F. J. MacWilliams proved an Extension theorem: Hamming isometries between linear codes over finite fields extend to monomial transformation. This result has been generalized by J. A. Wood who proved it for Frobenius rings. In this paper the Extension theorem for linear codes over a finite quasi-Frobenius module with commutative coefficient ring is proved. The main technique involves the description of quasi-Frobenius module in terms of character theory.
In this paper we propose an algorithm for finding subgraphs with adjusted properties of large social networks. The description of computational experiment which confirms the effectiveness of the proposed algorithm is given.
Various approaches for data storing and processing are investigated in the article. New algorithm to find paths in a huge graph is introduced.
This article describes the problem of analysis of social network graphs and other interacting objects. It also presents community detection algorithms in social networks, their classification and analysis. In addition, it considers applicability of algorithms for real tasks in social network graph analysis.
The calibration problem is considered for the accelerometer unit at a high-precision test bench. Besides instrumental errors of the accelerometer unit itself, possible faults of the test bench (which are accumulated during its operation) are taken into account. One of the main problems is to choose the optimal design of the angular unit positions. The guaranteed approach is proposed to determine this optimal design.
The “true form” of plane trees, i.e., the geometry of sets p −1[0, 1], where p is a Chebyshev polynomial, is considered. Empiric data about the true form are studied and systematized.
We classify quasi-simple finite groups of essential dimension 3.
In this paper, we prove that the cardinality of the set of all precomplete classes for definite automata is continuum
This paper deals with an extremal problem concerning hypergraph colorings. Let k be an integer. The problem is to find the value m(k,n) equal to the minimum number of edges in an n-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains at least k vertices of each color. In this paper, we obtain upper bounds of m(k,n) for small k and n, the exact value of m(4,8), and a lower bound for m(3,7).