MATHEMATICAL MODEL OF THE DEVELOPMENT OF A SINGLE TWIN LAYER IN METAL CRYSTALS

By analyzing the experimental data available in the scientific literature, a mathematical model of the development of a single twin layer in metal crystals has been obtained. The model has the form of a differential equation, the order of which is determined by the required accuracy of obtaining the results associated with the solution of this equation. Even in the linear approximation of one of the main parameters of the phenomenological model, the latter gives qualitatively the same dependences of the development of single twins under different loading conditions compared to the experiment. Despite a large number of experimental works devoted to twinning, there is still no rigorous quantitative theory of the development of twinning layers in different media and under different conditions. However, in these works, the mathematical approach was demonstrated only in relation to elastic twins. This work is an introduction to the creation of a quantitative theory of twinning in metal crystals. Comparisons with the experimental results of the proposed phenomenological model were limited in this work to the task of demonstrating the performance of the model in the sense of predicting the most specific effects of the development of twins under various conditions and loading modes. In particular, the model implies the effect of loss and subsequent restoration of hardening by twin boundaries during stress pulsations, the Bauschinger effect upon a change in the sign of the applied voltage, and a number of other effects observed experimentally on a number of different metal crystals.

THEORETICAL BACKGROUND FOR REFORM THE MONETARY SYSTEM OF UKRAINE

Introduction. Reforming the monetary system of Ukraine is necessary in order to bring it to a state that would meet the needs of socio-economic development of the country.Problem. Monetary reform in Ukraine can be carried out by trial and error, as was the case, for example, in the first half of the 1990s, and can be much more productive, based on the relevant theoretical principles.Purpose: highlighting those provisions of the basic theories of money, which in the current conditions can form a theoretical basis for monetary reform in Ukraine in its broadest sense, in terms of creating a fundamentally new structure and content of the monetary system.The presentation of the material of the article. When reforming the monetary system of Ukraine, it is necessary to focus on practically oriented provisions of basic theories of money. Within the framework of abstract theories, the following provisions can serve these purposes: metalistic theory - to displace the worst money with the best, to achieve a positive foreign trade balance, to pursue a policy of protectionism and exchange rate stabilization; commodity theory - on balancing the amount of money and commodity mass, the application of the gold coin standard, ensuring the independence of the central bank and changing the discount of securities depending on the needs of the economy; nominalist, in particular state, theory - on the maintenance of the state value of paper money. In the framework of applied theories of money, which are based on quantitative theory, the relationship between the mass of money and GNP is of practical importance. The classical quantitative theory of money is based on a direct relationship between them, the theory of neoclassical money (transactional, conjunctural and Cambridge) - indirect.Results and its discussion. It is shown that the Caesian theory of money is important for stimulating economic growth in Ukraine, and monetary theory, coordinated among themselves on the basis of neoclassical synthesis, is important for curbing inflation.Conclusions. Practically oriented provisions of abstract and applied theories of money can form the theoretical basis of monetary reform in Ukraine, but their use should be based on modern Ukrainian realities.Keywords: monetary system, monetary reform, money theory, commodity mass, money supply, price.

Predicting fringe visibility in dual-phase grating interferometry with polychromatic X-ray sources

Dual phase grating X-ray interferometry is radiation dose-efficient as compared to common Talbot-Lau grating interferometry. The authors developed a general quantitative theory to predict the fringe visibility in dual-phase grating X-ray interferometry with polychromatic X-ray sources. The derived formulas are applicable to setups with phase gratings of any phase modulation and with either monochromatic or polychromatic X-rays. Numerical simulations are presented to validate the derived formulas. The theory provides useful tools for design optimization of dual-phase grating X-ray interferometers.

On Proinov’s Lower Bound for the Diaphony

In 1986, Proinov published an explicit lower bound for the diaphony of finite and infinite sequences of points contained in the d−dimensional unit cube [Proinov, P. D.:On irregularities of distribution, C. R. Acad. Bulgare Sci. 39 (1986), no. 9, 31–34]. However, his widely cited paper does not contain the proof of this result but simply states that this will appear elsewhere. To the best of our knowledge, this proof was so far only available in a monograph of Proinov written in Bulgarian [Proinov, P. D.: Quantitative Theory of Uniform Distribution and Integral Approximation, University of Plovdiv, Bulgaria (2000)]. The first contribution of our paper is to give a self contained version of Proinov’s proof in English. Along the way, we improve the explicit asymptotic constants implementing recent, and corrected results of [Hinrichs, A.—Markhasin, L.: On lower bounds for the ℒ2-discrepancy, J. Complexity 27 (2011), 127–132.] and [Hinrichs, A.—Larcher, G.: An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77]. (The corrections are due to a note in [Hinrichs, A.—Larcher, G. An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77].) Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.

O REMÉDIO MONETÁRIO PARA ECONOMIA ANGOLANA NO QUADRO DO COMBATE DOS EFEITOS DA COVID-19

The purpose of this article is to assess the impacts of the monetary policy instruments adopted in Angola, within the framework of covid-19. Despite the vast literature associated with the understanding of inflationary processes, the option is to use the quantitative currency equation as a starting point, that is, the article presents the confrontation of two approaches, on the one hand, Milton Friedman's monetarists and on the other side the Structuralism of Raúl Prebisch. Based on the quantitative theory of money, Milton Friedman presents inflation as a purely monetary problem, while Prebisch, based on the fundamental assumptions of the market, presents inflation as well as a result of changes in real variables. The article ends by making a relatively historical incursion. inflation in Angola during the first quarter of 2020, showing that the monetary remedy for Angola should in fact result from a combination of the two approaches.