### Book

## Finite Difference Methods, Theory and Applications 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Revised Selected Papers

This book constitutes the thoroughly refereed conference proceedings of the 6th International Conference on Finite Difference Methods, FDM 2014, held in Lozenetz, Bulgaria, in June 2014. The 36 revised full papers were carefully reviewed and selected from 62 submissions. These papers together with 12 invited papers cover topics such as finite difference finite element methods and various its applications in physics, chemistry, biology and finance.

We deal with an initial-boundary value problem for the generalized time-dependent Schrödinger equation with variable coefficients in an unbounded $n$-dimensional parallelepiped ($n\geq 1$). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transparent boundary conditions is considered. We present its stability properties and derive new error estimates $O(\tau^2+|h|^2)$ uniformly in time in $L^2$ space norm, for $n\geq 1$, and mesh $H^1$ space norm, for $1\leq n\leq 3$ (a superconvergence result), under the Sobolev-type assumptions on the initial function. Such estimates are proved for methods with the discrete TBCs for the first time.

An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averages both in time and space. Stability in two norms is proved by the energy method. Also discrete transparent boundary conditions are rigorously derived for schemes by applying the method of reproducing functions. Results of numerical experiments are included as well.

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.

The purpose of the research is to substantiate the development of integral branch of modern psychology of personality which is defined as personology. The research stresses the need to change dominating analytical approaches to the study of personality for the synthetic approach defined as «science of synthesis». It will reflect multiple ties between different theories and consulting personality models; experience of creating a single semantic space for personality cognition; unity of theoretical, cultural and practical psychology of personality. This triple format of personology is focused on discovery and realization of self-cognition of the personality as well as personality of the personologist being the subject of hermeneutics, theoretical studies and practical activity. The research defines the subject of personology based on positions of synthesis as well as defines the foundation for integration of the personological knowledge, structure of personology, content, method and forms of interaction between cultural, fundamental and consulting psychology.

Contributions of the Thirteenth International Kazan summer scientific school-conference (Kazan, August 21-27, 2017).

A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.