African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1
ISSN: 1539-854X (Online) Subject area: Mathematics UGC CARE: UGC CARE JOURNAL Imapct Factor: 7.416 Editor in Chief: Dr Willaim Malesirs Kindly email your paper on : mbsresearchp@gmail.com
Fractional Runge-Kutta schemes for stochastic fractional equations Conflict of Interest
Stochastic fractional differential equations provide a flexible mathematical framework for processes in which hereditary memory and random fluctuations act simultaneously. Such models arise in anomalous diffusion, viscoelasticity, finance, biology and control, but their numerical treatment remains difficult because the Caputo derivative is nonlocal while the stochastic term is driven by nonsmooth Brownian paths. This paper develops a high-order fractional Runge-Kutta scheme for nonlinear stochastic fractional differential equations of Caputo type. The proposed stochastic fractional Runge-Kutta method combines a two-stage fractional drift approximation with an Itô-type stochastic increment and a memory quadrature correction. Under standard global Lipschitz and linear growth assumptions, we establish existence-compatible moment bounds, derive the local truncation estimate, prove mean-square stability for a scalar test equation, and obtain strong convergence in the mean-square norm. The stability result gives an explicit step-size criterion involving the fractional order, drift coefficient and diffusion intensity. Numerical experiments for linear and nonlinear test problems compare the proposed method with fractional Euler and fractional Milstein-type schemes. The results indicate improved error reduction and stable behaviour for fractional orders below one. Tables, convergence plots, stability diagrams and computational-cost graphs are supplied to support the analysis. The paper is written as a publication-ready applied mathematics article with theorem-proof structure, numerical validation and reproducible algorithmic details.
Dr. Dattatreya Hegde, Dr. Shivanandappa Doddagoudar, Dr. Geeta Hadimani,
Copyright (c) 2026 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
Separation Axioms, Connectedness and Metrizability in Neutrosophic Topological Spaces
This paper investigates separation axioms, connectedness and metrizability in neutrosophic topological spaces. Neutrosophic topology extends classical and fuzzy topology by assigning to each element a triple of truth-membership, indeterminacy and falsity-membership values. The paper first reviews the basic structure of neutrosophic sets, neutrosophic points, neutrosophic open sets and neutrosophic closed sets. It then develops a systematic account of neutrosophic separation axioms, including -, -, -, regularity and normality. The implications among these separation axioms are established, and examples are supplied to show that several converses fail. The connectedness section characterizes neutrosophic connectedness through the absence of proper neutrosophic clopen sets and relates it to continuous images and subspaces. The compactness section records basic covering properties and their interaction with continuous maps. The metrizability section introduces neutrosophic metrics, neutrosophic metric balls and sufficient conditions under which a neutrosophic topology is induced by a neutrosophic metric. Comparative tables and formal diagrams are included to distinguish classical, fuzzy, intuitionistic fuzzy and neutrosophic topological structures. The resulting article provides a consolidated theorem-proof framework suitable for further research in neutrosophic topology and related generalized topological systems.
Copyright (c) 2024 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
MATHEMATICAL MODELING AND AVAILABILITY ANALYSIS OF STEEL INDUSTRIAL SYSTEM IN HISAR DISTRICT
*]:pointer-events-auto R6Vx5W_threadScrollVars scroll-mb-[calc(var(--scroll-root-safe-area-inset-bottom,0px)+var(--thread-response-height))] scroll-mt-[calc(var(--header-height)+min(200px,max(70px,20svh)))]" dir="auto" data-turn-id="request-WEB:8ce09f34-84e7-460a-8f15-9bee58e16b3d-0" data-turn-id-container="request-WEB:8ce09f34-84e7-460a-8f15-9bee58e16b3d-0" data-testid="conversation-turn-2" data-scroll-anchor="false" data-turn="assistant"> This paper presents a mathematical modeling and availability analysis of a steel industrial system located in Hisar District Haryana employing the Regenerative Point Graphical Technique RPGT. The case study focuses on a stainless steel manufacturing plant comprising four essential subsystems Grinding Descaling Hot Steckel Mill and Cutter Machine configured in series. Each subsystems failure and repair rates are assumed to be constant and a comprehensive state transition diagram is constructed to depict all possible operational and failed states of the system. Using RPGT the study derives analytical expressions for critical reliability metrics including mean time to system failure MTSF system availability mean sojourn times server busy period and expected number of server visits. Numerical examples are provided to demonstrate the effect of varying failure and repair rates on system availability and profitability with results presented through tables and graphical illustrations. The findings offer valuable insights for plant management supporting improved decision making for reliability maintainability and profit optimization in the context of the steel industry in Haryana.
Regenerative Point Graphical Technique (RPGT)
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STATIC PLANE SYMMETRIC INTERACTING FIELDS IN GENERAL THEORY OF RELATIVITY
We have obtained the plane symmetric space time model in the presence of linearly coupled massless scalar field and source of free electromagnetic field with wet dark fluid by assuming. Further we discussed physical and kinematical properties of model. Since constant as and as . As the shear scalar is constant at the at the infinite future, this model is anisotropic in the nature throughout the evolution. Also, shows that the model does not approach the isotropy for large values of .
Copyright (c) 2022 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
Non-commutative algebra and ring theory investigate algebraic structures in which the multiplication operation does not satisfy commutativity, thereby extending classical commutative algebra into broader structural and categorical frameworks. This field studies non-commutative rings, modules, algebras, and their homological and representation-theoretic properties, emphasizing structural decomposition, radical theory, and ideal behavior. Central themes include simple and semisimple rings, Artinian and Noetherian conditions, Morita equivalence, and polynomial identity (PI) rings. Homological tools such as Ext and Tor functors provide insights into module resolutions and global dimensions, while localization and Goldie’s theory clarify structural aspects of non-commutative Noetherian rings. Applications extend to quantum groups, operator algebras, non-commutative geometry, and mathematical physics. By integrating structural theory with categorical and homological techniques, non-commutative algebra continues to play a foundational role in modern algebra and its interdisciplinary applications, offering deep connections between abstract theory and contemporary mathematical research.
Eigenvalues and Eigenvectors Theory and Practical Applications
Eigenvalues and eigenvectors are fundamental concepts in linear algebra that play a crucial role in both theoretical mathematics and a wide range of practical applications. They provide a powerful framework for understanding the behavior of linear transformations and the structural properties of matrices. Theoretically, eigenvalues and eigenvectors are essential in spectral theory, matrix diagonalization, and stability analysis, enabling the simplification and deeper interpretation of complex linear systems. From an applied perspective, these concepts are extensively used in solving differential equations, analyzing vibrations in mechanical systems, and studying stability in control and electrical engineering. In physics, they form the mathematical foundation of quantum mechanics and wave phenomena, while in modern computational fields, they are central to data science and machine learning techniques such as principal component analysis and spectral clustering. This paper aims to present an integrated overview of the theoretical foundations of eigenvalues and eigenvectors and to examine their diverse practical applications, highlighting their significance as a unifying tool across scientific and engineering disciplines.
ANALYTIC CONTINUATION OF COMPLEX MEASURES: A RIEMANN SURFACE PERSPECTIVE
This systematic and complete work presents a rigorous theoretical framework for the analytic continuation of complex probability measures, leveraging the intrinsic analytic structure embedded within their Fourier-Stieltjes transforms. The theory of holomorphic extension, a cornerstone of complex analysis, is here applied to generalize complex-valued measures from their original real domains into the complex plane. We establish a comprehensive system of fundamental results, including necessary and sufficient conditions for the existence and uniqueness of these continuations, providing both convergence theorems and explicit construction techniques essential for their effective realization. This treatment includes the derivation of novel extension theorems and a definitive characterization of the singularity structures—such as branch points, poles, and essential singularities—that arise in the complex domain.
Copyright (c) 2025 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
Spectral Graph Theory and Its Applications in Network Clustering
Spectral graph theory provides a rigorous mathematical foundation for analyzing the structural properties of complex networks through the study of eigenvalues and eigenvectors of graph-associated matrices. One of its most impactful applications lies in network clustering, where the objective is to partition a network into meaningful groups of nodes with dense internal connections and sparse external links. Spectral clustering leverages the eigen structure of the graph Laplacian to transform clustering into a low-dimensional representation problem, enabling efficient detection of communities even in high-dimensional, nonlinear, or noisy data. This approach has proven effective across diverse domains, including social networks, biological systems, image segmentation, and information retrieval. Recent advances integrate spectral methods with machine learning models and graph neural networks, improving scalability and robustness. This paper explores the theoretical foundations, methodologies, and applications of spectral graph theory in clustering, highlighting its strengths, limitations, and future research directions.
Higher Dimensional Generalization of Tolman’s Schwarzschild Interior Solution in General Relativity
Here in this interesting paper is dedicated to find and generalize the famous Richard C. Tolman’s Schwarzschild interior solution in higher dimensions. This solution is very important and useful in understanding and discussing the internal construction of stars. Max Wyman’s generalization has been also discussed to some extent. Energy density r and pressure p have been found. These solutions can be matched at the boundary with the exterior solution (Myers and Perry, 1986).
Spherically Symmetric Radiating Universe in General Relativity
The present paper provides an exact static spherically symmetric solution of Einstein’s field equations using the equation of state r = 3p and also with judicious choice of metric potential g44. We have also found and discussed various physical and geometrical properties of the model.
Copyright (c) 2025 African Diaspora Journal of Mathematics https://mbsresearch.com/
Some Anisotropic Spherically Symmetric Static Solutions Filled with Ferro Fluid
The present paper provides some static solutions of Einstein-Maxwell’s equations for anistropic ferrowfluid using spherically symmetric metric under different specific conditions. Various physical and geometric features have been found and discussed.
NON-LINEAR PARTIAL DIFFERENTIAL EQUATION BY IMPLEMENTING STANDARD AND NON-STANDARD VARIANCE SCHEME
In this study, the nonlinear Partial Differential Equation issue is solved using our nonstandard finite variance scheme. This section of the article will introduce the lemma for the discretization equation related to the positivity and roundedness requirements. Partial Differential equations are necessary in many engineering and research fields. The physical properties of their solutions are often diverse. We systematically develop unique non-standard finite difference techniques that reproduce three of these properties. The first feature is whether the fixed points of the associated universe independent equation are stable or unstable. Numerical experiments are provided.
Existence of Solutions for Partial Differential Equations
The existence of solutions for partial differential equations (PDEs) is a fundamental problem in mathematical analysis and applied mathematics, with implications across various fields such as physics, engineering, and economics. A partial differential equation relates a function of multiple variables to its partial derivatives, and solving these equations typically involves determining whether a function exists that satisfies the given equation under specified boundary or initial conditions. The existence of solutions to PDEs depends on the type of equation (e.g., elliptic, parabolic, hyperbolic) and the nature of the problem being considered. The study of these solutions is closely tied to the concept of well-posedness, which ensures that a problem has a solution, the solution is unique, and the solution's behavior depends continuously on the initial conditions. Several techniques are employed to prove the existence of solutions for PDEs. These methods involve converting the PDE into an optimization problem, typically by seeking the minimizer of an appropriate functional. This approach is often used for elliptic PDEs, such as the Poisson or Laplace equations, where solutions are obtained as critical points of functionals.Fixed-point results like Banach's Fixed-Point Theorem and Schauder's Fixed-Point Theorem are powerful tools for proving the existence of solutions to nonlinear PDEs. By reformulating the PDE as a fixed-point problem, these theorems provide conditions under which a solution exists. In many cases, classical solutions may not exist, especially for problems involving irregular data or non-smooth domains. In these instances, weak solutions, where the equation is satisfied in an integral sense, are considered. This approach is central in the theory of distributional solutions for PDEs. For boundary value problems, especially in the context of weak solutions, Galerkin’s method provides a finite-dimensional approximation of the infinite- dimensional solution space, thereby allowing for the existence of approximate solutions. Existence results for PDEs can often be derived using energy methods and Sobolev space theory, which provide the appropriate framework for handling weak and regular solutions. These methods are particularly useful in proving existence for nonlinear or time-dependent PDEs. For time-dependent PDEs, existence theorems often focus on both the local existence of solutions and their global behavior. Global existence guarantees that solutions exist for all times under certain conditions, providing stability to physical models like the heat equation or wave equation. In summary, the existence of solutions to partial differential equations ensures that mathematical models used to describe natural and engineering phenomena are meaningful and solvable. The development of existence theorems continues to be an area of active research, particularly for more complex PDEs, nonlinear equations, and systems of coupled PDEs, which require innovative mathematical tools and techniques. These results form the foundation for both analytical and numerical methods used to solve PDEs in real- world applications.
STUDY OF COMPARATIVE ANALYSIS OF RELATIVE BITOPOLOGICAL AND TOPOLOGICAL PROPERTIES
We critically examine relative bitopological inductive and covering dimension functions as well as to relative versions of Baire spaces for both the topological and the bitopological case. We show here that relative (bi) topological properties play a special role not only in the development of respective biotopological theories, but also generalise some of the known results. We extend it to the bitopological modifications of various types of relative regularity, relative complete regularity and relative regularity.
Dr. Govind Kumar Singh & Dr. Mukund Kumar Singh
The Foundations of Real Numbers: An Axiomatic Approach and Historical Perspective
This paper provides a comprehensive study of real numbers (), tracing their evolution from ancient philosophical dilemmas to modern axiomatic definitions. It delves into the historical motivations that necessitated a rigorous foundation for numbers, particularly the Pythagorean crisis stemming from the discovery of irrational quantities. The report then systematically explicates the axiomatic framework of real numbers, detailing the Field Axioms that define their algebraic structure, the Order Axioms that establish their linear arrangement, and most critically, the Completeness Axiom, which ensures the continuity of the real number line and distinguishes from other ordered fields like the rational numbers. A significant portion is dedicated to Dedekind's theory and Dedekind cuts as a primary method for constructing real numbers, illustrating how this formal approach fills the "gaps" inherent in the rational number system. The topological properties of real numbers, including their nature as a metric space and the concepts of limits and continuity, are also explored, highlighting their fundamental role in mathematical analysis. Finally, the report addresses pedagogical considerations for undergraduate students, offering insights into effective teaching strategies and common misconceptions encountered in the study of real analysis.
A Comparative Analysis of Various Techniques for Shortest Routes Network Problem
Computing constrained shortest Routes is basic to some significant network capacities, for example, QoS directing, MPLS Route choice, ATM circuit steering, and traffic designing. The problem is to locate the least expensive Route that fulfills certain imperatives. Specifically, finding the least expensive postponement obliged Route is basic for continuous information streams, for example, voice/video calls. Since it is NP-finished, much research has been planning heuristic algorithms that tackle the ε-estimation of the problem with a movable exactness. A typical methodology is to discretize (i.e., scale and round) the connection deferral or connection cost, which changes the first problem to a less difficult one reasonable in polynomial time. The proficiency of the algorithms legitimately identifies with the size of the blunders presented during discretization. In this paper, we propose various techniques for Shortest Routes Network Problem, which enable quicker algorithms to be planned. Diminishing the overhead of registering obliged shortest Routes is for all intents and purposes significant for the fruitful plan of a high-throughput preparing force and memory space.
Linear Programming Formulation of the Shortest Route Problem
Linear Programming is a basic programming definition problem. The greater part of the network problems can be figured as Linear Programming Problems and can be fathomed utilizing simplex technique calculation. In this segment, two Linear Programming definitions for the shortest-course problem are examined. These plans are commonly used to locate the shortest course between any two hubs in the network.
In the present paper, we have discussed and formed mathematical models for physician diagnosis problem, the hospital diet problem along with blood testing model and an optimal model for patient care. Here we have also provided significance and uses of our study.
Copyright (c) 2025 African Diaspora Journal of Mathematics ISSN: 1539-854X, https://mbsresearch.com/
Application of Goal Programming (G.P.) for Resource Allocation in Hospitals
The present paper provides an investigation on resource allocation problem in Hospital using goal programming. Here we have described a set of models to study this problem and discussed their application to a decision-making scenario in which surgical components of Hospitals must respond to a planned three year, 18% reduction in hospital funding. In this analysis we have taken the data of P.M.C.H., N.M.C.H. and Kurji Holy family hospital in Patna (for our convenience)
Here in this paper, solutions of Einstein-Cartan field equations have been obtained taking static spherically symmetric charged fluid sphere using judicious choice of matter distribution and charge distribution. We have also assumed that spins of individual particles are all aligned in radial direction. Various physical parameters like pressure, density and spin density have been evaluated and constants have been fixed using boundary conditions.
EXPLAIN A FEW OF THE IDEAS BEHIND THE FRAMES IN HILBERT AND BANACH SPACES IN RANDOM VARIABLES
Several functional-analytical characteristics of these decompositions are established in this paper, and their relevance to wavelet and gabor systems is illustrated. We start by showing that atomic decompositions and frames are stable under small perturbations. This is driven by similar classical perturbation results for bases, like the Paley-Wiener basis stability criteria and the Kato perturbation theorem. The methodological contributions
Thermal Instability of Suspended Particles in Parous Medium in Presence of Magnetic Field
The present paper provides an attempt to study the thermal instability of suspended particles through porous medium in presence of the variable magnetic field. We have given here formulation of the problem along with boundary conditions and dispersion relation. Here we have also discussed a variational principle in terms of Rayleigh number for the solution of the problem and instability conditions.
Effects of Magnetic Field on Fluid Flow and Heat Transfer in a Porous Medium Abstract: The interaction between magnetic fields and fluid flow in porous media has significant implications in engineering and geophysical applications. This study investigates
The interaction between magnetic fields and fluid flow in porous media has significant implications in engineering and geophysical applications. This study investigates the stability and behavior of a conducting fluid saturating a porous medium under the influence of a uniform magnetic field. Using the Brinkman model, we analyze the onset of convection and the impact of thermal boundary conditions. The external magnetic field is aligned with gravity, and solutions are derived for different boundary conditions, including rigid-rigid, rigid-free, and free-free configurations. Additionally, the study explores the effect of thermal radiation and suction/injection on fluid dynamics over a permeable stretching wall. The findings provide insights into optimizing heat transfer processes in magnetohydrodynamic systems and contribute to advancements in industrial applications such as cooling technologies and metallurgical processes.
The Development of the African American Literary Voice
“The Development of the African American Literary Voice” explores the development of the voice of the downtrodden in American literary canon to assert their rights and liberties as they fought for the same through different means in their real lives. The paper examines how the socio-political scenario of victimization due to white supremacist racist ideology had led to their victimization and how the Blacks fought their way forward to assert themselves as a part of the American nation. Fighting racial stereotypes and prejudices, the history of African Americans is long, and so is the literary rendition.
Copyright (c) 2019 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
ROLE OF E-COMMERCE IN PROCUREMENT MANAGEMENT
Procurement management plays a vital role in the success and efficiency of any organization's operations. With the advent of e-commerce, traditional procurement methods have undergone significant transformation. This paper explores the role of e-commerce in procurement management, examining its impact on efficiency, cost-effectiveness, transparency, and strategic decision-making processes. The integration of e-commerce platforms into procurement management processes has revolutionized the way organizations source goods and services. E-commerce facilitates a streamlined procurement process by providing access to a vast network of suppliers and vendors, thereby increasing competition and driving down costs. Moreover, the automation of procurement tasks, such as requisitioning, ordering, and payment processing, reduces the administrative burden on procurement professionals, allowing them to focus on strategic activities. E-commerce platforms also enhance transparency in procurement operations by providing real-time access to information regarding supplier performance, pricing trends, and market dynamics. This transparency enables organizations to make data-driven decisions and negotiate more favorable terms with suppliers. Additionally, e-commerce facilitates collaboration between procurement teams and other departments, such as finance and inventory management, through integrated systems and shared data repositories. e-commerce enables organizations to adopt strategic procurement practices, such as vendor consolidation, strategic sourcing, and demand aggregation, to optimize their procurement processes and achieve cost savings. By leveraging e-commerce analytics and reporting tools, organizations can identify opportunities for process improvement and cost optimization, leading to increased operational efficiency and competitiveness. e-commerce has become an indispensable tool in modern procurement management, offering numerous benefits, including enhanced efficiency, cost-effectiveness, transparency, and strategic decision-making capabilities. As organizations continue to embrace digital transformation, the role of e-commerce in procurement management will only grow in importance, enabling them to stay competitive in an increasingly dynamic business environment.
Copyright (c) 2019 Journals African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
Assessing the Performance Properties of Pre-test Estimator of Disturbance Variance in Linear Regression Model
This paper explores the performance properties of pre-test estimator of disturbance variance based on criteria such as bias and risk, under quadratic error loss, under different conditions. Attempt has also been made to carry out a comparative study of Pre-test estimator of disturbance variance with ordinary least squares and restricted least squares estimators.
Copyright (c) 2022 African Diaspora Journal of Mathematics https://mbsresearch.com/
Prospects and Challenges in Developing Homestays in Ayodhya
Homestays are a form of tourism experience itself, which allows tourists to experience the real culture and traditions of the host community very closely and get the opportunity to get involved with some. Homestays provide a diverse range of activities to give tourists a unique opportunity to experience the unique culture and traditions of the local people. The purpose of this paper is to analyze the prospects and problems in developing homestays in Ayodhya. Ayodhya is progressing toward massive inclusive tourism development, which includes accommodation, and the government's focus is also on Ayodhya's tourism expansion, which will create many opportunities for local communities to develop homestays as one of the economic sources and which will be the best alternative for budget travelers. This will bring light to the prospects and problems of developing homestays.
Ms. Arpita Mishra, Prof. Prateek Agrawal, Ms. Medha Jaiswal
Copyright (c) 2022 Ms. Arpita Mishra, Prof. Prateek Agrawal, Ms. Medha Jaiswal https://mbsresearch.com/
Review of Mathematical Approaches on Deteriorating Inventory Models
Deteriorating inventory models have garnered significant attention due to their relevance in various industries where products degrade over time. This review surveys mathematical approaches employed in tackling challenges posed by deteriorating inventory management.The first approach commonly employed is deterministic modeling, where continuous or discrete-time models are utilized to capture deterioration rates and demand patterns. These models often rely on differential equations or difference equations to describe inventory dynamics over time.Stochastic modeling is another avenue explored to address uncertainty in demand and deterioration rates. Stochastic differential equations or Markov processes are commonly used to model random variations, providing a more realistic representation of real-world inventory systems.Optimization techniques play a crucial role in determining optimal inventory policies under deteriorating conditions. Dynamic programming, stochastic optimization, and heuristic algorithms are frequently employed to find optimal ordering policies that minimize costs while ensuring adequate inventory levels.recent advancements in machine learning and data-driven approaches have led to the integration of predictive analytics in inventory management. Techniques such as neural networks and time series forecasting are applied to predict future demand and deterioration patterns, aiding in better decision-making.
Copyright (c) 2022 Journals African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/
Digital technologies and platforms can reduce transaction costs for businesses and facilitate access to new customers, both in domestic and foreign markets. Digitalization has a massive impact on the economic field, which plays a vital role in the development and advancement of society. Digitalization also plays a central role in extending the reach and impact of frontier technologies, many of which show great potential to enable the achievement of the Sustainable Development Goals. Government should focus on the improvement of digital infrastructure in the rural areas for the innovation of new generation technologies. Digitalization helps networking of people and things and the convergence of the real and virtual worlds that is enabled by information and communication technology.
Analyzing the Distribution of Pre-test Estimator of Error Variance in Linear Regression Model
In statistical inference, the estimation of error variance plays a crucial role in regression analysis and hypothesis testing. Using the available extraneous information, some improved estimators of error variance in the linear regression model may be constructed which combine both the sample and the non-sample information. A pre-test estimator of error variance is considered when prior information about regression parameters is available, influencing the estimation process. The modest aim of this article is to study and analyze distributional properties of a pre-test estimator of error variance in a linear regression model with numerical computation.
Copyright (c) 2020 African Diaspora Journal of Mathematics ISSN: 1539-854X, UGC CARE 1 https://mbsresearch.com/