ФУНДАМЕНТАЛЬНАЯ МЕТРОЛОГИЯ: БИКОЛЬЦОИДЫ И КОЛЬЦОИДЫ — ПЛОСКИЕ ВЕЩЕСТВЕННЫЕ АЛГЕБРАИЧЕСКИЕ КРИВЫЕ ШЕСТОГО ПОРЯДКА
FUNDAMENTAL METROLOGY: BIRINGOIDS AND RINGOIDS — FLAT MATERIAL ALGEBRAIC CURVES OF THE SIXTH ORDER
Сторінки: 220-231. Номер: №1, 2019 (269)
Автори:
В.Т. КОНДРАТОВ
Институт кибернетики им. В.М. Глушкова, г. Киев
V.T. KONDRATOV
V.M. Glushkov Institute of Cybernetics of National Academy of Science of Ukraine
DOI: https://www.doi.org/10.31891/2307-5732-2019-269-1-220-231
Рецензія/Peer review : 17.01.2019 р.
Надрукована/Printed : 15.02.2019 р.
Анотація мовою оригіналу
В работе дальнейшее развитие и исследование получили плоские вещественные алгебраические кривые шестого порядка — бикольцоиды и кольцоиды, используемые при решении задач теории и практики магнитополевых измерений, описании траектории движения отрицательно заряженных квазичастиц внутри механической системы замкнутого типа и совершаемой ими работе на отдельных участках этого пути. Построены графики бикольцоид и кольцоид с разными параметрами, графики левосторонней и правосторонней кольцоид, приведены условия и ограничения по их воспроизведению с помощью ППП Grapher 7.0. Работа представляет интерес для метрологов, специалистов, магистров и аспирантов, изучающих кривые шестого порядка и возможности их применения в метрологии.
Ключевые слова: кривые шестого порядка, аналитическое выражение, кольцоида, бикольцоида.
Розширена анотація англійською мовою
In the paper the further development and research have received flat material algebraic curves of the sixth order — biringoids and ringoids. It is ascertained, that the problem «about a parity between algebraic formulas and geometrical images» is one of fundamental problems of mathematics. The author in the world proves for the first time existence of flat material algebraic curves of the sixth order — biringoids and their special cases: link sided and right-hand ringoids the opened and closed types and other curves received at set restrictions of parameters of binary function of transformation and a range of change by a variable . For the first time in the world analytical expressions of flat material algebraic curves of the sixth order are deduced, the beginning is necessary to their researches and development. Demand the further research of the restrictions imposed on topology of a curve of the sixth order by directly its algebraic nature. Development of flat material algebraic curves of the sixth order is caused by necessity of the description of an average trajectory of movement negatively charged quasiparticles in mechanical system of the closed type and definition of made work on separate sites of this way at the decision of problems of the theory and practice magnetic-field measurements. In paper possibility of reception of curves both closed, and opened kinds is shown. Flat material algebraic curves of 6th order — biringoid, link sided and right-hand ringoids with different parameters are constructed, conditions and restrictions on their reproduction by means of the Grapher 7.0 are resulted. For the first time in metrology classification bikoltsoids which in enough full measure reflects all variety of flat material algebraic curves of 6th order is developed and resulted. Paper has scientific and practical value as promotes the decision of technical problems of the description of movement and others negatively charged quasiparticles in wave guides specified above a configuration.
Schedules of bikoltsoids and ringoids with different parameters, schedules link sided and right-hand ringoids are constructed, conditions and restrictions on their reproduction by means of the Grapher 7.0 are resulted. Work is of interest for metrologists, experts, masters and the post-graduate students studying curves of the sixth order and possibility of their application in metrology.
Keywords: curves of the sixth order, analytical expression, biringoid, ringoid.
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