Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

Reactions of the nitrate radical with a series of reduced organic sulphur compounds in air

A 480 L evacuable reaction chamber, equipped with FT-IR spectroscopy on-line and ion chromatography off-line, has been used to study the gas phase reaction between the nitrate radical, NO₃, and the reduced organic sulphur compounds CH₃CH₂SH, (CH₃CH₂)₂S, (CH₃CH₂)₂S₂, and CH₃CH₂SCH₃ in air. The products CH₃CH₂SO₃H, SO₂, H₂SO₄, CH₃CHO, and CH₃CH₂ONO₂ were identified and quantified in the reactions of the first three compounds, CH₃CH₂SH, (CH₃CH₂)₂S, and (CH₃CH₂)₂S₂. The reaction products were CH₃CH₂SO₃H, CH₃SO₃H, SO₂, H₂SO₄, CH₃CHO, and CH₂O in the reaction of CH₃CH₂SCH₃. On the basis of identified reaction products and intermediates observed in the infrared spectra, mechanisms are proposed for the reactions between the NO₃ radical and the four reduced organic sulphur compounds. The results of this study, together with those from previous experiments performed in this laboratory on CH₃SCH₃, CH₃SH, and CH₃SSCH₃ lead to the conclusion that all these species, in the reaction with the NO₃ radical, follow a similar degradation mechanism producing SO₂, H₂SO₄, R? SO₃H, R? CHO, and R? CH₂ONO₂, as the main reaction products. The inital step of the reaction of NO₃ with R? S? R and R? S? H type (R = CH₃, CH₂CH₃) reduced organic sulphur compounds was found to be H-atom abstraction, probably after the formation of an initial adduct. For the reaction between NO₃ and R? S? S? R type compounds, evidence for an addition-decomposition reaction, as the initial steps, was obtained. R? S·, R? S(O)·, and R? S(O)₂· appear to be formed as intermediates in all the reactions. © John Wiley & Sons, Inc.     

Aerosol formation and reaction pathways of atmospheric oxidation of dimethylsulfide

This paper concerns with three series of experiments about dimethylsulfide gas phase oxidation, carried out at increasing NOx level (< 20 ppb, 1 ppm, 10 ppm) to show the relation between the amounts of nitrogen oxides and the molar yields of sulfur containing products. DMSO, DMSO2, HCHO, HCOOH and SO2 were found as main reaction products. From these experiments and from preceding studies, a sensitive decrease in the quantity of total sulfur products in aerosol phase is underlined. This result derives from the reaction of NOx with CH3S(O)O2 and CH3S(O)OO radicals, which leads to stable intermediates as methylsulphonylperoxynitrate, MSPN, with a characteristic PAN-like structure.     

Reducibility and nonreducibility between equivalence relations

We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.

     

Non-treeability for product group actions

A product of two lcsc non-compact groups G ₁ × G ₂ acting freely by measure preserving transformation on a standard Borel probability space gives rise to a non-treeable equivalence relation unless both groups are amenable. Partially supported by NSF grant DMS 0140503     

The off-line group seat reservation problem

In this paper we address the problem of assigning seats in a train for a group of people traveling together. We consider two variants of the problem. One is a special case of two-dimensional knapsack where we consider the train as having fixed size and the objective is to maximize the utilization of the seats in the train. The second is a special case of two-dimensional bin packing where all requests must be accommodated while trying to minimize the number of passenger cars needed. For both variants of the problem we present a number of bounds and develop exact algorithms. Computational results are presented for various instances based on realistic data, and from the packing literature adapted to the problems addressed.     

Products and mechanism of the gas phase reaction between nitrate radical and arenes

Summary The reaction between the nitrate radical and ortho- and para-xylene and some deuterated analogues was studied in the gas phase in a 480 l reaction chamber. Sampling of the gas mixture and gas chromatography-mass spectrometry allowed to obtain kinetic isotope effect values in the range of 1.48–1.87. These were similar to the values of 1.25–1.67 observed in the oxidation of these substrates with cerium(IV) ammonium nitrate in acetonitrile. This suggests that the hydrogen abstraction mechanism commonly invoked for these reaction may compete with a single electron transfer and an addition of the nitrate radical to the aromatic compound in the rate-determining first reaction step. Lowering the concentration of dioxygen in the reaction gas mixture leads to an increase of the ratio nitrate ester/aromatic aldehyde.