Annotation: The article examines how prepayment affects the structure of forward contracts with deferred pricing. This tool allows you to distribute credit and price risks between the parties. The analysis shows that prepayment reduces the risk of non-payment for the recipient, but at the same time increases the likelihood of non-repayment of funds and creates liquidity constraints for the payer. And in the case of an "open price", it can increase the conflict of interests around its fixation. The findings can be used to develop prepayment conditions, types of collateral, and price fixing rules to increase the stability of transaction execution.

Annotation: At most large domestic enterprises, the HR department and the payroll department report to different managers, which creates a gap between HR decisions and their reflection in payroll calculations and increases the risks during inspections by regulatory authorities. The article examines the organizational and technological conditions under which a personnel evaluation system becomes an effective tool for enterprise management. Based on the author's management experience at three large enterprises – SE “Pivdennyi Sea Port Administration,” OilGasChem Service (OGC Service), and Lukoil Technologies Services Ukraine – a comparative analysis of personnel evaluation methods is conducted, the role of personnel commissions is characterized, and the author's HR-ERP system, implemented from scratch at two enterprises (OilGasChem Service (OGC Service) and Lukoil Technologies Services Ukraine), is described. It was found that combining a competency model, KPI approach, and performance review provides better management results than using each method separately. It was shown that combining the functions of the HR manager and the head of the payroll department in one position significantly reduces the number of calculation errors and ensures end-to-end consistency of personnel documentation and reporting. The scientific novelty is the concept of “live calculation” – an architectural solution in which any change in personnel status automatically and without delay recalculates accruals, which fundamentally distinguishes the system from standard solutions based on the paradigm of closing the calculation month.

Annotation: Jumping (plyometric) work can improve power, rate of force development, and jump performance, with some studies finding improvements comparable to the effects of traditional strength training/weightlifting for a range of speed-strength parameters. For strength athletes, the key question is not "should I jump?" but "how much should I jump" to achieve a stimulus without overloading the tendons or impairing recovery after lifting. This article proposes a practice-oriented model of "optimal volume" using clear metrics (contacts, intensity, frequency, weekly distribution) and based on data from systematic reviews/meta-analyses and methodological recommendations on plyometric volume.

Annotation: The article examines the theoretical and methodological foundations for the formation of hybrid development strategies of enterprises in the digital economy. The necessity of integrating traditional competitive strategies with digital business models, platform solutions, and data analytics tools is substantiated. The economic essence of the concept of a “hybrid enterprise development strategy” is clarified as an integrated system of strategic decisions that ensures the synergy of classical strategic management approaches and digital value creation mechanisms. A classification of hybrid strategies is proposed according to the vectors of digital transformation, including digital differentiation strategy, platform-product strategy, data-driven strategy, ecosystem strategy, and innovation-adaptive strategy. An integrated strategic management model considering the level of digital maturity of an enterprise and a system of performance indicators for evaluating the effectiveness of hybrid strategy implementation are developed. It is proved that the implementation of hybrid strategies enhances competitiveness, adaptability, and innovativeness of enterprises in a turbulent digital environment.

Annotation: This article explores the use of hand puppets and theatrical play techniques in educational and corrective–developmental work with children with autism spectrum disorders. The study analyses the psychoemotional and communicative characteristics of this group of children, as well as the limitations of traditional pedagogical approaches. A theatrical play–based approach is substantiated, in which the puppet character functions as a mediating tool that enables indirect pedagogical interaction. The paper outlines the methodological principles for organizing a theatrical play environment and describes the key stages of working with hand puppets. Observed outcomes of the practical application of the approach and the conditions supporting the sustainability of its effects in educational practice are also presented.

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Annotation: (Українська) В роботі розглядаються теоретичні передумови необхідності прогнозування соціально-економічних показників регіонального розвитку в рамках процесу стратегічного планування. Розкрито процес розробки економетричної моделі прогнозу та визначено основні характеристики та особливості трендових моделей соціально-економічного розвитку регіонів.

Annotation: Contemporary secondary education increasingly emphasises the development of students' capacity for meaningful learning, critical information analysis, and independent knowledge construction. This article examines project-based learning (PBL) as a pedagogical approach with significant potential for fostering learner autonomy, analytical thinking, and metacognitive skills within humanities subjects at the secondary school level. Drawing on a review of research in project-based and problem-oriented learning, as well as reflective analysis of pedagogical practice, the paper describes a staged model for organising project work within classroom time. Particular attention is given to the teacher's role as facilitator and to the significance of formative assessment and structured reflection throughout the learning process. The findings indicate that PBL, when implemented as a sequential, supported, and reflective process, promotes the formation of durable learning strategies, the development of student independence, and deeper engagement with humanities content. The practical contribution of the article lies in a step-by-step pedagogical model grounded in teacher reflection and adaptable to standard school curricula.

Annotation: (Українська) Акрилові нігті захопили косметичний ринок два десятиліття тому, але питання про те, що вони роблять з природною нігтьовою пластиною, довго нікого особливо не цікавило. Ця робота розбирає механізми пошкодження нігтів після акрилового нарощування та збирає докупи протоколи відновлення на основі клінічних даних 2017-2024 років. Виявилося: основна біда йде від механічного спилювання під час підготовки та зняття, хімічного протравлювання кислотними праймерами, зневоднення через розчинники та руйнування ліпідного захисту. Клінічно це виглядає як витончення пластини на 20-35%, розшарування, поздовжні тріщини, підвищена ламкість. Відновлення базується на припиненні травмування, поверненні вологи та ліпідів, застосуванні кератинових засобів та стимуляції зони росту. Повна регенерація займає 4-6 місяців за умови повної відмови від акрилу. Профілактика включає низькокислотні праймери, м'яку обробку поверхні, делікатне зняття та обов'язкові перерви між процедурами.

Annotation: Permanent makeup is one of the most sought-after cosmetic procedures. However, despite its popularity, there is a problem of skin microtrauma, which can occur due to incorrect choice of device and needle parameters. In this article, we will look at the key factors affecting the safety and effectiveness of permanent makeup. These factors include the diameter and configuration of the needles, the length of their tips, as well as the depth and rate of penetration of the pigment. Assessing the effect of these parameters on the skin and ways to optimize them will help minimize tissue damage and improve the safety of procedures. The article will provide recommendations for improving permanent makeup technologies, including the use of more accurate devices, optimizing needles, and developing better pigments.