arXiv subjects
Publications and source records attributed to Andrij Rovenchak.
In the article, theoretical principles and practical realization for the compilation of the concordance to "Perekhresni stezhky" ("The Cross-Paths"), a novel by Ivan Franko, are described. Two forms for the context presentation are proposed. The electronic version of this lexicographic work is available online.
The equivalence is established between the one-dimensional (1D) Bose-system with a finite number of particles and the system obeying the fractional (intermediate) Gentile statistics, in which the maximum occupation of single-particle energy levels is limited. The system of 1D harmonic oscillators is considered providing the model of harmonically trapped Bose-gas. The results are generalized for the system with power energy spectrum.
The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.
In the paper, the definition of clause suitable for an automated processing of a Ukrainian text is proposed. The Menzerath-Altmann law is verified on the sentence level and the parameters for the dependences of the clause length counted in words and syllables on the sentence length counted in clauses are calculated for "Perekhresni Stezhky" ("The Cross-Paths"), a novel by Ivan Franko.
In the paper, a complex statistical characteristics of a Ukrainian novel is given for the first time. The distribution of word-forms with respect to their size is studied. The linguistic laws by Zipf-Mandelbrot and Altmann-Menzerath are analyzed.