The index of an Eisenstein ideal and multiplicity one

Mathematische Zeitschrift - Mazur’s fundamental work on the Eisenstein ideal of prime level has a variety of arithmetic applications. In this article, we generalize some of his work to...     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Determination of docetaxel in rat plasma and its application in the comparative pharmacokinetics of Taxotere and SID530, a novel docetaxel formulation with hydroxypropyl‐β‐cyclodextrin

In this study, a sensitive, simple and reliable method for the quantification of docetaxel in rat plasma was developed and validated using liquid chromatography–tandem mass spectrometry (LC‐MS/MS). The plasma samples were prepared by protein precipitation, and paclitaxel was used as an internal standard (IS). Chromatographic separation was achieved using a Gemini C₁₈ column (2.0 × 150 mm, 5 µm) with a mobile phase consisting of 0.1% formic acid–acetonitrile (30:70, v/v). The precursor–product ion pairs used for multiple reaction monitoring were m/z 808.5 → 527.5 (docetaxel) and m/z 854.2 → 286.5 (IS, paclitaxel). A calibration curve for docetaxel was constructed over the range 1–1000 ng/mL. The developed method was specific, precise and accurate, and no matrix effect was observed. The validated method was applied in a comparative pharmacokinetic study in which two docetaxel formulations, SID530, a new parenteral formulation of docetaxel with hydroxypropyl‐β‐cyclodextrin (HP‐β‐CD), and Taxotere, were administered to rats at a dose of 5 mg/kg. For SID530 and Taxotere, the mean C₀ values were 1494 and 1818 ng/mL, respectively, and the AUC_last values were 837 and 755 h ng/mL, respectively. These two formulations did not show any statistical differences with regard to the pharmacokinetic parameters, thus establishing that the SID530 and Taxotere products are pharmacokinetically comparable in male rats. Copyright © 2012 John Wiley & Sons, Ltd.     

Phytohormone Supplementation Significantly Increases Growth of Chlamydomonas reinhardtii Cultivated for Biodiesel Production

Cultivation is the most expensive step in the production of biodiesel from microalgae, and substantial research has been devoted to developing more cost-effective cultivation methods. Plant hormones (phytohormones) are chemical messengers that regulate various aspects of growth and development and are typically active at very low concentrations. In this study, we investigated the effect of different phytohormones on microalgal growth and biodiesel production in Chlamydomonas reinhardtii and their potential to lower the overall cost of commercial biofuel production. The results indicated that all five of the tested phytohormones (indole-3-acetic acid, gibberellic acid, kinetin, 1-triacontanol, and abscisic acid) promoted microalgal growth. In particular, hormone treatment increased biomass production by 54 to 69 % relative to the control growth medium (Tris–acetate–phosphate, TAP). Phytohormone treatments also affected microalgal cell morphology but had no effect on the yields of fatty acid methyl esters (FAMEs) as a percent of biomass. We also tested the effect of these phytohormones on microalgal growth in nitrogen-limited media by supplementation in the early stationary phase. Maximum cell densities after addition of phytohormones were higher than in TAP medium, even when the nitrogen source was reduced to 40 % of that in TAP medium. Taken together, our results indicate that phytohormones significantly increased microalgal growth, particularly in nitrogen-limited media, and have potential for use in the development of efficient microalgal cultivation for biofuel production.     

Issue Information

An integrated finite element method (FEM) is proposed to simulate incompressible two‐phase flows with surface tension effects, and three different surface tension models are applied to the FEM to investigate spurious currents and temporal stability. A Q2Q1 element is adopted to solve the continuity and Navier–Stokes equations and a Q2‐iso‐Q1 to solve the level set equation. The integrated FEM solves pressure and velocity simultaneously in a strongly coupled manner; the level set function is reinitialized by adopting a direct approach using interfacial geometry information instead of solving a conventional hyperbolic‐type equation. In addition, a consistent continuum surface force (consistent CSF) model is utilized by employing the same basis function for both surface tension and pressure variables to damp out spurious currents and to estimate the accurate pressure distribution. The model is further represented as a semi‐implicit manner to improve temporal stability with an increased time step. In order to verify the accuracy and robustness of the code, the present method is applied to a few benchmark problems of the static bubble and rising bubble with large density and viscosity ratios. The Q2Q1‐integrated FEM coupled with the semi‐implicit consistent CSF demonstrates the significantly reduced spurious currents and improved temporal stability. The numerical results are in good qualitative and quantitative agreements with those of the existing studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Activation of α-Fe2O3 for Photoelectrochemical Water Splitting Strongly Enhanced by Low Temperature Annealing in Low Oxygen Containing Ambient

Photoelectrochemical (PEC) water splitting is a promising method for the conversion of solar energy into chemical energy stored in the form of hydrogen. Nanostructured hematite (α-Fe₂O₃) is one of the most attractive materials for a highly efficient charge carrier generation and collection due to its large specific surface area and the short minority carrier diffusion length. In the present work, the PEC water splitting performance of nanostructured α-Fe₂O₃ is investigated which was prepared by anodization followed by annealing in a low oxygen ambient (0.03 % O₂ in Ar). It was found that low oxygen annealing can activate a significant PEC response of α-Fe₂O₃ even at a low temperature of 400 °C and provide an excellent PEC performance compared with classic air annealing. The photocurrent of the α-Fe₂O₃ annealed in the low oxygen at 1.5 V vs. RHE results as 0.5 mA cm⁻², being 20 times higher than that of annealing in air. The obtained results show that the α-Fe₂O₃ annealed in low oxygen contains beneficial defects and promotes the transport of holes; it can be attributed to the improvement of conductivity due to the introduction of suitable oxygen vacancies in the α-Fe₂O₃. Additionally, we demonstrate the photocurrent of α-Fe₂O₃ annealed in low oxygen ambient can be further enhanced by Zn-Co LDH, which is a co-catalyst of oxygen evolution reaction. This indicates low oxygen annealing generates a promising method to obtain an excellent PEC water splitting performance from α-Fe₂O₃ photoanodes.     

Hydrogen production and photocatalytic activity of g-C3N4/Co-MOF (ZIF-67) nanocomposite under visible light irradiation

Herein, cobalt (Co)-based metal–organic zeolitic imidazole frameworks (ZIF-67) coupled with g-C₃N₄ nanosheets synthesized via a simple microwave irradiation method. SEM, TEM and HR-TEM results showed that ZIF-67 were uniformly dispersed on g-C₃N₄ surfaces and had a rhombic dodecahedron shape. The photocatalytic properties of g-C₃N₄/ZIF-67 nanocomposite were evaluated by photocatalytic dye degradation of crystal violet (CV), 4-chlorophenol (4-CP) and photocatalytic hydrogen (H₂) production. In presence of visible light illumination, the photocatalytic dye results showed that 95% CV degradation and 53% 4-CP degradation within 80 min. The H₂ production of the g-C₃N₄/ZIF-67 composite was 2084 μmol g⁻¹, which is 3.84 folds greater than that of bare g-C₃N₄ (541 μmol g⁻¹).     

Generation of single-crystalline domain in nano-scale silicon pillars by near-field short pulsed laser

We observe laser-induced grain morphology change in silicon nanopillars under a transmission electron microscopy (TEM) environment. We couple the TEM with a near-field scanning optical microscopy pulsed laser processing system. This novel combination enables immediate scrutiny on the grain morphologies that the pulsed laser irradiation produces. We find unusual transformation of the tip of the amorphous or polycrystalline silicon pillar into a single crystalline domain via melt-mediated crystallization. On the basis of the three-dimensional finite difference simulation result and the dark field TEM data, we propose that the creation of the distinct single crystalline tip originates from the dominant grain growth initiated at the apex of the non-planar liquid–solid interface. Our microscopic observation provides a fundamental basis for laser-induced conversion of amorphous nanostructures into coarse-grained crystals.