Chernoff efficiency of the sign and Wilcoxon tests for testing the symmetry hypothesis

The local Chernoff efficiency of the sign and Wilcoxon statistics are derived for the testing of symmetry on the basis of the analysis of the probabilities of large deviations of these statistics under the hypothesis and the alternative.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 101–107, 1989.     

Self-similar solution of the problem of pseudo-three-dimensional vertical hydraulic fracture propagation in an impermeable stratum

The initial stage of propagation of a vertical hydraulic fracture in an impermeable or low-permeability stratum is considered within the framework of the pseudo-three-dimensional Perkins-Kern model.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–86, November–December, 1995.     

Failure of an infinitely compressible composite containing a finite cylindrical crack in axial compression

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of the Ukraine. Translated from Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 15–23, September, 1995.     

Average and local magnetic moments on Fe atoms in microcrystalline and amorphous Fe100−xPx alloys

We have measured the concentration dependence of the average magnetic moment per Fe atom _Fe(x) in microcrystalline and amorphous Fe-P alloys obtained over a wide concentration range using electrochemical deposition. The model of local magnetic moments has been used to described _Fe(x). On the basis of this model the effects of phosphorus on the value _Fe are explained in terms of the parameters of the local environment of the Fe atom.     

Rotation in cosmology

Cosmological models for a universe with expansion and rotation are considered. In particular, we analyse some effects of the universal rotation on the observational cosmology. It is shown that pure cosmic rotation does not produce neither causality voilations, nor parallax effects, nor anisotropy of the microwave background radiation. It can be detected by studying angular dependence of standard cosmological tests, and is directly measurable via polarization observations. The latter are used to obtain experimental estimates for the direction and value of the rotation of the universeThis essay received the third award from the Gravity Research Foundation, 1991 — Ed.     

Déformations des algèbres de Lie locales et analogue du théorème d'algébricité de Carles

Sans résumé

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Synthesis of 1,3,4,6,7,11b-hexahydro[1,4]thiazino[3,4,-a]-isoquinolin-4-one,an analog of prasiquantel

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 994–996, July, 1992.     

Complexity of factorization and GCD computation for linear ordinary differential operators

This paper presents an algorithm of polynomial complexity for finding greatest common (right) divisors of families of linear ordinary differential operators. An algorithm is presented for factorization of operators into the product of irreducible operators with complexity significantly better than that of previously known algorithms. Estimates are given for the coefficients of the expansion of the fundamental solution of the corresponding linear differential equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 176, pp. 68–103, 1989.     

从数学解题看数学美

本论述了“教学好玩”(陈省身语)的五个方面；教学语言精确；教学发现(类比发现；归纳发现和直党发现)；教学解题思路；教学思想方法和数学应用都体现了教学关。