A critical survey of approximate scattering wave theories from random rough surfaces

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.     

Existence of standing waves for dirac fields with singular nonlinearities

We prove the existence of stationary states for nonlinear Dirac equations of the form (E) $$i\sum\limits_{\mu = 0}^3 {\gamma ^\mu \partial _\mu \psi - M\psi + F\left( {\bar \psi \psi } \right)\psi = 0,} $$ whereM>0 andF is a singular self-interaction. In particular, in the model case whereF(s)=?s ^?α, for some 0<α<1, and for every ω>M, there exists a solution of (E) of the form ψ(t, x)=e ^iωt?(x), wherex ₀=t andx=(x ₁,x ₂,x ₃), such that ? has compact support. IF 0<α<1/3, then ? is of classC ¹. If 1/3<α<1, then ? is continuously differentiable, except on some sphere {|x|=R}, where |??| is infinite.     

NMR spectra and structure of phospeorylated isothiocyanates

Conclusions The chlorides of dialkyl- and alkylenephosphorous acids react with trimethylsilyl isothiocyanate to give the isothiocyanates of the corresponding phosphorous acids. The reaction goes stereospecifically with a retention of the configuration at the phosphorus atom.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 1380–1383, June, 1976.     

Reaction of 2-diethylamino-3-diethylaminomethyl-1,3,2-benzoxazaphospholine with hydroxyl-containing compounds

The reaction of 2-diethylamino-3-diethylaminomethyl-1,3,2-benzoxazaphospholine with functionally substituted alcohols and phenols occurs with the cleavage of exocyclic P-N bond followed by N→P migration of the diethylaminomethyl group and formation of imidophosphonate dimers. A similar reaction with polyhydroxy compounds (diethylene glycol, glycerol) results in symmetrical and asymmetrical spirophosphoranes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1781–1784, October, 1993.