Convergence Analysis for a Finite Element Approximation of a Steady Model for Electrorheological Fluids

In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element approximation of the velocity and of the pressure, in a suitable functional setting

Phosphinosilylenes as a novel ligand system for heterobimetallic complexes

A dihydrophosphinosilylene iron complex [LSi{Fe(CO)(4)}PH2] has been prepared and utilized in the synthesis of novel heterobimetallic complexes. The phosphine moiety in this phosphinosilylene complex allows coordination towards tungsten leading to the iron-tungsten heterobimetallic complex [LSi{Fe(CO)(4)}PH2{W(CO)(5)}]. In contrast, the reaction of [LSi{Fe(CO)(4)}PH2] with ethylenebis(triphenylphosphine)platinum(0) results in the formation of the iron-platinum heterobimetallic complex [LSi{Fe(CO)(4)}PH{PtH(PPh3)(2)}] via oxidative addition

Facile rotation around a silicon-phosphorus double bond enabled through coordination to tungsten

Correction: Citation missing unintentionally. Missing intention is included in the additional file. To cite the Correction refer to DOI:10.1039/c5cc04247

A new method of quantization of classical solutions

Using stochastic quantization method we derive equations for correlators of quantum fluctuations around the classical solution in the massless phi^4 theory. The obtained equations are then solved in the lowest orders of perturbation theory, and the first correction to the free propagator of a quantum fluctuation is calculated.Comment: 8 page

Finite element approximation of the p(⋅)p(\cdot)-Laplacian

We study a~priori estimates for the Dirichlet problem of the $p(\cdot)$-Laplacian, $$-\mathrm{div}(|\nabla v|^{p(\cdot)-2} \nabla v) = f.$$ We show that the gradients of the finite element approximation with zero boundary data converges with rate $O(h^\alpha)$ if the exponent $p$ is $\alpha$-H\"{o}lder continuous. The error of the gradients is measured in the so-called quasi-norm, i.e. we measure the $L^2$-error of $|\nabla v|^{\frac{p-2}{2}} \nabla v$

Salvaging Affymetrix probes after probe-level re-annotation

Background: Affymetrix GeneChips can be re-annotated at the probe-level by breaking up the original probe-sets and recomposing new probe-sets based on up-to-date genomic knowledge, such as available in Entrez Gene. This results in custom Chip Description Files (CDF). Using these custom CDFs improves the quality of the data and thus the results of related gene expression studies. However, 44-71% of the probes on a GeneChip are lost in this re-annotation process. Although generally aimed at less known genes, losing these probes obviously means a substantial loss of expensive experiment data. Biologists are therefore very reluctant to adopt this approach. Findings: We aimed to re-introduce the non-affected Affymetrix probe-sets after these re-annotation procedures. For this, we developed an algorithm (CDF-Merger) and applied it to standard Affymetrix CDFs and custom Brainarray CDFs to obtain Hybrid CDFs. Thus, salvaging lost Affymetrix probes with our CDF-Merger restored probe content up to 94%. Because the salvaged probes (up to 54% of the probe content on the arrays) represent less-reliable probe-sets, we made the origin of all probe-set definitions traceable, so biologists can choose at any time in their analyses, which subset of probe-sets they want to use. Conclusion: The availability of up-to-date Hybrid CDFs plus R environment allows for easy implementation of our approach

Distribution of major anions and trace elements in the unsaturated zone at Franklin Lake Playa, California, USA

The composition of surficial salts formed near dry and drying saline lakes are partly the product of processes active in the unsaturated zone between the ground surface and the water table. These processes were investigated by determining the abundance of water-extractable solutes in sediment from the ground surface to the water table (~2.8 m) beneath Franklin Lake playa, California. Accumulation of solutes in the sediment is attributed to evaporation of aqueous solutions transported upward from the water table through the capillary fringe to an evaporation font that is currently 20-30 cm below the ground surface. Salts in the sediment from 0 to 20 cm depth are depleted in chloride and enriched in carbonate relative to deeper samples. Chloride depletion is most likely a product of selective dissolution by vertical recharge. The entire unsaturated zone contains greater amounts of carbonate than expected for evaporation of ground water and is best explained by preferential dissolution of more soluble salts in recharging precipitation but may also reflect the assimilation of CO2 as carbonate minerals precipitate. Variations in the concentrations of arsenic, molybdenum, tungsten, and uranium in the water-soluble fraction of the sediment are complex and suggest unique geochemical controls on the abundance of each element. The distribution of these trace element abundances indicates the arsenic is the element most likely to accumulate in near-surface salts

On the evaluation of some three-body variational integrals

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.Comment: 12 pages, 1 figure (PS) and 3 tables. Old figures 2 and 3 replaced by Tables I and III. A further table added. Paper enlarged giving some tips on the convergence of quadrature

SigWinR; the SigWin-detector updated and ported to R

<p>Abstract</p> <p>Background</p> <p>Our SigWin-detector discovers significantly enriched windows of (genomic) elements in any sequence of values (genes or other genomic elements in a DNA sequence) in a fast and reproducible way. However, since it is grid based, only (life) scientists with access to the grid can use this tool. Therefore and on request, we have developed the SigWinR package which makes the SigWin-detector available to a much wider audience. At the same time, we have introduced several improvements to its algorithm as well as its functionality, based on the feedback of SigWin-detector end users.</p> <p>Findings</p> <p>To allow usage of the SigWin-detector on a desktop computer, we have rewritten it as a package for R: SigWinR. R is a free and widely used multi platform software environment for statistical computing and graphics. The package can be installed and used on all platforms for which R is available. The improvements involve: a visualization of the input-sequence values supporting the interpretation of Ridgeograms; a visualization allowing for an easy interpretation of enriched or depleted regions in the sequence using windows of pre-defined size; an option that allows the analysis of circular sequences, which results in rectangular Ridgeograms; an application to identify regions of co-altered gene expression (ROCAGEs) with a real-life biological use-case; adaptation of the algorithm to allow analysis of non-regularly sampled data using a constant window size in physical space without resampling the data. To achieve this, support for analysis of windows with an even number of elements was added.</p> <p>Conclusion</p> <p>By porting the SigWin-detector as an R package, SigWinR, improving its algorithm and functionality combined with adequate performance, we have made SigWin-detector more useful as well as more easily accessible to scientists without a grid infrastructure.</p