To investigate the ordering and decomposition processes in Ti-Al-X [X = Si, Zr] alloys, the Monte Carlo simulations with first-principles parametrization of interatomic interactions were employed. It was shown that the processes of ordering and the precipitation in the Ti-Al system are closely related, and the stage of homogeneous ordering precedes the formation of ordered Ti₃Al particles. It was found that the duration of homogeneous ordering is very sensitive to the annealing temperature and composition of alloy, and that precipitation becomes preferable as the temperature rises. In particular, uniform ordering of alloy Ti-12 at % Al was found during long-term holding at temperature below 850 K, while annealing at 1000 K resulted in formation of ordered Ti₃Al particles. The obtained results agree well with the experimental data and allow explaining the features of the microstructure formed during annealing of the Ti-Al-X alloys.

Previous historical and philological commentaries on Nostradamus' "Prophecies" by Prof. Brind'Amour, R. Prevost, P. Guinard, A. Penzensky, and D. Crouzet have led to the unexpected conclusion that many quatrains are uninformative as predictions; moreover, some of them describe events preceding the moment of publication, raising questions about the predictor's motivation. Against the background of the increased interest in the development of cryptology methods in the first half of the 16th century, it is appropriate to assume the existence of a hidden message in the "Prophecies". Recent work by the author has shown that the text of the "Prophecies" contains two types of cipher. The modified algorithm "scytale" is apparently used to change the sequence of quatrains and assign them certain dates of real time. Additionally, a large graphical cipher is invisibly embedded in the text, so that specific words or letters, when mapped as stains on a plane in the coordinates "century number – quatrain number", lead to images of human faces. These images likely serve as illustrations to the prophetic text, however, their low quality and the cipher author's tendency towards surrealism make it difficult to identify the characters. The aim of this work is to propose a new method for processing the raw data to obtain higher-quality images, called the "smooth assembly" method, and to discuss Nostradamus' graphical cipher in a historical context. The results of the study suggest that Nostradamus' graphical cipher was a unique experiment in embedding images in text and had significant scientific value for the development of steganography in the 16th century. This leads to the assumption that, in addition to predictive motivation (or instead of it), the cipher author pursued a purely scientific goal – the creation of a new promising method of covert information transmission.

Despite the extensive bibliographical material, scientific study of the life and work of Nostradamus has only relatively recently begun. Currently, it includes a detailed examination of the predictor's biography and historical-philological commentaries on the quatrains. The unordered arrangement of the quatrains is one of the main problems hindering the understanding of the prophecies. In particular, it has been discovered that many quatrains describe presumed future events through comparison with the past, and therefore cannot be adequately understood without a reasoned arrangement by dates. Although Nostradamus himself unequivocally states in an epistle to King Henry II that the quatrains should be arranged using the biblical chronology he provided, with a reference point determined by the retrograde movements of planets (1606 year, as shown by prof. Brind'Amour), discussions of such cryptographic approaches were absent in Nostradamus literature until now. This work presents, for the first time, a detailed argument for the hypothesis that Nostradamus used a modified «scytale» algorithm to encrypt the correct sequence of quatrains and assign them certain dates. It is shown that the predictor indeed employed cyclically repeating biblical chronologies placed in the epistle to King Henry II for this purpose. The final date of the prophecies turns out to be the year 2242, close to the end of the 6000 years in the Jewish calendar (2240 AD) and the completion of the cycle of planetary epochs in the astrological concept of Abraham ibn Ezra (2241 AD), which aligns well with existing historical research. The results of the analysis indicate that although the «Prophecies» were published in parts, they form a coherent work following a strict plan. Consequently, the obtained results are relevant to the history of cryptography in Europe and have significant implications for a correct understanding of Nostradamus' texts.