2017
Том 69
№ 9

All Issues

Volume 58, № 6, 2006

Article (Russian)

On the dynamical equations of a system of linearly coupled nonlinear oscillators

Bak S. N., Pankov A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 723–729

We consider a system of differential equations that describes the dynamics of an infinite chain of linearly coupled nonlinear oscillators. Some results concerning the existence and uniqueness of global solutions of the Cauchy problem are obtained.

Article (Ukrainian)

On the Schur theorem for n-ary groups

Galmak A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 730–741

We prove n-ary analogs of the well-known Schur theorem on the finiteness of a commutator subgroup of a group whose center is of finite index.

Article (Ukrainian)

Structure of a permutable Munn semigroup of finite rank

Derech V. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 742–746

A semigroup any two congruences of which commute as binary relations is called a permutable semigroup. We describe the structure of a permutable Munn semigroup of finite rank.

Article (Russian)

Extremal problems dual to the Gauss variational problem

Zorii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 747–764

We formulate and solve extremal problems of potential theory that are dual to the Gauss variational problem but, unlike the latter, are always solvable. Statements on the compactness of classes of solutions and the continuity of extremals are also established.

Article (Russian)

On Frobenius groups with noninvariant factor SL 2(3)

Kozulin S. N., Senashov V. I., Shunkov V. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 765–777

We obtain a criterion for the unsimplicity of an infinite group containing the infinite class of the Frobenius groups $L_g = \langle a, g^{-1} a g\rangle$ with complement $SL_2 ( 3 )$.

Article (Ukrainian)

Convergence of the Galerkin method for a wave equation with singular right-hand side

Nomirovs'kii D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 778–786

We consider analogs of the Galerkin method for a linear wave equation of the fifth order with generalized functions on the right-hand side. Theorems on the convergence of an approximate method, depending on the order of singularity of the right-hand side, are proved.

Article (Ukrainian)

Mel’nikov-Samoilenko adiabatic stability problem

Prikarpatskii Ya. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 787–803

We develop a symplectic method for the investigation of invariant submanifolds of nonautonomous Hamiltonian systems and ergodic measures on them. The so-called Mel’nikov-Samoilenko problem for the case of adiabatically perturbed completely integrable oscillator-type Hamiltonian systems is studied on the basis of a new construction of “ virtual” canonical transformations.

Article (English)

Generalized solutions of mixed problems for first-order partial functional differential equations

Czernous W.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 804–828

A theorem on the existence of solutions and their continuous dependence upon initial boundary conditions is proved. The method of bicharacteristics is used to transform the mixed problem into a system of integral functional equations of the Volterra type. The existence of solutions of this system is proved by the method of successive approximations using theorems on integral inequalities. Classical solutions of integral functional equations lead to generalized solutions of the original problem. Differential equations with deviated variables and differential integral problems can be obtained from the general model by specializing given operators.

Brief Communications (Ukrainian)

Julia lines of entire functions of slow growth

Zabolotskii N. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 829–834

We obtain sufficient conditions under which the Julia lines of entire functions of slow growth do not have finite exceptional values.

Brief Communications (Russian)

On the uniqueness of a solution of the problem with oblique derivative for the equation Δ n v = 0

Kapanadze D. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 835–841

We prove the uniqueness of a solution of the problem with oblique derivative for the equation Δ n v = 0.

Brief Communications (Ukrainian)

Problem of interpolation of functions by two-dimensional continued fractions

Pahirya M. M., Svyda T. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 842–851

We investigate the problem of interpolation of functions of two real variables by two-dimensional continued fractions.

Brief Communications (Russian)

On the modularity of a lattice of τ-closed totally saturated formations of finite groups

Safonov V. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 852–858

We study τ-closed totally saturated formations of finite groups.

Brief Communications (Russian)

On calculation of integrals over spherical domains

Shamsiev E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 859–864

We construct cubature formulas for the computation of integrals over spherical domains containing less nodes as compared with known ones.