### Article

## Verification of an Entropy Dissipative QGD-Scheme for the 1D Gas Dynamics Equations

An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh $L^1$-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for $L^2$-dissipativity of the Cauchy problem for a linearized QGD-scheme.

We consider the Cauchy problem for the 1D generalized Schrὅdinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transpa\-rent boundary conditions (TBCs) has recently been constructed. Now we engage the global Richardson extrapolation in time to derive the high order method both with respect to space and time steps. To study its properties, we comment on its stability and give results of numerical experiments and enlarged practical error analysis for three typical examples. Unlike most common 2nd order (in either space or time step) methods, the proposed method is able to provide high precision results in the uniform norm by using adequate computational costs. It works even in the case of discontinuous potentials and non-smooth solutions far beyond the scope of its standard theory. Comparing our results to the previous ones, we obtain \textit{much more} accurate results using much less amount of both elements and time steps.

We study an explicit two-level in time and three-point symmetric in space finite-difference scheme for 1D barotropic and full gas dynamics systems of equations. The scheme is a linearization at a constant background solution (with an arbitrary velocity) of finite-difference schemes with general viscous regularization. We enlarge recently proved sufficient conditions (on the Courant-like number) for $L^2$-dissipativity in the Cauchy problem for the schemes by deriving new bounds for the commutator of matrices of viscous and convective terms. We deal with the case of a kinetic regularization in more detail and specify sufficient conditions in this case where the mentioned matrices are closely connected. Importantly, these new sufficient conditions rapidly tend to the known necessary ones as the Mach number grows. Also several forms of setting a regularization parameter are considered.

We consider an initial-boundary value problem for a 2D time-dependent Schrödinger equation on a semi-infinite strip. For the Numerov-Crank-Nicolson finite-difference scheme with discrete transparent boundary conditions, the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniqueness of a solution and the uniform in time $L^2$-stability (in particular, $L^2$-conservativeness) together with the error estimate $O(\tau^2+|h|^4)$ are proved. Due to the splitting, an effective direct algorithm using FFT in the direction perpendicular to the strip and solving of tridiagonal systems in its main direction is developed to implement the splitting method for general potential. We also engage the Richardson extrapolation in time to increase the error order with respect to time step and get the method of higher order both in space and time. Numerical results on the tunnel effect for smooth and discontinuous rectangular barriers are included together with the careful practical error analysis on refining meshes.

We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system.

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

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.

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.