On tails of stationary measures on a class of solvable groups

Let G be a subgroup of GL(R,d) and let (Qn,Mn) be a sequence of i.i.d. random variables with values in Rd?G and law μ. Under some natural conditions there exists a unique stationary measure ν on Rd of the process Xn=MnXn−1+Qn. Its tail properties, i.e. behavior of as t tends to infinity, were described some over thirty years ago by H. Kesten, whose results were recently improved by B. de Saporta, Y. Guivarc'h and E. Le Page. In the present paper we study the tail of ν in the situation when the group G₀ is Abelian and Rd is replaced by a more general nilpotent Lie group N. Thus the tail behavior of ν is described for a class of solvable groups of type NA, i.e. being semi-direct extension of a simply connected nilpotent Lie group N by an Abelian group isomorphic to Rd. Then, due to A. Raugi, (N,ν) can be interpreted as the Poisson boundary of (NA,μ).     

1H and 13C NMR Analysis of Poly(succinimide) Prepared by Microwave-Enhanced Polycondensation of L-Aspartic Acid

Poly(succinimide) (PSI) is a polymer of aspartic acid with interesting properties and numerous possible uses. Application areas include agriculture, cleaning agents, metallurgy, the building industry, wastewater treatment, medicine, pharmaceuticals, bioengineering, and many more. Therefore, the particular structure analysis is crucial for these purposes, especially considering possible reactions between monomer and solvent used in the polycondensation process. Moreover, utilization of microwave irradiation in such synthesis is conducive to reducing reaction time and improving yield. In this article, the detailed structure analysis of PSI prepared under microwave irradiation conditions as well as a comparison study with thermally synthesized PSI are presented.     

Water-Soluble Polymeric Carbon Nitride Colloidal Nanoparticles for Highly Selective Quasi-Homogeneous Photocatalysis

Heptazine-based polymeric carbon nitrides (PCN) are promising photocatalysts for light-driven redox transformations. However, their activity is hampered by low surface area resulting in low concentration of accessible active sites. Herein, we report a bottom-up preparation of PCN nanoparticles with a narrow size distribution (ca. 10±3 nm), which are fully soluble in water showing no gelation or precipitation over several months. They allow photocatalysis to be carried out under quasi-homogeneous conditions. The superior performance of water-soluble PCN, compared to conventional solid PCN, is shown in photocatalytic H₂O₂ production via reduction of oxygen accompanied by highly selective photooxidation of 4-methoxybenzyl alcohol and benzyl alcohol or lignocellulose-derived feedstock (ethanol, glycerol, glucose). The dissolved photocatalyst can be easily recovered and re-dissolved by simple modulation of the ionic strength of the medium, without any loss of activity and selectivity.     

Physicochemical characteristics of 2-, 3- and 4-methylpyridinium tetrachloroferrates(III)

The crystal structure of 2-methylpyridinium tetrachloroferrate(III) was determined. The iron cation is tetracoordinated by chloride anions, and it adopts a slightly distorted tetrahedral coordination with three angles smaller, two almost equal and one larger than the tetrahedral. The compound is isostructural with its 3-, and 4-methylpyridinium analogues. The thermal properties of 2-, 3- and 4-methylpyridinium tetrachloroferrates(III) have been studied using TG and DSC techniques. The compounds exhibit a high stability in the melt.      

Simultaneous quantification of Echinacea species, Flos Lonicerae, Radix Scutellaria and Fructus Forsythiae combinations by rapid resolution liquid chromatography

Echinacea angustifolia and E. purpurea are commonly used in North America for their anti-bacterial effects. Flos Lonicerae, Radix Scutellaria and Fructus Forsythiae are traditional Chinese medicinal herbs commonly used for the treatment of complaints such as pneumonia, acute upper respiratory tract infection, and acute bronchitis. A reproducible, simple, and reliable rapid resolution liquid chromatographic (RRLC) method has been developed to analyze extracts of products formulated containing E. angustifolia, E. purpurea, Flos Lonicerae, Radix Scutellariae and Fructus Forsythiae simultaneously in one run in less than 6 minutes. The method uses a C18-HST column, a mobile phase consisting of 0.1% aqueous phosphoric acid solution and acetonitrile, and UV detection at 327 nm and 229 nm. A stability test was performed that revealed that chlorogenic acid is more stable in acidic pH, and hence it is best to keep the extract of E. augustifolia, E. purpurea, Flos Lonicerae, Radix Scutellariae and Fructus Forsythiae in mild acidic conditions at approximately pH 5.     

Numerical Modeling of Salt Transport and Precipitation in Non-Isothermal Partially Saturated Porous Media Considering Kinetics of Salt Phase Changes

Water and salts strongly influence the durability of porous materials. One of the most adverse phenomena which is related to the salt and moisture presence in the pore system of building materials is salt crystallization. The process is associated with the supersaturation ratio. The salt phase change kinetics is taken into account during the modeling of coupled moisture, salt, and heat transport. To solve the set of governing, differential equations the finite element and the finite difference methods are used. Three different rate laws are assumed in modeling the salt phase change. The drying, cooling, and warming of the cement mortar sample, during which the salt phase change occurs, have been simulated using the developed software. The changes of salt concentration in the pore solution and the amount of precipitated salt due to variation of boundary conditions are presented and discussed. The results obtained in the numerical simulation assuming the first, second, and fourth order rate low indicate that the higher order of the rate law the longer time delay between the change of boundary conditions and the salt precipitation. Such an analysis might be very useful during the determination of the material parameters by solving the inverse problem.     

What physical phenomena can be neglected when modelling concrete at high temperature? A comparative study. Part 1: Physical phenomena and mathematical model

The paper deals with modelling of hygro-thermal performance and thermo-chemical degradation of concrete exposed to high temperature. Several possible simplifications in modelling of heat and mass transport phenomena in heated concrete are considered and their effect on the results of numerical simulations is analyzed.A mathematical model of concrete at high temperature, already extensively validated with respect to experiments, is used as the reference model. It is based on mechanics of multiphase porous media and considers all important couplings and material nonlinearities, as well as different properties of water above the critical point of water, i.e. 647.3 K (374.15 °C).In this part of the paper, first physical phenomena, as well as heat and mass flux and sources in a concrete element are studied, both during slow and fast heating process, to examine the relative importance of different flux components. Then, the mathematical model of concrete at high temperature, developed by Authors in the last 10 years, is briefly presented and for the first time all the constitutive relationships of the model are summarized and discussed in detail. Finally, the method of numerical solution of the model equations is thoroughly presented.In the companion paper (part II) a brief literature review of the existing mathematical models of concrete at high temperature and a summary of their main features and physical assumptions will be presented. Then, extensive numerical studies will be performed with several simplified models, neglecting chosen physical phenomenon or flux components, to evaluate the difference between the results obtained with the simplified models and with the reference model. The study will concern hygric, thermal and degradation performance of 1-D and 2-D axisymmetric concrete elements during fast and slow heating. The analysis will allow us to indicate which simplifications in modeling of concrete at high temperature are practically and physically possible, without generating excessive errors with respect to the full reference model.     

VoteDock: Consensus docking method for prediction of protein–ligand interactions

Molecular recognition plays a fundamental role in all biological processes, and that is why great efforts have been made to understand and predict protein–ligand interactions. Finding a molecule that can potentially bind to a target protein is particularly essential in drug discovery and still remains an expensive and time‐consuming task. In silico, tools are frequently used to screen molecular libraries to identify new lead compounds, and if protein structure is known, various protein–ligand docking programs can be used. The aim of docking procedure is to predict correct poses of ligand in the binding site of the protein as well as to score them according to the strength of interaction in a reasonable time frame. The purpose of our studies was to present the novel consensus approach to predict both protein–ligand complex structure and its corresponding binding affinity. Our method used as the input the results from seven docking programs (Surflex, LigandFit, Glide, GOLD, FlexX, eHiTS, and AutoDock) that are widely used for docking of ligands. We evaluated it on the extensive benchmark dataset of 1300 protein–ligands pairs from refined PDBbind database for which the structural and affinity data was available. We compared independently its ability of proper scoring and posing to the previously proposed methods. In most cases, our method is able to dock properly approximately 20% of pairs more than docking methods on average, and over 10% of pairs more than the best single program. The RMSD value of the predicted complex conformation versus its native one is reduced by a factor of 0.5 Å. Finally, we were able to increase the Pearson correlation of the predicted binding affinity in comparison with the experimental value up to 0.5. © 2010 Wiley Periodicals, Inc. J Comput Chem 32: 568–581, 2011