DSpace Собрание:
http://hdl.handle.net/11701/9242
2019-12-07T10:24:53ZOn the limiting behavior of a time-delay system’s solutions
http://hdl.handle.net/11701/10448
Название: On the limiting behavior of a time-delay system’s solutions
Авторы: Kuptsova, Svetlana E.; Kuptsov, Sergey Yu.; Stepenko, Nikolai A.
Краткий осмотр (реферат): In the present paper, we study motions of time-delay systems that have limiting behavior for
an unbounded increase in time in the case when the limit sets might not be invariant with
respect to initial differential-difference equations. The concept of an asymptotic quiescent
position for the trajectories of time-delay systems is introduced. By the use of the Lyapunov
functionals method, sufficient conditions for the existence of an asymptotic quiescent position
for systems of differential-difference equations were obtained. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are
obtained. Namely, the condition of the negativity of the time-derivative of Krasovskii
functionals is weakened.2018-06-01T00:00:00ZOn stabilization of a class of systems with time proportional delay
http://hdl.handle.net/11701/10447
Название: On stabilization of a class of systems with time proportional delay
Авторы: Zhabko, Aleksei P.; Tikhomirov, Oleg G.; Chizhova, Ol’ga N.
Краткий осмотр (реферат): In this paper, we investigate a possibility of the linear difference-differential system stabilization
with time proportional delay by the linear observation. Using the sufficient conditions
of asymptotic stability for the linear systems with linearly increasing delay, we obtain some
conditions of the asymptotic evaluation system existence for the original system. Then we use
the asymptotic evaluation system for the construction of the stabilizing control and derive
the sufficient conditions for the existence of such control.2018-06-01T00:00:00ZMathematical modelling of pulsativе blood flow in deformable arteries
http://hdl.handle.net/11701/10446
Название: Mathematical modelling of pulsativе blood flow in deformable arteries
Авторы: Tregubov, Vladimir P.; Ratkina, Svetlana V.
Краткий осмотр (реферат): The comprehensive analysis of structure and properties was performed for the blood and
blood vessels. This analysis shows that the blood may be considered as a liquid only in large
and middle vessels, where a diameter of vessel is much more than a dimension of blood
cells and their aggregates. In addition, taking into account the influence of complex internal
structure on its mechanical properties, it is necessary to consider it as a non-Newtonian liquid.
In this regard, the non-Newtonian liquid with the power connection of the stress tensor with
the strain velocity tensor was chosen for mathematical modelling of liquid. The pulsating flow
is created by the pulsating nature of the boundary condition for the blood flow at the input
cross-section. The vessels are considered as thick-walled cylinders with hyperelastic walls.
The interaction between blood and vessel wall is defined by means of semi-slip boundary
condition. Computer simulation was performed in software complex ANSYS with the use of
the direct conjugating module CFX and the module ANSYS “Multiphysics”. As a result, the
pressure and stress wave propagation on the vessel wall was obtained.2018-06-01T00:00:00ZThe entropy approach construction of the optimal structure of the chain of the automated identification systems basic stations for inland waterways
http://hdl.handle.net/11701/10445
Название: The entropy approach construction of the optimal structure of the chain of the automated identification systems basic stations for inland waterways
Авторы: Karetnikov, Vladimir V.; Vasin, Andrei V.
Краткий осмотр (реферат): The article deals with a constructive approach based on the entropy for constructing a
quasi-optimal chain of automated identification systems (AIS) base stations on the inland
waterways. The inland waterways of Russian Federation play an important role in providing
the transport process while transporting various types of cargo and passengers. Here is
a special way, it is worth noting the info-communication system of the first hierarchical
level of the vessel control system. This class of AIS is the most promising for large-scale
implementation of the inland waterways of Russian Federation. For the full-fledged operation
of such info-communication systems on the inland waterways of Russian Federation, it is
necessary to form a continuous information field, formed by sufficient overlapping of the
working zones of the operation of AIS base stations connected in a chain. To estimate the
optimal number of AIS base stations, we consider inland waterways as a fractal set. Therefore,
it is convenient to estimate the number of stations forming a continuous coverage zone in
terms of the Hausdorff measure. The problem is to find the minimal quantity of elements of
the r-network for different r. This number is calculated by means of r-entropy Hr of the set
under consideration. The entropy approach allows us to take into account the phenomenon
of collapse of AIS base station coverage zone in case of interference with a useful signal of a
spectrum-centered noise. This case corresponds to the entropy H of the set (the limit of Hr
when r tends to 0).2018-06-01T00:00:00ZSelection of homogeneous zones of agricultural field for laying of experiments using unmanned aerial vehicle
http://hdl.handle.net/11701/10444
Название: Selection of homogeneous zones of agricultural field for laying of experiments using unmanned aerial vehicle
Авторы: Bure, Vladimir M.; Mitrofanov, Evgenii P.; Mitrofanova, Olga A.; Petrushin, Aleksei F.
Краткий осмотр (реферат): An important stage in research aimed at solving the problems of accurate farming is the
laying of field experiments. A necessary condition for carrying out such experiments is to
ensure homogeneity of the selected land plot. Most of the existing techniques for isolating
homogeneous zones for conducting experiments are based on costly and labor-intensive
sampling and analysis of soil samples. An alternative and promising approach is the use
of an unmanned aerial vehicle. In work, all stages of choosing a homogeneous land plot with
the help of aerial photography are presented in sufficient detail. The object of the study
was a field with a long-term sowing of “goat” on the basis of the Menkovsky branch of
the Agrophysical Institute (Leningrad region). Aerial photography was carried out in 2015–
2017 with the help of an unmanned aerial vehicle “Geoscan 401”. The received data were
processed with the help of specialized software: crosslinking and alignment were carried out
in the Agisoft PhotoScan program; the thematic processing and allocation of homogeneous
areas of the field were carried out in the programs QGis and Saga Gis. To assess the state of
vegetation, the vegetative index NDVI (Normalized Difference Vegetation Index) was applied.
To cluster the homogeneous parts of the field in terms of NDVI parameters the ISODATA
algorithm (Iterative Self-Organizing Data Analysis Technique Algorithm) was applied. The
paper presents the results of clustering images of the same field in different time periods.
In the course of the work, intersections of these aerial photographs were constructed, four
clusters were identified, which are the intersection of the corresponding homogeneous zones
for the considered time periods. Accordingly, the laying of experiments is expedient to be
carried out on these sites, since the homogeneity present there seems more stable in dynamics.2018-06-01T00:00:00ZQuadratic and cubic Volterra polynomials: identification and application
http://hdl.handle.net/11701/10443
Название: Quadratic and cubic Volterra polynomials: identification and application
Авторы: Solodusha, Svetlana V.
Краткий осмотр (реферат): Volterra kernels identification is the main problem in constructing an input-output type
mathematical model of nonlinear dynamical system by a Volterra polynomial of Nth
order. Currently, various algorithms for solving this problem are proposed. Usually, it is
assumed that the decomposition of the dynamical system response y(t) into components
is preliminarily performed. Each of components is due to the influence of the concrete
integral term. In general, the separation problem is invariant with respect to a particular
family of test actions, and the choice of amplitudes of the test signals used to identify the
Volterra kernels is related to the necessary conditions for the solvability of the corresponding
multidimensional integral equations in special classes of functions. In the present paper,
existence theorems for solutions of two-dimensional and three-dimensional Volterra integral
equations of the first kind are given. This result is obtained in terms of the amplitudes of
the test signals. This will allow us to remove the arbitrariness in the choice of amplitudes
in construction of the quadratic and cubic Volterra polynomials in the case when external
action x(t) = (x1(t), x2(t))T is a vector function of time. Illustrative calculations are given
through the dynamic reference systems.2018-06-01T00:00:00ZDirect solution of a minimax location problem on the plane with rectilinear metric in a rectangular area
http://hdl.handle.net/11701/10442
Название: Direct solution of a minimax location problem on the plane with rectilinear metric in a rectangular area
Авторы: Plotnikov, Pavel V.; Krivulin, Nikolai K.
Краткий осмотр (реферат): A minimax single-facility location problem with rectilinear (Manhattan) metric is examined
under constraints on the feasible location region, and a direct, explicit solution of the problem
is suggested using methods of tropical (idempotent) mathematics. When no constraints are
imposed, this problem, which is also known as the Rawls problem or the messenger boy
problem, has known geometric and algebraic solutions. In the present article, a solution to
the problem is investigated subject to constraints on the feasible region, which is given by a
rectangular area. At first, the problem is represented in terms of tropical mathematics as a
tropical optimization problem, a parameter is introduced to represent the minimum value of
the objective function, and the problem is reduced to a parametrized system of inequalities.
This system is solved for one variable, and the existence conditions of solution are used to
obtain optimal values of the second parameter by using an auxiliary optimization problem.
Then, the obtained general solution is transformed into a set of direct solutions, written in
a compact closed form for different cases of relations between the initial parameters of the
problem. Graphical illustrations of the solution are given for several positions of the feasible
location region on the plane.2018-06-01T00:00:00ZEquilibrium route flow assignment in linear network as a system of linear equations
http://hdl.handle.net/11701/10441
Название: Equilibrium route flow assignment in linear network as a system of linear equations
Авторы: Krylatov, Alexander Yu.; Shirokolobova, Anastasiya P.
Краткий осмотр (реферат): Decision making requires possibilities to influence the object. In urban traffic area it is
crucial to influence traffic flows. However, first of all, decision maker needs comprehensive
information about traffic flows. From a practical perspective, the most valuable is information
about route flows, unlike information about link flows. In this paper, a route flow traffic assignment model in a linear network is studied. Linear road network (linear link performance
function) gives a chance to reduce traffic assignment problem to a system of linear equations
and conditions in the form of linear inequalities. The directed graph represents road network.
Route flow traffic assignment problem is presented as a nonlinear constrained problem. The
theorem about the reduction of a route flow traffic assignment problem in linear road network
to the system of linear equations is proved. Implementation of developed approach to an
example of the linear road network is disassembled in details.2018-06-01T00:00:00ZMathematical modeling of the deformation of composite plane with interface crack for semi-linear material
http://hdl.handle.net/11701/10440
Название: Mathematical modeling of the deformation of composite plane with interface crack for semi-linear material
Авторы: Domanskaya, Tatyana O.; Malkov, Venyamin M.; Malkova, Yulia V.
Краткий осмотр (реферат): The exact analytical solutions have been obtained for the nonlinear problems (plane-strain
and plane-stress) for the bi-material plane with an interface crack. The plane is formed
by joining of two half-planes made from different materials. Mechanical properties of halfplanes
are described with the model of semi-linear material. The application of this model
has allowed using the methods of the complex functions in the nonlinear boundary value
problems. For this particular case the problem is solved for the plane with a free interface
crack at given constant nominal (Piola) stresses at infinity. The expressions for nominal
stresses, Cauchy stresses and displacements are obtained. From the general solutions the
asymptotic expansions of these functions have been constructed in vicinities of crack tips. It
is established that in the nonlinear problem of uniaxial extension of a plane with a free crack
the formulas which give the crack disclosing differ by a constant factor from the formulas of
linear elasticity. The stress intensity factors (SIF) of nonlinear and linear problems coincide.
The nominal stresses have the root singularity at the tips of a crack; the Cauchy stresses
have no singularity.2018-06-01T00:00:00ZOn the diagonal stability of some classes of complex systems
http://hdl.handle.net/11701/10439
Название: On the diagonal stability of some classes of complex systems
Авторы: Aleksandrov, Alexander Yu.; Vorob’eva, Anna A.; Kolpak, Eugeny P.
Краткий осмотр (реферат): The paper deals with the problem of diagonal stability of nonlinear difference-differential
systems. Certain classes of complex systems with delay and nonlinearities of a sector type
are studied. It is assumed that these systems describe the interaction of two-dimensional
blockswith a delay in connections between the blocks. Two kinds of structure of connections
are investigated. For every kind, necessary and sufficient conditions for the existence of
diagonal Lyapunov—Krasovskii functionals are found. The existence of such functionals
guarantees the asymptotic stability of the zero solutions of considered systems for any
nonnegative delay and any admissible nonlinearities. These conditions are formulated in
terms of the Hurwitz property of specially constructed Metzler matrices. The proposed
approaches are used for the stability analysis ofsome models of population dynamics.
Generalized Lotka—Volterra models composed of several interacting pairs of predator-prey
type are investigated. With the aid of the Lyapunov direct method and diagonal Lyapunov—
Krasovskii functionals, conditions are derived under which equilibrium positions of the
considered models are globally asymptotically stable in the positive orthant of the state space
for any nonnegative delay. An illustrative example and results of the numerical simulation
are presented to demonstrate the effectiveness of the developed approaches.2018-06-01T00:00:00Z