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.

     

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 from twisted Coxeter groups

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

Locally toroidal regular polytopes of rank 4

The paper studies various relationships between locally toroidal regular 4-polytopes of types {6, 3,p} and {3, 6, 3}. These relationships are based on corresponding relationships between the regular honeycombs with the same Schläfli-symbol in hyperbolic 3-space. Also the paper discusses regular tessellations (secretions of rank 3) which are locally inscribed into regular 4-polytopes. In particular, this leads to local criteria for the finiteness of the polytopes.     

Cyclotomic factors of Coxeter polynomials

In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of nmod360, and come exclusively from spherical subdiagrams.     

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.     

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.     

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.