The occupation time of Brownian motion in a ball

LetW be a Wiener process of dimensiond3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot⁽¹⁶⁾ on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.     

Synthese und Charakterisierung neuer Cyclischer und acyclischer Silachalkogenane mit Disilanyleinheiten

Synthesis and Characterization of New Cyclic and Acyclic Silachalcogenanes with Disilanyl Units Synthesis and properties of (4-CH₃? C₆H₄)₃SiSiH₃, (C₆H₅)₂HSiSiH₂C₆H₅, C₆H₅Cl₂SiSiH₃, (C₆H₅)₂ClSiSiH₃, (H₃SiSiH₂)₂Se, H₃SiSiH₂ESiH₃, , as well as characterisation by IR-, MS-, NMR-spectroscopy are described. Reactions of phenylsubstituted disilanes with HCl in the presence of catalytic amounts of AlCl₃ provide chorinated chlorophenylsubstituted disilanes. Condensation of these chlorodisilanes with disilathiane or disilaselenane yield cyclic and acyclic silachalkogenanes containing disilanyl units. The structure of (C₆H₅)₃SiSiH₃ has been determined by X-ray analysis. The compound crystallizes in space group C2/c with the cell dimensions a = 16.366(2), b = 11.458(1), c = 19.719(2) Å, β = 110.93(1)°.     

Description of the turbidity measurements near the phase transition temperature of poly(N-isopropyl acrylamide) copolymers: the effect of pH, concentration, hydrophilic and hydrophobic content on the turbidity

Absorbance values between 300 and 800 nm of aqueous solutions of poly(N-isopropyl acrylamide-co-itaconic acid-9.80), poly(N-isopropyl acrylamide-co-itaconic acid-52.05) and poly(N-isopropyl acrylamide)s containing Tegomer H-Si 2111 end groups and/or blocks were measured using a Shimadzu 160-A UV-visible spectrometer. Turbidities obtained from these absorbance values were used to interpret the macromolecular phase transition from a hydrophilic to a hydrophobic structure of the polymers. The effects of comonomer type and content, concentration of the solutions, pH and temperature on the coil-globule transition were discussed in terms of turbidity form factor, β related to size and shapes of particles and calculated by using the simplified form of Debye equation.The results presented in this work show that the presence of Tegomer H-Si 2111 (Si containing end groups and/or blocks) or high amount of itaconic acid (IA) in the chains prevent a collapse transition from hydrated extended coils to hydrophobic globules, which aggregate and form a separate phase (β<2). Furthermore, it was observed that in the case of concentrated solutions intermolecular hydrophobic interactions between isopropyl groups overcame the repulsive forces resulting from the ionized carboxylic acid groups of IA or surface active nature of Si containing hydrophobic groups (β>2). This stage of the transition corresponds to macroscopic phase separation after an intramolecular process.     

Interaction of (1-phenylethyl)indole-2-carbonitrile with C-nucleophiles

Methods of obtaining ketones and enamino esters have been developed on the basis of reactions of 1-(1-phenylethyl)indole-2-carbonitrile with organomagnesium and organozinc compounds. Removal of a benzyl group from the indole nitrogen atom by the Grignard reagent has been discovered. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1179–1183, August, 2006.     

HPLC monitored synthesis of R2NCH2 substituted benzene derivatives used as (C,N)-ligands for organometallic compounds

2-(Diethylaminomethyl)phenyl bromide and 1,3-bis(dimethylaminomethyl)-benzene, useful ligands for the synthesis of hypervalent organometallic compounds, were prepared and characterized by NMR (¹H, ¹³C, 2D experiments) spectroscopy. Their synthesis was monitored by the HPLC method. The compounds were eluted on a Nucleosil 120 Si column (5 μm, 25×0.4 cm) with n-hexane at room temperature using a 1.0 ml/min flow-rate. The maximum values of absorbance for the studied compounds, excepting the diethylamine, were located in a narrow range around 212 nm, the wavelength used for their UV detection. The diethylamine was detected at 190 nm. The calibration curves are straight lines with correlation factors r>0.995. The HPLC data are in good agreement with those provided by NMR spectroscopy.     

Secure Direct Communication Using Ensembles with the Same Compressed Density Matrix

In this paper, a quantum secure direct communication protocol using ensembles with the same density matrix is proposed. The two communication parties can realize the message transmission using this method through a quantum channel, each bit of information can be transmitted using an ensemble and read out through global measurement.The eavesdropping behavior can be detected through the channel diagnoses.     

Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

Transformation of macromonomers into ring‐opening polymerization macroinitiators: A detailed initiation efficiency study

In the present study, n‐butyl acrylate macromonomer (BAMM) (M_n = 1900 g mol^?1; PDI = 1.96) has been synthesized via a high‐temperature polymerization process. Subsequently, the olefinic termini of the BAMM have been transformed into a diol via a dihydroxylation process using KMnO₄ as an oxidizing agent. The OH‐terminated macroinitiator pBA(OH)₂ has subsequently been employed for the ring‐opening polymerization (ROP) of ε‐caprolactone via various catalytic systems, that is, organo‐(1,5,7‐triazabicyclo[4.4.0]dec‐5‐ene), metal (tin(II) 2‐ethylhexanoate), and enzymatic catalysis (Novozym® 435). The obtained pBA‐b‐pCL block copolymers and the initiation efficiency of the BAMM macroinitiator have been investigated via size exclusion chromatography (SEC), electrospray ionization–mass spectrometry (ESI‐MS) hyphenated with SEC and liquid chromatography at the critical conditions of both poly(ε‐caprolactone) (pCL) and pBA. The in vitro enzyme catalysis (eROP) approach proved to be the most efficient catalysis system due to minor transesterification side reactions during the polymerization process. However, side reactions such as transesterifications occur in each catalytic system and—while they cannot be suppressed—they can be minimized. The species generated during the eROP process include the desired block copolymer pBA‐b‐pCL as main species as well as pCL homopolymer and residual macroinitiator pBA(OH)₂. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Exclusion process and droplet shape

We use a mathematical isomorphism between the one-dimensional exclusion process and the two-dimensional stochastic Ising model in the low-temperature limit to describe the typical instantaneous shape of a supercritical droplet. We derive, specifically, the exact asymptotic distribution of the boundaries of a (+1) spin region, confined to Z ₊ ² and subjected to a positive magnetic field. In an appropriate scaling, the boundary distribution converges to a deterministic continuum limit.On leave at the EPFL, CH-1015 Lausanne, Switzerland.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.