多元整系数多项式因式分解的一种理论和算法

本文将ｔ（ｔ是大于２的整数）元整系数多项式看成为系数为ｔ－２元整系数多项式的二元多项式，建立了多元整系数多项式因式分解的一种新理论，进而得到了分解多元整系数多项式的一个有力的算法。     

Noncommutative four-dimensional subalgebras of conformal algebra integrable in the space R1,3

D'alambert's equation is used as an example to study the possibilities of a new method of exactly integrating systems of linear differential equations — the method of noncommutative integration (NI). The results confirm that use of the NI is equivalent to complete separation of the variables in the case of four-dimensional subalgebras of conformal algebra. However, the method does simplify determination of the exact solution in this instance.Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 120–124, February, 1995.     

Axial Structure of the Field Intensity in Diffusion-Controlled Surface-Wave Produced Plasmas

Surface-wave gas discharges sustained under the conditions of a diffusion controlled regime are studied on the basis of the fluid plasma model. The self-consistent behaviour of the plasma density and of the field intensity along the discharge length is obtained. It is shown that the nonlinearity in the particle balance equation due to stepwise ionisation determines the plasma density in terms of the field intensity and ensures self-consistent behaviour of the wave ? discharge characteristics in a diffusion controlled regime.     

Interaction of a point vortex with boundary singularities of higher orders

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 167–168, May–June, 1993.     

THE SCHWARZIAN DERIVATIVE IN SEVERAL COMPLEX VARIABLES(II)

ＴＨＥＳＣＨＷＡＲＺＩＡＮＤＥＲＩＶＡＴＩＶＥＩＮＳＥＶＥＲＡＬＣＯＭＰＬＥＸＶＡＲＩＡＢＬＥＳ（ＩＩ）ＧＯＮＧＳＨＥＮＧＹＵＱＩＨＵＡＮＧＺＨＥＮＧＸＵＥＡＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＡｕｇｕｓｔ３０，１９９６．Ｄｅ...     

Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

Estimates of electron-positron pair production in the interaction of high-power laser radiation with high-Z targets

Electron-positron production processes occurring in the interaction of 10¹⁸–10²⁰ W/cm² laser radiation with high-Z targets are examined. Computational results are presented for the pair production and the positron yield from the target with allowance for the contribution of pair production processes due to electrons and bremsstrahlung photons. Monte Carlo simulations using the PRIZMA code confirm the estimates obtained. The possible positron yield from high-Z targets irradiated with 10²–10³ TW laser radiation is estimated to be 10⁹–10¹¹. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 4, 239–244 (25 February 1998)     

Magnetic and structural transitions in La1−x Sr x MnO3: T-x phase diagram

The electrical conductivity, magnetic susceptibility, magnetization, and submillimeter (v=5∓20 cm⁻¹) permittivity and dynamic conductivity of La_1−x Sr _x MnO₃ (0≤x≤ 0.45) single crystals are investigated. The anomalies in the temperature dependences of these quantities are identified with diverse magnetic and structural phase transformations, including antiferromagnetic and ferromagnetic ordering, structural transitions between strongly distorted (Jahn-Teller) and weakly distorted (pseudocubic) orthorhombic phases, structural transitions to a rhombohedral phase and unusual transitions to a polaron-ordering state. As a result, the complete T-x phase diagram of the system La_1−2x Sr _x MnO₃ is constructed in a wide interval of temperatures T=4.2∓1050 K and concentrations x=0−0.45. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 331–336 (25 August 1998)     

Numerical-analytic method for the investigation of multipoint boundary-value problems for systems of differential equations with transformed argument

The problem of existence and approximate construction is studied for the solution of a nonlinear system of differential equations with a transformed argument and linear multipoint boundary conditions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1581–1584, November, 1998.     

An algorithm for the single-input partial pole assignment problem

An algorithm for translating unstable eigenvalues of single-input partial pole assignment problems based on rank-one transformations is suggested. Special attention is paid to the practical case where translations are constructed using inexact spectral information provided by the Arnoldi procedure. Estimates of the resulting perturbations of stable and translated poles are derived. These estimates depend on the accuracy of spectral information about the unstable poles. The algorithm proposed is illustrated with numerical examples. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 5–28. Translated by A. Yu. Yeremin.