Synthesis of 2-Naphthylselenoacetic Acid Dialkylamides from 4-(2-Naphthyl)-1,2,3-selenadiazole

Russian Journal of General Chemistry - Under the action of potassium hydroxide, 4-(2-naphthyl)-1,2,3-selenadiazole readily decomposes with the evolution of nitrogen and the formation of potassium...     

Energy of a Relativistic Fermion in a Spherically Symmetric Potential Well of Finite Depth Near the Boundary of the Lower Continuum in a Two-Dimensional Space

Russian Physics Journal -     

A generating function for Rankin–Cohen brackets

We give a closed formula for the Rankin–Cohen formal covariant quantization in terms of generating functions of Jacobi polynomials.     

Motion of a charged particle in the field of a grounded conductive sphere

Motion of a charged particle in the field of a grounded conductive sphere is investigated. It is assumed that the field created by the sphere is quasi-static that implies limitation on particle velocities by nonrelativistic values and the possibility of neglecting magnetic interaction and heat losses. A classification is provided and possible particle trajectories are constructed in the examined case.     

Formylation of alkyl cyanofurylmethanphosphonates at the active methylene group

Alkyl cyanofurylmethanephosphonates are formylated with ethyl formate in the presence of sodium foil to form sodium derivatives of phosphonoacetic aldehyde. If phosphonoacetic aldehyde and nitrile groups occupy remote positions in the furan ring, the sodium derivative in DMSO solution exists in the form of carbanion carrying charge on the carbon atom adjacent to the aldehyde group. If the substituents are located at the adjacent carbons of furan ring, the solution equilibrium between the carbanionic (major product) and Z-enolate forms of salts is established. Alkylation of the formed salts with methyl iodide occurs exclusively at the oxygen atom to give methyl enolates. In most cases, a mixture of E-and Z-isomers is formed, the E one being prevailing. In the case of 2,5-location of the substituents in furan ring, the sodium salt is inactive, and the alkylation does not occur.     

Synthesis of (2-Ethoxy-2-oxoethylthio)methyl Derivatives of Furoic Acids and Attempts of Their Intramolecular Cyclizations under the Conditions of the Claisen Reaction

Based on reactions of phosphorylated derivatives of halomethylfuroic acid esters with thioglycolic acid ester in the presence of bases, a method for the synthesis of mono-and bisphosphosphorylated esters of (2-ethoxy-2-oxoethylthio)methyl derivatives of furoic acids, containing an ester group in the position adjacent to the sulfide moiety was developed. Obtained compounds are relatively easily metallized with potassium tert-butylate, but intramolecular cyclization proceeds smoothly only in the case of 5-(diethoxyphosphorylmethyl)-2-(ethoxycarbonylmethylthiomethyl)furan-3-carboxylic acid. The resulting 1,3-dicarbonyl derivative of 7H-thiopyrano[3,4-b]furan is hydrolytically unstable, but its enol O-methyl ether is stabile. Alkaline hydrolysis of the latter compound was studied, and it was shown that it proceeds at the ester as well as at the phosphonate group.     

Private Life of GL(5,ℤ)

In the paper, the (2, 3)-generation of GL(S, ℤ) is investigated. We reduce the problem to five specific pairs of matrices. Bibliography: 4 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 153–162.     

Synthesis and selected reactions of ethyl 5-(1-chloroethyl)-2-methylfuran-3-carboxylate

Ethyl 2-methylfuran-3-carboxylate is smoothly chloroethylated at 0°C in the 5 position of the ring. The resulting halide alkylates secondary amines but eliminates HCl with sodium diethyl phosphite under the Michaelis-Becker reaction conditions and with trimethyl phosphite under the Arbuzov reaction conditions. In the reaction with sodium diethyl phosphite, small amounts of 5-[1-(diethoxyphosphoryl)ethyl]furan-3-carboxylate and 5-ethylfuran-3-carboxylate are formed. In the Arbuzov reaction at a 1: 1.22 furan: trimethyl phosphite molar ratio, methyl 2,4-dimethyl-1-methoxy-1-oxo-1λ⁵-1,2-dihydrophospheto[3,2-b]furan-5-carboxylate was isolated.     

Synthesis of 5-acetyl derivatives of alkyl 2-furoates and 3-(2-furyl)acrylates

Methyl 5-acetyl-2-furoate has been prepared via oxidation of 5-(1-hydroxyethyl)-2-furoate with the Jones reagent. In turn, the starting compound has been synthesized via sequential chloroethylation of ethyl 2-furoate, substitution of chlorine with acetoxy group, and methanolysis of the acetate in presence of sodium methylate. The vinylog 2-furoate has been obtained as the major product via acetylation of ethyl 3-(2-furyl)-acrylate with acetic anhydride in the presence of magnesium perchlorate.

     

Differential symmetry breaking operators: I. General theory and F-method

We prove a one-to-one correspondence between differential symmetry breaking operators for equivariant vector bundles over two homogeneous spaces and certain homomorphisms for representations of two Lie algebras, in connection with branching problems of the restriction of representations. We develop a new method (F-method) based on the algebraic Fourier transform for generalized Verma modules, which characterizes differential symmetry breaking operators by means of certain systems of partial differential equations. In contrast to the setting of real flag varieties, continuous symmetry breaking operators of Hermitian symmetric spaces are proved to be differential operators in the holomorphic setting. In this case, symmetry breaking operators are characterized by differential equations of second order via the F-method.