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     

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.     

On the ultraviolet photodissociation of H(2)Te

The photodissociation of H(2)Te through excitation in the first absorption band is investigated by means of multireference spin-orbit configuration interaction (CI) calculations. Bending potentials for low-lying electronic states of H(2)Te are obtained in C(2v) symmetry for Te-H distances fixed at the ground state equilibrium value of 3.14a(0), as well as for the minimum energy path constrained to R(1)=R(2). Asymmetric cuts of potential energy surfaces for excited states (at R(1)=3.14a(0) and theta;=90.3 degrees ) are obtained for the first time. It is shown that vibrational structure in the 380-400 nm region of the long wavelength absorption tail is due to transitions to 3A('), which has a shallow minimum at large HTe-H separations. Transitions to this state are polarized in the molecular plane, and this state converges to the excited TeH((2)Pi(1/2))+H((2)S) limit. These theoretical data are in accord with the selectivity toward TeH((2)Pi(1/2)) relative to TeH((2)Pi(3/2)) that has been found experimentally for 355 nm H(2)Te photodissociation. The calculated 3A(')<--XA(') transition dipole moment increases rapidly with HTe-H distance; this explains the observation of 3A(') vibrational structure for low vibrational levels, despite unfavorable Franck-Condon factors. According to the calculated vertical energies and transition moment data, the maximum in the first absorption band at approximately 245 nm is caused by excitation to 4A("), which has predominantly 2(1)A(") ((1)B(1) in C(2v) symmetry) character.     

Imidoylketene-alpha-oxoketenimine and alpha-oxoketene-alpha-oxoketene rearrangements. 1,3-shifts of substituted phenyl groups

1,3-phenyl shifts interconvert imidoylketenes 1 and alpha-oxoketenimines 2 and, likewise, alpha-oxoketenes 3 automerize by this 1,3-shift. These rearrangements usually take place in the gas phase under conditions of flash vacuum thermolysis. Energy profiles calculated at the B3LYP/6-31G(d,p) and B3LYP/6311 + G(3df,2p)//B3LYP/6-31G(d,p) levels demonstrate that electron donating substituents (D) in the migrating phenyl group and electron withdrawing ones (W) in the non-migrating phenyl group, can stabilise the transition states TS1 and TS2 to the extent that activation barriers of ca. 100 kJ mol(-1) or less are obtained; i.e. enough to make these reactions potentially observable in solution at ordinary temperatures. The calculated transition state energies DeltaG(TS1) show an excellent correlation with the Hammett constants sigma(p)(W) and sigma(p+)(D).     

Ketene-ketenimine rearrangements in the gas phase and in polar media. 1,3-Migration intermediates and sequential transition states

[reaction: see text] Calculations of the activation barrier for the 1,3-shifts of substituents X in alpha-imidoylketenes 1 (HN=C(X)-CH=C=O), which interconverts them with alpha-oxoketenimines 3 (HN=C=CH-C(X)=O) via a four-membered cyclic transition state TS2 have been performed at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G* level. Substituents with accessible lone pairs have the lowest activation barriers for the 1,3-shift (halogens, OR, NR2). The corresponding activation barriers for the alpha-oxoketene-alpha-oxoketene rearrangement of 4 via TS5 are generally lower by 1-30 kJ/mol. A polar medium (acetonitrile, epsilon = 36.64) was simulated using the polarizable continuum (PCM) solvation model. The effect of the solvent field is a reduction of the activation barrier by an average of 12 kJ/mol. In the cases of 1,3-shifts of amino and dimethylamino groups, the stabilization of the transition state TS2 in a solvent field is so large that it becomes an intermediate, Int2, flanked by transition states (TS2' and TS2') that are due primarily to internal rotation of the amine functions, and secondarily to the 1,3-bonding interaction. In the case of the alpha-oxoketene-alpha-oxoketene rearrangement of 4, there is a corresponding intermediate Int5 for the 1,3-amine shift already in the gas phase.