In this paper the fundamental definitions like linear operator, norm of a linear operator, continuityand boundedness have been extended into fuzzy soft settings in a different notion. Also some theorems related to these concepts have been proved  and the famous Hahn Banach theorem is established.

Blockchain technology has revolutionized the way we think about secure and decentralized systems, yet its scalability challenges remain a significant barrier to widespread adoption. High transaction latency, limited throughput, and resource inefficiencies hinder its ability to support large-scale applications. This paper explores blockchain scalability through the lens of distributed computing, leveraging proven concepts such as sharding, parallelism, and load balancing to address these bottlenecks. We examine the interplay between Layer-1 and Layer-2 solutions, evaluate innovative consensus mechanisms, and highlight real-world implementations that demonstrate the potential of distributed computing techniques. Furthermore, we analyze the trade-offs between decentralization, scalability, and security, commonly known as the scalability trilemma. By integrating blockchain with cutting-edge distributed systems principles, this work aims to provide a roadmap for optimizing blockchain performance while maintaining its core ethos of decentralization and trustlessness. This perspective not only addresses immediate technical limitations but also opens avenues for future research and innovation in scalable blockchain systems.

The study investigated mathematics teachers’ assessment of the impact of universal Basic education (UBE) programme goals on the implementation of the 9-year Basic education mathematics curriculum. Based on the purpose of the study, three research questions and three hypotheses guided the study. The population consisted of all mathematics primary school teachers in Owerri Educational Zone of Imo State. A sample of one hundred and fifty (150) mathematics primary school teachers was randomly  drawn from two (2) local governments( 1 urban and 1 rural ) Areas. Researchers made four points modified likert-type of questionnaire titled MATA19EMC with reliability coefficient of 0.82 was used for data collection. The data generated were analyzed using mean, standard deviation and Z-test statistical tools. The results of the study showed that irrespective of gender mathematics teachers at the basic educational level had positive assessment of the impact of universal Basic Education on teachers training and re-training and provision of instructional facilities/ instructional materials, poor assessment about the impact of UBE on provision of mathematics laboratory at the Basic educational level was recorded. It was recommended among others that mathematics   laboratories should be provided in primary schools where mathematics teachers and pupils can use them to improve teaching and learning of mathematics.

Big data science has and is rapidly growing in the industries and is known to help in data analysis and forecasting. But the growth of data sharing in organizations creates many privacy problems especially in distributed environments. Discussing privacy preserving data sharing in Big Data analytics, this paper concentrates on distributed computing methods. It discusses techniques including encryption enhancement methods, differential privacy techniques, federated learning, and data access control techniques that maintain security and analysis capability. Also, it goes deeper into distributed structures such as blockchain and edge computing that allow secure sharing of the data.

Healthcare, finance, and smart cities are used as examples of these techniques in real-world contexts throughout the paper, stressing on the application of approaches to reduce privacy threats. Four issues, namely scalability, the computational load required when processing large datasets, adversarial attacks, and the potential solutions or improvements that may combat them, are presented. The paper concludes with future directions, such as quantum computing and real time analytics providing the guide path for developing sound privacy preserving methodologies in the Big Data domain. This research underlines the concerns regarding data use and protection, and serves as a starting point for analyzing possibilities of secure, moral and creative data sharing.

Efficient order fulfillment is a critical component of modern supply chain management, directly influencing customer satisfaction, operational efficiency, and business profitability. Oracle NetSuite Warehouse Management System (WMS) emerges as a robust solution, addressing challenges associated with traditional fulfillment processes such as inventory inaccuracies, delayed shipments, and high operational costs. This study explores the role of Oracle NetSuite WMS in streamlining order fulfillment processes, focusing on its features, functionalities, and real-world applications. Through a combination of qualitative and quantitative analyses, including case studies and performance metrics, this research highlights the system's impact on improving inventory accuracy, optimizing warehouse operations, and reducing order cycle times. The findings provide valuable insights for businesses seeking to enhance their fulfillment strategies, offering practical recommendations for implementation and future scalability.

Efficient warehouse layout design is pivotal in ensuring streamlined operations, cost reduction, and enhanced order fulfillment processes. This study investigates various techniques for optimizing warehouse layouts, including slotting optimization, zone-based picking, and the implementation of advanced automated systems like Automated Storage and Retrieval Systems (AS/RS). Leveraging a mixed-method approach, the research combines quantitative analysis of performance metrics with qualitative insights from industry practices to evaluate the impact of layout optimization on order picking time, travel distance, and labor productivity. Key findings reveal that slotting optimization reduces travel time by up to 30%, while zoning strategies enhance order picking speed by 40%. Advanced technological interventions, such as robotics and simulation models, further improve efficiency and accuracy while mitigating operational bottlenecks. This research highlights the transformative potential of integrating traditional and emerging technologies in warehouse layout optimization, providing actionable recommendations for practitioners and laying a foundation for future studies in dynamic optimization techniques.

Global supply chain has become complex and thus there is always need to look for new and effective ways that will help improve the efficiency, transparency and also the strength of the supply chain. In today’s supply chain management, artificial intelligence or AI has therefore taken on the role of a disruptive technology especially in the management of data integration. Machine learning, predictive analytics, and natural language processing technologies when applied can enhance business functioning, decision making processes and help to identify disruptions in near real time.

This paper aims to establish how AI is shaping supply chain management by progressing data integration approaches to unify systems, apply real-time analytics, and increase supply chain transparency. The chief use areas are inventory level management, demand forecasting, procurement planning, and logistic management as these functions are vital for cost cutbacks and operational efficiency.

However, the following issues are worth exploring: Data silos, integration issues, and ethical concerns, the following solutions: Use of blockchain, federated, learning, and unifying AI platforms. Examples from a flourishing retail to a struggling manufacturing plant and a logistics company are highlighted and great performance milestones of AI-oriented policies are revealed to be incomparable to traditional models.

These outcomes prove the significance of using AI technologies for meeting new requirements of modern supply chains and gaining benefits. Expanding opportunities of AI in SCM are presented as well as possibilities of the further use of quantum computing and other innovations based on sustainability, which constitute a set of directions on the transformation of the SCM environments.

As the digital world continues to expand and intertwine with every aspect of modern society, cyber threats are evolving at an unprecedented pace, both in complexity and frequency. Traditional cybersecurity measures, while effective in their time, increasingly struggle to address the sophisticated tactics employed by malicious actors. This pressing challenge has paved the way for the integration of Artificial Intelligence (AI) as a transformative solution in the realm of cybersecurity. AI's advanced capabilities, such as threat detection, predictive analytics, behavioral analysis, and automated response mechanisms, provide organizations with powerful tools to proactively identify vulnerabilities, prevent breaches, and respond to incidents in real-time. By analyzing vast amounts of data at incredible speeds, AI not only enhances accuracy but also significantly reduces the time required to address potential threats, thereby strengthening overall security infrastructure. Despite its promising advantages, the application of AI in cybersecurity is not without its hurdles. Challenges such as ethical considerations, the rise of adversarial AI techniques, the dependency on extensive and high-quality datasets, implementation complexities, and the substantial costs associated with deploying AI-powered systems present significant obstacles. Furthermore, the potential misuse of AI by cybercriminals adds another layer of complexity to its adoption. This article delves into the multifaceted role of AI in enhancing cybersecurity, providing an in-depth analysis of its benefits, limitations, and future prospects. It explores how organizations can leverage AI to transition from traditional, reactive defense strategies to proactive, adaptive security systems capable of safeguarding digital ecosystems against emerging and ever-changing threats. By embracing AI-driven innovations, the cybersecurity landscape can evolve into a more resilient and intelligent framework, empowering organizations to stay ahead of the curve in a rapidly advancing technological era.

Thanks to the high rates of growth of platform products, many industries have become unrecognizable from the traditional scheme and became integrated into a new economy that reflects the relations and mutual dependency of many different user groups. Such ecosystems, generated by platforms which act in multi-sided markets and connect producers and consumers of goods and services, have revolutionized several sectors, starting from transport to e-commerce, by employing technology as the main enabler of value creation at multiple levels. This article focuses on Understanding Platform Products and looks at characteristics of such products such as their reliance on network effects and ability to leverage growth. This allows the understanding of how and why a multitude of participants – consumers, producers, and third-party service providers – co-create value through interaction on the platform. How data analytics, AI, and real-time connectivity may improve the effectiveness and sustainability of platforms for users is discussed. First, there are some significant factors that should be taken into consideration when defining the success of the organizations in these markets on the one hand, the occupation of new markets should be understood as the ability of the companies to adapt to several aspects. This ranges from setting appropriate pricing strategies that would encourage the use of the platforms as well as measuring highly reliable governance frameworks that would ensure provision of accurate and trustworthy information and many other aspects that would enable organizations to carry out continuous innovation to adapt to competition. The strategies involve overcoming winner takes it all issues, regulatory attention and responding to sustainability questions are also discussed. In this case, the article uses case studies from successful platform businesses such as Amazon, Airbnb, and TikTok to identify and explore actionable strategies that firms can use to succeed in a platform ecosystem. This underlines the need to have a flexible and engaging platform which will also adhere to the right business practices. At last, the article looks at the further development of platform and identifies decentralization, blockchain and ethical artificial intelligence as future trends of the platform economy. Over the course of this research, I have endeavored to do just that to offer a practical and theoretical approach to the emergence of platform products and the management of multi-sided business models.