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The Fundamental Mathematics and Physics
V.V. Varlamov
Group Theoretical Description of Periodic System of Elements: III. 10-Periodic Extension
10-periodic extension of Mendeleev table is studied within group theoretical approach.
A multiplet structure is considered in detail for periods of the extended table. It is shown that period
lengths are defined by a structure of basic representation of the Rumer-Fet group. Theoretical
masses of elements are calculated for 10-th and 11-th periods. A notion of hypertwistor is introduced.
Keywords:
periodic law, Mendeleev table, Bohr model, Rumer-Fet group
A.K. Guts, V.N. Ivanov
Detection and Selection of Useful Discrete Signals in Periodic Discharges of Primary Particles
We study the problem of signal transmission using
discharges flows of primary particles and calculate the probability
of such signals registration, as well as probability of highlighting them
against the background of the Pousson noise. The computer simulations
of such useful signals and noises are discussed
Keywords:
Discharge of primary particles, signal transmission,
Poisson signals and noises, registration of useful signals
V.N. Borodikhin, M.M. Mikhailovskiy
Computer Simulation of the Nonequilibrium Critical Behavior of the Weakly Disordered Potts Model with the Number of Spin States \(q = 3\).
In this paper, by the method of short-time dynamics the behavior of weakly disordered three-dimensional
Potts model with the number of spin components equal to three was studied. The critical temperature value has been clarified.
For spin concentrations 0.95 critical indexes \(z\) and \(\nu\) were calculated.
Keywords:
phase transitions, Potts model, effect of impurities, critical dynamics
Applied Mathematics and Modeling
D.N. Gorelov
Reflections on Turbulence
The characteristic properties of the turbulent fluid flow
behind the plate are analyzed based on the hypothesis of L. Landau on the possibility
of using the ideal fluid model for the study of turbulent flows.
Keywords:
turbulent flow, separated flow, self-oscillations
Bautin S.P., Krutova I.Yu.
Linearized System of Gas Dynamics Equations When Taking Into Account the Action of Coriolis Force and Its Some Solutions
For the system of gas dynamics equations, taking into account the action of the Coriolis
force, the linearization is carried out in two cases: when the effect of gravity is and
when it is not taken into account. For linearized systems, their characteristics are defined. In the
case of a rectangular coordinate system, a partial splitting of the linear system of
equations iss carried out. Particular solutions in the form of standing and running waves
are found. The flow in the vicinity of the impenetrable horizontal plane is constructed.
Keywords:
system of equations of gas dynamics, Coriolis force, linearization, exact solutions
L.A. Volodchenkova, A.K. Guts
Interspecific Cmpetition in Forest Phytocenoses as a Strategic Bimatrix Game
The article examines the equilibrium in interspecific
competition in forest phytocenoses from the point of view of the
mathematical theory of games. Game strategies are described.
Various types of payoff matrices that can be used to describe the competition are analyzed.
Keywords:
interspecific competition, forest phytocenosis, game theory, Nash equilibrium
V.A. Shovin
Factor Analysis of Quality Indicators
The paper proposes new approaches for conducting factor analysis for qualitative indicators:
the approach of calculating quantitative indicators on the basis of multidimensional scaling and matrix of mutual
distances of objects; and a new approach to calculating the correlation matrix. Both methods can be preliminarily
used for quantitative factor analysis. Also we propose a new approach to reconstructing the distances of
objects and their location in a multidimensional space. The basis of the method is the principle of choosing the
nearest object from two other objects. As a result, the distances between all pairs of objects
are determined. Such a distance matrix is further used in the method of multidimensional scaling based on
the Verlet method. All objects are placed in a multidimensional space of the selected dimension.
This method of restoring distances between objects and placing them in a multidimensional space can also be used previously
for classical classification methods.
Keywords:
qualitative indicators, factor analysis, Verlet method, multidimensional scaling, distance reconstruction
Michael Beer, Afshin Gholamy, Vladik Kreinovich
A Theoretical Explanation for the Efficiency of Generalized Harmonic Wavelets in Engineering and Seismic Spectral Analysis
Wavelets of different shapes are known to be very efficient in
many data processing problems. In many engineering applications,
the most efficient shapes are shapes of a generalized harmonic
wavelet, i.e., a wavelet of the shape \(w(t)=t^a\exp(b\cdot t)\) for
complex \(b\). Similar functions are empirically the most successful
in the seismic analysis - namely, in simulating the
earthquake-related high-frequency ground motion. In this paper, we
provide a theoretical explanation for the empirical success of
these models.
Keywords:
Generalized harmonic wavelets, seismic spectral analysis, symmetries
Griselda Acosta, Eric D. Smith, Vladik Kreinovich
Why Patients Do Not Always Follow Doctor's Advice: Systems Approach Explains Empirical Observation
Empirical studies show that when a medical
doctor prescribes a medicine, only two third of the patients fill
the prescription, and of this filling-prescription group, only
half follow the doctor's instructions when taking the medicine. In
this paper, we show that a general systems approach - namely,
abstracting from the specifics of this situation - helps explain
these empirical observations. We also mention that systems
approach can not only explains this problem, it can also help
solve it - i.e., it can help increase the patients' adherence to
the doctors' recommendations.
Keywords:
doctor's recommendations, systems approach, Laplace Indeterminacy Principle
Julio C. Urenda, Vladik Kreinovich
Why Experts Sometimes Do Not Perform Well in Unusual Situations
We expect that the quality of experts' decisions increases with
their experience. This is indeed true for reasonably routine
situations. However, surprisingly, empirical data shows that in
unusual situations, novice experts make much better decisions than
more experienced ones. This phenomenon is especially unexpected for
medical emergency situations: it turns out that the mortality rate of patients
treated by novice doctors is a third lower than for patients
treated by experience doctors. In this paper, we provide a possible
explanation for this seemingly counterintuitive phenomenon.
Keywords:
experts, statistics, unusual vs. routine situations
Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
How We Can Explain Simple Empirical Memory Rules
Researchers have found out that normally, we remember about 30\% of
the information; however, if immediately after reading, we get a
test, the rate increases to 45\%. In this paper, we show that Zipf
law can explain this empirical dependence.
Keywords:
human memory; Zipf's law; empirical memory rules
Computer Science
S.V. Lejhter, S.N. Chukanov
The Use of Affine Normalization for Enhancement of the Accuracy of Images Comparison
The problem of comparing the forms of the source and terminal images is considered. For the analysis of images deformations, diffeomorphic transformations are used. For enhancement of an accuracy of comparing source image and terminal image, it is proposed to normalize these images. The original image is exposed to affine transformation and the cost functional between the transformed original and terminal images is minimized. The solution for a problem of the image form evolution is based on the using of simulated annealing algorithm.
Keywords:
pattern recognition, image normalization, affine transformations, simulated annealing algorithm
A.A. Senkovskaya
Modeling of Training Terms on the Basis of the Analysis of Working Educational Plans
The article describes the main approaches to the implementation of educational programs. It presents features of the modeling
of the learning process at various stages of the curricula organization. The possibility of reducing the duration of training due to the simulation of the curriculum as a directed graph is analyzed.
Keywords:
curriculum, oriented graph, modeling, educational process
D.N. Lavrov, A.P. Lapin, M.A. Kharlamova, I.A. Cherkashchenko
Text Processing with Phonetic and Thematic Markup for Displaying Texts of Dialect Corpus
The paper describes the developed finite state machine schemes
that underlie the development of a web application for the dialect corpus
of the Middle Irtysh. The paper proposes refinement of the structure
of an XML document representing a text recording of an interview with one or
more informants with phonetic and thematic markings. The study was carried out
with the financial support of the Russian Federal Property Fund in the
framework of the scientific project No. 18-012-00519.
Keywords:
web development, thematic markup, state machines, dialect corpus