Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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Name

Titov Nikolay Georgievich

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Honorary rank

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Kuban State University
   

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Articles count: 5

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267 kb

ADAPTIVE TIME SERIES MODELS OF A MOUNTAIN RIVER LEVEL

abstract 1141510109 issue 114 pp. 1517 – 1530 30.12.2015 ru 342
The article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
135 kb

CONSTRUCTING A THEORETICAL MODEL PREDICTING THE LEVEL OF WATER IN A MOUNTAIN RIVER IS USING MARKOV’S CHAINS

abstract 1141510110 issue 114 pp. 1531 – 1541 30.12.2015 ru 332
The article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
268 kb

FORECASTING THE WATER LEVEL IN A RIVER WITH THE ABRUPT FALLING WATER BASED ON KALMAN-BUSY FILTRATION

abstract 1041410058 issue 104 pp. 775 – 786 30.12.2014 ru 493
The technique of short-term forecasting of the water level in a vein of a mountain type river, based on a method of Kalman-Busy filtration in the make assumption of natural simplifications, characterized for natural objects is offered
481 kb

ON THE NUMERATIONS OF THE FINITE PARTIALLY ORDERED SETS

abstract 1181604006 issue 118 pp. 113 – 127 29.04.2016 ru 377
There is a widely known problem regarding the ordering of the partially ordered sets (Linear Ordering Problem). It boils down to finding the numerations of such sets. The main result of this article is a generalization of one of the known S. S. Kislitsyn's results about finding the number of numerations of finite partially ordered sets
204 kb

THE NUMBER OF LINEARLY ORDERABLE BINARY RELATIONS ON A FINITE SET

abstract 1291705014 issue 129 pp. 170 – 184 31.05.2017 ru 87
Partially ordered set is a basic concept of modern settheoretic mathematics. The problem of linear set ordering with given binary relations is well-known. Every partial order over a finite set can be linearly ordered, but not every binary relation over this set can be linearly ordered as well. Up to now, there is no known formula for calculating the number of partial orders over a given finite set. It appears that there is a formula for calculating linearly ordered binary relations over a finite set. This article is concerned with derivation of this formula. The fact from work of G.N. Titov [9] that a binary relation over a finite set is linearly ordered if and only if any diagonal block, derived from the binary relation matrix as a result of setting main diagonal elements to zero, contains at least one zero row (diagonal block of matrix means any matrix composed of elements at the crossings of rows and columns of a given matrix with the same numbers), plays a key role in process of corroboration. The main conclusion of the article is a theorem that allows to find the number of linearly ordered binary relations over a set of n elements using the formula. A recurrence formula for the number of linearly ordered (irreflexive) binary relations over a finite set of n elements, provided in the lemma, was derived as well
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