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.     

Application of Q-band electron spin echo spectrometer to investigation of glasses doped with rare earth ions

The Q-band electron spin echo (ESE) spectrometer which was created using modern microwave components is described. This simple incoherent apparatus was used with the X-band one for the study of phosphate and silicate glasses doped with non-Kramers rare earth Tb³⁺ ions. the EPR spectra measured by the ESE method have frequency independent peaks. The experimental results presumably show the existence of several types of paramagnetic centers in studied systems.     

Cauchy problem for convolution equations in spaces of analytic vector-valued functions

The present paper is devoted to the Cauchy problem of inhomogeneous convolution equations of a fairly general nature. To solve the problems posed here, we apply the operator method proposed in some earlier papers by the author. The solutions of the problems under consideration are found using an effective method in the form of well-convergent vector-valued power series. The proposed method ensures the continuity of the obtained solutions with respect to the initial data and the inhomogeneous term of the equation.     

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.     

Recyclization of the pyridine ring under the influence of nucleophiles

Alkyl- and dialkylanilines are formed by the action of primary and secondary amines on nitropyridinium salts. An alkylamino or dialkylamino group is included in the final product in the step involving the open form. Aqueous methylamine may lead to opening of the ring of nonquaternized nitropyridines with subsequent formation of the benzene ring of alkylanilines.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 98–102, January, 1979.     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

Synthesis,complexation, and photochemistry of benzobisthiazole-based bis(crown ether)

Benzobisthiazole-based bis(crown ether) was synthesized and its complexation with alkali and alkaline earth cations was studied. Photochemical transformations of the free ligand and its complexes with alkaline earth cations involve E,Z-photoisomerization and [2+2] photocycloaddition. Dedicated to Academician N. S. Zefirov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2056–2065, September, 2005.     

Synthesis of nitro and amino derivatives of benzothiacrown ethers

The condensation reaction of 1,2-bis(2-haloethoxy)-4-nitrobenzenes with acyclic α,ω-(oxa)alkanedithiols in the presence of alkali metal carbonates produced a series of nitrobenzodithiacrown ethers with macrocycles of different size. The structures of three ethers were established by X-ray diffraction. A new method was developed for the synthesis of nitrobenzomonothia-15-crown-5 ether. Nitro derivatives of benzodithiacrown ethers were tested as reagents for extraction of palladium(II), platinum(IV), and rhodium(III) from hydrochloric acid solutions. Extraction of Pd^II salts was found to be highly selective compared to that of Pt^IV and Rh^III salts. Benzodithia-15-crown-5 ether is the most efficient extractant for palladium(II). Reduction of nitrobenzothiacrown ethers with hydrazine hydrate in the presence of a platinum catalyst afforded their amino derivatives. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 958–966, May, 2007.