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## RNGAVXLIB: Program library for random number generation, AVX realization

We present the random number generator (RNG) library RNGAVXLIB, which contains fast AVX realizations of a number of modern random number generators, and also the abilities to jump ahead inside a RNG sequence and to initialize up to 1019 independent random number streams with block splitting method. Fast AVX implementations produce exactly the same output sequences as the original algorithms. Usage of AVX vectorization allows to substantially improve performance of the generators. The new realizations are up to 2 times faster than the SSE realizations implemented in the previous version of the library (Barash and Shchur, 2013), and up to 40 times faster compared to the original algorithms written in ANSI C.

In this update, we present the new version of the random number generator (RNG) library RNGSSELIB,which, in particular, contains fast SSE realizations of a number of modern and most reliable generators [1]. The new features are: (i) Fortran compatibility and examples of using the library in Fortran; (ii) new modern and reliable generators; (iii) the abilities to jump ahead inside a RNG sequence and to initialize up to 1019 independent random number streams with block splitting method.

We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in case where the random walk terminates at some boundary. We recently found that a finite step of the random walk produces a bias in the hitting probability and this bias vanishes in the limit of an infinitesimal step. Therefore, it is important to know how a change in the step size of the random walk influences the performance of simulations. We propose an algorithm with the most effective procedure for the step-length-change protocol.

The manual includes the general orientation information on quantitative and qualitative methods, necessary for experts without basic administrative education. With basic education the manual will be useful for experts not only expansion and fixing of knowledge, but also the annex to actual problems of the organization and management. Its feature that it assumes updating, fixing and judgment of knowledge of the subjects studied earlier, on other forms and training steps. The manual will have practical value for the students who are training on master programs for the Management direction.

Risk Management approach is an essential part of the project. Large industries and particular companies incorporate RM Culture. Statistics shows, that companies with Project Management (PM) Structure reduce cost ineffectiveness up to 20%. In oil and gas industry PM Risk Analysis (PRMA) has been widely used for the last years. Various models and procedures have been developed to manage projects of different scale. Nonetheless, Offshore Projects (OP) complexity, high uncertainty of technical, financial, market and government factors, as well as different sea conditions, still makes sense to improve general PRMA models according to the oil and gas OP features. Traditional RM tools and techniques are not appropriate to cope with complex projects in the Arctic. Companies will have to modify risk assessment process or look for new methods. The paper suggests OPRMM, where the attempt to implement PM tools and techniques together with mathematical modeling and expert assessment is made and institutional factors are included. Practically, it is founded on the comparison between offshore field development in the Barents Sea and the Kara Sea. The reason for research is debates around future Arctic oil and gas projects and their commercial potential. Several large projects with participation of major international companies in the Barents Sea and the prospectivity of the Kara Sea Projects in conditions of technology difficulties are under discussion and have not reached the investment project phase yet. OPRMM starts with identifying the key factors, which could affect offshore field development. Inside the investment regime modified real option value (ROV) model for OP is developed: stop option and scale transformation option. Basing on the binominal trees and Monte Carlo Simulation it is possible to see the perspectives of the OP at an early stage in the conditions of high uncertainty. Incorporating the ROV model into investment regime allows operator to choose the territory to explore. The research shows, that offshore projects in the Arctic offshore is not only under the pressure of internal corporative factors, but also under influence of external institutional factors. New tools and approaches will be required in Arctic projects where no one wants to be looking in the wrong place.

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.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

The Handbook of CO₂ in Power Systems' objective is to include the state-of-the-art developments that occurred in power systems taking CO₂ emission into account. The book includes power systems operation modeling with CO₂ emissions considerations, CO₂ market mechanism modeling, CO₂ regulation policy modeling, carbon price forecasting, and carbon capture modeling. For each of the subjects, at least one article authored by a world specialist on the specific domain is included.

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables