Elliptic bundle and generating operators

A hierarchy of Poisson Hamiltonian structures connected with an elliptic spectral problem is constructed. Generating operators connected with the Landau-Lifshits equations and asymmetric chiral 0(3)-field are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 161, pp. 76–87, 1987.The author is profoundly grateful to P. P. Kulish, A. G. Reiman, and M. A. Semenov-Tyan-Shanskii for interest in the present paper and helpful comments.     

Bahadur effectiveness of Watson-Darling goodness-of-fit tests

The rough asymptotic behavior of the probability of large deviations is found for Watson-Darling goodness-of-fit tests, which are centered versions of Kolomogorov-Smirnov statistics. Their Bahadur effectiveness is calculated and conditions for local asymptotic optimality for the alternative of translation are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 138–145, 1987.     

Production of light superpartners in π0 radiative decays

The production rate of light photinos in radiative pion decay \(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma\) is calculated. Experimental constraints on masses and mass splittings of scalar quarks imply the following upper bound on the decay rate \(BR(\pi ^0 \to \gamma \tilde \gamma \tilde \gamma ) \lesssim 10^{ - 16}\) .     

2-Amino-4,4-disubstituted-5-carboxymethyl-Δ2-1,3,4-oxadiazolin-4-ium chlorides and their recyclization in acetic anhydride

2-Methylamino-4,4-disubstituted-5-carboethoxymethyl-²-1,3,4-oxadiazolin -4-ium chlorides were obtained from the reaction of 1,1-disubstituted-4-methylsemicarbazides with ethyl propiolate in the presence of hydrochloric acid. After hydrolysis of the ester these chlorides recyclize in acetic anhydride to 1-substituted-3-acetoxy-1H-pyrazoles. The difference in the direction of ring opening with acetic anhydride in the betaines of 1,3,4-oxadiazolin-5-acetic acids and their thia-analogs has been demonstrated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1685–1688, 1992.     

Pseudo-cross-conjugated mesomeric betaines. 1. Synthesis of pseudo-cross-conjugated mesomeric betaines from quinoxaline derivatives

A new method for the synthesis of pseudo-cross-conjugated mesomeric betainic heterocyclic compounds with an angular nitrogen atom has been developed consisting in the reaction of 1,4-dielectrophile — -carbethoxy-2-(3-chloro)quinoxalylacetonitrile with azoles. Experimental regularities have been studied and a reaction mechanism has been proposed including the stage of formation of an ylide from a quaternary azolium salt. A pseudo-crossconjugated mesomeric betainic heterocyclic compound containing a thiazole ring compound has been synthesized for the first time.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1528–1533, November, 1992.     

3, 3, 3-Trifluoropropyl(methyl)cyclosiloxanes

The influence of the number of 3, 3, 3-trifluoropropyl(methyl)siloxane links (/) in the cyclotetrasiloxanes _mD_4-m, where D represents the dimethylsiloxane link and m=0–4, on the rearrangement of these compounds in acetone solution under the action of sodium siloxanolate has been studied. The rearrangement takes place with the formation of a linear polysiloxane the degradation of which yields, in addition to the initial ring, cyclosiloxanes with a different structure. The rate of rearrangement of _mD_4-m and of the formation of a linear polysiloxane rises with an increase in m from 0 to 3. The equilibrium concentration of the linear polysiloxane formed from _mD_4-m is inversely proportional to m. Results have been obtained on the kinetics of the formation of the cyclosiloxanes _mD_n, where m=0–5, n=0–5, and m+n=3–6, in the rearrangement of the rings D₃, ₂D₂, ₃D, and ₄. The reactivity of the siloxane links rises in the sequence (CH₃)₂Si-O-Si(CH₃)₂ < (CF₃CH₂CH₂)-(CH₃) Si-O-Si(CH₃)₂ <(CF₃CH₂CH₂) (CH₃)Si-O-Si(CH₃) (CH₂CH₂CF₃) . Because of the negative inductive effect transferred through the siloxane links, the 3, 3, 3-trifluoropropyl groups strongly activate the siloxane ring with respect to nucleophiiic reagents.For part I, see [3].     

Arylation of 2,5-dimethyl-4-phenylpyridine

The position of the pyridine ring is arylated by reaction of 2,5-dimethyl-4-phenylpyridine with phenyllithium and p-tolyllithium. Destructive oxidation of the diaryl-substituted pyridines primarily affects the pyridine ring.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1359–1361, October, 1970.     

Effect of hydrothermal treatment on catalytic properties of superhigh-silica zeolites

The effect of hydrothermal treatment of decationized superhigh-silica zeolite on the mechanism of n-hexane conversion has been studied. It has been established that thermosteam modification sharply decreases the cracking activity and increases the selectivity to aromatization reactions. Zeolite acidity markedly decreases, but its crystal structure does not become amorphous.

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