Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in (0, π). Two sequences of circle patterns are employed to approximate a given conformal map g and its first derivative. For the domain of g we use embedded circle patterns where all circles have the same radius decreasing to 0 and with uniformly bounded intersection angles. The image circle pattern has the same combinatorics and intersection angles and is determined from boundary conditions (radii or angles) according to the values of g′ (|g′| or arg g′). For quasicrystallic circle patterns the convergence result is strengthened to C ^∞-convergence on compact subsets.      

Development of a Simple,Rapid, and Robust Isocratic Liquid Chromatographic Method for the Determination of Pyrimethamine and its Synthetic Impurities in Bulk Drugs and Pharmaceutical Formulations

Pyrimethamine is an important antiparasitic drug in the treatment of malaria and toxoplasmosis and is often used in combination with either sulfadoxine, sulfalene, or sulfadiazine. Determining the content of pyrimethamine and investigating the related substances is currently possible applying either a compendial monograph utilizing thin layer chromatography as well as liquid chromatographic methods used by the respective manufacturers. To provide a simple method which is capable of determining the content of pyrimethamine and of resolving four of its potential synthetic impurities a very simple, cheap, precise, and accurate isocratic RP-HPLC method was developed. All analytes can be separated within a total runtime of 30 min and the method was linear within the concentration ranges of 0.12–0.740, 0.104–0.621, 0.120–0.710, 2.0–11.8, and 1.01–5.80 µg mL^?1 for pyrimethamine, impurity A, impurity B, impurity C, and impurity D, respectively. These substances were separated by employing a Eurospher-II C₁₈H column (250 × 4.6 mm, 5 µm particle size), a mobile phase being a mixture of a 0.05 M KH₂PO₄ buffer solution (pH 2.6) and methanol in the ratio 40:60 (v/v). The analysis was carried out at 30 °C, applying a flow rate of 1.2 mL min^?1, and a detection wavelength of λ = 215 nm. The coefficients of determinations (R ²) for the five analytes were greater than 0.994 for pyrimethamine and all impurities. Results of recovery studies were within the range of 89.1–105.1% for all substances. In all tested genuine batches of pyrimethamine raw material impurities within the specified limits were present which is concurrent with results obtained from using the present manufacturer’s method.     

Electrochemical Assay to Quantify the Hydroxyl Radical Scavenging Activity of Medicinal Plant Extracts

A new electrochemical assay has been developed which is based on quantifying the attack of OH^. radicals on a self‐assembled thiol monolayer on electrodes in the presence and absence of antioxidants. The OH^. radicals were produced in Fenton solutions. The radical scavengers diminish the concentration of the OH^. radicals in the Fenton solution, and the extent of thiol layer destruction is monitored with the help of a redox probe in solution, the signal of which is only generated at SAM‐free electrode surface. The results of the electrochemical assay were compared with those of the standard DPPH^. assay. In case of each plant extract, an excellent linear correlation was observed between the radical scavenging activity and the concentration of plant extracts; however, the scavenging properties of different plants strongly differ in the electrochemical and the DPPH^. assay. Since the proposed new method probes the reactivity of radical scavengers towards OH^., one of the most important reactive oxygen radicals in tissues, it is supposed to provide much more relevant information than the DPPH^. or other assays.     

[3+2] Cycloadditions of Metallo Nitrile Ylides and Metallo Nitrile Imines with Metal Carbonyl,Thiocarbonyl, and Isocyanide Complexes: Heterodimetallic Systems with Bridging Heterocycles [1]

The reactions of [Re(CO)₆]⁺, [FeCp(CO)₂CS]⁺ and [FeCp(CNPh)₃]⁺ with the metallo nitrile ylides [M^–{C⁺=N–C^–(H)CO₂Et}(CO)₅]^– (M = Cr, W) and the chromio nitrile imine [Cr^–{C⁺=N–N^–H}(CO)₅]^– (generated by mono‐α‐deprotonation of the parent isocyanide complexes) to give neutral 5‐metallated 1,3‐oxazolin‐ ( 1 ), 1,3‐thiazolin‐ ( 2 ), imidazolin‐ ( 3 , 4 ), 1,3,4‐oxdiazolin‐ ( 5 ), 1,3,4‐thiadiazolin‐ ( 6 ) and 1,3,4‐triazolin‐2‐ylidene ( 8 ) chromium and tungsten complexes represent the first all‐organometallic versions of Huisgen’s 1,3‐dipolar cycloadditions. The formation of 6 and 8 is accompanied by partial decomposition to (OC)₅Cr–C≡N–FeCpL₂ {L = CO ( 7 ), CNPh ( 9 )}. The structures of 4a and 5 have been characterized by X‐ray diffraction.     

Synthesis and crystal structure of CuZrTiO5—A new crystal structure type

A new compound, CuZrTiO₅, was synthesized as strongly pleochroic green crystals from the oxides between 995 and 1010 °C, 1 atm. Its crystal structure was determined by single crystal XRD, resulting in R (F²>2σ(F²))=0.032 and wR (all data)=0.079). CuZrTiO₅ is orthorhombic, space group P2₁2₁2₁, a=3.5871(3) Å, b=6.6968(4) Å, c=14.6679(9) Å, V=352.35(4) Å³, Z=4. The structure is topologically similar to In₂TiO₅ but differs in space group and cation coordination. CuZrTiO₅ has relatively regular TiO₆ polyhedra, but coordination is 7+1 for Zr, and 4+2 for Cu due to the Jahn-Teller effect. Ordering of the long Cu-O bonds causes reduction in symmetry relative to In₂TiO₅. Layers of Cu alternate with Ti+Zr on (001), giving rise to a distinct cleavage. Bond valence sums on Ti and Zr are far from ideal, which appears due to the limited ability of this structural topology to avoid close next-nearest neighbour distances.     

Standardization in allergen determination

An overview is given of sensitization and allergic reaction on food, along with minimal eliciting doses for selected allergens (milk, egg, peanut), followed by the legislative situation in the European Community, the USA, Canada, Australia/New Zealand and Japan. The main focus of the paper discusses methods for food allergen determination (chromatography, DNA-based, antibody-based) and their limitations. Special emphasis is given on antibody-based systems, which are at the moment the most advanced and validated methods available. Examples are given of the current status of standardization for egg, milk, nuts, prolamins, glutelins and for clinical validated reference samples from the EU project EuroPrevall. Recommendations for ongoing activities are also included.     

Computational homogenization and parameter-identification for heterogeneous inelastic materials

The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE² method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem is minimized using gradient-based optimization algorithms, where the gradient information is derived analytically within the discretized scheme. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A 43Ca and 13C NMR study of the chemical interaction between poly(ethylene-vinyl acetate) and white cement during hydration

⁴³Ca and ¹³C NMR methods were used to study the chemical interaction of poly(ethylene–vinyl acetate) (PEVAc) admixture in commercial-grade white cement. From ⁴³Ca NMR it is shown both that PEVAc induces modest changes in the hydrated cement structure, and that hydrated commercial cement is significantly more complex than models that have been used for its structure in past work. The ¹³C NMR results show that the PEVAc hydrolysis occurs early in the cement hydration acceleration period, with a rate well-fit by an exponential decay using a time constant of 6±1 days.