On a general class of graph polynomials

Let $\text{F}$ be a family of connected graphs. With each element α ∈ $\text{F}$, we can associate a weight w_α. Let G be a graph. An F-cover of G is a spanning subgraph of G in which every component belongs to $\text{F}$. With every F-cover we can associate a monomial π(C) = Π_αw_α, where the product is taken over all components of the cover. The F-polynomial of G is Σπ(C), where the sum is taken over all F-covers in G. We obtain general results for the complete graph and complete bipartite graphs, and we show that many of the well-known graph polynomials are special cases of more general F-polynomials.     

The interaction of oxygen and nitrogen with the niobium (100) surface: II. Reaction kinetics

Auger spectroscopy has been used to investigate the interactions of oxygen and nitrogen with both the (100) face niobium and with polycrystalline niobium. Sticking coefficients for both gases have been determined as a function of coverage. A temperature and concentration ependent segregation of oxygen at the surface has been observed even under conditions where the solid solubility of the bulk was not exceeded. A model to describe this segregation has been developed and extended to explain discrepancies in earlier investigations f the reaction of oxygen with niobium.     

Magnetic interactions of iron nanoparticles in arrays and dilute dispersions

The magnetic properties of monodisperse Fe nanoparticles with over 4 orders of magnitude difference in concentration are studied by a combination of ordinary and remanent hysteresis loops, zero field cooled magnetization as a function of temperature, and magnetic relaxation rates. We compare the behavior of dilute dispersions with different concentrations, dispersions, and arrays made from the same particles, and nanoparticle arrays with different particle sizes and separations. The results are related to theoretical predictions and are used to create a unified picture of magnetostatic interactions within the assemblies.     

Temperature-induced nucleation of poly(p-phenylene vinylene-co-2,5-dioctyloxy-m-phenylene vinylene) crystallization by HiPco single-walled carbon nanotubes

Hybrid systems of the conjugated organic polymer poly(p-phenylene vinylene-co-2,5-dioctyloxy-m-phenylene vinylene)(PmPV) and HiPco single-walled carbon nanotubes (SWNTs) are explored using spectroscopic and thermal techniques to determine specific interactions. Vibrational spectroscopy indicates a weak interaction, and this is further elucidated using differential scanning calorimetry (DSC), confocal laser scanning microscopy, temperature-dependent Raman spectroscopy, and temperature-dependent infrared spectroscopy of the raw materials and the composite. An endothermic transition is observed in the DSC of both the polymer and the 0.1% HiPco composite in the region of 50 degrees C. Also observed in the DSC of the composite is a double-peaked endotherm at -39 and -49 degrees C, which does not appear in the polymer. The Raman spectroscopy of the polymer upon increasing the temperature to 60 degrees C shows a diminished cis-vinylene mode at 1575 cm(-1), with an increase in relative intensity of the trans-vinylene mode at 1630 cm(-1). Partially irreversible change in isomerization suggests increased order in the polymer. This change in the polymer is also manifest in the Raman composite spectrum upon increase of the temperature to 60 degrees C, where the spectrum becomes abruptly dominated by nanotubes. Raman spectroscopy of the composite shows no change at -35 degrees C; however, infrared absorption measurements suggest that the transition at -35 degrees C derives from the polymer side chains. Here the composite at -35 degrees C shows a change in the absorbance of the polymer side chain aryl-oxide linkage at 1250 cm(-1) and alkyl-oxide stretch at 1050 cm(-1). Infrared spectra thus suggest that the transitions in the lower temperature region around -35 degrees C are side chain-induced, while Raman spectra suggest that the transition at 60 degrees C is backbone-induced. Furthermore, temperature cycling induces an irreversible decrease in the mean fluorescence intensity of the polymer, coupled with a further reduction in the mean fluorescence intensity of the composite. This suggests that an increase in crystallization of the composite is supported and enhanced by an increase in ordering of the polymer. Implications are discussed.     

The Farrell-Jones Isomorphism Conjecture for finite covolume hyperbolic actions and the algebraic -theory of Bianchi groups

We prove the Farrell-Jones Isomorphism Conjecture for groups acting properly discontinuously via isometries on (real) hyperbolic -space with finite volume orbit space. We then apply this result to show that, for any Bianchi group , , , and vanish for .

     

On the potentialities of nuclear gamma resonance (Mössbauer effect) spectroscopy as a new,low dose approach to cancer radiation therapy

The extension of a new, low dose, Mössbauer spectroscopy approach to cancer radiation therapy to “easy” isotopes other than Iron-57 is outlined. New in vitro studies using a number of cancer cell lines are reported.     

A variational principle for the scattered wave

A Schwinger-type variational principle is presented for the scattered field in the case of scalar wave scattering with an arbitrary field incident on an object of arbitrary shape with homogeneous Dirichlet boundary conditions. The result is variationally invariant at field points ranging from the surface of the scatterer to the farfield and is an important extension of the usual Schwinger variational principle for the scattering amplitude, which is a farfield quantity. Also, a generic procedure, physically motivated by the general principles of boundary conditions and shadowing, is presented for constructing simple trial functions to approximate the fields. The variational principle and the trial function design are tested for the special case of a spherical scatterer and accurate answers are found over the entire frequency range.     

Rapid removal of selected volatile organic compounds from gaseous mixtures using a new dispersive vapor extraction technique: A feasibility study

A new dispersive vapor extraction (DVE) technique for rapid removal of selected volatile organic compounds (VOCs) from gaseous mixtures was investigated. In this technique, less than 1.0 mL of a volatile solvent was vaporized for 8 min in a 250-mL flask containing a gaseous mixture. The flask was then cooled under running tap water for 2-3 min to induce condensation of the vapor and co-extraction of the VOCs from the headspace. The technique was tested over a concentration range of 4-23 ppb, and resulted in extraction efficiencies ranging from 80 to 97% for the VOCs tested. Because of its simplicity and the relatively short sampling time, DVE could potentially lead to high sample throughput and rapid air analysis.