### Book

## Mathematical Methods in Engineering

Peculiarities of lecturing discriminant analysis methods for training specialists in the field of "business informatics", that is, specialists for whom understanding the model, the algorithm for its practical implementation and approaches to assessing and analyzing the results obtained, are considered. And also - an understanding of purpose, where, when and how it is possible and necessary to use this method. All this determines the practical orientation of the lectouring process.

We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field F_p or F_{p^2} where *p* denotes a prime number ≥5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over F_{p_2} attaining the Drinfeld–Vladuts bound and on the descent of these families to the definition field F_p. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (Funct Approx Commmentarii Math, 55(2):177–197, 2016).

The expressive power of a new variant of temporal logic LP-CTL * is studied. In this logic, two classes of LP-1-LTL and LP-n-LTL formulas were distinguished and it was shown that the LP-1-LTL fragment more expressive than the known temporal logic of linear time LTL, and the LP-n-LTL fragment has the same expressive possibilities as the second-order monadic logic S1S.

We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing intersection numbers of 1- and 2-dimensional cycles are developed. Using these algorithms it is possible to construct a basis of the cohomology group from a given basis of the homology group of complementary dimension.

Two models of the tree modes of hash functions are introduced. For each model algorithms of computing of the hash code are formulated and their numerical characteristics are obtained. In terms of the constructed models we classify some existing algorithms for parallel hashing and identify some weaknesses of corresponding primitives.

We present an approach based on a two-stage ltration of the set of feasible solutions for the multiprocessor job-shop scheduling problem. On the rst stage we use extensive dominance relations, whereas on the second stage we use lower bounds. We show that several lower bounds can eciently be obtained and implemented.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.