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Том 217, № 2 (2016)
- Год: 2016
- Статей: 8
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14760
Article
Congruences on the Monoid of Monotone Injective Partial Self-Maps of Ln × lexℤ with Cofinite Domains and Images
Аннотация
We study congruences on the semigroup (ℤlexn) of monotone injective partial self-maps of the set of Ln × lexℤ with cofinite domains and images, where Ln × lexℤ is the lexicographic product of an n -element chain and a set of integers with ordinary linear order. The structure of the sublattice of congruences on (ℤlexn) contained in the least group congruence is described.
139-148
A Problem with Integral Conditions with Respect to Time for Shilov Parabolic Systems of Equations
Аннотация
In a domain specified in the form of the Cartesian product of an interval [0,T] and a space ℝp, we study a problem with integral conditions with respect to the time coordinate for Shilov parabolic systems of equations in the class of functions almost periodic with respect to the space variables. We establish a criterion of uniqueness and sufficient conditions for the existence of a solution of the problem. To solve the problem of small denominators encountered in the construction of the solution, we apply the metric approach.
149-165
Estimate of the Measure of Level Set for the Solutions of Differential Equations with Constant Coefficients
Аннотация
We establish the upper estimate of the measure of level set for the functions obtained as solutions of inhomogeneous ordinary differential equations with constant coefficients and right-hand sides without zeros in a certain interval. These estimates can be used for the investigation of entire and meromorphic functions, to study the problem of small denominators for partial differential equations, in the metric theory of Diophantine approximations, and in the theory of measure and integral.
166-175
Nonlocal Multipoint Problem for Differential-Operator Equations of Order 2n
Аннотация
We study a nonlocal multipoint problem for differential-operator equations of order 2n.The spectral properties of the operator of this problem are analyzed and the conditions for the existence and uniqueness of its solution are established. The solution of the problem is found in the form of expansion in series in the system of eigenfunctions. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.
176-186
Existence of Heteroclinic Traveling Waves in a System of Oscillators on a Two-Dimensional Lattice
Аннотация
By using the method of critical points and the concentration-compactness principle, we study the problem of existence of heteroclinic traveling waves for a system of linearly coupled nonlinear oscillators on a two-dimensional lattice.
187-197
Axisymmetric Resonant Vibrations and Vibration Heating of a Thermoviscoelastic Cylindrical Shell with Piezoelectric Sensors and Actuators
Аннотация
We consider a problem of axisymmetric forced resonant vibrations and dissipative heating of a viscoelastic cylindrical shell with piezoelectric sensors and actuators under monoharmonic loading. The viscoelastic behavior of the passive and piezoactive materials is described in terms of complex moduli depending on the temperature of vibration heating. On the basis of numerical calculations, we study the influence of the temperature dependence of the properties of materials on the dynamic characteristics, temperature of vibration heating, electric indications of a sensor, and active modal damping of the shell by the piezoactuator (with regard for the indications of the sensor).
198-209
Problem of Electroviscoelasticity for Multiply Connected Plates
Аннотация
We propose a method for the solution of the problem of electroviscoelasticity for multiply connected plates. By the method of small parameter, the problem is reduced to the recurrent sequence of problems of electroviscoelasticity that can be solved with the use of complex potentials. We propose a procedure for the determination, according to the complex potentials, of the approximate values of the principal characteristics of electroelastic state (stresses and the components of the vectors of induction and electric-field strength) at any time after the application of loading. As an example, we present the solution of the problem for a plate with elliptic hole. The results of numerical investigations reveal a strong influence of time on the values of the principal characteristics of the electroviscoelastic state.
210-228
Natural Vibrations of Parabolic Shells
Аннотация
The Rayleigh–Ritz method is used to analyze the natural vibrations of parabolic shells. The expressions for the kinetic and potential energies of a parabolic shell with fixed thickness are obtained. The properties of eigenfrequencies and eigenmodes of natural vibrations of the shells of different heights are investigated.
229-238