Limiting Properties of Random Graph Models with Vertex and Edge Weights

This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on edges and vertices and assuming that weights on edges are signed. We aim at an exposition that summarizes, simplifies, and extends proof ideas. We also study sparse graph asymptotics, showing convergence of the weighted random graphs to a certain weighted graph that can be constructed in terms of Poisson processes. We are motivated by numerous applications, ranging from ecology to parallel computing models. It is the latter set of applications that necessitates the introduction of vertex weights. Finally, we discuss some open problems and research directions.     

Quantitative characterization of TiO<Subscript>2</Subscript> nanoparticle release from textiles by conventional and single particle ICP-MS

TiO₂ is ubiquitously present in a wide range of everyday items, both as an intentionally incorporated additive and naturally occurring constituent. It can be found in a wide range of consumer products, including personal care products, food contact materials, and textiles. Normal use of these products may lead to consumer and/or environmental exposure to TiO₂, possibly in form of nanoparticles. The aim of this study is to perform a leaching test and apply state-of-the-art methods to investigate nano-TiO₂ and total Ti release from five types of commercially available conventional textiles: table placemats, wet wipes, microfiber cloths, and two types of baby bodysuits, with Ti contents ranging from 2.63 to 1448 μg/g. Released particle analysis was performed using conventional and single particle inductively coupled plasma mass spectrometry (ICP-MS and spICP-MS), in conjunction with transmission electron microscopy (TEM), to measure total and particulate TiO₂ release by mass and particle number, as well as size distribution. Less than 1% of the initial Ti content was released over 24 h of leaching, with the highest releases reaching 3.13 μg/g. The fraction of nano-TiO₂ released varied among fabric types and represented 0–80% of total TiO₂ release. Particle mode sizes were 50–75 nm, and TEM imaging revealed particles in sizes of 80–200 nm. This study highlights the importance of using a multi-method approach to obtain quantitative release data that is able to provide an indication regarding particle number, size distribution, and mass concentration, all of which can help in understanding the fate and exposure of nanoparticles.

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On the ergodicity conditions for stochastically recursive sequences

The ergodicity criterion for stochastically recursive sequences is given in terms of imbedded subsequences. Several examples are considered.     

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Experimental Techniques -     

Adsorption of fibrinogen on tantalum oxide, titanium oxide and gold studied by the QCM-D technique

The adsorption of human fibrinogen on tantalum oxide, titanium oxide and gold surfaces has been studied by quartz crystal microbalance with dissipation (QCM-D) at 37 degrees C. Two different protein concentrations have been used, one close to physiological concentration (1 mg/ml) and one significantly lower (0.033 mg/ml). To further characterize the adsorbed fibrinogen layer, the subsequent binding of both polyclonal and monoclonal antibodies of fibrinogen is studied. We found that the viscoelastic properties of the fibrinogen layer depends strongly on the initial protein concentration. The trend is generally seen for all three surfaces. The fibrinogen layer on gold and tantalum oxide is found to have the same viscoelastic properties, which are different from those found for the fibrinogen layer adsorbed on titanium oxide. The dependency of the surface chemistry on the viscoelastic properties of the fibrinogen layer is observed directly for the 0.033 mg/ml solution, and indirectly through the antibody response for the 1 mg/ml solution. From this we conclude that the orientation and/or denaturation of fibrinogen on a surface depends on the surface chemistry and the protein concentration in the solution, and that the binding of antibodies is a useful way to detect this difference.     

The determination of trace elements in aqueous media without preconcentration using a cryogenic hollow-cathode ion source

The glow discharge in a hollow cathode containing 20–50 μl of an aqueous sample held at liquid-nitrogen temperature is used as a source of ions in a double-focussing mass spectrometer. The device was tested with nine solutions containing an aggregate of seventy elements. Seven elements (F, P, S, Sc, Mn, Ni, and Ta) could not be determined because of interferences. The remainder of the elements could be determined at various detection limits ranging from sub-ng ml^?1 to μg ml^?1. Mercury (32 pg) could be detected in 20 μl of water in the presence of Tl, Pb, Bi, Th, U, and Al.     

Synthesis of asymmetric secondary phosphines by the cross coupling of arylhalides with silylphosphines

The cross coupling of aryl halides with alkyl(trimethylsilyl)phosphines catalyzed by zero-valent palladium complexes yields secondary alkylarylphosphoranes containing both electron-donor and electron-withdrawing substituents in the aromatic ring. The reversible disproportionation of alkylsilylphosphines to give AlkPH₂ and AlkP(SiMe₃)₂ was observed for the first time during this reaction. This disproportionation does not affect the yield of AlkArPH, which are formed in virtually quantitative yield, due to the high rate of cross coupling with AlkP(SiMe₃)H₂ and the reversibility of the disproportionation process.M. V. Lomonosov Moscow State University, 119899 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1645–1648, July, 1992.