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The article developed the mathematical model for the synthesis of ornamental images and implemented the software editor of ornamental images, based on symmetry theory. The paper shows the fundamental role of symmetry. It is analyzed that the symmetry theory methods are used in physics, chemistry, biology, and engineering. It was found that symmetry is based on transformation and storage. In addition, the symmetrical system is based on a set of invariants that are built according to certain rules.

Contemplating the works of monumental art that surround us in everyday life, you always see the numerous sculptural decorations of Lviv houses, carefully look at the wall paintings of temples, catch the glare of coloured stained glass windows. And the city itself, which has not been subjected to crushing destruction, not only has a considerable number of monumental architectural objects but also acts as a large complex representing the philosophy of different historical periods of society's existence. We see all this almost daily.

Today, Instagram social network is one of the most popular in Ukraine. In addition, it is the most dynamic web resource, because its developers regularly optimize all features. If it was previously used only as a platform for distributing photos and their short descriptions, today it is a resource that also plays an important role in creating and disseminating information and messages. It is a social network that has won a large audience, especially young people. That is why it also influences the formation of public opinion and the image of the country and its authorities.

In the article were researched the principles of building systems for observation and recognition of objects. Also we have given the classification of human faces recognition methods. Authors have analized the features of operetion for the progressive calibration network (PCN) for human face recognition. And finally has been created and tested the developed face recognition algorithm as the realized software system.

The images are one of the most used kinds of the information in modern information company. Therefore actual problems is the organization of protection from unauthorized access and usage. An important characteristic of the image is the presence of contours in the image. The task of contour selection requires the use of operations on adjacent elements that are sensitive to change and suppress areas of constant levels of brightness, that is, contours are those areas where changes occur, becoming light, while other parts of the image remain dark.

The article considers the issue of charismatic sacral architecture in Lviv within 1990 - 2000 years. It has been outlined a period, during which traditionalist or denominational stereotypes did not affect a process of sacral buildings design. Within this some unique structures has occurred, as a result of individual search of charismatic image of a sacral space. The active phase of this period lasted through the 1990s and 2000s.

The article deals with the correlation between the notions of symbol and image. The main attention is paid to the interpretation of symbol and image in various areas of Humanities, which allows to reveal substantial features of these terms. The terms “symbol” and “image” in semiotics and cultural studies have been analyzed. The interrelation of the terms “artistic symbol” and “artistic image” in literary theory has been discovered. According to the approaches to the study of linguistic terms, their terminological variability is substantiated.

In this article, a system of handwritten or printed text recognition in the image has been developed. Empirical methods of image processing and statistical models of machine learning and simulation are being developed in two directions: the detection of text on the image and the recognition of the text. Thus, in this paper, algorithmic software tools that combine these two areas in the software created for the operating systemiOS 11.0 or later for devices of the company Apple – iPhone, iPad that support this operating system are developed.

Images used as a stochastic signal are among the most commonly used types of information. Accordingly, the actual task is to protect such images from unauthorized access and use. This leads to the use of known classic encryption methods in the case of image encryption. Offered algorithms of encryption-decryption are intended for the use of images in grayscale and are based on using the ideas of basic RSA algorithm. Encryption – decryption can be carried out with extra noising and without too.

На основі короткої еволюційної інтроспекції образу висотної будівлі показано взаємозв’язок світоглядних, суспільних, виробничих факторів, що в ті чи інші періоди приводили до трансформації образу висотної будівлі від її виникнення в рамках “чиказької школи” до її перспектив на ХХІ століття.