Journal of Mathematical & Computer Applications
Journal of Mathematical & Computer Applications is an open access peer-reviewed journal from the publishers of Scientific Research and Community (SRC) which publishes articles in the form of written, video and power-point presentations from the arena of Mathematical & Computer Applications. The journal focuses to build up accessing the complete content of articles freely from online for reader’s perusal. Article acceptance will be in the form of research, review, case reports, analysis, magazines, editorials, opinion, communications, mini-review, short communications, picturized, book review, video type and power point presentations (PPTS). You can submit your articles through online: https://www.onlinescientificresearch.com/submit-online or through Email attachment: mathematics@onlinescientificresearch.info
The Education System and Artificial Intelligence - How It’s Going to Change the World
We posit two types of spontaneous symmetry breaking: one corresponding to the presence of a trivial vector bundle, the second corresponding to the presence of a nontrivial vector bundle. In their avatars, these resemble respectively the cases of type I and type II superconductivity. In the non-trivial case, the topology of the base space of the bundle enters fundamentally. Our applications will be to flavor symmetry breaking among the light quarks, so that the base space will be spacetime itself. In this case it is the SU(2)L and SU(3)L flavor symmetries themselves that are broken and the nature of such breaking is strongly restricted by the topology involved. Despite the negligible nature of any ambient gravitational intensities, we speculate that the topological change that must accompany the advent of mass could be the origin of this breaking and may give rise rise to both the Cabibbo angle and CP violation in the kaon system. We derive formulas for these parameters on the basis of this assumption.
Copyright (c) 2025 Journal of Mathematical & Computer Applications
Quantitative Verification of Microwave Heating Based on IR/FIR Spectrum Analysis
When DFT/MM-derived IR and FIR spectrum of materials is analyzed using their molecular models, their microwave thermal effect will be predicted and verified more quantitatively than the well-known heat output formula, P=1/2σ|E|2+πfε0εr”|E|2+πfμ0μr”|H|2.
OAuth 1.0 vs. OAuth 2.0: An In-Depth Analysis of Token Handling ,Client Authentication, and Developer Usability
OAuth (Open Authorization) is a widely adopted framework that allows third-party applications to access user resources without exposing user credentials. OAuth 1.0 and OAuth 2.0 are the two major versions of the protocol, each with distinct characteristics, advantages, and trade-offs. This paper provides an in-depth comparative analysis of OAuth 1.0 and OAuth 2.0, with particular emphasis on token handling, client authentication, and developer usability. By examining these critical components, the paper aims to provide a comprehensive understanding of how each version operates, the implications for security, and the experience for developers implementing these protocols.
Enhancing Regulatory Audit Readiness through Automated Data Lineage and Impact Analysis Using Azure Purview and SAP HANA
Data integrity is critical in Good Automated Manufacturing Practice (GxP) environments. This paper explores a cloud-based, automated data governance solution using Azure Purview and SAP HANA to enhance regulatory audit readiness. The proposed architecture automatically classifies metadata, tracks end-to-end data lineage, and visualizes access logs across regulated workflows in real time. It supports compliance with FDA 21 CFR Part 11, ISO 13485, and EU MDR, enabling faster, more transparent, and reliable audit responses while reducing manual overhead and human error.
Computer Vision in Automated Defect Detection for Manufacturing
Defect detection in additive manufacturing (AM) is crucial for maintaining quality and reliability across industries. Traditional methods primarily rely on manual inspection or isolated machine learning models, which often fail to generalize across varying defect types. This paper introduces a hybrid framework that integrates multiple Machine Learning algorithms, including convolutional neural networks (CNNs), support vector machines (SVMs), autoencoders, and explainability techniques such as SHAP and Grad-CAM. By leveraging the complementary strengths of these methods, the framework ensures both high detection accuracy and interpretability. The experimental evaluation is conducted using the MVTec Anomaly Detection dataset, which includes diverse defect types, and the results demonstrate significant improvements in classification performance and interpretability. The proposed approach paves the way for a more reliable and transparent AI-based defect detection system applicable across various manufacturing environments.
Integration of Email Security with ATD for Phishing and Malware Prevention
Email is the vector that is most exploited to deliver malware attacks and phishing. Traditional email security solutions only provide baseline protection, and they fail to detect any targeted, sophisticated, or zero-day threats. This white paper covers the integration of Advanced Threat Detection (ATD) with email security systems to address these gaps. The paper analyzes how combining behavior analysis, sandboxing, threat intelligence, and machine learning enhances the detection of malware attached to and socially engineered phishing emails. This paper discusses the real-world case studies, architectural models, practical recommendations, and performance trade-offs. The industry implementations present that the ATD-integrated email security improves the chance of decreasing the incident response time, improves the catch rates, and minimizes the false positives. This white paper discusses the future directions, XDR integration, AI-driven detection, and broader communication security as the next evolution in email threat defense.
A Framework of Economic Indicators for Transit-Oriented Development (Fei-Tod): A Case Study of Bandar Sunway, Malaysia
Transit-Oriented Development (TOD) has emerged as a potential solution to urban sprawl and traffic congestion in rapidly urbanizing Malaysian cities. However, the absence of standardised economic assessment tools has hindered effective TOD implementation and evaluation. This study aims to address this gap by developing a comprehensive Framework of Economic Indicators for Transit-Oriented Development (FEI-TOD) tailored to the Malaysian context, with a specific focus on Bandar Sunway as a case study. The research employs a mixed-method approach, integrating a systematic literature review using the PRISMA method, a three-round Delphi survey with TOD experts, and structured interviews with key stakeholders in Bandar Sunway. This methodological triangulation ensures the incorporation of global best practices, expert consensus, and local insights. The study systematically identifies common elements of successful TOD projects globally, compiles and evaluates potential economic indicators, and develops a context-specific framework for Bandar Sunway. The resulting FEI-TOD comprises 45 indicators across five categories: land use, density, transit facilities, value earnings, and economic attributes. This framework contributes to both the theoretical understanding of TOD's economic impacts and the practical implementation of sustainable urban development strategies in rapidly growing Malaysian cities. The FEI-TOD serves as a decision-support tool for urban planners, policymakers, and developers, facilitating evidence-based decision-making in TOD planning and implementation. The study's findings have significant implications for urban policy and practice in Malaysia, aligning with national urban development goals and the United Nations' Sustainable Development Goals, particularly SDG 11. The adaptability of the FEI-TOD suggests potential for broader application across diverse urban contexts in Malaysia and other rapidly urbanising regions.
Understanding Distance Metrics in KNN Imputation: Theoretical Insights and Applications
K-Nearest Neighbors (KNN) imputation is a widely used technique for handling missing data in machine learning and statistical modeling. The success of KNN imputation heavily depends on the choice of distance metric, as it determines the "closeness" of neighbors. This paper provides a comprehensive overview of the key distance metrics used in KNN imputation, including their theoretical background, mathematical formulations, use cases, and the implications of their selection on imputation outcomes [1-6].
Self-Cooling Simulated Annealing (SCSA) Algorithm for Nonlinear Least Square’s Data Analysis
A Self-Cooling Simulated Annealing (SCSA) algorithm is introduced for the optimization of nonlinear least-squares problems. In contrast to conventional simulated annealing techniques that require a predefined cooling schedule, the SCSA algorithm autonomously regulates system temperature based on the lowest figure of merit (ie. χ²) achieved at each iteration. The algorithm incorporates two key enhancements to improve efficiency: the separation of linear and nonlinear parameters, which reduces the dimensionality of the stochastic search space, and an adaptive Gaussian sampling mechanism that dynamically updates parameter-specific variances based on recent optimization history. A thermal resistance parameter (K) regulates the cooling rate and can be adjusted according to problem complexity. Performance benchmarking against standard Monte Carlo and gradient-based methods demonstrates that SCSA offers greater robustness in avoiding local minima and provides reliable convergence across varying levels of optimization difficulty. These characteristics make the method broadly applicable to nonlinear data analysis and other complex optimization tasks.
Geometric Constructions of Set Systems and Their Hypergraph Representations
We study t-designs of parameters (n, k, λ) over finite fields as group divisible designs and set systems admitting a transitive action of a linear group represented by an hypergraph G whose vertex set of size n is partitioned into sets of size k in such a way that every t sub set is contained in at least λ subsets of G. We relate the problem to the representation theory of the general linear group GL(n, Fq) and the constructions of AG codes over finite fields. As a byproduct we construct a RS code based encryption scheme
The Role of Machine Learning in Modern Software Development
The integration of machine learning (ML) into software applications is increasingly essential for enhancing functionality, decision-making, and performance in diverse fields. As industries strive to leverage intelligent systems, ML enables software to adapt dynamically, process large datasets efficiently, and deliver insights with minimal human intervention. This paper investigates the methodology of incorporating machine learning models into software systems, focusing on model selection, training, optimization, and real-time deployment. We present case studies on fraud detection systems and embedded applications, highlighting challenges, optimization techniques, and the role of continuous learning in maintaining model accuracy. Furthermore, the importance of explainable machine learning models for fostering user trust and understanding is emphasized. The paper concludes with discussions on the advantages and limitations of ML integration and future directions in enhancing model performance, scalability, and privacy-preserving capabilities, particularly in resource-constrained environments.
Azure Modernization Pathways: A Strategic Guide to Enhancing Legacy Application Performance
Business operations rely heavily on legacy applications, which often experience performance decline due to outdated technology that restricts agility and scalability, hindering innovation. This research examines how Microsoft Azure enhances legacy systems. It leverages its platform features, along with strategic modernization methods and specific services, to deliver measurable improvements in scalability, reliability, and cost efficiency. Microsoft Azure serves as a strategic catalyst, helping organizations transform their outdated applications into high-performing, resilient, and future-ready assets.
Intelligent Flaky Test Detection Using Historical Failure Patterns: An Ai-Driven Approach to Enhance Software Reliability
The burgeoning complexity of modern software systems, coupled with accelerated Continuous Integration/Continuous Deployment (CI/CD) pipelines, has exacerbated the pervasive challenge of flaky tests – non-deterministic failures that undermine developer confidence and impede release velocity. This paper introduces a novel, AI-driven framework engineered to proactively identify, diagnose, and mitigate flaky test failures by intelligently analyzing vast repositories of historical CI/CD data and a diverse array of external contextual signals. Our framework employs a sophisticated ensemble of machine learning models, including deep learning architectures for temporal pattern recognition and graph neural networks for dependency analysis, to precisely isolate the latent root causes of flakiness. Beyond mere detection, the system leverages Explainable AI (XAI) techniques to provide transparent insights into failure mechanisms and proposes intelligent remediation strategies, ranging from automated test quarantines and dynamic test re-prioritization to prescriptive recommendations for test refactoring or code modification. By continuously learning from evolving failure patterns, these AI models not only dramatically improve the stability and throughput of software delivery pipelines but also furnish invaluable, real-time historical insights into test reliability trends, empowering data-driven decision-making, fostering proactive quality assurance, and ultimately cultivating a culture of enhanced software quality and predictability
Engineering Intelligence: Fusing Agile, Devops and AI for Next Gen Software Development
As the complexity of software systems and customer expectations evolve organizations constantly seek to be at the forefront of innovative approaches for seamless, efficient and intelligent software delivery. The integration of Agile, DevOps and AI methodologies is an innovative evolution in the software engineering landscape. The article seeks to find the interplay between the three aspects and how they affect the software development lifecycle (SDLC) processes and product quality.
Orchestrating Microservices Across Hybrid Clouds with Kubernetes Federation
The proliferation of microservices and the increasing adoption of hybrid cloud strategies have introduced complex challenges in managing distributed workloads across multiple environments. Kubernetes Federation offers a compelling approach to orchestrating microservices across heterogeneous cloud infrastructures by enabling unified control, policy propagation, and service discovery across federated clusters. This paper investigates the practical and architectural considerations involved in implementing Kubernetes Federation in hybrid cloud scenarios. It outlines the architecture of Federation v2, emphasizing its components, capabilities, and limitations. Real-world use cases such as cross-cloud load balancing, disaster recovery, compliance enforcement, and multi-region deployments are explored to highlight the benefits of federated orchestration. An implementation framework is presented, including setup, deployment pipelines, and observability mechanisms. The paper also presents performance evaluations based on metrics like latency, availability, and failover efficiency, supported by empirical results from simulated environments. Key challenges such as network complexity, security considerations, and operational overhead are discussed in detail. The study concludes with recommendations for optimizing hybrid cloud operations using Kubernetes Federation, along with future research directions including integration with service meshes and autonomous orchestration. By bridging the gap between isolated clusters and unified governance, Kubernetes Federation emerges as a critical enabler of scalable, resilient, and policy-compliant microservice orchestration in hybrid cloud ecosystems.
Copyright (c) 2022 Journal of Mathematical & Computer Applications
Zero Trust Architecture in Kubernetes: Implementing Identity -Aware Network Controls
As Kubernetes continues to dominate the orchestration of cloud-native applications, traditional perimeter-based security models are proving inadequate in securing dynamic, distributed environments. Zero Trust Architecture (ZTA), built on the principle of never trust, always verify, offers a robust alternative by emphasizing identity, granular access control, and continuous verification. This paper examines the implementation of ZTA within Kubernetes, with a specific focus on identity-aware network controls. I explore how Kubernetes-native mechanisms, combined with tools like SPIFFE/SPIRE, service meshes Istio, and policy engines OPA/Gatekeeper, can be leveraged to enforce strong workload identity, mutual TLS (mTLS), and fine-grained authorization. By integrating these technologies, organizations can achieve micro-segmentation, limit lateral movement, and enforce least-privilege access across services. The article also presents a reference architecture for applying ZTA principles in Kubernetes and offers a step-by-step implementation strategy. Through case studies and performance evaluations, I demonstrate that identity-aware network controls not only enhance security posture but also support scalability and compliance in multi-tenant and regulated environments. Challenges such as operational complexity and tool interoperability are discussed, along with potential solutions and future directions. This work contributes a practical framework for Kubernetes security transformation and provides actionable insights for practitioners adopting Zero Trust in containerized ecosystems.
Copyright (c) 2023 Journal of Mathematical & Computer Applications
Metaverse Security: Decentralized Identity with DID Comm and Hyperledger Indy for Asset Tokenization
The metaverse is an emerging digital environment where virtual identities, assets, and interactions are becoming integral to online experiences. However, the decentralized and interconnected nature of this space introduces complex security challenges. This paper examines the integration of decentralized identity (DID) protocols, particularly leveraging Hyperledger Indy and Aries, to establish secure and verifiable digital identities for avatars. It also explores asset tokenization using ERC-1155 smart contracts, highlighting their potential for secure transactions while addressing associated vulnerabilities. Additionally, the paper addresses the security gaps in WebGL rendering and Unity SDKs, proposing a systematic approach to mitigate vulnerabilities like cross-site scripting (XSS). The proposed solutions aim to standardize identity protocols, strengthen asset tokenization security, enhance data privacy, and promote consistent security practices across metaverse platforms. This research contributes to creating a more secure, resilient, and user-centric metaverse environment.
Advanced Integration of Java EE Capabilities within CICS Liberty JVM Architecture
With the introduction of Liberty JVM within CICS (Customer Information Control System), IBM has enabled the deployment and execution of modern computing or APIs straight in CICS and executed them next to legacy applications written in COBOL, HLASM, and other languages. Using Java EE features brings enterprise-level capabilities like scalability, transactionality, security, and manageability. This integration of Java EE features also enhances the performance of Java applications deployed in CICS environments. This paper explores different Java EE features, such as Context and Dependency Injection (CDI), Enterprise Java Beans (EJB), Java Persistence API (JPA), Java Transaction API (JTA), Java Message Service (JMS), and more, available to Java applications deployed into the CICS Liberty JVM environment. It also explores how the Liberty JVM supports each feature and how the integration with CICS works in each case.
Containerization on z/OS: Running Applications with z/OS Container Extensions (zCX)
z/OS Container Extensions, or zCX in short, offer a revolutionary way to run container workloads based on Linux natively on IBM Z within the z/OS environment. This paper takes a deep dive into zCX architecture to understand its components, integration with the workload of z/OS, operational mechanics for deploying containerized applications, and unique advantages compared to standalone implementations of Linux on IBM Z. This paper also looks into some examples of how to build and run a "Hello World" Java application and demonstrate tight integration with z/OS subsystems like CICS and DB2. The paper concludes by evaluating zCX's role in modern application development and its potential to streamline hybrid workloads.
In this paper, the possibility of finding a simple proof of Fermat’s Last Theorem is discussed by using the principles of elementary algebra instead of using the Modularity theorem. For an odd prime n the Fermat’s diophantine equation xn = yn + zn gives rise to an equation of (n − 1) th degree which can be proved to be irreducible over the field Q of rational real numbers by using Eisenstein’s criterion. This proves the theorem for any odd prime n. For n = 4 we use a method of reductio-ad-absurdum to prove the theorem. Finally, we deduce Beal’s conjecture.
Max / Min(a, b, c) stands for the Largest/Least among the numbers a, b and c
Optimizing Email Campaigns based on Pricing Variability
Email marketing is now a mainstay in most e-commerce customer engagement platforms especially considering dynamic pricing and personalized campaign tactics. This paper explores how pricing-based cohort segmentation can best optimize email campaigns by identifying the appropriate consumer groups sensitive to price changes so marketers can adjust the timing and content of their campaigns for maximum engagement and conversion. Three effective strategies identified in this paper for cohorts and their related targeted email dispatch are leveraging user behavior data, real-time pricing adjustments, and automation. Beyond that, the paper includes a review of challenges like synchronization issues, as well as data privacy issues, while incorporating real-world case studies demonstrating the impact of cohort-based strategies on campaign performance. The future directions discussed look into the role of AI and machine learning in generating higher accuracy levels for cohort segmentation and personalization, which shall serve as the road to refined data driven email marketing strategies for e-commerce
Goldbach’s Conjecture, which was announced in 1742, asserts that each even positive integer greater than or equal to 4 is the sum of two prime integers. Thus, e.g., 12 = 5 + 7. Prior to this paper, the Conjecture was still unproved.
A Very Short Proof of Fermat’s Last Theorem
Fermat’s Last Theorem was originally stated by the 17th century mathematician Pierre de Fermat (1601-65). In the margin of an ancient Greek text on number theory that he was studying, he wrote: “There are no positive integers such that xn + yn = zn for n greater than 2. I’ve found a remarkable proof of this fact, but there is not enough space in the margin [of the text] to write it.”
The Selection of the Competitors for the NCAA Football Championship: A Retrospective
A collection of various team rating, and ranking, strategies are described as well as some hybrid combinations of these strategies. How closely these approaches have matched the consensus regarding who the top college football teams have been, since the inception of having teams compete on the field for that sport’s national championship, is examined along with an evaluation of how well some of these methodologies have matched the current committee who decides which teams will be invited to this competition.
A Simple Elementary Proof of Fermat's Last Theorem
In this article we attempt to describe a short proof of Fermat's Last Theorem. The Fermat's diophantine equation xn = yn + zn gives rise to an equation of (n-1)th degree, which can be proved to have no positive rational roots. This proves the case for any odd prime n. For n = 4 we use the principle of reductioad-absurdum along with a polynomial equation of degree 3. Further Beal's conjecture is examined and proved to be true.
Copyright (c) 2024 Journal of Mathematical & Computer Applications
Insider threats have been discussed in this review based on two selected articles adopting the SWOT analysis. It outlines the advantages and disadvantages of the existing approaches and technologies used in the detection, gaps in resources, funding, and organization, opportunities to advance cooperation and development of new methods and strategies, and risks in the extrapolation of tactics and compliance issues. The information presented focuses on the prevention and control of insiders and the major strategies proposed, stressing the use of technological, behavioral, and organizational measures. Further studies should focus on the use of analytics, communication with stakeholders, and adjustments in security management to improve an organization's protection against insider threats.
AutoPureData: Automated Filtering of Undesirable Web Data to Update LLM Knowledge
Up-to-date and reliable language models are consistently sought after and are essential in various applications. Typically, models are trained on a fixed dataset and then deployed globally. However, the knowledge of the models becomes outdated. Enabling automatic updation of AI knowledge using web data involves significant concerns regarding the model’s safety and quality due to a threat from unsafe and undesirable text across the web. The purity of new data was essential for updating knowledge of language models to maintain their reliability. This paper proposes Auto Pure Data, a system that automatically collects and purifies web data. The system loaded a sample of web data. Utilizing existing trusted AI models, it successfully eliminated unsafe text with an accuracy of 97% and undesirable text with an accuracy of 86%, demonstrating the system’s effectiveness in purifying the data. The system ensures that only meaningful and safe text can be used to update LLM knowledge. The pure text was then optimized and stored in a vector database for future querying. It was found that LLM can fetch new data from the vector DB. The LLM writes the RAG query in English, even if the user’s query is in another language, proving that the system can perform cross-lingual retrieval. This paper proposes a method to maintain the accuracy and relevance of up-to-date language models by ensuring that only purified data was used to update LLM knowledge. This work contributes to updating knowledge of chatbots using meaningful and safe text, enhancing their utility across various industries, and potentially reducing the risks associated with outputs caused by unsafe or impure data. Code is available at https://github.com/Pro-GenAI/AutoPureData.
The Unit Gompertz Regression Model with Applications to COVID-19 Data in Brazil
In this paper, based on the unit Gompertz distribution, a new regression model for the unit interval has been introduced. In this model, the parameterization is done based on the median of the distribution. The estimation of the model parameters is done by maximum likelihood method. Monte Carlo simulations, to show the performance of maximum likelihood estimators are performed. Finally, using Covid-19 data in Brazilian capital cities, the unit Gompertz regression model performance better than the popular beta and Kumaraswamy regression models.
Streamlining Payment Process in Cloud Enterprise Resource Planning Application
In the current landscape of the organization, multiple disparate payables applications are used to manage and execute payments directly to banks, leading to significant challenges in tracking, organizing, accounting, and reporting on payables invoices and payment transactions. This fragmented approach results in inefficiencies and inaccuracies, hindering effective financial management and decision-making. To address these issues, the organization aims to streamline its payment process by centralizing all payables invoices from various systems into the Oracle Cloud Enterprise Resource Planning (ERP) application via an integrated Platform as a Service (iPaaS) middleware. By consolidating the payment process within the Oracle Cloud Payment system, the organization expects to achieve significant improvements in operational efficiency. This centralized approach will provide a single source of truth for all payment-related data, facilitating better tracking and control of financial transactions. The streamlined process will enhance the organization’s ability to generate accurate and timely financial reports, ensure compliance with regulatory requirements, and improve overall financial governance. Additionally, the Oracle Cloud ERP’s robust reporting and analytics capabilities will enable better decision-making by providing comprehensive insights into the organization’s financial health. This strategic initiative will enable the organization to improve financial reporting, enhance compliance, and reduce the risks associated with managing multiple payment channels. This also eliminates the inefficiencies associated with multiple payment systems, reducing operational risks, and establishing a scalable, future-proof financial infrastructure that can support the organization’s growth and evolving business needs.
Index Terms-Oracle Cloud Fusion Accounts Payables
Integrate Large Language Models (LLMs) with Computer Vision in the Field of Robotics for Computer Vision Image Processing, Simultaneous Localization and Mapping and to Prevent/Secure Robot Malfunctions
The development of robotics has affected many parts of the world, but the application of robotic systems in complex environments is still a concern. This paper proposes GANs and robotics computer vision to enhance image processing and SLAM, which are key for autonomous navigation. The methodology quantitatively compares different SLAM systems using various environments, including traditional ones and those supplemented by GANs. There is a higher accuracy of localization and mapping, better performance in complex environments with abundant visual elements, and higher computational efficiency. This paper will present an innovative application of GANs in robotics vision and, in the process, establish a new benchmark for how robotic systems perceive the actual world. This study, therefore, is part of the advancement of robotic systems. It provides a novel approach to using GANs as a robot vision tool and offers empirical evidence that the traditional robotic platform can be integrated with machine learning.