Kriterien für das Zerfallen von Gruppen über Subnormalteilern

Ohne Zusammenfassung     

Identifiability of chemical reaction networks

We consider the dynamics of chemical reaction networks under the assumption of mass-action kinetics. We show that there exist reaction networks for which the reaction rate constants are not uniquely identifiable, even if we are given complete information on the dynamics of concentrations for all chemical species of . Also, we show that there exist reaction networks such that their dynamics are identical under appropriate choices of reaction rate constants, and present theorems that characterize the properties of , , that make this possible. We use these facts to show how we can determine dynamical properties of some chemical networks by analyzing other chemical networks.     

Spectroscopic investigations and crystal structure from synchrotron powder data of the inclusion complex of beta-cyclodextrin with atenolol

Inclusion complexes of atenolol with beta-cyclodextrin (beta-CD) in aqueous solution have been investigated with (1)H NMR and UV-vis spectroscopy. The stoichiometry of this inclusion complex was established to be equimolar (1:1) and its stability constant was determined by UV-vis spectroscopy. The crystal structure of the beta-CD-atenolol (1:1) inclusion compound has been solved from synchrotron powder diffraction data using direct-space search techniques. The crystal structure model and (1)H NMR data are in good agreement and, with support of Hyperchem MM+ molecular dynamics results, suggest which protons are likely to be involved in the inclusion process that leads to the supramolecular architecture of this guest-host complex.     

Simultaneous determination of bisphenol A, triclosan, and tetrabromobisphenol A in human serum using solid-phase extraction and gas chromatography-electron capture negative-ionization mass spectrometry

This study aimed at optimizing and validating a sensitive method for simultaneous determination of bisphenol A (BPA), triclosan (TCS), and tetrabromobisphenol A (TBBPA) in human serum using solid-phase extraction (SPE) and gas chromatography coupled to electron-capture negative-ionization mass spectrometry (GC-ECNI/MS). Sample preparation involved denaturation of serum proteins with formic acid followed by SPE on an Oasis HLB cartridge. Fractionation was performed on Florisil from which the phenolic compounds were eluted with methanol-dichloromethane (DCM) (5:1, v/v). The phenolic fraction was further derivatized with pentafluoropropionic acid anhydride (30 min at 70 degrees C). Further liquid-liquid partitioning using hexane-DCM (4:1, v/v) and K(2)CO(3) 3% aqueous solution was used to eliminate excess reagent and acidic by-products formed during derivatization. The cleaned extract was injected into a GC-ECNI/MS system operated in selected ion monitoring mode. For thorough method validation, each step of the procedure was rigorously optimized. The method limits of quantitation for BPA, TCS, and TBBPA were 0.28 ng mL(-1), 0.09 ng mL(-1) and 0.05 ng mL(-1), respectively. Furthermore, the method was applied to 21 Belgian human serum samples. The median concentrations obtained for BPA (0.71 ng mL(-1)) and TCS (0.52 ng mL(-1)) in Belgian human serum samples were similar to previously reported data for human fluids. Slightly higher levels of TBBPA (0.08 ng mL(-1)) were found in Belgium samples compared to Norwegian serum.     

Thermal behavior of Co<Subscript>x</Subscript>Fe<Subscript>3−x</Subscript>O<Subscript>4</Subscript>/SiO<Subscript>2</Subscript> nanocomposites obtained by a modified sol–gel method

The thermal behavior of Co_xFe_3?xO₄/SiO₂ nanocomposites obtained by direct synthesis starting from nonahydrate ferric nitrate and hexahydrate cobalt nitrate in different ratios with and without the addition of 1,4-butanediol was studied. For the synthesis of Co_xFe_3?xO₄ (x = 0.5–2.5) dispersed in the silica matrix a wide Co/Fe molar ratio was used. The decomposition processes, formation of crystalline phases, gases evolvement and mass changes during gels annealing at different temperatures were assessed by thermal analysis. The absence of succinate precursor and a low mass loss were observed in the case of the gel obtained in the absence of 1,4-butanediol. In case of gels obtained using a stoichiometric ratio of Co/Fe, no clear delimitation between Co and Fe succinates was observed, while for samples with a Fe or Co excess, the formation of the two succinates was observed. The evolution of the crystalline phase after annealing (673, 973 and 1273 K) investigated by X-ray diffraction analysis and Fourier transformed infrared spectrometry revealed that in samples with Fe excess, stoichiometric Fe/Co ratio or low Co excess, the cobalt ferrite (CoFe₂O₄) was obtained as a single phase, while in samples with higher cobalt excess, olivine (Co₂SiO₄) as a main phase, cobalt oxide and CoFe₂O₄ as secondary phases were obtained after annealing at 1273 K. The SEM images confirmed the nanoparticles embedding in the silica matrix, while the TEM and X-ray diffraction data showed that the obtained nanoparticles’ size was below 10 nm in most samples.     

Bernstein-type operators on a triangle with all curved sides

We construct and analyze Bernstein-type operators on triangles with curved sides, their product and Boolean sum. We study the interpolation properties and approximation accuracy. Using the modulus of continuity we also study the remainders of the corresponding approximation formulas. Finally, there are given some particular cases and numerical examples.     

A comparison between iterative methods by using the basins of attraction

There exists a real competition between authors to construct improved iterative methods for solving nonlinear equations. In this paper, by using computer experiment, we study the basins of attraction for some of the iterative methods for solving the equation P(z) = 0, where P:C→C is a complex coefficients polynomial, and this allows us to compare their performances (the area of convergence and theirs speed). The beauty fractal pictures generated by these methods are presented too.     

On Essential Self-Adjointness for Magnetic Schrödinger and Pauli Operators on the Unit Disc in $${\mathbb {R}^2}$$

We study the question of magnetic confinement of quantum particles on the unit disk \({\mathbb {D}}\) in \({\mathbb {R}^2}\) , i.e. we wish to achieve confinement solely by means of the growth of the magnetic field \({B(\vec x)}\) near the boundary of the disk. In the spinless case, we show that \({B(\vec x)\ge \frac{\sqrt 3}{2}\cdot\frac{1}{(1-r)^2}-\frac{1}{\sqrt 3}\frac{1}{(1-r)^2\ln \frac{1}{1-r}}}\) , for \({|\vec x|}\) close to 1, insures the confinement provided we assume that the non-radially symmetric part of the magnetic field is not very singular near the boundary. Both constants \({\frac{\sqrt 3}{2}}\) and \({-\frac{1}{\sqrt 3}}\) are optimal. This answers, in this context, an open question from Colin de Verdière and Truc (Ann Inst Fourier 2011, Preprint, arXiv:0903.0803v3). We also derive growth conditions for radially symmetric magnetic fields which lead to confinement of spin 1/2 particles.     

Counting chemical compositions using Ehrhart quasi-polynomials

To count the number of chemical compositions of a particular mass, we consider an alphabet ${\mathop{\bf a}}$ with a mass function which assigns a mass to each letter in ${\mathop{\bf a}}$ . We then compute the mass of a word (an ordered sequence of letters) by adding the masses of the constituent letters. Our main interest is to count the number of words that have a particular mass, where we ignore the order of the letters within the word. We show first that counting the number of words of a given mass has a geometric interpretation, whose solutions are called Ehrhart quasi-polynomials, a class of functions defined on integers. These special functions are “periodic” in the sense that they use the same polynomial every λ steps. In addition to discovering the connection between counting compositions and Ehrhart quasi-polynomials, we also find number theoretic results that greatly reduce the number of candidates for the period, λ. Finally, we illustrate the usefulness of these results and the use of a software library named barvinok (by Verdoolaege et?al.) by applying them to eight different classes of chemical compositions, including organic molecules, peptides, DNA, and RNA.     

Analysis of a two-dimensional nonsmooth Poincaré-like map

A two-dimensional nonsmooth Poincaré-like map is investigated in the present work. The map generalizes in some sense the so-called Nordmark map, which is related to one-dimensional impacting oscillators near grazing points, and constitutes an intuitive basis for dynamics related to degenerate grazing in such oscillators.