Formal Sciences

Abstract -/- The Recursive-Collapse-Recombination (RCR) Model is a metastable, autopoietic, non-hierarchical, non-binary, and non-linear framework that defines reality as a continuously generative process. It describes how recursion (self-reinforcing structures), collapse (destabilization and phase shifts), and recombination (adaptive restructuring) interact to produce emergent, dynamic systems. Unlike equilibrium-based models, RCR establishes metastability as the core condition of reality, ensuring ongoing transformation rather than static resolution. The model is mathematically formalized to apply across domains, from physics and cognitive science to social structures and (...) AI systems. By framing reality as an interplay of recursion, collapse, and recombination, RCR reveals why deterministic reductionism fails and why reality remains an open-ended generative structure rather than a closed, finite system. -/- Keywords -/- Recursive-Collapse-Recombination (RCR) -/- Metastability -/- Phase Transitions -/- Nonlinear Systems -/- Emergence -/- Self-Organization -/- Autopoiesis -/- Indeterminacy -/- Reality Structuring -/- Generative Systems -/- --- -/- License (CC BY 4.0) -/- This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). -/- ✔ Share — Copy and redistribute the material in any medium or format. ✔ Adapt — Remix, transform, and build upon the material for any purpose, even commercially. -/- Attribution Requirement: You must give appropriate credit, provide a link to the license, and indicate if changes were made. This must be done in a reasonable manner, but not in any way that suggests endorsement by the original author. -/- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits. (shrink)

The ever-growing volume of scientific research challenges for traditional publishing models. This necessitates innovative approaches to journal editing and adopting by Artificial Intelligence (AI) in publication. This scoping review aims to explore the emerging trends shaping the field of journal editing by AI. Literature employed to search relevant databases published between 2008 and 2024. A total of 25 studies met the inclusion criteria. The review synthesizes key trends of inclusion of the technological tools integration for manuscript processing, the rise of (...) open-access publishing models, and evolving considerations around research ethics. The study underscores the pivotal role of emerging trends in shaping the future of scientific publishing. It offers valuable perspectives for editors to adeptly maneuver through the evolving terrain of scholarly communication. By suggesting possible best practices, it serves as a beacon for maintaining editorial excellence. Furthermore, it identifies critical domains warranting deeper exploration, thereby setting the stage for continuous advancement in the field. This forward-looking approach not only facilitates informed decision-making but also fosters a proactive stance towards embracing change in scientific discourse. (shrink)

Until, 1971, articles were not freely accessible to everyone online. Project Gutenberg made the dream a reality. Exorbitant increases in the cost of print journals have forced publishers to reduce their publications and turn them from the print to the electronic journal (e-journal) medium. Higher visibility of Open Access (OA) leads to a higher number of citations, better h-index of authors and the Impact Factor (IF) of journals, which gains the popularity of e-journals. However, authors face a problem in predatory (...) journals, Article Processing Charges (APC), etc. It is not late to write this article for in-depth understanding of e-journals and the impact of Artificial Intelligence (AI) in academic scholarships, especially for novice readers, authors, and researchers. This article also depicts what important things you need to keep in mind when publishing your article to go to a higher level in the era of electronic publication. (shrink)

Việc bài nghiên cứu bị từ chối là một thực tế mà tất cả các học giả phải đối mặt trên con đường học thuật. Mặc dù việc này có thể ảnh hưởng tiêu cực đến sự tự tin, sức khỏe tinh thần và khả năng bền bỉ theo đuổi nghề của các nhà nghiên cứu, nó vẫn được xem là cơ chế “lọc” quan trọng nhằm phân biệt giữa những nghiên cứu đạt và không đạt tiêu chuẩn. Tuy nhiên, (...) gia tăng sự khắt khe trong quá trình đánh giá và phản biện chưa hẳn chỉ mang lại toàn kết quả tích cực. -/- . (shrink)

Abstract: As artificial intelligence (AI) technologies rapidly evolve and permeate various aspects of society, the need for effective regulation and governance has become increasingly critical. This paper explores the current landscape of AI regulation, examining existing frameworks and their efficacy in addressing the unique challenges posed by AI. Key issues such as ensuring compliance, mitigating biases, and maintaining transparency are analyzed. The paper also delves into ethical considerations surrounding AI governance, emphasizing the importance of fairness and accountability. Through case studies (...) of different regulatory approaches and their outcomes, the paper highlights both successes and areas for improvement. Finally, it offers insights into future directions for AI regulation, advocating for innovative policies and enhanced international cooperation to ensure that AI technologies are developed and deployed responsibly. This comprehensive analysis aims to contribute to the ongoing discourse on creating robust regulatory mechanisms that can keep pace with the rapid advancement of AI. (shrink)

This book serves as an introduction to mathematical logic for STEM (Science, Technology, Engineering, and Mathematics) students, written for undergraduates (in particular, 1st and 2nd year undergraduates). A focus on this book is on logical thinking, not simply rote memorization, with a focus on examples and analogies relevant to students aimed at becoming technical leaders and problem solvers. This book includes propositional logic, set theory, functions and relations, and more, with coding examples provided in the Python programming language.

This mixed methods study investigates whether technology mediated collaborative practices during a professional development (PD) session led to growth in the collective efficacy of 21 special education teachers at an independent 1-12 school in Southeastern Virginia. This school specializes in individualized instruction for students with learning differences not limited to Autism Spectrum Disorder, Attention Deficit Hyperactivity Disorder, Specific Learning Disability, and their comorbidities. Teacher collective efficacy, which subsumes cohesive perceptions of classroom learning and behavior management, has been shown as strongly (...) related to student achievement and healthy school culture. Mastery experiences with specific tasks related to teaching and learning can spur collective efficacy. Cutting-edge technologies (Vibe and Newline collaborative all-in-one hardware and software interfaces) were used to engage teachers in an interdisciplinary vision boarding activity to outline academic, social, and technological goals within and across subject areas. Teachers also engaged in a behavior management reflection exercise. Pre- and post-survey analysis was conducted using a paired samples t-test, showing overall growth in collective efficacy after the brief PD session. Regression analyses revealed that technology savvy teachers grew most in collective efficacy. Network analysis of vision board output and a descriptive analysis of the behavior management surveys showed that teachers became united in interdisciplinary goals for learning, and in strategies for behavior management through conversational practices. (shrink)

In the presently unfolding deepfake era, recurrent inflationary algorithmic superintelligence (ASI) achievement claims degenerated from being a mere reflection of an exaggerated but candid initial enthusiasm to becoming a convenient tool for misdirection facilitating epistemic perpetuum mobile (EPM) scams. This transdisciplinarily conceived paper compactly analyzes the underlying ASI definition avoidance problem which emerged from interactions between three major epistemic trends in the ASI debate: boomerism, doomerism and pragmatism. Via taking a fourth external perspective entertained by a fictive entity called Cyogenes (...) who volunteers as a philosopher and criticizes contemporary conventions (inspired by the ancient Cynicism lived by early Greek philosophers including Antisthenes and Diogenes of Sinope), the paper highlights key strengths but also particularly pitfalls within those three aforementioned epistemic trends all of which face the ASI definition avoidance problem – clearing the way for global EPM scams. After this philosophical analysis, a deflationary account of ASI (i.e. the epistemic perpetuum mobile) is discussed. Thereafter, practical cybersecurity-oriented threat models and defenses against EPM scams are formulated. In brief, fruitless EPM scams unnecessarily risk intensifying the near-term existential risk of epistemic self-sabotage and reinforcing totalitarian aspirations. (shrink)

Much ado – and increased complexity – is generally the case when it comes to checking formally the (intended) meaning of programs, as formal semantics for programs are typically extrinsic to both them and the formal grammars that generate the programming languages in which they are written. The van Wijngaarden grammars, on the contrary, have an intrinsic semantics in the sense that their rules contain or express the (intended) meaning of the terminal strings generated by them. This intrinsicness allows for (...) preservation of meaning both in syntactic change and context-sensitive conditions. In order better to show the intrinsicness of the semantics of the van Wijngaarden grammars I contrast them with the attribute grammars, a frequent choice when the semantic analysis of programming languages is called for (e.g., in compilation). (shrink)

Abstract: The integration of artificial intelligence (AI) into mental health care has the potential to revolutionize the field by enhancing diagnostic accuracy, personalizing treatment, and improving access to care. This paper explores the advancements in AI technologies applied to mental health, including machine learning algorithms for diagnosis, natural language processing for therapeutic applications, and predictive analytics for personalized care. It also examines the ethical and practical challenges associated with these technologies, such as privacy concerns, algorithmic bias, and the need for (...) regulatory frameworks. By analyzing current applications and emerging trends, this paper aims to provide a comprehensive overview of how AI can transform mental health care while addressing the associated challenges and opportunities. (shrink)

Abstract: The integration of artificial intelligence (AI) into drug discovery is revolutionizing the pharmaceutical industry by accelerating the development of novel therapeutics. AI-powered tools enable researchers to process vast datasets, identify drug candidates, and predict their efficacy and safety with unprecedented speed and accuracy. This paper explores the transformative impact of AI on drug discovery, highlighting key advancements in machine learning algorithms, deep learning, and predictive modeling. Additionally, it addresses the challenges associated with AI implementation, including data quality, regulatory hurdles, (...) and ethical considerations. By analyzing case studies of AI-driven pharmaceutical breakthroughs, this paper underscores AI's potential to streamline drug development, reduce costs, and address unmet medical needs. The future of drug discovery is poised to shift dramatically as AI continues to advance, offering promising solutions for improving human health. (shrink)

Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another model. Nonetheless, I argue that certain kinds of high-dimensional effective model building, and effective field theory construction in quantum field theory, can be viewed as special cases of manifold learning. I argue that this helps to shed light on all of these techniques. (...) First, it suggests that the effective model building procedure depends upon a certain kind of algorithmic compressibility requirement. All three approaches assume that real-world systems exhibit certain redundancies, due to regularities. The use of these regularities to build simplified models is essential for scientific progress in many different domains. (shrink)

Abstract: As the frequency and sophistication of cyberattacks continue to rise, organizations face increasing challenges in safeguarding their digital infrastructures. Traditional cybersecurity measures often struggle to keep pace with rapidly evolving threats, creating a pressing need for more adaptive and proactive solutions. Artificial Intelligence (AI) has emerged as a transformative force in this domain, offering enhanced capabilities for detecting, analyzing, and preventing cyberattacks in real- time. This paper explores the pivotal role of AI in strengthening cybersecurity defenses by leveraging machine (...) learning algorithms, predictive analytics, and automation to anticipate and mitigate potential threats before they manifest. Furthermore, it examines AI's ability to evolve with emerging attack vectors, providing a dynamic response to an ever-changing threat landscape. The paper also addresses the limitations and ethical considerations surrounding AI-driven cybersecurity, advocating for a balanced approach to its deployment. Through this exploration, the research underscores how AI is redefining the future of cyber defense by shifting the focus from reactive to proactive strategies. (shrink)

Purpose: This article aims to analyze and summarize the practical experience of deploying and integrating platforms for open journals, conferences, and repositories with support for the Open Archives Initiative Protocol for Metadata Harvesting (OAI-PMH). It highlights the errors and challenges that journal and repository managers and administrators, as well as conference organizers, may encounter and offers recommendations to prevent and avoid these issues. Design / Method / Approach: The research is based on the analysis of real cases of deploying platforms (...) for open science, including the analysis of errors and difficulties encountered during this process. The methodology includes the analysis of real-world cases, applying methods such as testing, validating the OAI-PMH protocol, observation, and studying regulatory and technical documents. Findings: Key errors and difficulties that organizers may face when creating open journals, conferences, and repositories with OAI-PMH support have been identified. Specific solutions are proposed to ensure the reliable operation of the metadata harvesting protocol (PMH), initial setup, and further integration of these platforms. Theoretical Implications: The study extends the understanding of the problems and challenges in the field of open science, particularly concerning the organizational and technical aspects of platforms with OAI-PMH support. Practical Implications: Practical recommendations are provided for administrators and managers of open journals, conferences, and repositories to avoid common mistakes and effectively use OAI-PMH to ensure data interoperability and accessibility. Originality / Value: The article presents an original analysis of real cases of implementing and integrating platforms with OAI-PMH support, making it a valuable resource for practitioners in the context of deploying platforms for open science. Research Limitations / Future Research: The study is limited to the analysis of specific cases and does not cover all possible aspects of deploying and integrating web applications with OAI-PMH support. Future research may focus on the quantitative analysis of the effectiveness of implementing these platforms and their long-term impact on open science. Paper Type: Case Study / Practitioner Paper. (shrink)

The rapid digitalization of various societal sectors in Ukraine, including public services, banking, e-learning, and logistics, emphasizes the need for enhanced practical IT competencies among students. Despite the widespread availability of digital devices, educational curricula often lack tasks that provide hands-on experience with configuring networks and operating systems. This study aimed to address this gap by updating the curriculum of the "Information Processes and Methods of Their Algorithmization" course to focus on practical tasks that involve creating and configuring information resources. (...) To achieve this, the Debian operating system was chosen due to its flexibility, low resource requirements, and compatibility with outdated hardware. Key tasks included configuring services for business and home use, such as remote server access, secure file sharing, web hosting, and office environments with essential software like LibreOffice and Thunderbird. Performance metrics, including memory usage and disk space utilization, were evaluated for different configurations of the operating system, demonstrating its efficiency even on low-resource systems. The results highlight Debian as a cost-effective and adaptable solution for both educational and small-scale business needs, fostering practical IT skills while minimizing hardware expenses. In comparison, Ubuntu Server was found to be more advanced yet resource-intensive, making it better suited for corporate environments. This study underscores the potential of open-source solutions like Debian for improving IT education and promoting their broader adoption in academic and business contexts. (shrink)

Today, the space industry is undergoing a period of significant technological advancement. Continuous progress in additive manufacturing technologies and the adoption of modern materials for 3D printing are driving this transformation. This trend has intensified competition among various space companies—both state-owned and private—each striving to introduce innovative and unique solutions. FlightControl Propulsion, a private space company in Ukraine, is one such example. This study focuses on the design of the power frame for a low-thrust liquid rocket engine. Power frames in (...) rocket engines must withstand significant mechanical loads. The application of topology optimization and high-strength steels enables the development of compact and efficient power frames that are substantially lighter than traditional designs. Additive manufacturing not only significantly reduces the production time of various parts and assemblies but also offers nearly unlimited possibilities for creating complex geometric shapes. What was previously challenging or even impossible to manufacture using conventional methods has now become feasible. This work examines a component fabricated using Selective Laser Melting (SLM) technology. A structured algorithm for topology optimization is described, along with the fundamental principle of the SIMP (Solid Isotropic Material with Penalization) topology optimization method. Numerical modeling of the stress-strain state for the initial design variant is performed using the finite element method (FEM) in a computer-aided engineering (CAE) environment. A computational finite element mesh is generated, and the safety margins of the design are evaluated. Following topology optimization, the final design variant is determined, and numerical modeling of the stress-strain state is repeated for the optimized design. The final design is then prepared for manufacturing and subsequent experimental testing. (shrink)

Purpose. The purpose of this study is to explore vectorization as an engineering technique to improve the performance and readability of Python code, particularly in data processing tasks. We aim to demonstrate the benefits of vectorization through practical examples involving the handling of missing data. Design / Method / Approach. To achieve the research goals, we performed a comparative analysis between loop-based and vectorized implementations. Specifically, two versions of a function were developed to identify columns containing missing values within a (...) dataset. These implementations were tested on two real-world datasets. We compared execution time and code readability. Findings. The findings showed that vectorization resulted in substantial performance improvements, reducing execution time by hundreds of times compared to traditional loop-based methods. Additionally, the vectorized code was more compact, leading to greater readability and ease of maintenance. Theoretical Implications. Vectorization provides a higher level of abstraction for performing operations on data structures. This allows developers to focus on algorithmic logic rather than managing iterative control structures, contributing to broader discussions on optimizing computational efficiency in Python. Practical Implications. For data engineers and analysts, vectorization represents a highly effective solution for optimizing Python code. It significantly accelerates data-intensive tasks, such as missing data imputation, data analysis, and machine learning, making it an essential tool for enhancing productivity in data-driven environments. Originality / Value. This study presents a practical approach to optimizing Python code through vectorization. It is valuable for professionals seeking to improve efficiency in their workflows. Research Limitations / Future Research. The limitation of this research lies in its focus on a single problem – missing data imputation. Future research should expand the scope to other computational areas, such as image processing and simulation modeling, or examine the use of vectorization alongside Just-In-Time (JIT) compilation using tools like Numba to further boost Python's performance. Paper Type. Practitioner Paper. (shrink)

This mixed methods case study employed Vygotsky’s theory to show how peer and teacher contingent support created individualized zones of proximal development for three students with learning differences in a high school makerspace class at a special education institution. Our results expand extant literature by highlighting the intra- and interpsychological potential of makerspace curricula, specifically for students with learning differences. We employ mixed methods analyses of self-reported responses related to emergent problem navigation, a narrative of class fieldnotes, and visuals of (...) whole class projects to describe full class and individual project-based learning activities. Aggregated results from three students showcase stability in design thinking perceptions through the course of weekly whole class design challenges involving TinkerCAD, Homestyler, and material fabrication techniques. A single student example articulates how similar self-reported perceptions were observed in the non-linear development of an individual project for an end-semester Arts Festival. (shrink)

The advent of AI calls for an existential self-redefinition of humanity. It necessitates the establishment of a pluralistic global humanist culture that enables us to coexist in the new world of active media and autopoietic technology. In this paper, related philosophical questions give rise to the proposal of a novel metaculture that elevates human heritages and cultural memories to the plane of a digital AI- based infrastructure. I argue for a balanced and holistic approach to human-to-human and human–AI interactions and (...) metaculture that can be developed in the form of combinatorial “metagames” that reflect the potential of human consciousness, transcend the boundaries between technology, human embodiment and biology, the arts, sciences and humanities, and philosophy, and, finally, include the element of meaningful coincidence and spontaneity “in the second potency.” Hermann Hesse’s final novel, The Glass Bead Game, offers a key to understanding this basic idea. His vision is extremely relevant today. Based on this, the concept of cultivating global cultural memories through innovative aesthetic-epistemic “Glass Bead Games 2.0” is discussed further from a systematic angle. To complement this, reference is also made to Hesse’s own source of inspiration: Novalis’s “encyclopedist” approach interlinks aesthetic and epistemic productivity in a way that could become a major starting point to create a new holistic metaculture in the Age of AI. (shrink)

L’informatisation de la société se poursuit à un rythme effréné. Cependant, pour développer les technologies modernes de l’information, la complexité croissante du monde réel doit être modélisée, ce qui nécessite de revoir la façon de réaliser une modélisation conceptuelle. Cette étude propose que la notion souvent négli-gée de « système » doive être un construit distinct et fondamental pour la modéli-sation conceptuelle, et argumente en faveur de son intégration, de même que l’intégration de concepts connexes, tels que l’émergence, dans les (...) approches existantes de la modélisation conceptuelle. L’étude procède à une synthèse de l’ontologie des systèmes et de la théorie générale des systèmes. Ces éléments fondamentaux de la modélisation sont ensuite utilisés pour proposer un modèle CESM+ pour la modélisation conceptuelle fondé sur des systèmes. Plusieurs nouvelles notations de modélisation conceptuelle sont introduites. La modélisa-tion systémique est ensuite appliquée à une étude de cas sur le développement d’une plateforme de science citoyenne. L’étude de cas montre le potentiel de l’approche systémique pour la théorie et la pratique. L’article avance des recom-mandations sur la façon d’intégrer des systèmes dans des projets existants et suggère des voies de recherche sur la modélisation conceptuelle. (shrink)

Purpose. The main goal of the research was development and testing of the methodology of automated processing and analysis of multispectral satellite images of medium spatial resolution for the detection of deforestation. Design / Method / Approach. Experimental testing of the proposed methodology was carried out in the south-west of Ivano-Frankivsk and the south-east of Zakarpattia Oblasts using free archival images of the visible and IR ranges from Sentinel-2A/B satellites. Findings. The results obtained during the conducted research confirmed the possibility (...) and high efficiency of using images from Sentinel-2A/B satellites to detect and assess the dynamics of felling of wild and protected forests. In only one test area, the area of identified fellings in 2 years amounted to more than 300 hectares. Theoretical Implications. The paper shows the advantages of using the normalized difference index of time changes NDI for a given pair of satellite images of different times and selected spectral channels. Thanks to NDI, the accuracy and stability of the results of the detection of temporal changes increases, as well as the influence of such factors as differences in the illumination of different time images, the presence of scattered clouds, aerosol haze, absorption of radiation by the atmosphere, etc., is reduced. Practical Implications. Due to the high degree of automation, the developed technique can be implemented as a software in the form of a geo-informational web service that can function in the interests of a wide range of public services. Originality / Value. During the study, the necessary stages and sequence of processing remote sensing data were determined, and methods, algorithms and software tools for processing images were selected, and proprietary algorithms and programs were developed to increase the degree of automation and efficiency of image processing, as well as to improve the user interface. Research Limitations / Future Research. This study was limited to the use of multispectral imagery from the Sentinel-2A/B satellites (MSI imager). Future studies involve the use of additional data from Landsat-7 (ETM+ imager), Landsat-8 (OLI imager), Landsat-9 (OLI-2 imager) and Terra (ASTER imager). Paper Type. Applied research, methodological article. (shrink)

Purpose. The purpose of the study is to analyze the accumulated experience in designing rocket engines using computer-integrated technologies, and to identify current areas of development of this issue and tools for solving scientific and practical problems. Design / Method / Approach. The study is based on the analysis of the accumulated experience in the design of rocket engines using computer-integrated technologies. The researchers developed a design algorithm, a modeling algorithm, and a mathematical model for calculating the parameters of liquid-propellant (...) rocket engines and solid-propellant rocket engines. The analysis process covers the design stages with the introduction of the latest digital tools. Findings. The article identifies key areas for modernizing the rocket engine design process. New methods for modeling and analyzing the design stages using computer-integrated technologies have been developed, which allows to increase the efficiency and accuracy of design. Theoretical Implications. The work confirms the importance of using computer-integrated technologies to optimize and improve the rocket engine design process. The theoretical conclusions emphasize the importance of these technologies in ensuring the accuracy and quality of the design of the latest rocket engine models. Practical Implications. The results obtained can be used to improve the design process at modern rocket engine development enterprises. This will increase the competitiveness of such companies and their leading positions in the engineering services market. Originality / Value. The originality of the study lies in an integrated approach to analyzing the rocket engine design process using the latest computer-integrated technologies. The proposed tools and models are new and have significant value for the further development of the industry. Research Limitations / Future Research. The study is limited to the analysis of certain stages of design and the use of individual tools. Further research could focus on expanding the range of digital tools and improving mathematical models for other types of rocket engines. Paper Type. Practitioner Paper, Review of Methods. (shrink)

The Yang-Mills mass gap problem has stood as one of the most profound unresolved questions in theoretical physics for nearly half a century. Despite extensive efforts, a rigorous mathematical proof of the mass gap's existence in Yang-Mills theory has remained elusive—until now. -/- The proof presented in this work represents not merely a technical achievement, but a fundamental paradigm shift in our understanding of the mathematical structures underlying physical reality. By rigorously demonstrating that the mass gap arises as a direct (...) consequence of the gauge-invariant constraint structure of Yang-Mills theory, we overturn decades of conventional assumptions and reveal a startling truth: what we perceive as physical laws are in fact mathematically unavoidable necessities emerging from the very consistency conditions required for a well-defined quantum field theory. (shrink)

Unified Proof Set: Introducing the Next Paradigm of Understanding This set of interconnected papers collectively introduces a groundbreaking framework to achieve a Unified Field Theory (UFT), solving two of the Millennium Prize Problems (Riemann Hypothesis and Navier-Stokes Existence and Smoothness), and providing a comprehensive explanation for relational dynamics in science, ethics, and the cosmos. Papers in the Unified Proof Set 0. Introduction to the Unified Proof Set Abstract : This paper introduces the overarching purpose and framework of the Unified Proof (...) Set. It outlines the interconnected nature of the subsequent works, offering insights into their individual contributions while presenting a unified vision. 01. Relational Unity Equation of the Unified Field: Explained Abstract : A user-friendly breakdown of the Equation of Relational Unity, designed for both scientific and lay audiences. This paper provides an intuitive understanding of the mathematical framework that supports the Unified Field Theory. 1. Hyper-Conjugation: Achieving Unified Field Theory Abstract : Hyper-conjugation is introduced as the foundational mechanism enabling the mathematical representation of the Unified Field. By integrating relational dynamics and harmonic systems, this framework establishes a robust pathway to unify microcosmic and macrocosmic phenomena. 2. The Implicate Order: A New Paradigm for Universal Understanding Abstract : This work bridges the physical and metaphysical through a comprehensive exploration of the implicate order, synthesizing the relational coherence that emerges from entangled systems and their interplay within the unified field. 3. The Equation of Relational Unity Abstract : The centrepiece of the Unified Proof Set, this paper introduces the mathematical equation underpinning the Unified Field. The Equation of Relational Unity establishes a framework where harmonic coherence and energy flow govern all physical and relational dynamics across dimensions. 4. A Mathematical Proof for Ethics and Stability Abstract : Expanding on the implications of the Unified Field, this paper offers a mathematical proof for ethical behaviour as a stabilizing mechanism within dynamic systems. The work explores the relationship between coherence, intention, and the emergent harmonics of stability. 5. Resonance and Symmetry: A New Framework for the Riemann Hypothesis Abstract : This paper recontextualizes the Riemann Hypothesis through resonance and symmetry principles derived from the Unified Field Theory. The solution highlights the harmonic consistency within prime number distribution, offering a novel mathematical approach. 6. Unified Resonance in Fluid Dynamics: A Novel Proof for Navier-Stokes Existence and Smoothness Abstract : Building on the relational principles of the Unified Field, this work solves the Navier-Stokes Existence and Smoothness problem. The proof demonstrates how fluid motion remains stable through harmonic resonance, bridging chaos and coherence. Purpose of the Unified Proof Set The Unified Proof Set represents the culmination of decades of inquiry into the nature of existence. It seeks to bridge scientific, mathematical, ethical, and philosophical paradigms, providing a harmonious framework for future research and application. This work not only resolves significant open questions in mathematics and physics but also offers humanity a blueprint for sustainable, ethical, and innovative solutions to its most pressing challenges. Protection and Use Statement This work is published under the Creative Commons Attribution 4.0 International (CC BY 4.0) license, allowing for redistribution and adaptation, provided that proper attribution is given to the author. Any derivative works must explicitly credit the original creator and clearly distinguish modifications from the original content. The author asserts the originality and integrity of this work, intending it to be used ethically and for the advancement of science, knowledge, and humanity. Any misuse, misrepresentation, or unethical application of this work is strictly discouraged. For citation, acknowledgment, and further inquiries, please reference the DOI provided or contact the author directly. Eliahi Priest The Priest Group Pty Ltd AUSTRALIA. (shrink)

The primary purpose of this study was to examine the intricate relationship between enrichment programs, pedagogical preparedness, and the mathematical proficiency of pre-service teachers. Employing a quantitative research design, the study utilized a descriptive-correlational method to establish the relationship between variables. A comprehensive sampling was used and adapted well-structured survey questionnaires were distributed to gather relevant data from the participants. Correspondingly, the data analysis was performed using statistical tools such as mean and standard deviation, Pearson’s correlation coefficient (r), and regression (...) analysis to distill complex data into meaningful insights and answer the research objectives. The findings revealed that the levels of both enrichment programs and pedagogical preparedness among pre-service teachers were very high, indicating that they are always manifested and consistently implemented. Additionally, the level of mathematical proficiency was found to be high, suggesting that the pre-service teachers frequently exhibited strong mathematical skills. There is a confirmation that the levels of enrichment programs and pedagogical preparedness have a significant relationship with mathematical proficiency. Therefore, this connects to the idea that enrichment programs and pedagogical preparedness influence the mathematical proficiency of pre-service teachers. These findings emphasize the importance of integrating comprehensive enrichment programs and adaptive pedagogical strategies into teacher training, enabling pre-service teachers to develop advanced mathematical understanding and effective teaching practices. Continuous professional development tailored for pre-service teachers, complemented by peer mentoring, seminars, and collaborative training within and beyond schools, can further refine teaching skills and enhance mathematical proficiency. By fostering this holistic approach, the study contributes to improving teaching effectiveness and student outcomes, promoting a culture of excellence in mathematics education. (shrink)

У монографії поглиблено науково-методологічні підходи та запропоновано практичні рекомендації щодо удосконалення управління та застосування управлінського інструментарію підвищення ринкової капіталізації машинобудівних підприємств на основі вартісної концепції. Розкрито теоретичні основи управління ринковою капіталізацією підприємства на основі вартісної концепції. Здійснено оцінювання вартості машинобудівних підприємств України, аналіз формування ринкової капіталізації та оцінювання впливу зміни складових вартості досліджуваних підприємств на її цільове значення. Удосконалено механізм управління ринковою капіталізацією підприємств на основі вартісної концепції, оцінено вплив стимулюючих інструментів на підвищення ринкової капіталізації, запропоновано систему управлінських рішень з (...) оптимізації структури капіталу та визначено її вплив на зміну вартості та ринкової капіталізації машинобудівних підприємств. Видання розраховане на наукових працівників, викладачів ЗВО, керівників підприємств, а також усіх, хто має намір поглибити знання з управління бізнесом. (shrink)

Gender inequality generates negative consequences for the economy, social sphere, and often the environment at the level of individual countries and the world. In this way, inequality creates a gender gap. The issue of reducing the gender gap was highlighted in the Sustainable Development Goals and drew scientists' attention from various fields and international organizations to a multifaceted study of the gender gap phenomenon at different levels. The article analyzes available indicators that measure the gender gap and the conducted earlier (...) research on the factors that influence gender equality. We chose the Global Gender Gap Index. We found a statistically significant impact on the gender gap: the share of women in the total population, the level of achievement of the Sustainable Development Goals, the level of democracy, and GNI per capita. Thus, by accelerating the achievement of sustainable development goals and implementing democratic reforms, countries are reducing the gender gap in society. Our study did not confirm the statistically significant inverse relationship between fertility rates and the gender gap, which was previously established based on incomplete statistical information. Also, the gender gap is not affected by the country's population growth or by the country's belonging to one of the four groups by per capita income. The impact of migration processes on gender equality requires an in-depth and additional analysis based on data showing the impact of migration movements influenced by the war between Russia and Ukraine. (shrink)