Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid

In this paper, we obtain a nonlinear Poisson structure and two first integrals in the problem of the plane motion of a circular cylinder and n point vortices in an ideal fluid. This problem is a priori not Hamiltonian; specifically, in the case n= 1 (i.e., in the problem of the interaction of a cylinder with a vortex) it is integrable.     

Rolling of a non-homogeneous ball over a sphere without slipping and twisting

Consider the problem of rolling a dynamically asymmetric balanced ball (the Chaplygin ball) over a sphere. Suppose that the contact point has zero velocity and the projection of the angular velocity to the normal vector of the sphere equals zero. This model of rolling differs from the classical one. It can be realized, in some approximation, if the ball is rubber coated and the sphere is absolutely rough. Recently, J. Koiller and K. Ehlers pointed out the measure and the Hamiltonian structure for this problem. Using this structure we construct an isomorphism between this problem and the problem of the motion of a point on a sphere in some potential field. The integrable cases are found.      

NMR spectra of pyrimidines

The chemical shifts of the protons in the even positions of the pyrimidine ring in 2- and 4-substituted pyrimidines in dimethyl sulfoxide solutions were determined. The correlation equations that link the relative chemical shifts (with allowance for corrections for the magnetic anisotropy of the substituents and the ring) with the F and R substituent constants were calculated. The ratios obtained were analyzed by comparison with the corresponding correlation equations for monosubstituted benzenes. The reasons for the significant increase in the transmission of the conjugation effects of the substituents to the even positions of the pyrimidine ring as compared with the meta positions of the benzene ring and the appreciable weakening of the conductivity of their inductive effects when the heteroring nitrogen atom is situated between a resonating proton and the substituent are discussed.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 673–677, May, 1978.     

Influence of electronegative substituents on the electronic spectra of the porphyrins in the form of dications

The positions of the electronic absorption bands and also the intensities of the Soret bands of the porphyrins with ethoxycarbonyl substituents in the form of dications have been calculated by the LCAO MO method in Huckel's approximation. Comparison with the experimental results shows good agreement.     

Pyrimidines

The condensation of -substituted acetophenones with benzylidenebisurea in an acid medium has given 5-R-2-oxo-4,6-diphenyl-1,2,3,4-tetrahydropyrimidones. The analogous condensation of propiophenone forms 5-methyl-2-hydroxy-4,6-diphenylpyrimidine. The tetrahydro derivatives obtained are readily dehydrogenated to 5-R-2-hydroxy-4,6-diphenylpyrimidines.For part XX, see [1].     

Pyrimidines

The reaction of cyclohexanone with arylidenebisureas (e.g. benzal-bisurea) in an acid medium has given 4, 4-diaryl-2, 2-dioxo-5, 5-trimethylene-6, 6-spirobishexahydropyrimidines (II). The acid hydrolysis of IIa (aryl-C₆H₅) in the presence of 2, 4-dinitrophenylhydrazine leads to the 2, 4-dinitrophenylhydrazone of 2-hydroxy-8-oxo-4-phenyl-5, 6, 7, 8-tetrahydroquinazoline (IV). Compound IV was also obtained by the ozonization of 2-acetoxy-8-benzal-4-phenyl-5, 6, 7, 8-tetrahydroquinazoline (IX) and subsequent decomposition of the ozonide with a solution of 2, 4-dinitrophenylhydrazine. The structure of the compounds obtained was confirmed by means of their IR, UV, and PMR spectra. Corresponding 6, 6-spirobishexahydropyrimidines have also been obtained from 2-methylcyclohexanone, acetone, and methyl ethyl ketone and benzalbisurea.For part XIV, see [1].     

Pyrimidines

A new method was developed for the synthesis of substituted pyrazolo[3,4-d]pyrimidines by the condensation of 1-alkyl(aryl)-3- and 5-aminopyrazoles with arylidenebisureas.See [1] for communication XXVIII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 535–539, April, 1971.     

Pyrimidines

2-Diazoacetyl-4, 6-diphenylpyrimidine is prepared from 2-chloro-4, 6-diphenylpyrimidine via the nitrile and the corresponding acid, and it is readily converted to 2-bromoacetyl and 2-chloroacetyl-4, 6-diphenylpyrimidine. It was not possible to bring about the Wolff reaction.For Part IV see [12].     

Pyrimidines

The corresponding 2-pyrimidoylacetate esters (I, II) and 2-pyrimidoyl-acetonitrile (V) were obtained by condensation of pyrimidine-2-carboxylic acid esters with methyl acetate or acetonitrile. The structures of the tautomeric forms were determined by IR and PMR spectroscopy. The effect of a solvent and protonation of the pyrimidine ring on the ketone-enol equilibrium was examined.