A remark on quasianalytic vectors for a pair of anticommuting operators

We prove that two self-adjoint operators that anticommute on the dense invariant domain of their common quasianalytic vectors are strongly anticommuting. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii, Zhurnal, Vol. 49, No. 6. pp. 878–880, June, 1997.     

ZD-coradical of aKI-group

We consider existence and completability of the ZD-coradical of a group in which all the subgroups of the commutant are invariant.Kiev Polytechnical Institute. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 120–124, 1991.     

On the stability of a trivial invariant torus of one class of impulsive systems

We consider the problem of asymptotic stability of the trivial invariant torus of one class of impulsive systems. Sufficient criteria of asymptotic stability are obtained by the method of freezing in one case, and by the direct Lyapunov method for the investigation of stability of solutions of impulsive systems in another case. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 338–349, March, 1998.     

Groups in which the commutant is generated by invariant cyclic subgroups

We study groups in which the commutant is generated by invariant cyclic subgroups. Existence of a hypercentral coradical in a periodic group is proved and a completability criterion is derived for some subgroups of the coradical.Kiev Polytechnical Institute. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 74, pp. 85–88, 1992;     

Group analysis of boundary-value problems of mathematical physics

We obtain conditions for invariance and invariant solvability of boundary-value problems of mathematical physics. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 140–144, January, 1999.     

On invariant tori of countable systems of differential equations with delay

We obtain conditions for the existence and smoothness of invariant tori of countable systems of differential equations with delay. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1292–1295, September, 1999.     

Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable hamiltonian systems. I

By using the Cartan differential-geometric theory of integral submanifolds (invariant tori) of completely Liouville-Arnol’d integrable Hamiltonian systems on the cotangent phase space, we consider an algebraic-analytic method for the investigation of the corresponding mapping of imbedding of an invariant torus into the phase space. This enables one to describe analytically the structure of quasiperiodic solutions of the Hamiltonian system under consideration. Academician. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 51, No. 10, pp. 1379–1390, October 1999.     

On the stability of solutions of a quasilinear uncertain system

We generalize the Lyapunov direct method, which can be used for establishing new conditions of the uniform asymptotic stability of solutions of an uncertain system with respect to an invariant moving set. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 458–465, April, 1999.     

Isomorphisms of combinatorial block decompositions of three-dimensional manifolds

For three-dimensional manifolds with the structure of a combinatorial block complex, we construct an invariant that allows one to verify the existence of isomorphisms, between these manifolds. For complexes of small dimensionality, we solve the problem on the possibility of extending the isomorphisms of subcomplexes to those of complexes. Shevchenko National University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal., Vol. 51, No. 4, pp. 568–571, April, 1999.     

Gaussian and non-Gaussian limit distributions of estimates of the regression coefficients of a long-memory time series

We obtain Gaussian and non-Gaussian distributions of estimates of regression coefficients of a long-memory time series. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 931–939, July, 1999.     

Normal structure of the jonquere group over a field of characteristic zero

The lattice of normal divisors of the Jonquere group over a field of characteristic zero is described. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 692–698, June, 1994.     

A modified projection-iterative method for solution of a singular integral equation with parameters and small nonlinearity

We suggest a modified version of the projection-iterative method of solving a singular integral equation with parameters and small nonlinearity. Kiev Polytechnic Institute, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 418–422, March, 1999.     

On the Levy-Baxter theorems for shot-noise fields. II

We establish sufficient conditions under which shot-noise fields with a response function of a certain form possess the Levy-Baxter property on an increasing parametric set. Kiev Polytechnic Institite, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 12–31, January, 1999.     

Periodic solutions of a weakly nonlinear system of partial differential equations with pulse influence

We establish conditions of the existence of solutions periodic in t with period T for a weakly nonlinear system of partial differential equations with pulse influence. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 601–605, April, 1997.     

On necessary conditions for the weak regularity of a linear extension of a dynamical system on a torus

We give a necessary condition for the weak regularity of a linear extension of a dynamical system on a torus in the form of Fourier series with respect to a part of the variables. Kiev Polytechnical Institute, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol 50, No. 3, pp. 424–425, March, 1998.     

Optimization of a system of linear differential equations with random coefficients

We consider a system of differential equations with controls that are linearly contained in the right-hand sides. We establish a necessary condition for the optimal control that minimizes a quadratic functional. Kiev National Economic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 556–561, April, 1999.     

Stability of one difference equation with positive coefficients

We consider a linear homogeneous difference equation of ordern with positive coefficients, which is presented in the normal form. We obtain necessary and sufficient conditions for the stability and asymptotic stability. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1276–1280, September, 1990.     

On one generalization of the averaging method

We consider one case where it is possible to establish sufficient conditions for the convergence and analyticity of matrix series used for the construction of a system of moment equations. Kiev National Economic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 906–911, July, 1997.     

A functional limit theorem of the type of the law of large numbers for random reliefs

For a random function dependent on time and on a point of a space with measure, we find an asymptotic expression for the measure of the region in which values of the function do not exceed a given level. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 542–552, April, 1999.