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Fundamental mathematics and physics
A.K. Guts
On Sources of Antigravitation
The formula for the “gravitational” force in a constant static spherical-symmetric space-time,
allowing to describe the change of gravity to antigravity, is given. Possible sources of antigravitation are analyzed.
Keywords: antigravitation, source of antigravitation
A.N. Kabanov
Center Series of The Group of Unitriangular Automorphisms
of a Free Leibniz Algebra
The center series of the group of unitriangular automorphisms of a free
Leibniz algebra over an arbitrary field is described.
Keywords: Leibniz algebra, unitriangular automorphism, hypercenter.
T.K. Rustjumov, S.T. Rustjumova
Edge Connectivity of Polyhedra Vertices
At the beginning of the article the authors show unusual and still unknown
property of vectors by a concrete example in the 3–dimensional space. The concept
of ”conical basis” is introduced upon which new properties of vector space are proved
for vector spaces of any finite dimension.
Keywords:vector space, vector, cone, polyhedral cone, finitely generated cone, polytope,
polyhedra, inequality
O. Kosheleva, V. Kreinovich
Experimentally Observed Dark Matter Confinement Clarifies a Discrepancy in Estimating the Universe’s Expansion
Speed
It is well known that our Universe is expanding. In
principle, we can estimate the expansion speed either directly, by
observing the current state of the Universe, or indirectly, by
analyzing the cosmic background radiation. Surprisingly, these two
estimates lead to somewhat different expansion speeds. This
discrepancy is an important challenge for cosmologists. Another
challenge comes from recent experiments that show that, contrary
to the original idea that dark matter and regular (baryonic)
matter practically do not interact, dark matter actually
"shadows" the normal matter.
In this paper, we show that this "dark matter confinement" can
explain the discrepancy between different estimates of the
Universe's expansion speed. It also explains the observed
ratio of dark matter to regular matter.
Keywords: dark matter, Universe's expansion speed
O. Kosheleva, V. Kreinovich
Derivation of GrossPitaevskii Version of Nonlinear Schroedinger Equation from Scale Invariance
It is known that in the usual 3-D space, the
Schroedinger equation can be derived from scale-invariance. In
view of the fact that, according to modern physics, the actual
dimension of proper space may be different from 3, it is desirable
to analyze what happens in other spatial dimensions \(D\). It turns
out that while for \(D\ge 3\) we still get only the Schroedinger's
equation, for \(D=2\), we also get the Gross-Pitaevskii version of a
nonlinear Schroedinger equation that describes a quantum system of
identical bosons, and for \(D=1\), we also get a new nonlinear
version of the Schroedinger equation.
Keywords: scale-invariance, nonlinear Schroedinger equation,
Gross-Pitaevskii equation, system of identical bosons
A.M. Pownuk, V. Kreinovich
Why Linear Interpolation?
Linear interpolation is the computationally simplest
of all possible interpolation techniques. Interestingly, it works
reasonably well in many practical situations, even in situations
when the corresponding computational models are rather complex. In
this paper, we explain this empirical fact by showing that linear
interpolation is the only interpolation procedure that satisfies
several reasonable properties such as consistency and
scale-invariance.
Keywords: linear interpolation, scale-invariance
Applied Mathematics and Modeling
S.N. Astrakov, A.G. Kvashnin, L.A. Korolenko
Building Cost-Effective Sensor Networks
In this paper, we present methods for designing wireless sensor networks with
the use of models of the regular circular coverage. The problem dealt with in this work
is building the most efficient sensor network at a given complexity of its structure.
When solving this problem, the cost of a typical sensor and expenses to run the sensor
network are taken into account. The size of the effective area of sensors corresponds to
radii of circles. Complexity of the structure of a sensor network is defined by the
number of different sizes of circles (one, two or more types) and by a method of
positioning the circles. Accordingly, principles of classification of the regular
coverage are offered which are based on a notion of the minimum fragment. Methods of
calculating optimum number of sensors for bounded regions at a given structure of the
regular sensor network are presented.
Keywords: sensor networks, circular models of coverage, density of coverage, regular
structure of coverage, cost optimization.
L.A. Volodchenkova, A.K. Guts
The Equilibrium Dynamics of Soil Fertility in Arid and Humid Regions
The article investigates the equilibrium dynamics in the sense of Nash of
soils in arid and humid regions in the framework of the differential games theory.
Keywords:
The Nash equilibrium, model of soil, soil fertility, arid region, differential
games.
E.V. Vorozhtsov, V.P. Shapeev
Application of the Integral Form of Collocation Equations
and Differential Matching Conditions in the Method
of Collocations and Least Squares
. To increase the accuracy of computations by the method of collocations and
least squares (CLS) it is proposed to increase the number of degrees of freedom with the
aid of the following two techniques: an increase in the number of basis vectors and the
integration of the linearized partial differential equations (PDEs) over the subcells of
each cell of a spatial computational grid. It is shown that the proposed new versions of
the CLS method possess a higher accuracy than the previous versions of this method.
Furthermore, the version of the CLS method, which employs the integral form of
collocation equations, needs a lesser number of iterations for its convergence than the
“differential” CLS method.
Keywords: method of collocations and least squares, preconditioning, Krylov subspaces,
multigrid, collocation of integral relations, Navier–Stokes equations.
S.N. Chukanov, S.V. Lejhter
Constructing Metamorphosis of Pixel Images for the Objects
on the Basis of Solving Euler-Poincare Equations
This work considers comparison of two images (original and target) that
are represented by black and white pixels to each correspondingly. The problem
can be solved by detecting diffeomorphism that would allow to match deformed and
template images. Solution to the problem is based on the method of constructing a
minimized functional, which characterizes evolution process of the diffeomorphic
transformation of the image from initial to the final one and “penalty charge” for the
deviation of the image path from the required trajectory. An algorithm for solving
the diffeomorphic transformation equation is developed on the basis of the gradient
descent method. The considered problem of comparing two images can be used for
constructing optimal metamorphosis of images, when there is no exact correspondence
between the target image and the final image of the diffeomorphism. The designed
algorithms can be used through a biometrical system, in images and subjects
classification systems, machine vision systems, images and patterns recognition, tracking
systems.
Keywords: pattern recognition, Euler-Poincare equation, diffeomorphism, metamorphosis
approach.
Computer Science
E.A. Tyumentcev
About the Formalization of the Software Development Process
In the book ”Mythical man-month, or How software systems are created,” Brooks
refers to several studies on the basis of which it can be concluded that the productivity
of the work of programmers, measured in the number of lines of code per time, decreases
as the size of the program project grows. In this paper, we describe the formalization of
the software development process, as the process of editing the source code of the
program, with the help of which the laboriousness function is defined, and a sufficient
condition for the constant productivity of the programmers, independent of the size of
the project, is derived.
Keywords: formalization, development process, software, productivity, Brooks, Mythical
man-month.
U.A. Osipova, D.N. Lavrov
Application of Cluster Analysis by the K-Means Method
for the Classification of Scientific Texts
The article discusses the construction of software to develop recommendations
for the appointment of UDC. The development is based on the k-means method.
Keywords: method of k-means, lemmatization, TF-IDF.
Information Security
D.M. Brechka, A.A. Litvinenko
Investigation of Methods of Information Hiding in the Mpeg Video Stream
The article discusses the methods of information hiding in the MPEG-4 video
stream using the H.264 codec. To test the possibility of embedding of information in the
video stream, there was chosen method of embedding in the coefficients of the discrete
cosine transform. The ability of embedding and retrieving of information was tested on
modified OpenH264 codec.
Keywords: codec, MPEG-4, H.264, embedding data, video stream, information hiding.
A.K. Guts, E.P. Enns
Program for Simulation of Computer Network and Network Attacks
We present a computer program that simulates the work of computer network
and allows us to demonstrate the result of malicious attacks on network using several
existing network vulnerability.
Keywords: computer network, network attacks, attack simulation, computer program.
A.V. Kostylev, D.N. Lavrov, A.K. Guts
Identification of Suicidal Groups and Violators of Copyright in Social Networks
In this paper, the task is to develop software that allows you to automate the
search for groups and users in social networks that host suicidal materials and materials
that violate copyright in the network. As a social network for exploring the possibility
of such a search, the social network “VKontakte” — the largest social network of the CIS
was chosen. The latent semantic analysis algorithm was based on the developed software.
The main variants of the algorithm and the most adequately working on real data version
is selected.
Keywords:
classification of texts, latent-semantic analysis, copyright, offenses, social
networks, suicidal groups.