Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N^1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.     

The Volterra operator is a compact universal quasinilpotent

Every compact quasinilpotent Hilbert space operator can be uniformly approximated by operators that are similar to the Volterra operator in L²([0,1],dx).     

Solid phase extraction for the speciation and preconcentration of inorganic selenium in water samples: A review

Selenium is an essential element for the normal cellular function of living organisms. However, selenium is toxic at concentrations of only three to five times higher than the essential concentration. The inorganic forms (mainly selenite and selenate) present in environmental water generally exhibit higher toxicity (up to 40 times) than organic forms. Therefore, the determination of low levels of different inorganic selenium species in water is an analytical challenge. Solid-phase extraction has been used as a separation and/or preconcentration technique prior to the determination of selenium species due to the need for accurate measurements for Se species in water at extremely low levels. The present paper provides a critical review of the published methods for inorganic selenium speciation in water samples using solid phase extraction as a preconcentration procedure. On the basis of more than 75 references, the different speciation strategies used for this task have been highlighted and classified. The solid-phase extraction sorbents and the performance and analytical characteristics of the developed methods for Se speciation are also discussed.     

Thermal desorption gas chromatography with mass spectrometry study of outgassing from polymethacrylimide foam (Rohacell®)

Polymethacrylimide foams are used as light structural materials in outer‐space devices; however, the foam closed cells contain volatile compounds that are outgassed even at low temperatures. These compounds ignite as plasmas under outer‐space radiation and the intense radio‐frequency fields used in communications. Since plasmas may cause spacecraft fatal events, the conditions in which they are ignited should be investigated. Therefore, qualitative and quantitative knowledge about polymethacrylimide foam outgassing should be established. Using thermogravimetric analysis, weight losses reached 3% at ca. 200°C. Thermal desorption gas chromatography with mass spectrometry detection was used to study the offgassed compounds. Using successive 4 min heating cycles at 125°C, each one corresponding to an injection, significant amounts of nitrogen (25.3%), water (2.6%), isobutylene (11.3%), tert‐butanol (2.9%), 1‐propanol (11.9%), hexane (25.3%), propyl methacrylate (1.4%), higher hydrocarbons (11.3%), fatty acids (2.2%) and their esters (1.3%), and other compounds were outgassed. Other compounds were observed during the main stage of thermal destruction (220–280°C). A similar study at 175°C revealed the extreme difficulty in fully outgassing polar compounds from polymethacrylimide foams by baking and showed the different compositions of the offgassed atmosphere that can be expected in the long term.     

Growth rate and shape as possible control mechanisms for the selection of mode development in optimal biological branching processes

Recently three branching modes were characterized during the formation of the lung in mice. These modes are highly stereotyped and correspond to domain formation, planar bifurcation and three dimensional branching respectively. At the same time it is proved that although genetic control mechanisms are presumably related to the selection of any of these modes, other external factors will most probably be involved in the branching process during development. In this paper we propose that the underlying controling factors might be related to the rate at which the tubes that form the lung network grow. We present a mathematical model that allows us to formulate specific experimental predictions on these growth rates. Moreover we show that according to this formulation, there is an optimization criterion which governs the branching process during lung development, namely, efficient local space filling properties of the network. If there is no space limitation the branches are allowed to grow freely and faster, selecting one branching mode, namely, domain formation. As soon as volume constraints appear the growth rate decreases, triggering the selection of planar and orthogonal bifurcation.     

On new computational local orders of convergence

Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of convergence is analyzed. Three of the new definitions given here do not involve the unknown root. Numerical experiments using adaptive arithmetic with multiple precision and a stopping criteria are implemented without using any known root.     

Elimination for Generic Sparse Polynomial Systems

We present a new probabilistic symbolic algorithm that, given a variety defined in an n-dimensional affine space by a generic sparse system with fixed supports, computes the Zariski closure of its projection to an ?-dimensional coordinate affine space with ?<n. The complexity of the algorithm depends polynomially on some combinatorial invariants associated to the supports.     

The Isolation of Single MMX Chains from Solution: Unravelling the Assembly–Disassembly Process

Herein, we provide a systematic theoretical and experimental study of the structural and optical properties of MMX (M=metal, X=halide) chains. The influence of solvent, temperature, and concentration has been analyzed to find suitable parameters for initial building‐block associations in solution. By using density functional calculations, we have computed the dissociation energy of different MMX oligomers (up to the tetramer) in the gas phase. On the basis of these findings, we discuss the most likely disassembly scenario and propose a new interpretation of these compounds. We also calculated the charge redistribution that occurs upon MM+XMMX binding in vacuum. Time‐dependent density functional theory (TDDFT) is used to calculate the UV/visible spectra of different MMX chains up to the tetramer in the gas phase. The implications of these theoretical findings in the analysis of our experiments are discussed in the text. The overall body of data presented suggests a new way of looking at such linear structures. By taking into account these new data, we have been able to isolate single/few MMX chains on mica.     

Characterization of grape seed procyanidins by comprehensive two-dimensional hydrophilic interaction × reversed phase liquid chromatography coupled to diode array detection and tandem mass spectrometry

In this work, the development and optimization of a new methodology to analyze grape seed procyanidins based on the application of two-dimensional comprehensive LC is presented. This two-dimensional method involves the use of a microbore column containing a diol stationary phase in the first dimension coupled to either a C₁₈ partially porous short column or a C₁₈ monolithic column in the second dimension. The orthogonal hydrophilic interaction?×?reversed phase liquid chromatography (HILIC×RP-LC) system is interfaced through a ten-port two-position switching valve. The optimized HILIC×RP-LC separation followed by diode array and tandem mass spectrometry detection (HILIC×RP-LC-DAD-MS/MS) made possible the direct analysis of a complex grape seed extract and allowed the tentative identification of 43 flavan-3-ols, including monomers and procyanidin oligomers till a polymerization degree of 7 units with different galloylation degrees. To the best of our knowledge, this is the first time that this powerful analytical technique is employed to characterize complex procyanidin samples. This work successfully demonstrates the great capabilities of the HILIC×RP-LC-DAD-MS/MS coupling for the direct analysis of very complex natural samples like grape seeds.

Zn incorporation and (CuIn)1−xZn2xSe2 thin film formation during the selenization of evaporated Cu and In precursors on Al:ZnO coated glass substrates

CuInSe₂ thin films with typical 1.0 eV gap energy and tetragonal chalcopyrite structure have been obtained on soda–lime glass substrates by the reaction of sequentially evaporated Cu and In layers with elemental selenium vapor, at 500 °C in flowing Ar. When analogous deposition and reaction processes were performed on Al:ZnO coated glasses, some increment in the band gap energy and diminution in the crystalline interplanar spacings have been detected for the resulting films with an extent that depends on the Cu/In atomic ratio of the evaporated precursor layers. This fact has been related to Zn incorporation into the selenized film, with quaternary (CuIn)_1−xZn_2xSe₂ compound formation that is influenced by the presence of copper selenide phases during the reaction process. Such deductions are supported by the optical, structural and compositional characterizations that have been performed comparatively on samples prepared by selenization of evaporated metallic precursors with two different Cu/In ratios (0.9 and 1.1) on bare and Al:ZnO coated glass substrates.