Цитата с сайта ВАК: "Научные периодические издания, удовлетворяющие достаточному условию, текущие номера которых или их переводные версии на иностранном языке включены в хотя бы одну из систем цитирования (библиографических баз) Web of Science, Scopus, Web of Knowledge, Astrophysics, PubMed, Mathematics, Chemical Abstracts, Springer, Agris, GeoRef, являются включенными в Перечень" (Список ВАК). LNCS (Lecture Notes in Computer Science) - Научное периодическое издание, включенное в систему цитирования Springer. Тем самым, входит в "Список ВАК". In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them featuring the cutpoint additive distances. These include the path distances, the reliability distance, the walk distances, and the logarithmic forest distances among others. We discuss a number of connections between these and other distances.

We investigate relationships in the Kalman algebra, viewed as an algebra over the algebra induced by the coefficients of the characteristic polynomial of the state matrix. To this end we introduce the categories BSS and BSSstrict associated with relationships in some basis of the Kalman algebra and also with reconstruction of relationships from known fragments. On these categories we construct the structures of the symmetrical monoidal category induced by addition and multiplication in the Kalman algebra. We investigate the properties of some of the most important classes of morphisms, in particular, we describe the structure and the action of the automorphism group.

A multiple objective dynamical problem under uncertainty is solved for an optimal combination of outcomes and risks. A linear-quadratic form is considered, which leads to an explicit solution for a fairly wide class of problems.

Abstract: The walk distances in graphs have no direct interpretation in terms of walk weights, since they are introduced via the logarithms of walk weights. Only in the limiting cases where the logarithms vanish such representations follow straightforwardly. The interpretation proposed in this chapter rests on the identity ln det B = tr ln B applied to the cofactors of the matrix I−tA, where A is the weighted adjacency matrix of a weighted multigraph and t is a sufficiently small positive parameter. In addition, this interpretation is based on the power series expansion of the logarithm of a matrix. Kasteleyn (Graph theory and crystal physics. In: Harary, F. (ed.) Graph Theory and Theoretical Physics Academic, London, 1967) was probably the first to apply the foregoing approach to expanding the determinant of I−A. We show that using a certain linear transformation the same approach can be extended to the cofactors of I−tA, which provides a topological interpretation of the walk distances.

Построено обобщение структуры почти произведения и почти комплексной структуры на гладком многообразии. Построены тензорные инварианты таких структур (тензорные поля типа (2,1) и дифференциальные 2-формы) . Построенные инварианты используются для классификации уравнений Монжа-Ампера и систем Якоби.