Mappings of finite distortion: Removable singularities

We derive sufficiently sharp local dimension-free estimates for volumes of sublevel sets of analytic functions in the unit ball of ℂ ⁿ The research was partially supported by the United States-Israel Binational Science Foundation.     

Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.     

Structure and reactivity of the polarised liquid–liquid interface: what we know and what we do not

Charge transfer phenomena at the interface between two immiscible electrolyte solutions (ITIES) are electrochemical reactions taking place in soft media. Owing to their liquid nature, the ITIES shows a large panel of electrochemical reactions including electron transfer reactions, ion transfer reactions, coupled electron–ion transfer reactions or biomimetic redox reactions. Nevertheless, the mechanisms by which these reactions proceed are yet to be fully understood. The goal of this short review is to summarise the work accomplished over the past decades towards the elucidation of the structure and reactivity at the ITIES, highlighting the main questions still to be answered.     

Size-dependent structural evolution and chemical reactivity of gold clusters.

Ground-state structures and other experimentally relevant isomers of Au(15) (-) to Au(24) (-) clusters are determined through joint first-principles density functional theory and photoelectron spectroscopy measurements. Subsequent calculations of molecular O(2) adsorption to the optimal cluster structures reveal a size-dependent reactivity pattern that agrees well with earlier experiments. A detailed analysis of the underlying electronic structure shows that the chemical reactivity of the gold cluster anions can be elucidated in terms of a partial-jellium picture, where delocalized electrons occupying electronic shells move over the ionic skeleton, whose geometric structure is strongly influenced by the directional bonding associated with the highly localized "d-band" electrons.     

Effect of pH on growth and fatty acid composition ofLactobacillus büchneri andLactobacillus fermentum

Growth and fatty acid composition of two lactobacilli,Lactobacillus büchneri andLactobacillus fermentum, were studied at different pHs of the media in a small-scale fermenter with particular interest in lactobacillic acid production of the cultures. Generally, the total fatty acid content of the bacterial cells increased with increasing culture age. The production of lactobacillic acid was affected in the two lactobacilli by both culture age and pH of the media, but in a very different manner. In L.büchneri cultures, the relative proportion of lactobacillic acid was highest when the pH was lowest (pH 4.5), whereas inL. fermentum cultures, the proportion of lactobacillic acid was highest at pH 7.0. The pH of the medium affected not only the relative proportion of lactobacillic acid, but also biomass production and total fatty acid accumulation of the cultures. Thus, by controlling the pH of the cultures, the volumetric yield of lactobacillic acid could be improved considerably compared to cultures without pH control.     

Multivariate Gaussian criteria in SMAA

We consider stochastic multicriteria decision-making problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions. In many real-life problems the uncertainties of criteria measurements may be dependent. However, it is often difficult to quantify these dependencies. Also, most of the existing methods are unable to handle such dependency information.In this paper, we develop a method for handling dependent uncertainties in stochastic multicriteria group decision-making problems. We measure the criteria, their uncertainties and dependencies using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. Based on the simulation results, we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies. We then use the SMAA-2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions. We demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated European electricity market.     

Molecular dynamics simulations of conserved Hox protein hexapeptides. I. Folding behavior in water solution

Molecular dynamics simulations of hexapeptides TFDWMK and LFPWMR; the highly conserved regions of Hox proteins Hox B1 and Hox B8, respectively, are carried out starting from extended structures to investigate their conformational space in water solution. In addition, we have studied TADWMK and TADAMK, where the aromatic residues Phenylalanine and Tryptophan were successively substituted for Alanine to investigate effects from the presence/absence of aromatic amino acids and interactions between them to folding behavior. The backbone of the hexapeptides in all simulations folds to a similar conformation found in experimental studies in solution. Intramolecular, hydrophobically driven interactions between the aromatic residues and internal hydrogen bonds are found to stabilize the conformations.