The National Pedagogical Dragomanov University is a Ukrainian University in Kyiv, which has III-IV accreditation level.Post address: 01601,Ukraine, Kyiv, Pyrohova str., 9.
We study topological, metric and fractal properties of set of numbers [0;1] with given asymptotic mean of digits in their ternary representation. We investigate connection of these numbers and numbers with a given frequency of digits.
In the paper we describe some properties of function y=r(x)=lim_n→∞1/n∑^∞_k=1α_k(x), where x=∑^∞_k=1α_k(x)4^-k of 4-adic digits asymptotic mean of fractional part of real number x, particularly properties of it's level sets S_θ={x: r(x)=θ, θ=const, 0⩽ 3}, if all 4-adic digits frequencies exist, i.e. ν_i(x)=lim_n→∞n^-1#{k: α_k(x)=i, i⩽ n}, i=0,1,2,3. We provided an algorithm of constructing point from the set S_θ, and proved continuality and every where density of the set. We found conditions of zero and full Lebesgue measure and estimates of Hausdorff-Besicovitch fractal dimension.
Background: In the context of rapid societal changes and increasing demands for professional competence, coaching has emerged as a recognised method for improving employee productivity, motivation, and personal development across industries. Objective: This study aimed to summarise existing scientific evidence on the effectiveness of coaching interventions in various professional fields and to identify key factors influencing their outcomes. Methodology: The research design followed a systematic and transparent protocol consistent with the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines, ensuring methodological rigour and replicability. The meta-review encompassed empirical studies published between 2016 and 2025 that examined the effectiveness of coaching interventions across professional domains, particularly in business management and healthcare systems. Comprehensive database searches were conducted in Scopus, Web of Science, PubMed, PsycINFO, and Google Scholar, yielding 54 studies that met the inclusion criteria. Of these, only 11 randomised controlled trials (RCTs) provided complete statistical indicators necessary for the computation of the effect size (Hedges’ g), representing a combined participant pool of 15,278 individuals. The mean effect size and heterogeneity were subsequently calculated in relation to the duration, format, and methodological characteristics of the coaching interventions to identify key determinants of their overall efficacy. Results: The meta-analysis indicated a significant positive impact of coaching on professional performance, emotional competence, self-awareness, and goal attainment, with a moderate overall effect size (Hedges’ g ≈ 0.58). Higher effectiveness was observed in long-term programmes, individual coaching formats, cognitive-behavioural approaches, externally assessed outcomes, and in the fields of digital transformation management and healthcare. Conclusion: Coaching interventions significantly and positively influence professional outcomes, with the highest benefits in individualised, long-term applications within management and healthcare. Unique Contribution: This study integrates large-scale empirical evidence to clarify which structural and methodological factors enhance coaching effectiveness, offering practical insights for program design in diverse professional sectors. Key Recommendation: Future research should focus on the interaction between coaching duration, delivery format, and assessment method, as well as on sector-specific customisation to optimise program effectiveness.
In the paper we study transformations of the interval [0;1) and functions that preserve the asymptotic mean r of the digits in the s–adic representation of a number x, r(x)=lim_n→∞1/n∑^n_i=1α_i(x) specify the necessary and sufficient conditions for a transformation to belong to this class
The journal retracts the article “System-Cluster Technology of e-Learning Improvement under the Conditions of COVID-19” [...]
