NIEZMIENNE URZĄDZENIA PIEZOREZONANSOWE NA PODSTAWIE ADAPTACYJNYCH WIELOCZĘSTOTLIWOŚCIOWYCH SYSTEMÓW Z PROGNOZOWANYM STANDARDEM

The paper presents conceptual provisions for the construction of invariant multi-frequency piezoelectric resonance devices with a predictive reference model. The law of the optimal control of the system in real time is formulated, aimed at minimizing energy costs to ensure the trajectory of the system. The results of piezoelectric resonance system mathematical modelling in the conditions of temperature and vibration perturbations are presented.W artykule przedstawiono koncepcyjne zasady konstruowania niezmiennych wieloczęstotliwościowych piezoelektrycznych urządzeń z predykcyjnym modelem odniesienia. Zostało sformułowane prawo optymalnego sterowania systemem w czasie rzeczywistym, aby przy minimalnych stratach energii zapewnić trajektorię ruchu systemu. Przedstawiono wyniki matematycinvariant multi-frequency piezoelectric resonance system, optimal control, mathematical modelznego modelowania układu piezorezonansowego w warunkach zaburzeń temperatury i drgań

Mathematical modelling of running crown forest fires

Adapted mathematical model of running crown forest fire propagation is considered. Simplifying assumptions, equations of the model, initial and boundary conditions, finite diference approximations are introduced. The results of computer modelling and the peculiarities of forest fire behavior in heterogeneous forests are discusse

Principles and solutions for integrating computer algebra tools and applications based on open semantic technologies

The paper discusses the principles of integration of computer algebra systems and the Ecosystem of Intelligent Computer Systems of a new generation (OSTIS Ecosystem). The feasibility of such integration, various options for such integration, the advantages and disadvantages of these options are shown. The implementation of the proposed approach is considered using the example of an intelligent learning system indiscrete mathematics

Extensional Flow of a Free Film of Nematic Liquid Crystal with Moderate Elasticity

Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale a weakly elastic model due to Cummings et al. [European Journal of Applied Mathematics 25 (2014): 397-423] to describe a case of moderate elasticity. The resulting system of two nonlinear partial differential equations for sheet thickness and axial velocity is nonlinear and fourth order in space, but still represents a significant reduction of the full system. We analyze solutions arising from several different boundary conditions, motivated by the underlying application, with particular focus on dynamics and underlying mechanisms under stretching. We solve the system numerically, via collocation with either finite difference or Chebyshev spectral discretization in space, together with implicit time stepping. At early times, depending on the initial film shape, pressure either aids or opposes extensional flow, which changes the shape of the sheet and may result in the loss of a minimum or maximum at the moving end. We contrast this finding with the cases of weak elasticity and Newtonian flow, where the sheet retains all extrema from the initial condition throughout time.Comment: Copyright (2023) M.J. Taranchuk, L.J. Cummings, T.A. Driscoll, and R.J. Braun. This article is distributed under a Creative Commons Attribution (CC BY) License. The following article has been submitted to Physics of Fluids. After it is published, it will be found at https://aip.scitation.org/journal/ph

Отдельные аспекты туристского обслуживания в Полоцкой культурно-туристской зоне

The article focuses on the importance and need for the development of tourist and recreational services in the Republic of Belarus. The presence and distribution of historical and cultural values inside it is analyzed and exemplified by the Polotsk cultural and tourist zone, the main indicators are broken down by administrative districts of hotels and accommodation facilities, the dynamics of the number of objects representing catering services in the districts can be traced, a tangible emphasis is placed on the role agro farmsteads The uneven distribution of all components of tourist services is emphasized. A complex of numerous effective measures for a radical improvement of the hotel service is proposed and justified. The article contains the necessary tabular and cartographic evidence.В статье акцентируется внимание на значимость и необходимость развития в Республике Беларусь туристско-рекреационного обслуживания населения. Анализируется на примере Полоцкой культурно-туристской зоны наличие и распределение внутри нее историко-культурных ценностей, приводятся и оцениваются основные показатели в разрезе административных районов деятельности гостиниц и средств размещения, прослеживается динамика количества объектов, представляющих услуги питания на территории районов, ощутимый упор делается на роль агроусадеб. Подчеркивается неравномерный характер распределения всех компонентов туристского обслуживания. Предлагается и обосновывается комплекс многочисленных действенных мер по радикальному улучшению гостиничного сервиса. Статья содержит необходимый табличный и картографический доказательный материал