Моделирование и прогнозирование в управлении: методы и технологии: материалы 2-й Международной научно-практической конференции
This article considers the subject of interdisciplinary interaction among specialists working in exact and social sciences as a practice of exchanging ideas about social reality; mutual adaptation of these ideas; empirical verification of the universal formal logic rules applied to specific tasks of sociological research. Such formulation of the subject goes beyond the problem of adapting educational programs to “literacy classes” for potential partners. It is maintained that in inter-professional communication it is important to formulate conceptual systems of common use not “in general”, not for all possible cases, but with regard to the problem addressed by consolidated effort. For such conceptual systems we use the term “common language area” according to the ideas of epistemologists (Ilya Kasavin). Elements of these conceptual systems include paradigms, concepts, tools and procedures mobilized for collaborative work. Readers are offered a description of the experience of cooperation between mathematicians and sociologists in 1990–2010s in the qualitative analysis of sociological data — which is an area of concern for both sociology and exact methods. To find a cooperative solution, we needed to develop a system of basic propositions regarding the object and purpose of the research; to put together a structure of sociological data suitable for using the proposed formal tool; to carry out empirical verification of the formalized language of logic-mathematical reasoning. This work has made it possible to explicate the opportunities and limitations when it comes to interpreting results. The article draws conclusions about the specifics of communication in a team of specialists, including sociologists and mathematicians, and about the development of a common language area in the field of cooperation that deals with qualitative analysis of sociological data. Our experience of cooperation in using formalized qualitative analysis of sociological data shows that, when it comes to the need to solve a common problem, partner role relations turned out to be the most effective (rather than role pairs such as “teacher-student” or “seller-buyer”).
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l 2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l 2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.
In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.