Billiards and Teichmüller curves on Hilbert modular surfaces

This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

     

Regular polytopes from twisted Coxeter groups

Dedicated to Professor L. Danzer on the occasion of his 60th birthday     

Facets with fewest vertices

Forv>d≧3, letm(v, d) be the smallest numberm, such that every convexd-polytope withv vertices has a facet with at mostm vertices. In this paper, bounds form(v, d) are found; in particular, for fixedd≧3, $$\frac{{r - 1}}{r} \leqslant \mathop {\lim \inf }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \mathop {\lim \sup }\limits_{\upsilon \to \infty } \frac{{m(\upsilon ,d)}}{\upsilon } \leqslant \frac{{d - 3}}{{d - 2}}$$ , wherer=[1/3(d+1)].     

Amenability,Poincaré series and quasiconformal maps

Summary Any coveringYX of a hyperbolic Riemann surfaceX of finite area determines an inclusion of Teichmüller spaces Teich(X)Teich(Y). We show this map is an isometry for the Teichmüller metric if the covering isamenable, and contracting otherwise. In particular, we establish <1 for classical Poincaré series (Kra's Theta conjecture).The appendix develops the theory of geometric limits of quadratic differentials, used in this paper and a sequel.Research partially supported by an NSF Postdoctoral Fellowship     

Development and validation of a glass-silicon microdroplet-based system to measure sulfite concentrations in beverages

Sulfite is often added to beverages as an antioxidant and antimicrobial agent. In fermented beverages, sulfite is also naturally produced by yeast cells. However, sulfite causes adverse health effects in asthmatic patients and accurate measurement of the sulfite concentration is therefore very important. Current sulfite analysis methods are time- and reagent-consuming and often require costly equipment. Here, we present a system allowing sensitive, ultralow-volume sulfite measurements based on a reusable glass-silicon microdroplet platform on which microdroplet generation, addition of enzymes through chemical-induced emulsion destabilization and pillar-induced droplet merging, emulsion restabilization, droplet incubation, and fluorescence measurements are integrated. In a first step, we developed and verified a fluorescence-based enzymatic assay for sulfite by measuring its analytical performance (LOD, LOQ, the dynamic working range, and the influence of salts, colorant, and sugars) and comparing fluorescent microplate readouts of fermentation samples with standard colorimetric measurements using the 5,5′-dithiobis-(2-nitrobenzoic acid) assay of the standard Gallery Plus Beermaster analysis platform. Next, samples were analyzed on the microdroplet platform, which also showed good correlation with the standard colorimetric analysis. Although the presented platform does not allow stable reinjection of droplets due to the presence of a tight array of micropillars at the fluidics entrances to prevent channel clogging by dust, removing the pillars, and integrating miniaturized pumps and optics in a future design would allow to use this platform for high-throughput, automated, and portable screening of microbes, plant, or mammalian cells.

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Ion chromatographic determination of nitrate and nitrite in vegetable and fruit baby foods

An ion chromatographic method was developed for the determination of nitrate and nitrite in vegetable and fruit baby foods. The introduction of nitrate or nitrite to food may be natural or artificial as a preservative. Because of the higher pH found in babies' stomachs, nitrate can act as a reservoir for the production of nitrite by nitrate-reducing bacteria that can be harbored in the intestinal tract. This problem does not exist in adults because of the lower pH of the adult stomach. Exposure to nitrite by infants can result in methemoglobinemia (blue baby syndrome). There are also indications that carcinogenic nitrosamines can be formed from nitrates at the higher pH. These gastric conditions disappear at approximately 6 months of age. In this method, nitrate and nitrite were separated on a hydroxide-selective anion exchange column using online electrolytically generated high-purity hydroxide eluant and detected using suppressed conductivity detection. Average recoveries of spiked nitrite residue ranged from 91 to 104% and spiked nitrate residue ranged from 87 to 104%. This method and the AOAC Official Method yield comparable results for samples containing incurred nitrate residue. In addition, this method eliminates the hazardous waste associated with the use of cadmium found in the AOAC Official Method.     

Regular Polytopes of Nearly Full Rank: Addendum

A small family of regular polytopes of nearly full rank was omitted from the earlier paper with this title. This omission is rectified here.     

Simultaneous quantification of levofloxacin,pefloxacin, ciprofloxacin and moxifloxacin in microvolumes of human plasma using high‐performance liquid chromatography with ultraviolet detection

Levofloxacin, pefloxacin, ciprofloxacin and moxifloxacin are four fluoroquinolones used in the treatment of serious bacterial infections. The antibacterial activity of fluoroquinolones is concentration dependent. Therefore, therapeutic drug monitoring in daily clinical practice is warranted to ensure the therapy's efficacy and prevent bacterial resistance. The purpose of the present study was to develop a method using high‐pressure liquid chromatography with an ultraviolet detector for simultaneous quantification of these four fluoroquinolones in human plasma. A 50 μL aliquot of plasma was precipitated by 200 μL of methanol using gatifloxacin as internal standard. The chromatographic separation was performed on a Kinetex XB‐C₁₈ column using a mobile phase composed of a mixture of orthophosphoric acid 0.4% (v/v), acetonitrile and methanol at a flow rate of 1.2 mL/min. Dual UV wavelength mode was used, with levofloxacin and moxifloxacin monitored at 293 nm, and pefloxacin and ciprofloxacin monitored at 280 nm. The calibration was linear over the ranges of 0.125–25 mg/L for levofloxacin, 0.1–20mg/L for moxifloxacin and 0.05‐10 mg/L for both pefloxacin and ciprofloxacin. Inter‐ and intra‐day trueness and precision were <13% for all the compounds under study. The proposed method was simple, reliable, cost‐effective and suitable for therapeutic drug monitoring or pharmacokinetics studies.     

A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient

We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as

$?F(x,u,Du,D^{2}u)=\lambda c(x)u+〈M(x)Du,Du〉+h(x)$

in a bounded domain with a Dirichlet boundary condition; here $\lambda \in \mathbb{R}$, $c,h\in L^p(\mathrm{\Omega })$, $p>n\ge 1$, $c?0$ and the matrix M satisfies $0<{\mu }_{1}I\le M\le {\mu }_{2}I$. Recently this problem was studied in the “coercive” case $\lambda c\le 0$, where uniqueness of solutions can be expected; and it was conjectured that the solution set is more complex for noncoercive equations. This conjecture was verified in 2015 by Arcoya, de Coster, Jeanjean and Tanaka for equations in divergence form, by exploiting the integral formulation of the problem. Here we show that similar phenomena occur for general, even fully nonlinear, equations in nondivergence form. We use different techniques based on the maximum principle.We develop a new method to obtain the crucial uniform a priori bounds, which permit to us to use degree theory. This method is based on basic regularity estimates such as half-Harnack inequalities, and on a Vázquez type strong maximum principle for our kind of equations.     

Photon Equivalents as a Parameter for Scaling Photoredox Reactions in Flow: Translation of Photocatalytic C−N Cross‐Coupling from Lab Scale to Multikilogram Scale

With the development of new photocatalytic methods over recent decades, the translation of these chemical reactions to industrial‐production scales using continuous‐flow reactors has become a topic of increasing interest. In this context, we describe our studies toward elucidating an empirically derived parameter for scaling photocatalytic reactions in flow. By evaluating the performance of a photocatalytic C?N cross‐coupling reaction across multiple reactor sizes and geometries, it was demonstrated that expressing product yield as a function of the absorbed photon equivalents provides a predictive, empirical scaling parameter. Through the use of this scaling factor and characterization of the photonic flux within each reactor, the cross‐coupling was scaled successfully from the milligram scale in batch to a multi‐kilogram reaction in flow.