1,2,4-Azadiphosphole

tert-Butylaminophosphaalkyne 4 is shown to dimerize in alkaline medium to 1-tert-butyl-3-tert-butylamino-1,2,4-azadiphosphole 1 —the first representative of 1,2,4-azadiphospholes. The structure of 1 has been determined by IR and ³¹P NMR spectroscopy and by X-ray crystallography. Compound 1 crystallizes in the triclinic space group P¯1 with a = 10.356(7), b = 11.817(5), c = 11.830(3) Å, α = 88.51(3), β = 78.61(4), γ = 77.05(4)°, V = 1383(1) ų, Z = 4 (two independent molecules).     

Highly unsaturated phosphorus compounds: Trimeric and dimeric sulfides of a α,β‐di‐tert‐butyl vinyl phosphaalkyne

The first examples of sulfides of a 1,3,5‐triphosphabenzene were synthesized by the sulfurization of parent 1,3,5‐triphosphabenzene 2 . Disulfide 7 was found to be remarkably thermally stable, the stability likely coming from the contribution of resonance forms 7A and 7B . In addition to two hydrolysis products of trisulfide 8 , which can be anticipated in unsaturated phosphorus chemistry, a new and not trivial bicyclic bridgehead five‐membered heterocycle 10 was isolated among the decomposition products of 8 . © 2010 Wiley Periodicals, Inc. Heteroatom Chem 22:114–118, 2011; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20664     

A new method for the preparation of diphenylboryldipivaloyl phosphide

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2670–2671, November, 1990.     

Synthesis and steric structure of 2,2-disubstituted 5-phenyl-1,3,5-dioxaphosphorinanes

Conclusions Phenylbis(l-ethoxyalkyl)phosphines and 2,2-disubstituted 5-phenyl-l,3,5-dioxaphosphorinanes, with their conformational equilibrium shifted in the direction of the form with an axial orientation of phenyl at the phosphorus atom, were obtained by the reaction of phenylbis(hydroxymethyl)phosphine with aldehyde and ketone acetals, respectively.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2506–2509, November, 1986.     

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.     

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.     

Synthesis of C-(N,N-dialkylamino)phosphaalkenes

New C-(N,N-dialkylamino)phosphaalkenes were synthesized by the reaction of phenylphosphine with amidacetals. Such compounds may also be synthesized by the reaction of bis(trimethylsilyl)phenylphosphine with amidacetals.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1639–1641, July, 1990.     

Phosphorylated Allenes in the Cycloaddition Reactions

Abstract

The reactions of phosphorus-containing allenes with the derivatives of phosphorus of low coordination are investigated. The interaction of the l -vinyl-l-phosphoryloxy-3,3-di-methylallene with (dimethylaminomethylidene)phenylphosphine was shown to occur over 1,3-diene system according to Diels-Alder reaction. The formation of the six-membered heterocycle was accompanied by changing the coordination of the phosphorus atom from P^II to P^III. The reaction of the phosphorus containing 1,3-dipole (diethylaminobenzylidene)-aminodimethoxyphosphine with 1-vinyl-1-phosphoryloxy-3,3-dimethylallene was found to give the seven-membered aza-phosphepin. The changing of methoxy-radicals by ethoxy-groups in benzylideneaminophosphine leads to azaphos-phorins as products. The formation of the seven-membered adduct in this case is small. The two-step mechanism of these reactions with the initial attack of atom P at central carbon atom of allene is in agreement with kinetic, thermochemical and ³¹P-NBR data.