On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

Some properties of weight functions in Tauberian theorems. II

New representations for weight functions in Tauberian theorems are derived. The representations are given by recurrent formulae. Obtained results are used to study properties of the weight functions

Some properties of weight functions in tauberian theorems

The rate of convergence for weight functions series in Tauberian theorems is obtained. Numerical results demonstrate required rate of convergence. Some asymptotic properties of hypergeometric functions are obtained as auxiliary results

EU Cultural Projects in Ukraine and the Impact of the Pandemic on Their Realization

События 2014 года стали поворотными в истории культурного самоопределения Украины. В обществе произошел давно наметившийся цивилизационный раскол. Тесные культурно-исторические связи ЕС и Западной Украины позволяют рассматривать последнюю в качестве части западной цивилизации.The events of 2014 marked a turning point in the history of cultural self-determination in Ukraine. There has been a long-standing division of civilization in society. Close cultural-historical ties between the EU and Western Ukraine make it possible to consider the latter as part of Western civilization

Alliance of Russia, Iran and Turkey in Syria: Perspectives of Maintenance of the Alliance

Целью данного исследования является определение перспектив сохранения союза России, Ирана и Турции в Сирии путем анализа экспертных оценок.The purpose of this study is to determine the prospects for the alliance between Russia, Iran and Turkey in Syria by analyzing expert assessments

Space Weather and Its Impact on Psycho-Emotional State of the Inhabitants of Different Latitudes

Purpose of the research was to conduct a comparative analysis of the psychological characteristics of the inhabitants of the northern and middle latitudes, depending on their psychological sensitivity to changes in geomagnetic disturbances Materials and Methods: The study included 78 relatively healthy volunteers (women and men, the average age of 44.2[36.7; 54.3] years) living in the polar (Tiksi), subpolar (Yakutsk) and middle (Saratov) latitudes. Monitoring of the studied indicators was carried out during March and April 2016. To achieve this goal, the following methods were used: the Spielberger-Khanin scale for reactive (situational) and personal anxiety; E. Heim's technique for revealing individual coping strategies; the projective psycho-geometric test. Every day, during March and April 2016, the Kp-index, an integral indicator of changing geomagnetic disturbance was used. Depending on the identified matches, the peak values of the reactive anxiety by Spielberger-Khanin and Kp-index (not less than 60% of cases), all volunteers were divided into 2 groups. Group 1 included persons with similar overlap and, therefore, carriers of psychological sensitivity to changes in the action of heliogeomagnetic factors. Group 2 included persons without a specified sensitivity, (i.e., no coincidences). Results: In the course of the study, both coinciding and latitude-related differences in the psychological characteristics of different groups of volunteers were established. In the inhabitants of the polar and subpolar latitudes, especially in Group 1, the behavioral sphere was the most vulnerable (no constructive coping strategies). In addition, their changes in the emotional sphere contributed to the manifestation of aggressiveness and suppression of emotions against the background of general concentration, purposefulness and integrity of the individual. Regardless of the latitude of residence, volunteers, psychologically sensitive to changes in heliogeomagnetic factors, were more constructive in the emotional sphere, and the least in the behavioral, which gives reason to state that, depending on the factors of space weather, the behavior of the individual is the most vulnerable

From subgaussianity to stochastic approximation and modelling

The modern theory of subgaussian random variables and processes was created by independent efforts of several research schools from France, USA and Ukraine. Professor Yu.Kozachenko was a founder and leading figure of this research direction of the Ukrainian probability school. An outline of Professor Yu.Kozachenko's contribution to the theory of sub-Gaussian random variables and processes is presented. The class of $\varphi$-subgaussian random variables is introduced and its key property is discussed. Then it is demonstrated how these results can be used in stochastic approximation and modeling. In particular, applications to approximation of trajectories of $\varphi$-subgaussian random processes with given accuracy and reliability are discussed. Two important clases of algorithms from the signal processing theory, the Shannon sampling method and wavelet decompositions, are used as examples. Some personal memories of the author about Yu. Kozachenko are included at the end of the paper.Key words: Yu.Kozachenko, subgaussian, stochastic approximation, stochastic modelling.Pages of the article in the issue: 84 - 88Language of the article: Ukrainia

On fractional spherically restricted hyperbolic diffusion random field

The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial–temporal homogeneous and isotropic random fields and their spherical restrictions are studied. The spectral representations of these fields are derived and the associated angular spectrum is analysed. The obtained mathematical results are illustrated by numerical examples. In addition, the numerical investigations assess the dependence of the covariance structure and other properties of these fields on the orders of fractional derivatives