Headings of the journal
"Educational Resources and Technologies"

Annotation: According to the methodology developed by the author, two one-parameter classes of integer sequences are introduced and investigated in the paper. The first class provides an interpolation between a sequence of powers of two and a sequence of Catalan numbers, and the second class provides an interpolation between a sequence of powers of two and a sequence of Bell numbers. In order to obtain various interpretations of the numbers of the considered classes, T-models and permutations by Lehmer codes are used. These interpretations are based on the recursive construction of sequences of numerical tables of a special kind defining T-models and the properties of permutations by Lehmer codes. The method used leads to simple algorithms for constructing two classes of permutation sets corresponding to the introduced classes of numerical sequences. On the basis of the obtained classes of permutation sets, it is also possible to set probability distributions. The representation of elements of the second class of numerical sequences using Stirling numbers of the second kind allows us to match the class of ordered partitions of sets into a certain number of blocks to the corresponding class of permutation sets. For the numbers of the studied classes of sequences, the relations for their q-analogues are obtained.

Annotation: The article describes the features of information interaction in a human-machine system. The structure and features of the human-machine system are described. It is shown that a significant difference between a man-machine system and other systems is the inclusion of human resources in its composition. Human participation and abilities affect the outcome of a human-machine system. The human-machine system is interpreted as an organizational technological information complex. The article shows the importance of information models and information technologies for human-machine systems. Two system models of a man-machine system are described: weakly formalized and formalized. The models complement each other. The article describes the significance of visual models for a human-machine system. Different types of information interactions are shown. The visual model allows information interaction in a human-machine system for a real situation. The importance of information units in the formation of information and visual models is described. The article describes the basic principles of information interaction in a human-machine system. The article compares the algorithmic information processing system and the man-machine system.

Annotation: Zen tradition, which is recorded in texts, and which is presently integrated into various spheres of human activity – philosophy, literature, art, psychology, – is considered in the current paper. Special attention is paid to the brief revision and systematization of texts on the example of translations and research of Doctor of Philosophy Yevgenia Vladimirovna Zavadskaya. The main ideas of Zen Buddhism are revealed in the works of the author, which can be an important support for the competent presentation and interpretation of this teaching in modern society, which connects Western culture and Zen Buddhism. This aspect can be seen in philosophy, literature and art, through which Zen penetrates the expanses of the West, and later the Soviet Union. The purpose of the investigation is to analyze the works of Ye. V. Zavadskaya as an attempt to predict the prospects for the development of cultures. The process of integrating Zen ideas into European culture is considered in the paper, which is considered as a springboard between humanitarian knowledge and the practical application of this knowledge. The main research methods are hermeneutical and dialectical.

Annotation: The article proposes a new technique for interpolating integer sequences. It is demonstrated on classes interpolating sequences between Catalan numbers and factorials and between Bell numbers and factorials as well. This technique is based on T-models and Lehmer permutations codes. T-models are specified recursively by sequences of special type numerical tables. It allows us to obtain algorithms for solving a number of emerging problems. Integer sequences correspond to T-models whereas sets of numbers (codes) of their elements are also constructed for the latter. Using this technique the article introduces the classes of generalized Catalan and Bell numbers, as well as their q-analogues. Their extension leads to the sequence interpolation problem solution. We also find the permutation classes corresponding to sequences and given by sets of Lehmer codes. This approach greatly simplifies the construction of permutation classes that were previously obtained in computer science articles by means of removing the permutations with given patterns.

Annotation: The information morphism as a key technology for creating a mixed reality is investigated. The content of mixed reality as a new educational technology is revealed. The similarities and differences between mixed reality, virtual reality, and augmented reality are shown. It is shown that mixed reality is realized by means of multimedia. The variety of information morphism as a technology of information interaction is revealed. The requirements necessary for the implementation of this technology are formulated. The transformation of a theoretical conceptual model in the information field into a model of information construction, which serves as the basis for building information models of objects and processes, is considered. Information models of processes and objects make it possible to build virtual reality. It is shown that mixed reality is constructed as a synthesis of virtual reality, information situation and spatial reality. The structure of interrelated information models of objects and processes in the construction of mixed reality is presented. The advantages of using mixed reality in the educational process are revealed due to the properties of variability, high adaptation to innovations, the possibility of presenting retrospective facts and models in the course of training.