This study introduces a hybrid calculation-estimation framework to optimize flow field designs for vanadium redox flow batteries (VRFBs), prioritizing directly calculable geometric and physical parameters over empirically fitted coefficients to enhance model fidelity and predictive accuracy. A fully validated three-dimensional multi-physics model, coupling fluid dynamics with electrochemical kinetics, is developed to systematically evaluate three distinct flow field architectures: a conventional serpentine design, a nature-inspired biomimetic leaf-venation network, and a modified serpentine channel featuring embedded micro-pillar perturbators. Comparative analysis reveals that biomimetic design achieves the most favorable trade-off between hydraulic and electrochemical performance. Its low-resistance, hierarchically branched architecture facilitates uniform electrolyte distribution across the porous electrode, resulting in a 35% reduction in pressure drop and a corresponding 3.2% increase in net system efficiency relative to the conventional baseline. In contrast, while the perturbator-enhanced design achieves the highest limiting current density (190 mA cm⁻²) by inducing localized vortex mixing to enhance mass transport, this gain is offset by a significant increase in pumping losses. The findings underscore that directly calculated parameters such as branching geometry and flow path length are critical drivers of performance. This work provides a principled modeling strategy and offers generalizable design guidelines, demonstrating that nature-inspired engineering is a key pathway toward developing next-generation, high-efficiency VRFB systems.

Mathematics underpins scientific advancement and fuels innovation across disciplines. In the next decade, the convergence of differential equations and control theory with emerging technologies, especially artificial intelligence and machine learning will redefine modeling, prediction, and decision-making for complex systems. This integration enhances predictive fidelity, reveals latent structure in high-dimensional data, and accelerates discovery cycles. Recent work in environmental forecasting illustrates these gains, where deep learning has achieved high-accuracy prediction of atmospheric variables and pollutant concentrations. Multi-scale modeling will be central to linking phenomena across spatial and temporal ranges, enabling impactful applications from nanotechnology to fluid dynamics. Parallel progress in fractal geometry offers new tools to analyze, quantify, and optimize intricate structures and dynamics, informing studies of urban growth, heterogeneous media, and chaotic flows. AI-assisted control strategies are poised to transform healthcare, autonomous systems, and communication networks by delivering adaptive, data-driven policies that improve robustness, efficiency, and safety. This review synthesizes the state of the art at the intersection of differential equations, control processes, and AI, surveying methodological advances, benchmark applications, and emerging computational pipelines. It also identifies open challenges including model interpretability, data scarcity across scales, stability guarantees for learning-based controllers, and reproducible evaluation protocols that demand tightly coordinated, interdisciplinary research. By unifying mathematical rigor with AI-driven inference and control, the field is positioned to build more predictive, reliable, and efficient solutions for the next generation of scientific and engineering problems.

In the paper, we propose a fuzzy logic controller system to be implemented for smart mobility management in the 5G wireless communication network. Mobility management is considered as a main issue for all-IP mobile networks future generation. As a network-based mobility management protocol, Internet Engineering Task Force developed the Proxy Mobile IPv6 (PMIPv6) in order to support the mobility of IP devices, and many other results were presented to reduce latency handover and the amount of PMIPv6 signaling, but it is not enough for the application needs in real-time. The present paper describes an approach based on the IEEE 802.21 Media Independent Handover (MIH) standard and PMIPv6, so we present a new vertical handover algorithm for anticipating handover process efficiently. Our object is to propose a smart mobility management that contribute in 5G wireless communication system network operating functions. Two proposed dynamic thresholds were successfully made to guaranty process triggering, and a new primitive MIH is proposed for signaling a needed handover to be done. Simulation results demonstrate a significant reduction of the handover delay, packet loss, handover blocking probability and signaling overhead. Simulation results and tests are accomplished.

Advances in differential equations and control theory are reshaping how secure, efficient medical data-exchange systems are designed. In parallel, blockchain offers decentralized trust, cryptographic integrity, and auditable access control for healthcare networks. Yet the choice of storage and transmission architecture strongly affects scalability, latency, privacy, and cost. This work investigates how mathematical modeling via differential equations and modern control processes can be coupled with blockchain to strengthen security and interoperability across distributed healthcare systems. We comparatively examine three deployment models: (1) on-chain storage, (2) off-chain, cloud-backed storage with blockchain access control, and (3) local institutional storage integrated with federated learning. On-chain designs maximize transparency and tamper-resistance but incur substantial computation and storage overhead. Off-chain approaches improve scalability while retaining verifiable control through the ledger. Local storage with federated learning safeguards patient privacy by keeping raw data within institutions and sharing only encrypted updates or proofs on chain. Persistent challenges include storage bloat, network delays, heterogeneous regulations, and evolving attack surfaces. To address these issues, we outline optimization strategies grounded in system dynamics stability analysis, resource allocation, and control-oriented tuning to balance throughput, privacy, and reliability. The study synthesizes theoretical insights with implementation considerations, offering a unified perspective on building resilient, performant, and privacy-preserving medical data-exchange frameworks that leverage blockchain under mathematically principled control.

한국멀티미디어학회(The Journal of Curriculum Evaluation)

The psychological well-being of parents of children diagnosed with cancer is a crucial yet often overlooked aspect of pediatric oncology. These parents frequently experience high levels of stress, anxiety, and depression, which can undermine their emotional resilience and ability to support their child’s treatment. Despite the substantial mental health burden they face, structured psychological interventions remain inconsistently implemented across healthcare systems. This study explores the psychological challenges encountered by parents of children undergoing cancer treatment, examines existing gaps in mental health support, and evaluates the effectiveness of structured interventions in reducing emotional distress. A comprehensive systematic review of existing literature, combined with qualitative analysis of clinical observations, was conducted. Additionally, the study integrates advancements in computer science, particularly artificial intelligence (AI)-driven mental health tools, telehealth platforms, and data-driven predictive models, to assess their role in enhancing psychological interventions. The analysis includes a comparative evaluation of psychological support programs across different healthcare models, with a particular focus on the Bright IDEAS program and its impact on alleviating parental distress. The findings indicate that parents frequently endure significant psychological strain, yet formal psychological support services remain fragmented and insufficient in many clinical settings. Evidence suggests that Cognitive Behavioral Therapy (CBT), mindfulness-based interventions, and structured peer support programs are among the most effective strategies for reducing parental anxiety and improving emotional well-being. Moreover, AI-powered chatbots, mobile health (mHealth) applications, and digital cognitive therapy tools show promise in providing scalable and personalized mental health support. However, challenges persist in ensuring standardized implementation and equitable access to these interventions. The study highlights the urgent need for integrated psychological support frameworks within pediatric oncology, incorporating digital mental health solutions to enhance accessibility, personalization, and efficiency. Healthcare policymakers and providers should prioritize the adoption of evidence-based psychological interventions, leveraging computational advancements to ensure their effectiveness in diverse clinical environments. Future research should emphasize longitudinal studies and empirical data collection to further validate the impact of these interventions and refine best practices for their implementation.