Improved limits on the mass of the tau neutrino

Several methods to determine (or set an upper bound on) the mass of the tau neutrino are described. The decay spectrum of \(\tau \to e\bar \nu _e \nu _\tau \) near the high center-of-mass electron-energy end is particularly sensitive to the tau-neutrino mass. It is shown that an upper bound of 20 MeV or lower may be feasible. In addition, improved limits on the mass and mixing angle of a heavy component of the tau-neutrino may be readily obtained. We also discuss the purely leptonic decays of theD andF mesons, and show how measurements of the ratiosB(D→τν_τ/B(D→μν_μ,B(F→τν_τ/B(D→μν_μ can be sensitive to tau-neutrino masses of 30 MeV or greater.     

Über Pterinchemie. 49. Mitteilung. Eine neue Synthese von 5-Formyl-6, 7-dimethyl-5,6,7,8-tetrahydropterin und 5,6,7-Trimethyl-5,6,7,8-tetrahydropterin

Starting with 5-formyl-6,7-dimethyl-5,6,7,8-tetrahydropterine (II), a new synthesis of 5,6,7-trimethyl-5,6,7,8-tetrahydropterine (III) is described. Thereby the chemical behaviour of the 5-formyl group in II is investigated, in order to enable the unequivocal differentiation between formylation at position 5 and at position 10 in folic and tetrahydrofolic acid derivatives. ¹³C-NMR. spectra of II and III are discussed.     

Über Pterinchemie. 79. Mitteilung. 13C-und 15N-NMR.-spektroskopische Untersuchungen an der (6RS)-5, 10-Methylen-5, 6, 7, 8-tetrahydro-L-folsäure; eindeutiger Beweis ihrer Struktur

¹³C- and ¹⁵N-NMR.-Spectroscopic Studies on (6RS)-5, 10-Methylene-5, 6, 7, 8-tetrahydro-L -folic Acid; Unequivocal Proof of thier Structure The existence of a 5, 10-methylene bridge in the title compound has been established with the help of ¹⁵N-NMR, and ¹³C-NMR. spectroscopy. The simultaneous coupling of ¹³C(11) with ¹⁵N(5) and ¹⁵N(10) proves that C(11) must be bound as a methylene bridge to both N-atoms. Some other aspects of the NMR. spectra of the compound are discussed. Synthesis of the title product with the label ¹⁵N is described.     

Über Pterinchemie. Mitteilung. Die Kristallstruktur von 5,6,7-Trimethyl-5,6,7,8-tetrahydropterindihydrochlorid-monohydrat

The crystal structure of 5,6,7-trimethyl-5,6,7,8-tetrahydropterine-dihydrochloride-monohydrate The crystal structure of the title compound has been determined by X-ray analysis (direct methods) and refined with 947 structure amplitudes to R = 0.026. The crystal system is orthorhombic, space group Pna2₁, with unit cell dimensions a = 14.081, b = 14.623, c = 6.773 Å. The molecule is protonated at the N(1)- and N(5)-position. The tetrahydropyrazine ring exists in a conformation in which C(6) deviates markedly from the mean plane of the other five atoms. The CH₃-groups at N(5) and C(6) possess a trans configuration with a pseudoaxial and an axial conformation respectively. The CH₃-groups at C(6) and C(7) in return possess the cis configuration, whereby the CH₃-group at C(7) occupies an equatorial conformation.     

Polymerization studies on allylic compounds. III. α(substituted methyl)styrenes

The free-radical polymerization of a series of α-(substituted methyl)styrenes was investigated. These compounds were found to be inactive in homopolymerizations but copolymerized with methyl methacrylate and styrene with a retarding effect. Copolymerization characteristics were followed by rate and viscosity measurements.     

Longitudinal nuclear relaxation measurements in hcp H2

Measurements of T₁ in the hep phase of H₂, over the temperature range 2°–12°K and the ortho concentration range between 0.5 and 0.97 are presented. At temperatures below 10°K, the thermally activated self-diffusion is negligible and the mechanism for nuclear relaxation is that attributed by Moryia and Motizuki and by Harris to intramolecular dipolar interaction, modulated by intennolecular electric quadrupole-quadrupole (EQQ) interaction. The gaussian approximation for the correlation function was used by these authors to predict T₁. From the comparison between experiment and theory, we determine the EQQ parameter Γ/k_B to be 0.67°K. Above 10°K the effect of diffusion influences T₁, and the experimental results for an 88 per cent ortho H₂ sample up to the melting point suggest that the relaxation mechanisms resulting from EQQ interaction and diffusion are not independent of one another.     

Projective Modules over the Non-Commutative Sphere

The positive cone of the K₀-group of the non-commutative sphereB is explicitly determined by means of the four basic unboundedtrace functionals discovered by Bratteli, Elliott, Evans andKishimoto. The C*-algebra B is the crossed product A x Z₂ ofthe irrational rotation algebra A by the flip automorphism defined on the canonical unitary generators U, V by (U) = U*,(V) = V*, where VU = e²ⁱ UV and is an irrational real number.This result combined with Rieffel's cancellation techniquesis used to show that cancellation holds for all finitely generatedprojective modules over B. Subsequently, these modules are determinedup to isomorphism as finite direct sums of basic modules. Italso follows that two projections p and q in a matrix algebraover B are unitarily equivalent if, and only if, their vectortraces are equal: [p] = [q]. These results will have the following ramifications. They areused (elsewhere) to show that the flip automorphism on A isan inductive limit automorphism with respect to the basic buildingblock construction of Elliott and Evans for the irrational rotationalgebra. This will, in turn, yield a two-tower proof of thefact that B is approximately finite dimensional, first provedby Bratteli and Kishimoto.     

Planar graphs,Hamilton cycles and extreme independence number

If a graph has too many edges, it must be Hamiltonian. We show how to construct graphs near the threshold: they have as many edges as possible without sacrificing planarity but are not Hamiltonian. We base our construction on the concepts of independent sets and 1-toughness.The work of the author was partially supported by CNPq-Brasil.