The evolution of subcritical Achlioptas processes

In Achlioptas processes, starting from an empty graph, in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the evolving graph. AlthouSgh the evolution of such ‘local’ modifications of the Erd?s–Rényi random graph process has received considerable attention during the last decade, so far only rather simple rules are well understood. Indeed, the main focus has been on ‘bounded‐size’ rules, where all component sizes larger than some constant B are treated the same way, and for more complex rules very few rigorous results are known. In this paper we study Achlioptas processes given by (unbounded) size rules such as the sum and product rules. Using a variant of the neighbourhood exploration process and branching process arguments, we show that certain key statistics are tightly concentrated at least until the susceptibility (the expected size of the component containing a randomly chosen vertex) diverges. Our convergence result is most likely best possible for certain generalized Achlioptas processes: in the later evolution the number of vertices in small components may not be concentrated. Furthermore, we believe that for a large class of rules the critical time where the susceptibility ‘blows up’ coincides with the percolation threshold. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 174–203, 2015     

The Janson inequalities for general up‐sets

Janson and Janson, ?uczak and Ruciński proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up‐sets (increasing events) of a special form—each event is the intersection of some subset of a single set of independent events (i.e., a principal up‐set). We show that these inequalities in fact hold for arbitrary up‐sets, by modifying existing proofs to use only positive correlation, avoiding the need to assume positive correlation conditioned on one of the events. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 391–395, 2015     

A general hilbert space approach to wavelets and its application in geopotential determination

A general approach to wavelets is presented within a framework of a separable functional Hilbert space H. Basic tool is the construction of H-product kernels by use of Fourier analysis with respect to an orthonormal basis in H. Scaling functions and wavelet are defined in terms of H-product kernels. Wavelts are shown to be ‘building blocks’ that decorrelate the data. A pyramid scheme provides fast computation. Finally, the determination of the earth's gravitational potential from single and multipole expressions is organzied as an example of wavelet approximation in Hilbert space structure.     

Properties of nanometric and micrometric multilayered films made of three conducting polymers

The electrochemical, electrical and morphological properties of multilayered films formed by alternated layers of poly(3,4-ethylenedioxythiophene), polypyrrole, and poly[N-(2-cyanoethyl)pyrrole], which were prepared by electrochemical layer-by-layer deposition, have been investigated and compared with those of multilayered films formed by two conducting polymers. Results indicate that the electrochemical behavior of the films formed by three conducting polymers depends on the micrometric or nanometric thickness of the layers. Thus, the electroactivity increases until the thickness of these films reaches a threshold value (∼2 μm), while the electrostability of the films is very remarkable when their thickness is close to ∼4 μm or higher. On the other hand, comparison between multilayered systems made of two and three conducting polymers indicates that the third component introduces heterogeneity in the interfaces between consecutive layers, reducing the ability to store charge. Among the latter, multilayered films formed by poly(3,4-ethylenedioxythiophene) and polypyrrole have been found to be particularly electroactive and electrostable. The surface morphology and topography of the layers have been used to rationalize the electrochemical properties of the different materials.     

Interfacial properties of emulsions stabilized with surfactant and nonsurfactant coated boehmite nanoparticles

The properties of emulsions stabilized with surface-modified boehmite particles of 26 and 8 nm in diameter have been investigated. The surface-modified particles were prepared by mixing aqueous dispersions of cationic boehmite particles with aqueous solutions of the surfactant p-dodecylbenzenesulfonic acid (DBSA) or the nonsurfactant p-toluenesulfonic acid (TSA). For the 26 nm particles, interfacial tension measurements indicate that p-dodecylbenzenesulfonic acid partitions between the particle surface and the oil-water interface, while p-toluenesulfonic acid remains on the particle surface. The partitioning of p-dodecylbenzenesulfonic acid supports the formation of emulsions, although in the absence of the particles the same surfactant concentration is not sufficient for emulsion stabilization. Due to the fast exchange kinetics, p-dodecylbenzenesulfonic acid is gradually replaced by particles. At equilibrium, the interfacial tension in the presence of the surface-modified particles is between the values for the pure particles and the pure surfactant solutions. However, the interfacial tension is independent of the surfactant concentration used in the preparation of the particles. Reducing the particle size to 8 nm leads to increased emulsion stability, and thus, the minimum particle concentration required to prepare stable emulsions was reduced to 0.1 g/L. However, above approximately 3.5 mmol/L of the sulfonic acids, the small particles dissolve slowly, and the emulsion stability is lost. This mechanism can be used to trigger the collapse of the emulsions.     

Chromatographic peak deconvolution of constitutional isomers by multiple-reaction-monitoring mass spectrometry

Highly efficient and sophisticated separation techniques are available to analyze complex compound mixtures with superior sensitivities and selectivities often enhanced by a 2nd dimension, e.g. a separation technique or spectroscopic and spectrometric techniques. For enantioselective separations numerous chiral stationary phases (CSPs) exist to cover a broad range of chiral compounds. Despite these advances enantioselective separations can become very challenging for mixtures of stereolabile constitutional isomers, because the on-column interconversion can lead to completely overlapping peak profiles. Typically, multidimensional separation techniques, e.g. multidimensional GC (MDGC), using an achiral 1st separation dimension and transferring selected analytes to a chiral 2nd separation are the method of choice to approach such problems. However, this procedure is very time consuming and only predefined sections of peaks can be transferred by column switching to the second dimension. Here we demonstrate for stereolabile 1,2-dialkylated diaziridines a technique to experimentally deconvolute overlapping gas chromatographic elution profiles of constitutional isomers based on multiple-reaction-monitoring MS (MRM-MS). The here presented technique takes advantage of different fragmentation probabilities and pathways to isolate the elution profile of configurational isomers.     

Screening of degradation products,impurities and precursors of chemical warfare agents in water and wet or dry organic liquid samples by in-sorbent tube silylation followed by thermal desorption–gas chromatography–mass spectrometry

A standard method used by inspection teams of the Organisation for the Prohibition of Chemical Weapons (OPCW) for preparation of aqueous samples requires several extraction and derivatization steps. This results in tedious and time consuming on-site analysis. A simple thermal desorption–gas chromatography–mass spectrometry (TD–GC–MS) method was developed to analyse for a broad range of degradation products, impurities and precursors of chemical warfare agents (CWA) in water solutions and wet or dry organic liquid samples. The method is fast, sensitive, requires only microliter volumes of sample and enables the simultaneous determination of a wide range of compounds with widely differing polarity, volatility and reactivity. The applicability of the method was demonstrated by successful analysis of five OPCW Official Proficiency Test samples.     

A Cyclopeptide‐Derived Molecular Cage for Sulfate Ions That Closes with a Click

The 2:1 sandwich‐type complexes formed between a cyclopeptide with alternating L ‐proline and 6‐aminopicolinic acid subunits and inorganic anions can be stabilized by covalently linking a tris‐alkyne and a tris‐azide derivative of this peptide through copper‐catalyzed azide–alkyne cycloaddition. The resulting triply linked bis‐cyclopeptide can interact with anions such as sulfate ions in aqueous solution by including them into the cavity between the two cyclopeptide rings, where they can form hydrogen bonds to amide NH groups, distributed along the inner surface. The binding kinetics of this system differ significantly from those of a bis‐cyclopeptide that contains only one linker because the rate of guest exchange is considerably slower. Thermodynamically, the stability of the sulfate complex of the triply linked bis‐cyclopeptide approaches a log K_a value of 6 in H₂O/CH₃OH 1:1 (v/v) which is, however, only approximately one order of magnitude larger than affinity of the more flexible monolinked analogue. Titration calorimetry revealed that this behavior is mainly due to the change in the binding enthalpy from exothermic to endothermic upon increasing the number of linkers. Results from NMR spectroscopy and X‐ray crystallography indicate that the mono‐ and triply linked bis‐cyclopeptides adopt similar conformations in their complexes with sulfate ions, but the complex formation is enthalpically unfavorable for the cage. The substantial entropic contribution to sulfate complexation of this receptor more than compensates for this disadvantage, so that the overall sulfate affinity of both bis‐cyclopeptides ends up in the same range. These investigations provide important insight into the structure–property relationships of such receptors, thus leading the way to further structural improvement.     

Thermal evolution of ceramic powders surrounding the YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7–x</Subscript> composition

Organometallic-derived ceramic compositions surrounding YBa₂Cu₃O_7–x (123) were evaluated via DTA-TG runs and dilatometric densification. The compositions were either Y, Ba or Cu deficient respect to 123. For the Yttrium deficient compact the presence of liquids containing 0–1.3 mole %YO_1.5—capable of dissolving the 123 grains—can promote a rapid sintering behavior. For Copper deficient compact the main densification/contraction mechanisms were delayed till 985 °C. For both Barium and Copper deficient compacts a strong exudation of liquids was detected at 990 °C and 1020 °C, respectively.