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Fundamental mathematics and physics
V.V. Varlamov
About Axiom System of Nonlocal Quantum Theory
An axiom system of nonlocal quantum theory is defined within Heisenberg-Fock
conception. A notion of single quantum system lies in the ground of axiomatics.
A generating kernel of this system is an abstract \(C^\ast\)-algebra. It is shown that different
concrete realizations of the operator algebra depend on the structure of generators of
the group of a fundamental symmetry (these generators are joined to energy operator).
In the case of generators of the conformal group, we have a state spectrum
defined within Rumer-Fet representation, that leads to a group-theoretical description
of Mendeleev periodic system.
Keywords: single quantum system, Heisenberg-Fock conception, operator algebra,
complex envelopes, conformal group, Mendeleev periodic system.
A.G. Grin'
On the Attraction of Symmetric Functions from Dependent Variables to the Normal Law
The necessary and sufficient conditions for attracting a certain class of
functions from dependent random variables to a normal law are obtained. These
conditions include the so-called minimal conditions of weak dependence.
Keywords: symmetric functions of random variables, attraction to the normal law, minimal conditions of weak dependence.
I.A. Eganova, W. Kallies
Foundation of Minkowski's World as a Mathematical Structure: to the Answer for Riemann's Question
In the given article B. Riemann's gnoseological question about an internal
cause of initiation of metric relations in space with respect to the World of
events (space-time) is raised. On the whole, the relevance of Riemann's question for
space-time is shown: its decision visualizes the physical foundation of Minkowski's
World, gives new notations about interconnections in the World of events and appreciably
new methods for experimental investigations. An executed in the article
conceptual review of historical development of A.D. Alexandrov's approach to the
Riemann's question is made according to the following plan. 1. Previously, it was
shown that Alexandrov's approach is completing the definite sequence of investigations,
namely of H. Minkowski, A.A. Friedman, and N.A. Kozyrev, in the World
of events history. 2. Further, along Alexandrov's line, it is determined that on the
basis of Friedman's and J.L. Synge's analysis of methods of temporal intervals measurements
and G.J. Whitrow's decision of the problem of the standard clock choice
an innate (a priori) interconnection of simultaneous world events, that is able to
create the space-time metric, is revealed. 3. Then we are taking into consideration
that the essence of physical processes, which are used for the temporal intervals
measurements, indicates in fact some way to finding a possibility of observations of
a certain physical phenomenon which is connected with the a priori interconnection
of simultaneous world events. Some mathematical relation indicating that as this
phenomenon figures the revealed and successively learned by Kozyrev distance-type
action of external irreversible processes changing the internal state of any complex,
structured systems, that can be in various internal states, is obtained and analyzed.
This phenomenon, in principle, justifies the known I. Prigogine's notations about a
constructive function of irreversible processes in the appearance, existence, and evolution
of complex systems. 4. And finally, some results of astronomical observations,
which testify about properties of the Minkowski's World structure, are considered and
new possibilities for investigations of various branches of science are enumerated.
Keywords: Minkowski's World, World of events, space-time, space-time metric, measurements of temporal intervals, standard clock problem, irreversible processes.
A.N. Kabanov
The Upper Hypercentral Series of the Group of Unitriangular Automorphisms of a Free Leibniz Algebra
The upper hypercentral series of the group of unitriangular automorphisms
of a free Leibniz algebra over an arbitrary field is described. The length of this series
is obtained.
Keywords: Leibniz algebra, unitriangular automorphism, hypercenter.
N.V. Michailova
Problem-Oriented Justification of the Modern Mathematical Analysis
Formation of the mathematical analysis revealed a contradiction between
its ability to receive concrete mathematical results and specific difficulties of its justification. Article considers problem-oriented justification of the mathematical
analysis.
Keywords: justification of the modern mathematical analysis, problem-oriented approach, philosophy of mathematics aspects.
V.I. Strunin, V.V. Shkurkin, A.A. Lyahov
Software and Hardware Equipment for Probe Diagnostics of Low-Temperature Plasmas
Automated system for probe measurements in low-temperature plasmas is considered. To acquire of current-voltage characteristics a multifunctional data-acquisition board is used. The double differentiation of characteristics is provided by the programmed digital filter. The test probe characteristic of air lower pressure plasma was obtained and the electron energy distribution function was recovered from it. The influence of filter's parameter on the accuracy of electron mean energy measurements is also discussed.
Keywords: Langmuir probe, Savitsky-Goley filter, differentiation of experimental curves, automated measurements.
R. Martinez, V. Kreinovich
Does the Universe Really Expand Faster than the Speed of Light: Kinematic Analysis Based on Special Relativity and Copernican Principle
In the first approximation, the Universe�s expansion is described by the Hubble�s law v = H � R, according to which the relative speed v of two
objects in the expanding Universe grows linearly with the distance R between them. This law can be derived from the Copernican principle, according to
which, cosmology-wise, there is no special location in the Universe, and thus, the expanding Universe should look the same from every starting point. The
problem with the Hubble�s formula is that for large distance, it leads to nonphysical larger-than-speed-of-light velocities. Since the Universe�s expansion
is a consequence of Einstein�s General Relativity Theory (GRT), this problem is usually handled by taking into account GRT�s curved character of spacetime.
In this paper, we consider this problem from a purely kinematic viewpoint. We show that if we take into account special-relativistic effects when
applying the Copernican principle, we get a modified version of the Hubble�s
law, in which all the velocities are physically meaningful � in the sense that
they never exceed the speed of light.
Keywords: cosmological expansion, Copernican principle, special relativity, faster-than-speed-of-light.
Applied Mathematics and Modeling
S.L. Deryabin, A.S. Kiryanova
Mathematical Modeling of Fluid Flows Under Gravity is Appearing as a Result Of Damage to the Dam
The paper examines the three-dimensional isentropic flows of a
polytropic gas under the action of gravity. As a mathematical model, a system
of equations of gas dynamics for a polytropic gas is used. With the polytropic
index \( \gamma=7.02 \), this system describes the movement of water. The system introduces
an orthogonal curvilinear coordinate system. To formulate the problem of the
disintegration of a special discontinuity, the system makes a degenerate change of
variables, namely: dependent and independent variables change roles. In new
variables, an initial-boundary value problem with data on the sound characteristic
and an additional condition is posed for the system. The solution of the
initial-boundary value problem is constructed in the form of power series. The
convergence of the constructed series in the region from the surface of a weak
discontinuity to the gas-vacuum boundary is proved. To determine the law of motion
of the gas-vacuum boundary, a quasilinear system of partial differential equations
is written out, which, with the help of the characteristic parameter, reduces to a
system of ordinary differential equations.
Keywords: polytropic gas, vacuum, force of gravity, the gas dynamics equations,
gas-vacuum boundary, initial-boundary value problem, Riemann problem, centered wave.
A.B. Krohaleva, V.M. Belov
The Human Factor in the System of Socially Significant Activity
In article the entity and a role of a human factor in an assessment of
quality of socially important activities are considered. The evolution of this category
is provided, since the period of operations of neoclassics until now. Determination of a human
factor in the context of socially important activities is offered. For the description
of component composition of an integral index of a human factor the classification by
different bases is provided: the form of the embodiment, the nature of interaction in
system, the content of knowledge, the subject of a human factor. Basic approaches
to an assessment of a human factor are analyzed. The two-component model of an
assessment of a human factor in socially important activities, consisting of units of
qualitative and quantitative analysis of data with use of linguistic, mark and interval
scales, is offered. The quantitative component represents an integral assessment of the
measured characteristics by means of a complex of medical instruments and devices,
combinations of psychophysiological tests. The qualitative component contains an
assessment of difficult formalized characteristics in the conditions of uncertainty of
basic data.
Keywords: human factor, fuzzy logic, interval analysis, quality assessment, socially significant activity.
A.A. Senkovskaya
Modeling the Distribution Process of the Department's Teaching Load Using a Greedy Algorithm
The main reasons for the need to automate the process of distribution of
the academic load of the department are presented. The mathematical formulation
of the load distribution problem of the department is formulated. The main algorithms
realizing the assigned task are considered, in particular greedy algorithms aimed at
optimization of this automated process.
Keywords: optimization, modeling, teaching load, greedy algorithm.
A.M. Pownuk, O. Kosheleva, V. Kreinovich
Towards Decision Making under General Uncertainty
There exist techniques for decision making under
specific types of uncertainty, such as probabilistic, fuzzy, etc.
Each of the corresponding ways of describing uncertainty has its
advantages and limitations. As a result, new techniques for
describing uncertainty appear all the time. Instead of trying to
extend the existing decision making idea to each of these new
techniques one by one, we attempt to develop a general approach
that would cover all possible uncertainty techniques.
Keywords: decision making, general uncertainty, fuzzy uncertainty, probabilistic uncertainty.
F. Zapata, O. Kosheleva, V. Kreinovich
Why Stable Teams Are More Efficient in Education
It is known that study groups speed up learning.
Recent studies have shown that stable study groups are more
efficient than shifting-membership groups. In this paper, we
provide a theoretical explanation for this empirical observation.
Keywords: study groups, stable groups, shifting-membership groups.
O. Kosheleva, V. Kreinovich
The Onsager Conjecture: A Pedagogical Explanation
In 1949, a Nobelist Lars Onsager considered
liquid flows with velocities changing as \(r^\alpha\) for spatial
points at distance \(r\), and conjectured that the threshold value
\(\alpha=1/3\) separates the two possible regimes: for \(\alpha>1/3\)
energy is always preserved, while for \(\alpha<1/3\) energy is
possibly not preserved. In this paper, we provide a simple
pedagogical explanation for this conjecture.
Keywords: Euler equations, hydrodynamics, Onsager conjecture.
Computer Science
Heuristic Network for Chatbot Program
An efficient algorithm for the heuristic network, with some properties similar to a recurrent neural network, for a virtual companion program is proposed in the article. The
algorithm is improved with the use of an explanatory dictionary of the Russian
language. A generator of new responses on the basis of statistical information knowledge base
is introduced in the heuristic network.
Keywords: chatbot, virtual companion, recurrent neural network, heuristic network.
L. Brunoni, O. Beaudet-Labrecque
Smart Contracts and Cybercrime: a Game Changer?
The purpose of this paper is to provide a brief explanation regarding
the authors� current research in the field of the possible uses of smart contracts
in cybercrime, focusing in particular on how the technology could provide a
substitute for trust both in client-criminal transactions and in transactions
taking place within criminal organizations. The authors share the conviction
put forward by Alharby and Moorsel [1] in their 2017 analysis of blockchain-based smart contracts that there is a �lack of studies on criminal activities
in smart contracts�: while quality research does exist, including a paper by
Juels et al. [2] detailing three types of such activities that can be facilitated
by the technology, it is evident that the subject deserves a more widespread
attention. Quality research, in fact, could play an important role in aiding
authorities and regulators to understand the issue and react accordingly.
Keywords: smart contracts, blockchain, cybercrime, cybersecurity, criminal behavior.