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The Fundamental Mathematics and Physics
V.A. Erovenko
Essential Spectra of Ordinary Differential Operators II. Stability of Spectra
The article contains precise formulas for finding of the essential spectra
that are revolted with asymptotically constants on infinity in coefficients with use of
rather compact and rather small indignations on infinity in Lebesgue spaces of \(L^{p}\).
These formulas are new analogs of the classical theorem of Weyl.
Keywords:
perturbation theory of operators, essential spectra, ordinary differential operators
M.N. Boldyreva, A.A. Magazev, I.V. Shirokov
Classification of Yang - Mills Fields Admitting Integrals of Motion for the Wong Equations
In the paper, we investigate the gauge fields that are characterized by the existence of non-trivial integrals of motion for the Wong equations.
For the gauge group \(SU(2)\), the class of fields admitting only the isospin first integrals is described in detail.
All gauge non-equivalent Yang - Mills fields admitting a linear integral of motion for the Wong equations are classified in the three-dimensional Euclidean space.
Keywords:
Yang--Mills field, the Wong equations, integral of motion, gauge transformation
M.N. Podoksenov, V.V. Chernykh
Autoisometries and Autosimilarities of Lie Algebra \(\mathcal{A}(1)\oplus \mathcal{R}^2\)
We consider four-dimensional Lie algebra \(\mathcal{A}(1)\oplus \mathcal{R}^2\) endowed with Lorentzian
scalar product. We find all the one-parameter groups of isometries and similarities, which are simultaneously
automorphisms of Lie algebra, and also we find the conditions of existence of such one-parameter group.
Conditions of existence are associated with the location of ideals with respect to isotropic cone.
Keywords:
Lie algebra, Lorentzian metrics, automorphism, similarity, isometry
S.A. Terentyev, A.K. Guts
The Analyticity Domain of Spectral Density of the Electromagnetic Field in a Vertically Inhomogeneous Conductive Medium
The electromagnetic field in electrical exploration
problems is often represented as integrals with a fast-oscillating
nucleus. When calculating these integrals on a computer, it is
necessary to deform the contour of integration into the plane of
the complex variable. The article studies the allowable
deformation region of the integration contour in the case of a
non-uniform medium, in which strong and weak solutions of
electromagnetic field are analytical. The source of the field is a
vertical dipole. A similar problem was solved for a horizontally
layered medium with a harmonious electrical or magnetic dipole as
a source.
Keywords:
Electrical exploration, electromagnetic
field of vertical electric or magnetic dipole, fast-oscillating
integrals, deformation contour, complex plane, absence of singular
points, deformation domain
Olga Kosheleva, Vladik Kreinovich
On Geometry of Finsler Causality: For Convex Cones, There Is No Affine-Invariant Linear Order (Similar to Comparing Volumes)
Some physicists suggest that to more adequately describe the causal structure of space-time, it is
necessary to go beyond the usual pseudo-Riemannian causality, to a more general Finsler causality. In this general
case, the set of all the events which can be influenced by a given event is, locally, a generic convex cone, and not
necessarily a pseudo-Reimannian-style quadratic cone. Since all current observations support pseudo-Riemannian
causality, Finsler causality cones should be close to quadratic ones. It is therefore desirable to approximate a
general convex cone by a quadratic one. This can be done if we select a hyperplane, and approximate intersections of
cones and this hyperplane. In the hyperplane, we need to approximate a convex body by an ellipsoid. This can be done in
an affine-invariant way, e.g., by selecting, among all ellipsoids containing the body, the one with the smallest
volume; since volume is affine-covariant, this selection is affine-invariant. However, this selection may depend on the
choice of the hyperplane. It is therefore desirable to directly approximate the convex cone describing Finsler
causality with the quadratic cone, ideally in an affine-invariant way. We prove, however, that on the set of convex
cones, there is no affine-covariant characteristic like volume. So, any approximation is necessarily not
affine-invariant.
Keywords:
space-time geometry, Finsler spaces, causality
Applied Mathematics and Modeling
A.V. Eremeev, A.V. Spirov
Estimates from Evolutionary Algorithms Theory Applied to Directed Evolution
The field of evolutionary computation emerged in the area of
computer science due to transfer of ideas from biology and
developed independently for several decades, enriched with
techniques from probability theory, complexity theory and
optimization methods. Our aim is to consider how some recent
results form the theory of evolutionary computation may be transferred back into biology. It
has been noted that the non-elitist evolutionary algorithms optimizing Royal Road fitness
functions may be considered as models of evolutionary search for
the synthetic enhancer sequences “from scratch”.
This problem asks for a tight cluster of supposedly unknown motifs
from the initial random (or partially random) set of DNA sequences
using SELEX approaches. We apply the upper bounds on the expected
hitting time of a target area of genotypic space
in order to upper-bound the expected time to finding a
sufficiently fit series of motifs in a SELEX procedure. On the other hand,
using the theory of evolutionary computation, we propose an upper bound on the expected
proportion of the DNA sequences with sufficiently high fitness at
a given round of a SELEX procedure. Both approaches are
evaluated in computational experiment, using a Royal Road fitness function
as a model of the SELEX procedure for regulatory
FIS factor binding site.
Keywords:
runtime analysis, SELEX procedure, Royal Road function, enhancer
L.A. Volodchenkova, A.K. Guts
Mycelial Growth Analysis Based on the Chanter-Thornley Model
The Chanter-Thornley mycelial growth model is
analyzed with point of view of the mathematical bifurcation theory.
It was shown that one can observe not only the
continuous growth of the mycelium, but also its saltatory evolution.
Keywords:
mycelium, Chanter-Thornley model, saltatory growth, bifurcation theory
Bautin S. P., Bugaenko A. A., Krutova I. Yu.
Particular Solutions of a Linearized System of Gas Dynamics Equations in the Absence of Gravity
Taking into Account the Actions of the Coriolis Force
For the system of gas dynamics equations, taking into account the action of the Coriolis force, linearization
is carried out in case when the effect of gravity is not taken into account. Particular solutions in the form of running waves are found.
Keywords:
system of equations of gas dynamics, Coriolis force, linearization, exact solutions
D.N. Gorelov
On a Singularity of the Cauchy Integral over a Closed Contour
A study is made of the parametric singularity of the Cauchy integral
that arises when the sides of a closed loop come together. Formulas are obtained
that relate the values of the Cauchy integral on different sides of an extremely narrow contour.
Keywords:
Cauchy integral, Sokhotsky-Plemel formulas, parametric singularity of the Cauchy integral
D.N. Gorelov
A Parametric Feature of a Three-Dimensional Analogue of the Cauchy Integral
The existence of a parametric singularity of a three-dimensional analogue
of the Cauchy integral over a closed surface is proved. This feature arises when
the sides of a closed surface approach each other. Formulas are obtained that relate
the values of the analogue of the Cauchy integral on different sides of an extremely narrow surface.
Keywords:
Cauchy integral, parametric singularity of the Cauchy integral
Griselda Acosta, Eric D. Smith, Vladik Kreinovich
How to Explain That Changes in Elderlies Depression Level Are Uniformly Distributed
Changes in the elderlies depression level result from a large
number of small independent factors. Such situations are ubiquitous
in applications. In most such cases, due to the Central Limit
Theorem, the corresponding distribution is close to Gaussian. For
the changes in the elderlies depression level, however, the
empirical distribution is far from Gaussian: it is uniform. In this
paper, we provide a possible explanation for the emergence of the
uniform distribution.
Keywords:
elderlies depression, uniform distribution, changes in depression level
Computer Science
L.A. Volodchenkova, D.V. Kozirev
Creation of the Server Side of the Programm for Remote Data Storage
In this article the programm interface (API) of the server side of the cloud data storage is created.
Keywords:
cloud storage, server side, software interface
A.I. Gorev, E.G. Gorev
About the Applicability of Existing Data Processing Algorithms to Big Data
The processes of obtaining BIG DATA during operation of computer technologies,
the purpose of which is not to create data arrays, are defined. However,
the use of the obtained data can have a great positive effect.
Keywords:
big data, structured data, automated information systems
Education
Griselda Acosta, Eric D. Smith, Vladik Kreinovich
Confirmation Bias in Systems Engineering: A Pedagogical Example
One of the biases potentially affecting systems engineers is the confirmation bias,
when instead of selecting the best hypothesis based on the data, people stick to the previously-selected
hypothesis until it is disproved. In this paper, on a simple example, we show how important it is to take
care of this bias: namely, that because of this bias, we need twice as many experiments to switch
to a better hypothesis.
Keywords:
confirmation bias, systems engineering, hypothesis testing