reduction of the spinel by silicon during the deposition of silicon on the Czochralski spinel in helium. Both the electrical data of 1 μm thick films and the physical nature of the deposits prior to complete coverage of the substrate lead to the conclusion that the hole mobilities in silicon on spinel are limited primarily by the impurities introduced into the deposit by reaction of the substrate with the deposition constituents, and that the impurities are incorporated into the deposit mainly prior to complete coverage of the surface and are concentrated in a thin layer in the silicon near the silicon-substrate interface.     

Counting codes over rings

We extend the definition of free codes to codes over local rings and arbitrary Frobenius rings. The number of free codes over finite Frobenius rings is determined by calculating the number for local rings and applying the Chinese Remainder Theorem. A formula for the number of codes of arbitrary type over a finite chain ring is given and this is applied to determine the number of linear codes over a finite principal ideal ring.     

Maximum distance separable codes over {\mathbb{Z}_4} and {\mathbb{Z}_2 \times \mathbb{Z}_4}

Known upper bounds on the minimum distance of codes over rings are applied to the case of ${\mathbb Z_{2}\mathbb Z_{4}}$ -additive codes, that is subgroups of ${\mathbb Z_{2}^{\alpha}\mathbb Z_{4}^{\beta}}$ . Two kinds of maximum distance separable codes are studied. We determine all possible parameters of these codes and characterize the codes in certain cases. The main results are also valid when ?? = 0, namely for quaternary linear codes.     

CYCLIC CODES OVER FORMAL POWER SERIES RINGS

In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.     

Intramolecular pyridone/enyne photocycloaddition: partitioning of the [4 + 4] and [2 + 2] pathways

Intramolecular photocycloaddition (>290 nm) between a 1,3-enyne and a 2-pyridone is far more selective than the intermolecular version; a three-atom linkage both controls regiochemistry and separates the [2 + 2] and [4 + 4] pathways. All four head-to-head, head-to-tail, tail-to-head, and tail-to-tail tetherings have been investigated. Linkage via the ene of the enyne leads to [2 + 2] products regardless of alkene geometry, whereas linkage through the yne results in [4 + 4] cycloadducts. The bridged 1,2,5-cyclooctatriene products of [4 + 4] cycloaddition are unstable and undergo a subsequent [2 + 2] dimerization reaction.     

Fabrication of bovine serum albumin nanotubes through template-assisted layer by layer assembly

One-dimensional protein nanostructures have many potential applications in the biomedical field. In this article, protein nanotubes have been fabricated via sequential filtration of bovine serum albumin (BSA) solution at pH 3.8 and 7.0 through the nanochannels of anodic aluminum oxide templates. The morphology of the nanostructures has been examined using scanning electron microscopy and transmission electron microscopy. Circular dichroism and UV/Vis spectroscopy have been used to select experimental conditions such as the pH values and the etching solution to release the fabricated protein nanotubes to minimize potential damage to the bioactivity of BSA. These results indicate that much more study needs to be done to strengthen the mechanical stability of the protein nanotubes and to better control their morphology.     

Preliminary limits on the WIMP-nucleon cross section from the cryogenic dark matter search (CDMS)

We are conducting an experiment to search for WIMPs, or weakly-interacting massive particles, in the galactic halo using terrestrial detectors. This generic class of hypothetical particles, whose properties are similar to those predicted by extensions of the standard model of particle physics, could comprise the cold component of nonbaryonic dark matter. We described our experiment, which is based on cooled germanium and silicon detectors in a shielded low-background cryostat. The detectors achieve a high degree of background rejection through the simultaneous measurement of the energy in phonons and ionization. Using exposures on the order of one kilogram-day from initial runs of our experiment, we have achieved (preliminary) upper limits on the WIMP-nucleon cross section that are comparable to much longer runs of other experiments.