The present research aims to introduce a brand new theoretical framework for solving multi-dimensional fractional partial differential equations (FPDEs) by developing a novel integral transform tool called the Double Mohand-Generalized ARA Transform (DM-GART). The DM-GART is a triple-integral operator that applies the Mohand transform twice—once in each spatial variable x and y and the ARA transform once in the temporal variable t; the adjective “Double” refers specifically to the double spatial application of the Mohand transform. The theoretical properties and existence/uniqueness results of this newly developed integral transform are rigorously established in a Banach fixed-point theorem setting. The newly developed integral transform tool is then synergistically combined with the Adomian Decomposition Method (ADM) to produce a novel technique called the Coupled Double Mohand-Generalized ARA Decomposition Method (CDM-GADM). The CDM-GADM is applied for solving generalised fractional biological population equations. The technique is assessed by comparing exact solutions with N-term series solutions for N = 4, 6, and 8. From the results obtained in Tables 3–10, it can be noted that with an increase in the terms from N = 4 to N = 8, the absolute errors decrease several orders of magnitude; the absolute errors for N = 8 are as low as 10⁻¹⁰ for α = 1.0 at smaller values of time. The results are obtained in the form of convergent series characterized by the Mittag-Leffler function, validating the efficiency of the proposed method. A tolerance of ε = 10⁻⁶ is used as the practical stopping criterion.

This research uses an advanced intuitionistic fuzzy optimization framework to study the Multi-Objective Emission and Economic Load Dispatch (MEELD) issue under ambiguous and imprecise operational conditions. Because fuel cost and pollution emissions must be minimized simultaneously while carefully adhering to power balancing calculations, generator capacity limitations, and system operational constraints, the MEELD problem is intrinsically complicated. A strong optimization method that can manage uncertainty and decision ambiguity is required because of these competing goals. In order to overcome this difficulty, a mathematical model that incorporates vagueness related to system characteristics and decision variables is developed in both fuzzy and intuitionistic fuzzy contexts. The intuitionistic fuzzy model, in contrast to other fuzzy methods, takes membership, non-membership, and hesitation degrees into account, offering a more thorough depiction of uncertainty. Using intuitionistic fuzzy aggregation operators, a structured solution approach is suggested to convert the multi-objective optimization problem into an equivalent single-objective formulation. A three-unit thermal power generation system, which is frequently used as a benchmark in MEELD research, is used to illustrate the efficacy of the suggested methodology. The intuitionistic fuzzy optimization method effectively accomplishes an ideal trade-off between economic and environmental goals, according to simulation data. When compared to conventional optimization techniques, the resulting solutions show better compromise solutions, increased flexibility, and improved convergence characteristics. In summary, the MEELD problem continues to be a crucial component of contemporary power system operation, especially when considering sustainable energy management and environmental requirements. For large-scale power system applications needing simultaneous economic and emission optimization, the suggested intuitionistic fuzzy optimization approach offers a technically sound and effective framework for decision-making.

Optimizing load balancing in cloud-based healthcare systems is critical for improving system performance, particularly in terms of reducing latency, increasing throughput, and enhancing task completion time. This study investigates the impact of optimization algorithms, specifically Genetic Algorithm (GA) and Simulated Annealing (SA), on the efficiency of cloud resource allocation in healthcare applications. Additionally, we incorporate queuing theory and stochastic processes to model the task arrival and server load dynamics. By applying these optimization techniques, the system performance was evaluated, showing significant improvements in the key performance metrics. The results highlighted a 50% improvement in latency, 50% increase in throughput, and 25% reduction in task completion time. The optimized system demonstrated enhanced resource utilization, ensuring more efficient real-time data processing in cloud healthcare environments. The proposed approach shows promising results for future applications in dynamic healthcare workload management.

The success of a software system mostly depends on how effectively and carefully the requirements are understood, prioritized, and handled. Defects, cost escalation and project failure often occur because of misconception of requirements. While current requirement engineering methods have tried to solve these problems, still there are many that struggle to classify perfectly and prioritize needs. This is especially applied for non-functional requirements, where systematic validation remains as a notable gap in the process. This study suggests a structured FR/NFR Defect Decision Ontology Framework that combines ontology-based thinking including machine learning techniques. The framework is performed on a dataset consisting of 6,086 requirements (3,964 FRs and 2,122 NFRs). Defects are automatically identified by using ontology-driven rules, which leads to 458 defective occurrences. Evaluation has been done with a layered 80/20 train–test split with 10-fold cross-validation. FR/NFR classification, defect detection, defect type classification, and severity classification are four classification tasks which are performed by using models such as Naive Bayes, Support Vector Machine (SVM), Logistic Regression, and Random Forest. The result shows strong performance with the highest accuracy, 87.68% for FR/NFR classification, 97.29% for defect detection, 88.76% for defect type classification, and 82.02% for severity classification. The findings indicate that NFR defects are more complex and less traceable than FR defects. The framework will help to improve both accuracy and understandability that supports more effective requirement analysis and decision-making in software engineering.

Combining Near Field Communication (NFC) technology with Secure Hash Algorithm (SHA) 256-bit encryption into smart homes may offer new opportunities to improve the security and usability of today’s homes. The goal of this paper is to explore a new way to automate home functions using NFC to authenticate users and share information seamlessly, while also using SHA 256-bit for secure encryption of sensitive information. By using this combined technology, homeowners will be able to securely operate their smart home devices through NFC-enabled Smartphone’s or wearable devices rather than having to remember complicated passwords or use complicated authentication methods. Because all communications between each user’s device and the smart home hub will be securely encrypted with SHA 256, protected from unauthorized access or tampering, the transferred data will be both confidential and have its integrity preserved. Additionally, because of the flexibility of the described system, it will be possible to easily integrate existing smart homes into a single platform and support users in many different applications, such as home security, energy management, remote monitoring, etc. Performance testing and validation will continue throughout this process. Then we demonstrate the way technology presented in this paper has improved both security and user experience in a smart home environment. The research presented will advance the technology used in smart homes through the use of NFC with SHA-256-based hashing for integrity and authentication to create a stable and user friendly method for providing security, as well as efficiency, in home automation.

We study the prime spectrum of idealistic S-algebras, defined via an algebraic structure with a complete lattice of ideals and a suitable notion of prime ideals. The spectrum is equipped with a natural topology and is shown to form a spectral space, possessing key properties such as compactness, separation, and sobriety. We further establish that the spectrum construction is functorial and provides a correspondence between minimal prime ideals and irreducible components under appropriate conditions. Examples are included to illustrate the role of the underlying structure, showing that the existence of minimal primes depends critically on the ideal-theoretic properties.

This dissertation presents a numerical investigation of the two-dimensional incompressible Navier-Stokes equations, focusing on the classic Lid-Driven Cavity problem. The study develops a computational fluid dynamics (CFD) solver from first principles using the Finite Difference Method (FDM) on a structured Cartesian grid, providing a funda- mental understanding of the pressure-velocity coupling in viscous flows. The numerical framework employs the Projec- tion Method, originally proposed by Chorin, to enforce the incompressibility constraint. This operator-splitting technique solves an intermediate velocity field which is subsequently projected onto a divergence-free space via a Pressure Poisson Equation (PPE). The governing equations are discretized using second-order central differences for spatial derivatives and a first-order explicit Euler scheme for time integration. The solver is validated at a Reynolds number of Re = 100. The simulation results successfully capture the characteristic flow features, including the primary central vortex and the corner recirculation eddies. Quantitative validation is performed by comparing the vertical centerline velocity profiles against the established benchmark data of Ghia et al. The results demonstrate excellent agreement with the benchmark solutions, confirming that the developed solver correctly resolves the physics of wall-bounded shear flows. This work establishes a robust foundational framework for simulating viscous incompressible flows and highlights the efficacy of the Projection Method for fundamental CFD applications.

A stochastic programming (SP) problem involves some or all of the parameters or variables being uncertain. Uncertainty is typically expressed as a probability distribution on the parameters. In reality, despite its precise description, uncertainty can manifest in various forms, ranging from a limited number of possible outcomes to precise joint probability distributions. In the water supply system, weather patterns (in the rainy season the rainfall is very high compared to the other seasons), water demand, and water availability are a few uncertain parameters. These uncertainties might not be sufficiently taken into account by conventional deterministic optimization techniques, resulting in less-than-ideal results. The water supply model will be enhanced in this study by SP ideas, resulting in a more stable and adaptable optimization strategy. In this research, we first analyze a 2-stage SP model by capturing more sample data and show the comparison of capturing more and less sample data. We will extend the 2-stage SP model to a 3-stage SP model by using the tree algorithm, and we will show the comparison between these two-stage and three-stage SP models.