Sofic groups and diophantine approximation

We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic. © 2007 Wiley Periodicals, Inc.     

A study of high transverse momentum π0's at ISR energies

We present a study of the transverse momentum spectrum of π⁰'s produced at c.m. angles θ = 90° and 53° in pp collisions at √s = 23.6, 30.8, 45.1, 53.2, and 62.9 GeV. The experiment was performed with a lead-glass detector. The data can be described with the usual parametrization $\text{p}{}_{\mathrm{<mtext>T</mtext>}}{}^{\mathrm{?n}}\text{?;(x}{}_{\mathrm{<mtext>T</mtext>}}\text{, θ)}$, with n = 7.2 ± 0.2. Comparison between the 90° and 53° data further indicates no appreciable dependence on θ, at least for x_T < 0.3. Two-particle inclusive cross sections for π⁰'s produced alongside are also presented. They are observed to have a dependence upon the transverse momentum of the dipion similar to that of single-particle cross sections and with the same value of n. Two-photon decays of η mesons are observed between 3 and 4 GeV/c transverse momentum with a production cross section half of that of π⁰.     

Problèmes rencontrés dans mon parcours mathématique : un bilan

Sans résumé Texte remanié de l’allocution prononcée par l’auteur au Colloque tenu en son honneur à Paris, en septembre 1988.     

The electronic states of carbon monofluoride: Low-lying valence states

Multiconfiguration Hartree-Fock calculations are reported on the low-lying valence states, the X²Π, ⁴Σ^?, B²Δ, and ²Σ^± states, of carbon monofluoride. The wavefunctions describe dissociation of the molecule to the correct atomic limits and take account of the atomic 2s-2p near-degeneracy effect. For the ground state the calculations give (with experimental values in parentheses): a bond length of 1.286 Å (1.2667 Å), a fundamental frequency of 1292 cm^?1 (1308 cm¹), and a dissociation energy of 3.93 eV (5.5 ± 0.1 eV). A ⁴Σ^? state arising from the $\text{C}\text{(}{}^3\text{P) +}\text{F}\text{(}{}^2\text{P)}$ manifold is calculated to lie just 2.66 eV above the ground state. The B²Δ state, calculated adiabatic excitation energy 6.59 eV (6.12 eV), is found to dissociate to $\text{C}\text{(}{}^1\text{D) +}\text{F}\text{(}{}^2\text{P)}$ via a potential maximum. Calculations are also reported on a repulsive ²Δ state arising from ground state atoms.     

Novel N-aryl and N-heteroaryl sulfamide synthesis via palladium cross coupling

A novel and efficient synthesis of N-aryl and N-heteroaryl sulfamides via an intermolecular palladium-catalyzed coupling process has been developed. The reactions proceeded with good to excellent yields and were tolerant of a wide range of functional groups. [reaction: see text]     

A measurement of the proton-proton cross section at the CERN ISR

We present a measurement of the total cross section σ_t in proton-proton collisions at the CERN ISR. The method involves determination of the total interaction rate and machine luminosity. A two-arm scintillation hodoscope observes ～ 90% of the total interaction rate, while a streamer chamber is employed for event topologies missed by the main trigger. An increase of about 10% in σ_t is observed in the energy range √s = 23.6 to √s = 62.8 GeV/c in agreement with previous experiments.