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Titov Nikolay Georgievich

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## Articles count: 5

• pdf  273.659kb doc 273.659kb Views: 842 Date: 30.12.2015
Description
The article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
• pdf  492.810kb doc 492.810kb Views: 789 Date: 29.04.2016
Description
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
• pdf  208.521kb doc 208.521kb Views: 623 Date: 31.05.2017
Description
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
• pdf  138.528kb doc 138.528kb Views: 860 Date: 30.12.2015
Description
The article presents a technique of short-term forecasting of water level in the river bed of a mountain type using Markov’s chains
• pdf  274.348kb doc 274.348kb Views: 1197 Date: 30.12.2014
Description
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