## Mathematical Structures and Modeling ¹2(50)

 Mathematical Structures and Modeling. - Omsk : OmSU, 2019. ¹2(50), 120 p. ISSN (print): 2222-8772 ISSN (online): 2222-8799 For researchers, post-graduate students and senior students. Journal issue in one file

The Fundamental Mathematics and Physics

This paper is devoted to the two essential circumstances that should be taken into account when using the new standard (prototype) of mass - the kilogram, primarily, in the procedure of measuring mass by means of the Kibble balance, i.e.: the innate interconnection in the World of events (in space-time) and the belonging of the mass standard to complex structured objects. In the three sections of the paper (sec. 2 - sec. 4) the main traits of the mentioned above circumstances are discussed and illustrated, due to (sec. 1) the decision of the International Committee for Weights and Measures on redefining the prototype of the kilogram after 20 May 2019. In the limelight is a phenomenon of change of mass of a complex organized object due to change of its inner energy that is associated with the phenomenon of initializing influence of external irreversible processes that belongs to temporal aspect of the objective reality. Theoretical considerations (sec. 2) are supported with direct and clear experimental material (sec. 3 and sec. 4). In conclusion, general recommendations on measuring mass of structured (on atomic level) object by means of the Kibble balance, that follow from the discussed circumstances, are given.
Keywords: mass prototype, kilogram, Kibble balance, innate (a priory) interconnection, World of events (space-time), structured objects, open systems, irreversible processes

It is shown how the idea of the view of the World may proceed not from “what the World is made of”, but from what samples (patterns) it is made of. Such patterns can be so-called physical structures of Novosibirsk physicist V.I. Kulakov, generalized later by G.G. Mikhailichenko and Yu.S. Vladimirov. We show that physical structures detect their presence in socio-psychological relationships of people, in economic relations of people, enterprises and economies, in botany. Moreover, it is shown that the structures of Kulakov-Vladimirov suggest us how we can change the physical laws.
Keywords: Kulakov structures, physics, sociology, psychology, micro-economy, macro-economy, botany, Lem cosmogony

Mourat Tchoshanov, Olga Kosheleva, Vladik Kreinovich
Summation of Divergent Infinite Series: How Natural are the Current Tricks

Infinities are usually an interesting topic for students, especially when they lead to what seems like paradoxes, when we have two different seemingly correct answers to the same question. One of such cases is summation of divergent infinite sums: on the one hand, the sum is clearly infinite, on the other hand, reasonable ideas lead to a finite value for this same sum. A usual way to come up with a finite sum for a divergent infinite series is to find a 1-parametric family of series that includes the given series for a specific value $$p = p_0$$ of the corresponding parameter and for which the sum converges for some other values $$p$$. For the values $$p$$ for which this sum converges, we find the expression $$s(p)$$ for the resulting sum, and then we use the value $$s(p_0)$$ as the desired sum of the divergent infinite series. To what extent is the result reasonable depends on how reasonable is the corresponding generalizing family. In this paper, we show that from the physical viewpoint, the existing selection of the families is very natural: it is in perfect accordance with the natural symmetries.
Keywords: divergent infinite series, symmetries

Applied Mathematics and Modeling

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. 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

L.A. Volodchenkova, A.K. Guts
Equilibrium Dynamics of Undecomposed Litter in Forest Ecosystems

In the article the Nash equilibrium states for undecomposed litter in forest ecosystems within the framework of the theory differential games are investigated. It is shown that in equilibrium the decay of litter goes at a lower speed.
Keywords: The Nash equilibrium, forest ecosystem, litter, vegetation, differential games

Computer Science

A.A. Senkovskaya, I.I. Furayeva
Analysis of the Source Data in the Task of Curriculum Optimization

The principles of the influence of working curricula on the teaching load as a whole and on the final schedule of classes in the end, as well as the need to optimize them are presented. It is shown that a preliminary analysis of the source data reduces the number of variables studied. The selection of the algorithm is carried out for the subsequent analysis of the working curricula.
Keywords: curriculum optimization, modeling, reducing the number of variables

Olga Kosheleva, Vladik Kreinovich
Was There a Pre-Biblical 9-Ary Number System?

In the Biblical Hebrew, in general, numbers were represented in decimal form. For example, a representation of 123 consists of three symbols that represent 100, 20, and 3. However, there are exceptions to this rule: for two numbers, 15 and 16, representation involve number 9, not number 10: 15 is represented as 9 + 6, and 16 as 9 + 7. Maybe this means that in the past, people used a 9-ary number system? In this paper, we explain why this hypothesis makes sense, how it explains that this system disappeared, and how we can use this hypothesis to further spice up'' the teaching of different number systems.
Keywords: 9-ary system, seven plus minus two law, ternary number system, Biblical mathematics, teaching number systems

Information Security

Olga Kosheleva, Vladik Kreinovich
Why STEM?

Is the idea of combining science, technology, engineering, and mathematics into a single STEM complex a fashionable tendency, as some educators think - or is there a deep reason behind this combination? In this paper, we show that the latest developments in Theory of Computation make such a union necessary and desirable.
Keywords: STEM, theory of computation, feasible algorithms, NP-complete problems

Olga Kosheleva, Julian Viera, Vladik Kreinovich
From Gig Economy to Gig Education

Modern economy has benefited from gig economy idea, where, instead of hiring permanent employees, a company assigns each task to the person who is the most efficient in performing this task. This way, each task is performed in the best possible way - by a person who is the most suited for this job. Why not extend this idea to education? Every student deserves the best possible teacher in every topic. So why not have a teacher who is the best in town in explaining quadratic equations teach quadratic equations to all the students from the town? In this paper, we describe this proposal and its logistics in some detail.
Keywords: gig economy, sharing economy, gig education

Olga Kosheleva, Julian Viera, Vladik Kreinovich
Should School Feel Like a Family: Lessons from Business Controversy as Interpreted by Decision Making Theory

Traditional business theory promoted the ideal of business as a family: everyone should feel good about each other, all employees should feel good working together towards a joint goal. Recently, however, researchers claim that this well-promoted ideal is unattainable, it is a ruse causing everyone to overwork. Instead, these researchers propose a non-emotional collaboration of adults working temporarily on a joint project. In this paper, we show that this new trend is not just based on anecdotal evidence, it actually has a solid foundation in decision theory. So maybe we should apply this new trend to teaching too - and place less emphasis on the need for everyone to become friends and for team-building? Maybe - like the new business trend suggests - we should reserve our feeling for our real families?
Keywords: decision making theory, emotions, business practices, education