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On the stability of the zero solution of a periodic reversible secondorder differential equation
No full textThe problem of the stability of the zero solution of the second-order differential equation
describing the periodic perturbations of an oscillator with a nonlinear reducing force is
studied. The problem in the autonomous case was solved by A.M. Lyapunov. The so called
transcendental case when all members of the decomposition of the right part of the differential
equation into series are to be taken into account, is considered. This case takes place
for reversible differential equations, i. e. equations that do not change when time is replaced by the opposite value. The problem is solved by the methods of the KAM theory, according
to which in any neighborhood of the equilibrium position at the origin of the phase
plane there are periodic invariant two-dimensional tori that separate the three-dimensional
configuration space. These tori are considered as two-dimensional periodic invariant surfaces
covering the time axis from where the stability (non-asymptotic) of the zero solution
followed. The problem to be solved is characterized by the fact that the unperturbed part
of the equation contains a dissipative term (a term dependent on velocity) which has the
same order of smallness as the restoring force. It is established that if a dissipative part
of the perturbation is small enough then the unperturbed movement is stable according to
Lyapunov
Ultrapowers of Banach algebras
No full textIn this paper, we consider ultrapowers of Banach algebras as Banach algebras and the
product (J,U) on the second dual of Banach algebras. For a Banach algebra A, we show
that if there is a continuous derivation from A into itself, then there is a continuous derivation
from (A
∗∗
, (J,U)) into it. Moreover, we show that if there is a continuous derivation
from A into X∗∗, where X is a Banach A-bimodule, then there is a continuous derivation
from A into ultrapower of X i. e., (X)U. Ultra (character) amenability of Banach algebras
is investigated and it will be shown that if every continuous derivation from A into (X)U
is inner, then A is ultra amenable. Some results related to left (resp. right) multipliers on
(A
∗∗
, (J,U)) are also given
Gravitational instability of gasdust circumnuclear disks in nearby galaxies
No full textUsing the two-dimensional multi-component hydrodynamical simulations, we study the effect
of dust on the development of instability in the gas-dust mini-disks observed in the
central regions of galaxies. The dust is coupled with the gas gravitationally and by means
of a friction force depending on the velocity difference between the two components. The
presence of dust leads to the instability of a mini-disk and the development of a spiral
structure observed in the gas-dust mini-disks. The spiral structure is multi-armed, which
is caused by a dominance of the high order Fourier harmonics in the unstable modes. The
instability of gas-dust circumnuclear disks is an important mechanism for explaining the
activity of galactic nuclei associated with the accretion of matter onto a central black hole.
We find that the admixture of dust with a dust-to-gas ratio of 10–20% significantly destabilizes
the gas-dust disk
Criminal law guarantees of human dignity and development of biotechnology
No full textThe article examines the impact of biotechnology progress on changing criminal law. The author
concludes that somatic rights do not constitute a new generation of human rights but enrich
the dignity of the individual. Due to the natural nature of these rights, they can only be
regulated to a small extent by law, which also limits the possibility of imposing prohibitions.
Criminal law must address the task of guaranteeing the dignity of the individual. There is a need
for clearer regulation of circumstances that exclude the crime of an act, such as the consent
of the victim and reasonable risk. Criminalization of biotechnology applications where there
were no signs of abuse should be considered unreasonable. Scientific progress has created
uncertainty in the application of certain rules of criminal law. This requires the improvement of
sentencing rules and the calculation of the statute of limitations of criminal prosecution. The
need to criminalize new types of acts against the person, to introduce responsibility for crimes
against artificial organs, as well as organs and tissues separated from a person, was analyzed.
Issues of criminal legal assessment of illegal acts with human embryos are considered. It was
concluded that it is necessary to include genetic information in the area of privacy protected
by criminal law. An analysis of the development vectors of criminal law shows the impossibility
of effective deterrence by prohibitions of certain ways of self-determination of the individual.
The Russian legislator in this matter shows reasonable restraint. When further improving the
criminal law, it is unacceptable to use the design of formal offences. As criminal-forming signs
of prohibited acts, there can be both objective characteristics (the method of medical intervention
caused by harm) and subjective ones — motive, purpose (for example, performing a sex
reassignment operation for unlawful purposes). This will allow criminal law not to stand in the
way of biotechnological progress, helping medical legislation determine some boundaries. The
article analyses the norms of criminal law, the provisions of international conventions, and the
practice of constitutional proceedings
Cultural relations of the Russian Federation and the Republic of Austria at the beginning of the 21st century
No full textThe present study is devoted to the analysis of the Russian-Austrian cultural relations in the
beginning of the 21st century. In the article an attempt to identify and assess current trends and forms of cultural dialogue between Russia and Austria, the factors which influence bilateral
cooperation, as well as to assess the prospects of cultural relations has been made on the
basis of extensive source materials and research literature. Modern cultural relations between
the two countries reflect the general trends and peculiarities of modern bilateral interaction,
are characterized by diversity and depth. Bilateral cultural exchange involves not only capitals,
major cities, but also the regions. Cultural cooperation between the Russian Federation and
the Republic of Austria today is based on a solid legal framework, which is replenished with
new documents on both the current programs of cultural exchange and strategic issues. A relevant
trend of the modern cultural cooperation is institutionalization. This feature is reflected
in the modern dialogue between Russia and Austria. Cultural centers, public and state organizations
are successful actors of bilateral cooperation, they bring together a wide audience of
participants and contribute to the development of cultural contacts on an ongoing basis. Particular
attention in the article is paid to a new format of bilateral cultural cooperation between
Russia and Austria — the cross-years of cultures, which have become traditional large-scale
events of bilateral exchange. This format contributes to the regionalization of interaction and
has an impact on economic, political dialogue and investment policy. The conclusions of the
study allow identifying the potential of bilateral cooperation between the Russian Federation
and the Republic of Austria and forecasting the possible prospects of the cultural dialogue.
The chronological framework of this article is the beginning of the 21st to 2020
Assessing the risks of spatial disintegration in a state with a multinuclear territorial and political structure (on the example of Bolivia)
No full textThis article carries out an assessment of risks of spatial disintegration using a methodology developed
by the authors. The methodology makes it possible to quantify the danger of weakening,
disruption, and destruction of the system-forming links between the administrative-territorial
units of the country. The authors have identified seven factors of spatial disintegration: historical,
socio-economic, domestic political, ethno-cultural, military-strategic, transport, and foreign
policy. As an example of testing this technique, Bolivia was chosen as a state that has patterns
of economic, political, socio-cultural development characteristic of most Latin American countries.
But unlike most of them, Bolivia has a multi-core territorial and political structure: in the
political field, the actual (La Paz) and constitutional (Sucre) capitals compete with an alternative
pole of growth — the city of Santa Cruz de la Sierra in the flat east of the country. The Santa Cruz
Department initiates and coordinates various innovations and projects aimed at increasing the
autonomy of the east of the country or federalization of Bolivia. The calculations have shown
that Bolivia has significantly higher risks of potential disintegration compared to several Latin
American states (Mexico, Venezuela, Chile). Modern Bolivia is a contradictory system of two
heterogeneous socio-cultural, economic and political regions — the mountainous West, inhabited
by Aymara and Quechua, that economic development is based on the mining industry,
and the plain East, populated by Creoles and Guarani, economically stimulated by natural gas
production and more intensive agriculture. It is determined that the departments of Santa Cruz
and Tarija have the greatest risks of spatial disintegration within Bolivia
The mentions about ancient Slavs (aṣ-Ṣaqālibah) by «the father of the Muslim historiography» aṭ- Ṭabarī (839–923)
No full textThe author of this article extracted all historical, geographical and ethnographical materials
(including legendary) concerning the ancient Slavs of the Eastern Balkans and Asia Minor mentioned in
the multivolume «History of the Prophets and Kings» (Ta’rīḫ ar-Rusul wa-l-Mulūk) by «the father of the
Muslim historiography», an Arabic spoken Iranian Muḥammad b. Ǧarīr (Djarir) aṭ-Ṭabarī (839–923), which
outlines the general history from the Creation to 302 AH (914/5). The extracted passages are from a classic
edition carried out in three series and 15 volumes by the eminent Dutch Arabist Michael Jan de Goeje
(1836–1909) in Leiden (Annales quos scripsit Abu Djafar Mohammed ibn Djarir at-Tabari / Cum aliis
ed. M. de Goeje. Series I–III. Lugduni Batavorum, 1879–1901). The selected passages are translated from
Classical Arabic into Russian for the first time. The detailed text notes and scholarly comments based on
the historical and geographical narratives of the Antiquity, Pre-Islamic Middle East, Christian and Muslim
Orient are attached to the translated materials as well. They are also based on the world’s leading scientific,
reference (encyclopedic) and educational publications.The reported study was funded by the Russian Foundation for Basic Research,
project number 20-09-00010
Complement to the Hölder inequality for multiple integrals. II
No full textThis article is the second and final part of the author’s work published in the previous
issue of the journal. The main result of the article is the statement that if for functions γ1 ∈ Lp1 (Rn), . . . , γm ∈ Lpm(Rn), where m 2 and the numbers p1, . . . , pm ∈ (1,+∞]
are such that 1
p1
+ . . . + 1
pm
< 1 the “non-resonant” condition is fulfilled (the concept
introduced by the author in the previous work for functions from spaces Lp(Rn), p ∈
(1,+∞]), then: supa,b∈Rn
[a,b]
m
k=1
[γk(τ) +Δγk(τ )] dτ
C
m
k=1
γk +Δγk
L
pk
hk
(Rn), where
[a, b] — n-dimensional parallelepiped, the constant C > 0 does not depend on functions
of Δγk ∈ Lpk
hk
(Rn) and Lpk
hk
(Rn) ⊂ Lpk (Rn), 1 k m are some specially constructed
normalized spaces. In addition, in terms of the fulfillment of some non-resonant condition,
the paper gives a test of a boundedness of the integral from the product of functions when
integrating over a subset of Rn
Heat and radiative fluxes in strongly nonequilibrium flows behind shock waves
No full textState-to-state and two-temperature theoretical models for high-temperature strongly nonequilibrium
reacting and radiating air flows are developed in the framework of the generalized
Chapman—Enskog method. In the theoretical approach, the sets of governing
equations for coupled fluid dynamics, chemical kinetics, internal energy transitions and
radiation are derived; the algorithms for the calculation of state-resolved transport coefficients
are developed and implemented. The proposed models are applied for 1-D simulations
of shock waves in air under high-temperature conditions observed in flight experiments. Nonequilibrium mixture composition, temperatures and pressure profiles are obtained and
compared for various models of chemical reaction rate coefficients. Flow variables strongly
depend on both the kinetic-theory approach and chemical reaction model; species molar
fractions and temperature show significantly different behaviour for the state-to-state and
two-temperature simulations. Transport properties and radiative fluxes are calculated as
functions of the distance from the shock front. It is found that diffusion provides a major
contribution to the total energy flux whereas the role of heat conduction is weak due to
the compensation effects. It is shown that under considered conditions, two-temperature
models are not applicable for correct predictions of radiative heating.The work is supported by the Russian Science Foundation (project no. 22-11-00078)