Spatial characterization of the transversal structure of rotationally symmetric pulsed beams

A simple analytical model is proposed to describe the transversal spatial structure of a tridimensional rotationally symmetric pulsed beam. The spatial behaviour of the pulse amplitude is shown to be linked to its (measurable) second- and higher-order intensity moments, namely, beam width, quality parameter and kurtosis. As an illustrative experimental example, this model has been applied to high-quality TEA CO2 laser pulses. This revised version was published online in November 2006 with corrections to the Cover Date.     

Greatly attenuated experimental autoimmune encephalomyelitis in aquaporin-4 knockout mice

Background  

The involvement of astrocyte water channel aquaporin-4 (AQP4) in autoimmune diseases of the central nervous system has been suggested following the identification of AQP4 autoantibodies in neuromyelitis optica, an inflammatory demyelinating disease.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

Reaction of 1,2-borylphosphinoethene with thiocyanates. Molecular and crystal structure of 2,2,3-tributyl-4,5,5-triphenyl-6-methylthio-1,5,2-azaphosphoniaboratacyclohexa-3,6-diene

The reaction of 1,2-borylphosphinoethenes with alkylthiocyanates leads to formation of substances having the structure of 6-alkylthio-1,5,2-azaphosphoniaboratacyclohexa-3,6-dienes in the crystal state. The structure of the compounds has been proven by x-ray diffraction analysis of 2,2,3-tributyl-4,4,5-triphenyl-5-methylthio-1,5,2-azaphosphoniaboratacyclohexa-3,6-diene. The heterocyclic moiety of the molecule is planar within 0.010(2) Å. The methylthio group lies practically in the plane of the heterocycle.Deceased.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan Scientific Center, Russian Academy of Sciences, 420083 Kazan. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1638–1644, July, 1992.     

Electrochemical reduction and structural properties of borylphosphinoethene derivatives

The intramolecular coordination bonds between phosphoryl-, thio-, and selenophosphoryl groups and boron facilitate the electrochemical reduction of borylphosphinoethene derivatives as compared with their noncyclic analogs. In 1-dibutylboryl-2-diphenylphosphino-1-butyl-2-phenylethene reception of the first electron takes place in the C=C bond. In the oxide, sulfide, and selenide, the electron-accepting centers are most likely the P-C₁ and P=R (R=S, Se) bonds.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 24–27, January, 1990.     

Substitution of the chr-O fragment in 1,3,2,5-dioxaboraphosphorinanes

Conclusions 1,3,2,5-Dioxaboraphosphorinanes react with aldehydes having electron-withdrawing groups to form the corresponding 4,6-disubstituted dioxaboraphosphorinanes.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2412–2414, October, 1988.