We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

In this article, we consider the problem of planning maintenance operations at a locomotive maintenance depot. There are three types of tracks at the depot: buffer tracks, access tracks and service tracks. A depot consists of up to one buffer track and a number of access tracks, each of them ending with one service track. Each of these tracks has a limited capacity measured in locomotive sections. We present a constraint programming model and a greedy algorithm for solving the problem of planning maintenance operations. Using lifelike data based on the operation of several locomotive maintenance depots in Eastern polygon of Russian Railways, we carry out numerical experiments to compare the presented approaches.

Let L = −div(A∇) be a uniformly elliptic operator in Rn with real, symmetric, measurable coefficients. We study the identity of two families of Besov spaces Bs,L p,q and Bs p,q , where the former one is defined using the heat semigroup of L, while the latter one is defined in a classical way, using the metric structure of Rn. A sharp range of parameters p, q, s ensuring the identity Bs,L p,q = Bs p,q is given by a Hardy– Littlewood–Sobolev–Kato diagram.

The article discusses the problems of introducing digital technologies into the decision-making process in the energy sector. For this purpose, two types of digital decision-making technologies are analyzed. The first technology - direct, which today is the main (traditional), is that the decision is made by a person - a decision maker, and a computer program acts as an “advisor” - a decision support system. The development of this technology is associated with the development of “active advisers”, when, after the implementation of the decision, a comparison is made of the decision made by the decision maker and the decision proposed by the “adviser” on the basis of so-called “recalculating models”. In the second technology (let's call it inverse), the decision is made by a computer program, and the person only observes and analyzes, without interfering in the decision-making process (with the exception of force majeure situations). In this technology, a decision support system is transformed into a decision-making system, and a decision maker becomes a decision analyst. However, the decision-making mechanism is developed by the head and other stakeholders who are responsible for the results of the operation. The necessary conditions for the effective functioning of both technologies are, firstly, the interest of participants in the presentation of reliable information required for decision-making, and secondly, interest in the implementation of decisions made (conditions of L.V. Kantorovich - V.M. Glushkov). The article provides a comparative analysis of these technologies and provides examples of their practical implementation.