DSpace Общество:http://hdl.handle.net/11701/64562018-12-15T05:31:03Z2018-12-15T05:31:03ZAbout book “Mathematical Petersburg”http://hdl.handle.net/11701/151402018-12-14T00:02:26Z2018-12-01T00:00:00ZНазвание: About book “Mathematical Petersburg”
Краткий осмотр (реферат): About book “Mathematical Petersburg”2018-12-01T00:00:00ZIn memoriam of Veniamin Vladimirovich Vityazevhttp://hdl.handle.net/11701/151392018-12-14T00:02:29Z2018-12-01T00:00:00ZНазвание: In memoriam of Veniamin Vladimirovich Vityazev
Краткий осмотр (реферат): In memoriam of Veniamin Vladimirovich Vityazev2018-12-01T00:00:00ZIn memoriam of Gennadii Alekseevich Leonovhttp://hdl.handle.net/11701/151382018-12-14T00:02:25Z2018-12-01T00:00:00ZНазвание: In memoriam of Gennadii Alekseevich Leonov
Краткий осмотр (реферат): In memoriam of Gennadii Alekseevich Leonov2018-12-01T00:00:00ZModeling of energy characteristics of atmospheric boundary layerSolovev, Sergey Yu.Khrapunov, Evgenii F.http://hdl.handle.net/11701/151372018-12-14T00:02:28Z2018-12-01T00:00:00ZНазвание: Modeling of energy characteristics of atmospheric boundary layer
Авторы: Solovev, Sergey Yu.; Khrapunov, Evgenii F.
Краткий осмотр (реферат): The paper contains some experimental data obtained in modeling the atmospheric boundary
layer in the Landscape Wind Tunnel, a new test facility of the Krylov State Research
Centre. The test facility, measurement techniques and test data processing methods are
described. The atmospheric boundary layer is modelled in the long test section of this wind
tunnel using vortex generators in the form of cones and prism-shaped discrete roughness
elements. All flow characteristics are measured using thermoanemometry techniques. A case
study of modeling the average and pulsation velocity profile is used to demonstrate that the
atmospheric boundary layer can be modelled not only in terms of average characteristics
but also in terms of the main energy characteristics with acceptable accuracy for engineering
applications. Modelled average characteristics have been verified by comparing the
experimental data with the data contained in regulatory documentation on determination
of natural wind loads. Correct reproduction of energy characteristics is ensured based on
agreement with the known energy relationships: “−5/3” law, approximations of Davenport,
Karman, Liepmann. It is concluded that, in principle, special-purpose wind tunnels with
long test sections are able to simulate the main characteristics of atmospheric boundary
layer for various types of terrain.2018-12-01T00:00:00ZEnergy dissipation during vibrations of non-uniform composite structures. 2. Method of solutionParshina, Ludmila V.Ryabov, Victor M.Yartsev, Boris A.http://hdl.handle.net/11701/151362018-12-14T00:02:23Z2018-12-01T00:00:00ZНазвание: Energy dissipation during vibrations of non-uniform composite structures. 2. Method of solution
Авторы: Parshina, Ludmila V.; Ryabov, Victor M.; Yartsev, Boris A.
Краткий осмотр (реферат): This paper describes the method of numerical solution to decaying vibration equations for
heterogeneous composite structures. The system of algebraic equations is generated through
Ritz method using Legendre polynomials as coordinate functions. First, real solutions are
found. To find complex natural frequencies of the system, the obtained real natural frequencies
are taken as initial values, and then, by means of the third-order iteration method,
complex natural frequencies are calculated. The paper discusses the convergence of numerical solution of the differential equations describing the motion of layered heterogeneous
structures, obtained for unsupported rectangular two-layered plate. Bearing layer of the
plate is made of unidirectional CRP, its elastic and dissipation properties within the investigated
band of frequencies and temperatures are independent on vibration frequency.
The bearing layer has one of its outer surfaces covered with a layer of “stiff” isotropic
viscoelastic polymer characterized by temperature-frequency relationship for the real part
of complex Young’s modulus and mechanical loss factor. Validation of the mathematical
model and of the numerical solution method performed through comparison of calculation
results for natural frequencies and loss factor versus test data (for two composition variants
of two-layered unsupported beam) has shown their good correlation.2018-12-01T00:00:00ZExistence of liouvillian solutions in the problem of motion of a dynamically symmetric ball on a perfectly rough sphereKuleshov, Alexander S.Katasonova, Vera A.http://hdl.handle.net/11701/151352018-12-14T00:02:26Z2018-12-01T00:00:00ZНазвание: Existence of liouvillian solutions in the problem of motion of a dynamically symmetric ball on a perfectly rough sphere
Авторы: Kuleshov, Alexander S.; Katasonova, Vera A.
Краткий осмотр (реферат): The problem of rolling without sliding of a rotationally symmetric rigid body on a sphere
is considered. The rolling body is assumed to be subjected to the forces, the resultant of
which is directed from the center of mass G of the body to the center O of the sphere, and
depends only on the distance between G and O. In this case, the solution of this problem
is reduced to solving the second-order linear differential equation over the projection of the
angular velocity of the body onto its axis of symmetry. Using the Kovacic algorithm, we
search for Liouvillian solutions of the corresponding second order linear differential equation.
We prove that all solutions of this equation are Liouvillian in the case when the rolling
rigid body is a nonhomogeneous dynamically symmetric ball. The paper is organized as
follows. In the first paragraph, we briefly discuss the statement of the general problem of
motion of a rotationally symmetric rigid on a perfectly rough sphere. We prove that this
problem is reduced to solving the second order linear differential equation. In the second
paragraph, we find Liouvillian solutions of this equation for the case, when the rolling rigid
body is a dynamically symmetric ball.2018-12-01T00:00:00ZSpecificity of the Darboux mechanism rectilinear motionBurian, Sergei N.http://hdl.handle.net/11701/151342018-12-14T00:02:29Z2018-12-01T00:00:00ZНазвание: Specificity of the Darboux mechanism rectilinear motion
Авторы: Burian, Sergei N.
Краткий осмотр (реферат): Mechanisms of a parallel structure may have singularities in configuration space in which
system controllability may be lost or additional instantaneous degrees of freedom may
appear. These features have kinematic base. But interest is also represented by geometric
singularities, when the mechanism in some configuration could change the type of motion.
The example of a mechanism with branch points, the Darboux mechanism, is considered. It
is proved that this hinged mechanism can transform the rotational motion of one rod into
a (strictly) rectilinear motion of its vertex H. The rods of Darboux’s mechanism can form
geometric figures, such as triangles and a square (with diagonals drawn). In the “square”
configuration of the mechanism the branch point arises: the vertex H can move both along
the straight line L and along the curve γ. The rank of the holonomic constraints of the
system in singular point falls by one. For a rectilinear motion of the vertex H, the Lagrange
equation of the second kind is written in terms of the coordinate of H. The coefficients of
this equation smoothly extend through the branch point. The “limiting” behavior of reaction
forces in rods is analyzed when the mechanism moves to the branch point. An external force
that does not work on the point H leads to unlimited reactions in the rods. Kinematics at
the branch point are studied. The inverse problem of dynamics at a point where the rank
of holonomic constraints is not maximal is solvable. The Lagrange multipliers of Λi at the
branch point are not uniquely determined, but the forces corresponding to them acting on
the vertices of the mechanism are uniquely determined.2018-12-01T00:00:00ZA method for finding the optimal solution of a differential inclusionFominyh, Alexander V.http://hdl.handle.net/11701/151332018-12-14T00:02:25Z2018-12-01T00:00:00ZНазвание: A method for finding the optimal solution of a differential inclusion
Авторы: Fominyh, Alexander V.
Краткий осмотр (реферат): In the paper, we study a differential inclusion with a given continuous convex multivalued
mapping. For a given finite time interval, it is required to construct a solution of the
differential inclusion, that satisfies the given initial and the final conditions and minimizes
the integral functional. With the help of support functions, the original problem is reduced
to minimizing some functional in the space of partially continuous functions. In the case of
continuous differentiability of the support function of a multivalued mapping with respect to
the phase variables, this functional is Gateaux differentiable. In the paper, Gateaux gradient
is found, necessary conditions for the minimum of the given functional are obtained. On
the basis of these conditions, the method of the steepest descent is applied to the original
problem. Numerical examples illustrate the constructed algorithm realization.2018-12-01T00:00:00ZInverse shadowing in actions of Baumslag—Solitar groupFadeev, Aleksei V.http://hdl.handle.net/11701/151322018-12-14T00:02:28Z2018-12-01T00:00:00ZНазвание: Inverse shadowing in actions of Baumslag—Solitar group
Авторы: Fadeev, Aleksei V.
Краткий осмотр (реферат): In parallel with the shadowing theory (which is now very well-developed), the theory of
inverse shadowing was developed. The main difference between the two theories is that the
shadowing property means that we can find an exact trajectory near an approximate one
while the inverse shadowing means that given a family of approximate trajectories we can
find a member of this family that is close to any chosen exact trajectory. We generalise the
property of inverse shadowing for group actions and prove the absence of this property for
some linear actions of the Baumslag—Solitar group which is often considered as a source
of counterexamples.2018-12-01T00:00:00ZOne property of bounded complexes of discrete Fp[π]-modulesPodkopaev, Oleg B.http://hdl.handle.net/11701/151312018-12-14T00:02:25Z2018-12-01T00:00:00ZНазвание: One property of bounded complexes of discrete Fp[π]-modules
Авторы: Podkopaev, Oleg B.
Краткий осмотр (реферат): The goal of this note is to give a proof of the following proposition. Let π be a profinite group
and K
∗ be a bounded complex of discrete Fp[π]-modules. Assume all Hi(K
∗
) are finite
abelian groups. Then there exists a quasiisomorphism L
∗ −→ K
∗, where L
∗ is a bounded
complex of discrete Fp[π]-modules such that all Li are finite abelian groups. This is an
analogue for discrete Fp[π]-modules of a well-known lemma about bounded complexes of Amodules
(say, concentrated in nonnegative degrees), where A is a Noetherian commutative
ring, that establishes the existence of a quasiisomorphism between any such complex and
a complex of finitely generated A-modules that are free except, possibly, the one in degree
0. This lemma plays the key role in the proof of a base change theorem for cohomology of
coherent sheaves on Noetherian schemes, that in turn, can be used to prove a theorem of
Grothendieck about the behavior of dimensions of cohomology groups of a family of vector
bundles on a flat family of varieties.2018-12-01T00:00:00Z