Heavy-tailed phase-type distributions: a unified approach

Extremes - A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being...     

Fractional square functions and potential spaces

Carlos Segovia and Richard Wheeden defined fractional square functions involving fractional derivatives. They obtained characterizations of potential spaces via square functions. Our aim in this paper is to reconsider the ideas of Segovia and Wheeden under the light of the semigroups of operators. We develop a quite general theory of fractional square functions associated to certain classes of operators. We present some examples of differential operators where our theory applies. We recover in a more compact way the results of Segovia and Wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and Ornstein–Uhlenbeck operators.     

Organotin catalysts in organosilicon chemistry

Organotin compounds are best known in the chemical industry as PVC stabilizers, polyurethane foam formers and antifungal agents. However, they have also been widely used in the silicon industry for decades for curing organosilicon polymers, despite the fact that neither the mechanism through which the siloxane bonds are formed nor their inherent toxicity are completely understood. This review gives an account of the use of organotin compounds in the preparation of diverse polysiloxane‐containing materials via cross‐linking with either organic or inorganic polymers. As they are common ingredients for this application, a brief outline of the preparation of relevant silicon‐containing compounds, as well as their reactivity, are given. In addition, since there is some evidence that stannasiloxanes formed in situ during the reaction play a determinant role as intermediates in the reaction mechanism, an overview of the synthesis and reactivity of Sn‐O‐Si‐containing compounds is also presented. Copyright © 2012 John Wiley & Sons, Ltd.     

The Compound Poisson Limit Ruling Periodic Extreme Behaviour of Non-Uniformly Hyperbolic Dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of certain non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.     

Facile and template‐free method toward chemical synthesis of polyaniline film/nanotube structures

A facile and template‐free method is reported to synthesize a new thin film structure: polyaniline (PANI) film/nanotubes (F/N) structure. The PANI F/N is a 100‐nm thick PANI film embedded with PANI nanotubes. This well‐controlled method requires no surfactant or organic acid as well as relatively low concentration of reagents. Synthesis condition studies reveal that aniline oligomers with certain structures are responsible for guiding the growth of the nanotubes. Electrical characterization also indicates that the PANI F/N possesses similar field‐effect transistor characteristics to bare PANI film. With its 20% increased surface‐area‐to‐volume (S/V) ratio contributed by surface embedded nanotubes and the excellent p‐type semiconducting characteristic, PANI F/N shows clear superiority compared with bare PANI film. Such advantages guarantee the PANI F/N a promising future toward the development of ultra‐high sensitivity and low‐cost biosensors © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3973–3979     

Experimental and Kinetic Modeling Study of C2H2 Oxidation at High Pressure

A detailed chemical kinetic model for oxidation of acetylene at intermediate temperatures and high pressure has been developed and evaluated experimentally. The rate coefficients for the reactions of C₂H₂ with HO₂ and O₂ were investigated, based on the recent analysis of the potential energy diagram for C₂H₃ + O₂ by Goldsmith et al. and on new ab initio calculations, respectively. The C₂H₂ + HO₂ reaction involves nine pressure‐ and temperature‐dependent product channels, with formation of triplet CHCHO being dominant under most conditions. The barrier to reaction for C₂H₂ + O₂ was found to be more than 50 kcal mol^?1 and predictions of the initiation temperature were not sensitive to this reaction. Experiments were conducted with C₂H₂/O₂ mixtures highly diluted in N₂ in a high‐pressure flow reactor at 600–900 K and 60 bar, varying the reaction stoichiometry from very lean to fuel‐rich conditions. Model predictions were generally in satisfactory agreement with the experimental data. Under the investigated conditions, the oxidation pathways for C₂H₂ are more complex than those prevailing at higher temperatures and lower pressures. Acetylene is mostly consumed by recombination with H to form vinyl (reducing conditions) or with OH to form a CHCHOH adduct (stoichiometric to lean conditions). Both C₂H₃ and CHCHOH then react primarily with O₂. The CHCHOH + O₂ reaction leads to formation of significant amounts of glyoxal (OCHCHO) and formic acid (HOCHO), and the oxidation chemistry of these intermediates is important for the overall reaction.     

The Reactivity of Polymersome Encapsulated Hemoglobin with Physiologically Important Gaseous Ligands: Oxygen, Carbon Monoxide and Nitric Oxide

Two distinct preparations of amphiphilic diblock copolymer vesicles (i.e. polymersomes), composed of (poly(ethylene oxide)-poly(butadiene)) (PEO-PBD), with molecular weights of 1.8 kDa and 10.4 kDa, offering different hydrophobic membrane thicknesses, were used to encapsulate the oxygen (O(2)) storage and transport protein hemoglobin (Hb) for possible application as a red blood cell (RBC) substitute. Key biophysical properties as well as the kinetics of polymersome encapsulated Hb (PEH) interaction with physiologically important gaseous ligands (O(2), carbon monoxide and nitric oxide) were measured as a function of the hydrophobic membrane thickness of the PEH particle. Taken together, the results of this work show that PEHs exhibit biophysical properties and retarded ligand binding/release kinetics (compared to cell-free Hb), which are similar to the behavior of RBCs. Therefore, PEHs have the potential to serve as safe and efficacious RBC substitutes for use in transfusion medicine.