On the domain of attraction of an operator between supremum and sum

Summary Between the operations which produce partial maxima and partial sums of a sequenceY ₁,Y ₂, ..., lies the inductive operation:X _n =X _n-1(X _n-1+Y _n ),n1, for 0<<1. If theY _n are independent random variables with common distributionF, we show that the limiting behavior of normed sequences formed from {X _n ,n1}, is, for 0<<1, parallel to the extreme value case =0. ForFD() we give a full proof of the convergence, whereas forFD()D(), we only succeeded in proving tightness of the involved sequence. The processX _n is interesting for some applied probability models.     

The synthesis and reactivity of polysilylacetylenes: Diels—Alder reactions to give bis (silyl) benzenes

Six bis(silyl)acetylenes (XMe²Si? C?C? SiMe₂X) with the following varied silicon substituents X were prepared: 1 (Me, Me); 2 (H, H); 3 (C1, H); 4 (CI, CI); 5 (MeO, H); 6 (MeO, MeO). While 1 and 2 may be prepared by the reaction of dilithio- or bis(bromomagnesium)-acetylide with the appropriate chlorosilane, similar reactions designed to give 3–6 yielded oligomers, XMe₂Si? (? C?C? SiMe₂)_n? X, 7, X=CI, MeO, as the major products, indicating that the acetylenic functionality on silicon activates the chlorosilane towards nucleophilic substitution. Compounds 3 and 4 were prepared by free radical chlorination of 2. Methanolysis of 3 and 4 gave quantitative yields of 5 and 6 respectively. Compounds 1–6 undergo a Diels–Alder reaction with α-pyrone to produce, after loss of carbon dioxide, bis(silyl)-substituted benzene derivatives. The order of reactivity has been determined to be: 4=6>3=5>1>2, indicating that chloro or alkoxy substituents favor the cycloaddition with 2- pyrone. The adducts formed by compounds 3–6 undergo an unusually facile hydrolysis or elimination to give 1,1,3,3-tetramethyl-1,3-disila-2-oxaindane.     

Gravity-driven azimuthal flow of a layer of thixotropic fluid on the inner surface of a horizontal tube

The gravity-driven azimuthal flow of a layer of thixotropic paint on the inner surface of a horizontal tube is studied, considering surface tension effects. Using the lubrication theory, it was shown that a non-linear, fourth-order partial differential equation governs the time evolution of the paint layer thickness distribution along the azimuthal coordinate. Three parameters arise in the analysis, namely, the Bond number and two rheology-related parameters. The governing equation is integrated via a second-order accurate finite-difference scheme. The results showed that, in situations where the capillary force dominates (Bo < 1), displacement of the paint after application is very slow. For situations where the gravity force dominates (Bo > 1), an undulation on the interface arises near the tube bottom at sufficiently large times.     

On Criticality for Competing Influences of Boundary and External Field in the Ising Model

We continue a study of Schonmann (1994), Schonmann and Shlosman (1996), and Greenwood and Sun (1997) regarding the competing influences of boundary conditions and external field for the Ising model. We find a critical point B ₀ in the competing influences for low temperature in dimension d 2A7E; 2.     

Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise

We consider estimation of the drift function of a stationary diffusion process when we observe high-frequency data with microstructure noise over a long time interval. We propose to estimate the drift function at a point by a Nadaraya–Watson estimator that uses observations that have been pre-averaged to reduce the noise. We give conditions under which our estimator is consistent and asympotically normal. Its rate and asymptotic bias and variance are the same as those without microstructure noise. To use our method in data analysis, we propose a data-based cross-validation method to determine the bandwidth in the Nadaraya–Watson estimator. Via simulation, we study several methods of bandwidth choices, and compare our estimator to several existing estimators. In terms of mean squared error, our new estimator outperforms existing estimators.     

Synthesis and in vitro photodynamic activity of novel galactose-containing phthalocyanines

A novel series of silicon(IV) phthalocyanines with one or two axial acetal-protected galactose substituent(s) have been prepared by typical substitution reactions. The compounds exhibit a high photodynamic activity against HepG2 human hepatocarcinoma cells with IC₅₀ values down to 0.10 μM.     

Evaluation of process parameters of ultrasonic treatment of bacterial suspensions in a pilot scale water disinfection system

In this study, several process parameters that may contribute to the efficiency of ultrasound disinfection are examined on a pilot scale water disinfection system that mimics realistic circumstances as encountered in an industrial environment. The main parameters of sonication are: (i) power; (ii) duration of treatment; (iii) volume of the treated sample. The specific energy (E_s) is an indicator of the intensity of the ultrasound treatment because it incorporates the transferred power, the duration of sonication and the treated volume. In this study, the importance of this parameter for the disinfection efficiency was assessed through changes in volume of treated water, water flow rate and electrical power of the ultrasonic reactor. In addition, the influences of the initial bacterial concentration on the disinfection efficiency were examined. The disinfection efficiency of the ultrasonic technique was scored on a homogenous and on a mixed bacterial culture suspended in water with two different types of ultrasonic reactors (Telsonic and Bandelin). This study demonstrates that specific energy, treatment time of water with ultrasound and number of passages through the ultrasonic reactor are crucial influential parameters of ultrasonic disinfection of contaminated water in a pilot scale water disinfection system. The promising results obtained in this study on a pilot scale water disinfection system indicate the possible application of ultrasound technology to reduce bacterial contamination in recirculating process water to an acceptable low level. However, the energy demand of the ultrasound equipment is rather high and therefore it may be advantageous to apply ultrasound in combination with another treatment.