Headings of the journal
"Educational Resources and Technologies"

Annotation: Many thinkers have tried to prove that we live in a simple world, yet man complicates it, but this is not the case. The world is complex independently of us. Firstly, there is a plethora of objects in the world, secondly, it is constantly changing and, thirdly, it is heterogeneous. Plurality, versatility and heterogeneity are already sufficient qualities to recognize the complexity of the world. Micro, macro and mega levels are challenging from the Big Bang itself. If we take social reality, then here we also observe a complication associated with the increase in the number of homo sapience on Earth. As demographic indicators grow, the level of competition increases, sustainable objects become hybrids, verity becomes post-truth, and the state of society becomes chaosmos. Purpose of the work: to present a methodology of complexity in a new technological order. Applied research methods: structural analysis, system analysis, factor analysis, synergetics. As a result of the conducted research, the following Results were obtained: 1) speed is considered as a factor of complexity; 2) the cognitive conditions of complexity are considered; 3) the adaptive capabilities of society to complexity are conceptualized as a new normality, representing the convergence of modern social processes while preserving identities and boundaries of interpretation.

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.