Charge-transfer transitions and optical spectra of chromites

Specific features of charge-transfer states and charge-transfer transitions of the O2p→Cr3dtype in octahedral complexes (CrO6)9- have been considered in the cluster approximation. Reduced matrix elements of the electric-dipole moment operator on many-electron wave functions, which are the initial and final states for charge-transfer transitions, are calculated. The results are parameterized, and the relative intensities of different allowed charge-transfer transitions in the absence of mixing of different charge-transfer configurations with identical symmetry are calculated. This mixing is taken into account within the Tanabe-Sugano theory, and the true energies and intensities of many-electron charge-transfer transitions are obtained. The Coulomb interaction between 2p electrons of O 2- ligands and 3d electrons of the central Cr3+ ion in (CrO6)9- cluster is considered. The influence of this interaction on the optical spectra is found to be insignificant. Simulation of the optical spectra of chromium oxides has shown the presence of a band of complex charge-transfer transitions composed of 33 lines with a total width of about 8 eV. The model spectrum is in adequate agreement with the experimental data, which indicates limited applicability of the widespread view that charge-transfer transition spectra have a simple structure. © Pleiades Publishing, Ltd., 2013

Data Analysis on the Basis of Numerals Statistics

Two approaches to content analysis of text data are suggested, both based on the statistical study of numerals occurrence in texts. The first approach is related to counting the frequency distribution of various leading digits of numerals occurring in the text. These frequencies are unequal: the digit 1 is strongly dominating; usually, the incidence of subsequent digits is monotonically decreasing. The frequencies of occurrence of the digit 1, as well as, to a lesser extent, the digits 2 and 3, are usually a characteristic author's style feature, manifested in all (sufficiently long) literary texts of any author. This approach is convenient for testing whether a group of texts has common authorship: the latter is dubious if the frequency distributions are sufficiently different. The second approach is the extension of the first one and requires the study of the frequency distribution of numerals themselves (not their leading digits). The approach yields non-trivial information about the author, stylistic and genre peculiarities of the texts and is suited for the advanced stylometric analysis. The proposed approaches are illustrated by examples of computer analysis of the literary texts in Lithuanian – by S. Daukantas, A. Baranauskas, Maironis, and J. Tumas-Vaižgantas

Numerals in authorial Turkish-language texts and the stylometric analysis

Two approaches to the statistical analysis of texts are suggested, both based on the study of numerals occurrence in coherent texts. The first approach is related to the study of the frequency distribution of various leading digits of numerals occurring in the text. These frequencies are unequal: the digit 1 is strongly dominating; usually, the incidence of subsequent digits is monotonically decreasing. The frequencies of occurrence of the digit 1, as well as, to a lesser extent, the digits 2 and 3, are usually a characteristic author's style feature, manifested in all (sufficiently long) texts of any author. This approach is convenient for testing whether a group of texts has common authorship: the latter is dubious if the frequency distributions are sufficiently different. The second approach is the extension of the first one and requires the study of the frequency distribution of numerals themselves (not their leading digits). The approach yields non-trivial information about the author, stylistic and genre peculiarities of the texts and is suited for the advanced discourse analysis. This paper deals with the application of the second approach to the literary texts in Turkish. We have analysed almost the whole corpus of works by are illustrated by examples of computer analysis of the literary texts by O. Pamuk and Y. Kemal - two of Turkey's most prominent novelists. The hierarchical cluster analysis based on the occurrence of numerals in the texts by Pamuk and Kemal shows the author, genre, and chronology differences of numerals usage in the literary texts of these authors. © The Authors, published by EDP Sciences, 2021.We believe that the methodology we are developing can be a useful addition to the traditional stylometric practices of taking into account the length of sentences and words, the frequency of use of service words and certain significant parts of speech, etc. This work was supported by a grant from the Russian Foundation for Basic Research, project No. 19-012-00199A, “A New Method of Text Attribution Based on Statistics of Numerals”. This work was partially supported by a scholarship from the Slovak Academic Information Agency

Discrete Nonholonomic LL Systems on Lie Groups

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.Comment: 32 pages, 13 figure

Taxation issues facing small business in the Russian Federation

The paper outlines the issues related to the taxing facing small businesses in the Russian Federation. The foreign experience concerning the effectiveness of small business taxation was also studied. The relevance relates to the study of the issues of small business development in Russia and the economy as a whole. The purpose of the work is to analyze foreign experience in the sphere of small business management and to solve some problems of its development in Russia. Research methods are descriptive, analytical, and structural method that allowed analyzing the existing foreign practices in the sphere of supporting and functioning of small business abroad as well as problems preventing the development of small business in Russia. The paper examines some problems of taxation facing small enterprises. The foreign experience of tax system functioning of small enterprises is analyzed. Comparing the basic principles of the functioning of tax systems in Russia and abroad, the main tasks of reforming modern taxation in Russia are identified

A novel method of stylometry based on the statistic of numerals

A new method of statistical analysis of texts is suggested. The frequency distribution of the first significant digits in numerals of English-language texts is considered. We have taken into account cardinal as well as ordinal numerals expressed both in figures, and verbally. To identify the author's use of numerals, we previously deleted from the text all idiomatic expressions and set phrases accidentally containing numerals, as well as itemizations and page numbers, etc. Benford's law is found to hold approximately for the frequencies of various first significant digits of compound literary texts by different authors; a marked predominance of the digit 1 is observed. In coherent authorial texts, characteristic deviations from Benford's law arise which are statistically stable significant author peculiarities that allow, under certain conditions, to consider the problem of authorship and distinguish between texts by different authors. The text should be large enough (at least about 200 kB). At the end of {1, 2, ⋯, 9} digits row, the frequency distribution is subject to strong fluctuations and thus unrepresentative for our purpose. The aim of the theoretical explanation of the observed empirical regularity is not intended, which, however, does not preclude the applicability of the proposed methodology for text attribution. The approach suggested and the conclusions are backed by the examples of the computer analysis of works by W.M. Thackeray, M. Twain, R. L. Stevenson, J. Joyce, sisters Bront.e, and J.Austen. On the basis of technique suggested, we examined the authorship of a text earlier ascribed to L. F. Baum (the result agrees with that obtained by different means). We have shown that the authorship of Harper Lee's "To Kill a Mockingbird" pertains to her, whereas the primary draft, "Go Set a Watchman", seems to have been written in collaboration with Truman Capote. All results are confirmed on the basis of parametric Pearson's chi-squared test as well as non-parametric Mann-Whitney U test and Kruskal-Wallis test. Copyright © 2018 Institute of Computer Science