http://dspace.nbuv.gov.ua:80/handle/123456789/111459 2026-04-06T07:18:35Z 2026-04-06T07:18:35Z http://dspace.nbuv.gov.ua:80/handle/123456789/113743 2017-02-14T01:02:43Z 2016-01-01T00:00:00Z

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2016-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/113379 2017-02-08T01:03:12Z 2016-01-01T00:00:00Z

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2016-01-01T00:00:00Z Сарычев, О.П. http://dspace.nbuv.gov.ua:80/handle/123456789/112894 2017-01-30T01:03:05Z 2016-01-01T00:00:00Z

Линейная авторегрессия со случайными коэффициентами на основе метода группового учёта аргументов в условиях квазиповторных наблюдений Сарычев, О.П. Предложен критерий регулярности с разбиением выборок наблюдений на обучающие и проверочные подвыборки в условиях квазиповторных наблюдений для моделирования в классе авторегрессионных уравнений со случайными коэффициентами. Выявлено условие редукции оптимальной авторегрессионной модели, которое зависит от параметров модели и объемов выборок.; Запропоновано критерій регулярності з розбиттям вибірок спостережень на навчальні та перевірні підвибірки за умов квазіповторних спостережень для моделювання в класі авторегресійних рівнянь з випадковими коефіцієнтами. Виявлено умову редукції оптимальної авторегресійної моделі, що залежить від параметрів моделі і обсягів вибірок.; Introduction and purpose: The linear autoregression equation is traditional mathematical object in the theory and practice of the Group Method of Data Handling (GMDH). In 80-th years of the last century academician O.G. Ivakhnenko often posed such tasks in connection with so-called “the objective system analysis (OSA)” and then, as a rule, as criterion of selection of models (parameter of quality of regression equation) the criterion of regularity of GMDH was applied. The developed criterion is the criterion of regularity which is constructed with dividing of observations on training and testing subsamples in conditions of quasirepeated observations. Methods: Object of research is process of modelling in a class of autoregression equations in conditions of uncertainty on structure of regressors. In this theoretical article we used the multivariate statistical analysis, the regression analysis, the theory of matrixes, the mathematical analysis and the Group Method of Data Handling. Results: For modeling in a class of autoregression equations the criterion of regularity with dividing of observation sample on training and testing subsamples in conditions of quasirepeated observations is offered. It is proved, that the optimum set of regressors exists. The condition of a reduction of optimal autoregression equation is obtained. This condition depends on parameters of autoregression equation and volumes of samples. Conclusion: The developed criterion of regularity allows solving a problem of structural identification in a class of autoregression equations in conditions of quasirepeated observations and can be recommended at the decision of various scientific and practical problems.

2016-01-01T00:00:00Z Петренюк, Д.А. http://dspace.nbuv.gov.ua:80/handle/123456789/112893 2017-01-30T01:03:04Z 2016-01-01T00:00:00Z

Граціозні дерева. Аналіз проблеми та перспективи Петренюк, Д.А. Запропоновано аналіз результатів щодо гіпотези про граціозність дерев. Розглянуто два підходи до питання правдивості гіпотези про дані дерева, описано основні класи таких дерев, способи отримання більших дерев з менших, а також результати комп’ютерних обчислень стосовно граціозності дерев. Подано деякі аргументи проти гіпотези про граціозність дерев.; Предложен анализ результатов относительно гипотезы о грациозности деревьев. Рассмотрены два подхода к вопросу истинности гипотезы о данных деревьях, основные классы грациозных деревьев, способы получения больших деревьев из меньших, а также результаты компьютерных вычислений о грациозности деревьев. Приведены некоторые аргументы против гипотезы о грациозности деревьев.; Graceful Tree Conjecture is one of the most popular math conjectures. It was formulated almost half a century ago, but even today it is still far from being completely solved. A. Krishnaa in 2004 and J. Gilbert in 2009 [19] proposed their proofs of the Conjecture, but they turned out to be wrong or incomplete. The article contains a brief review of the state of art in solving the Conjecture, including some results that have been proposed by the author. Graceful labeling of undirected graph G with n edges is an injection from vertex set of graph G to {0, 1, 2, ..., n} such that all the induced edge labels are different. Induced edge label is the absolute value of the difference between the labels (numbers) of the two end-vertices of the edge. A graph is graceful if it admits graceful labeling. The Graceful Tree Conjecture claims that all trees are graceful. There are two approaches to solving the Graceful Tree Conjecture. The first is to prove gracefulness and obtain graceful labeling algorithms for certain classes of trees; if once gracefulness of all classes of trees is shown, then the Conjecture is proved. For today, gracefulness is proved for stars, paths, caterpillars, olive trees, some subclasses of lobsters (firecrackers, (2,2)-caterpillars, lobsters with perfect matchings), banana and generalized banana trees, and some other classes. Many methods of combining few graceful trees to obtain a new bigger graceful tree have been found. Another approach to solving the conjecture is to use computer to check if all trees with number of vertices not exceeding a given value are graceful. This approach can provide new graceful labeling algorithms and can be also used to disprove the Conjecture, once at least one tree that does not admit graceful labeling is found. However, no such tree has been found so far. It has been proved that all the trees having not more than 35 vertices are graceful. Despite all the positive results, some researchers express serious doubts about the truthfulness of the Conjecture. They point out that the most graceful labeling methods have been designed for trees with regular or very simple structure, while there are no proofs of gracefulness for sufficiently irregular trees. However, the majority or researchers tend to believe that the Graceful Tree Conjecture is true and will be once proved completely.

2016-01-01T00:00:00Z