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     

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.     

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.     

Network dimensionality and ligand flexibility in lanthanide terephthalate hydrates

Various lanthanide open framework materials incorporating the terephthalate (TP) entity were prepared using hydrothermal synthesis methods at a moderate temperature of 170 °C. The compounds Nd₂(TP)₃(H₂O)₄(1), Er₂(TP)₃(H₂O)₄(2), Yb₂(TP)₃(H₂O)₂(3), Yb₂(TP)₃(H₂O)₆(4), and Yb₂(TP)₃(H₂O)₈·2H₂O (5), were characterized by single crystal structural analysis and FT-IR spectroscopy. While compounds 1 and 2 have been reported before on the basis of powder X-ray diffraction, the structural characterization of any ytterbium terephthalate species is unprecedented. Compounds 1-5 crystallize in triclinic settings with space group P-1. The compounds are compared with their previously reported Er and Tb-counterparts and the reduction of the dimensionality of the resulting networks from 3D over 2D to 1D with increasing level of hydration is discussed. Compounds 1, 2, and 3 with the lowest water content assemble in three-dimensional network lattices. Compounds 4 and 5, however, form 2D layered systems and 1D rod like chains, respectively, which are held together by hydrogen bonds originating from coordinating H₂O. The crystal lattices of the 3D networks experience higher levels of tension as can be seen by increasing out-of-plane torsion with regard to the terephthalate carboxylate groups. Moreover, there seems to be a correlation between the level of strain on the aromatic ligands and the reduction of the number of carboxylate oxygen atoms that are part of the coordination polyhedra.     

Complete subgraphs of the graphs of convex polytopes

It is shown that if three vertices of the graph G(l') of a convex 3-polytope P are chosen, then G(P) contains a refinement of the complete graph C₄ on four vertices, for which the three chosen vertices are principal (that is, correspond to vertices of C₄ in the refinement). In general, all four vertices may not be preassigned as principal. For dimensions d?4, simple (simplicial) d-polytopes are constructed whose graphs contain sets of three (four) vertices, which cannot all be principal in any refinement of C₄₊₁.     

The phase behavior of a polymer‐fullerene bulk heterojunction system that contains bimolecular crystals

Polymer:fullerene blends have been widely studied as an inexpensive alternative to traditional silicon solar cells. Some polymer:fullerene blends, such as blends of poly(2,5‐bis(3‐tetradecylthiophen‐2‐yl)thieno[3,2‐b]thiophene (pBTTT) with phenyl‐c71‐butyric acid methyl ester (PC₇₁BM), form bimolecular crystals due to fullerene intercalation between the polymer side chains. Here we present the determination of the eutectic pBTTT:PC₇₁BM phase diagram using differential scanning calorimetry (DSC) and two‐dimensional grazing incidence X‐ray scattering (2D GIXS) with in‐situ thermal annealing. The phase diagram explains why the most efficient pBTTT:PC₇₁BM solar cells have 75–80 wt % PC₇₁BM since these blends lie in the center of the only room‐temperature phase region containing both electron‐conducting (PC₇₁BM) and hole‐conducting (bimolecular crystal) phases. We show that intercalation can be suppressed in 50:50 pBTTT:PC₇₁BM blends by using rapid thermal annealing to heat the blends above the eutectic temperature, which forces PC₇₁BM out of the bimolecular crystal, followed by quick cooling to kinetically trap the pure PC₇₁BM phase. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011