EPH-International Journal of Mathematics and Statistics
EPH – International Journal of Mathematics and Statistics ISSN: 2208-2212 Publisher: Southern Cross Academic Press Frequency: Quarterly Language: English Access Type: Open Access Visit Publisher Website EPH – International Journal of Mathematics and Statistics is a premier peer-reviewed, open-access academic journal dedicated to publishing original research that advances mathematical theory and statistical methodology. The journal follows a rigorous double-blind peer review process and operates under a fully open access model, ensuring global visibility and accessibility of high-quality scholarly research and academic excellence.
CLIMATE VARIABILITY AND HYDROCLIMATIC CHANGE IN RANCHI, JHARKHAND, INDIA: TRENDS IN RAINFALL AND TEMPERATURE DURING 2000-2025
Climate change is one of the most severe environmental challenges of the twenty first century that has been affecting the regional climate systems, hydrological processes, ecosystem dynamics and the human livelihoods. Information on long-term climatic variations at the regional scale is needed to facilitate the development of effective adaptation and mitigation strategies. This study examines the variations in monthly climatic parameters of rainfall and temperature over Ranchi District of Jharkhand, India for the period 2000 to 2025. Rainfall variability and dependence on the monsoons, temperature trends and climate anomalies were assessed using annual, seasonal and monthly analysis. The results show that annual rainfall has increased slowly by no more than 22.3 mm per year while mean temperature has increased by no more than 0.038 °C per year. The mean annual rainfall for the study period was 1468.6 mm with almost 81.5% of it falling in the southwest monsoon season. There was large interannual variation, with the highest recorded in 2025 (2553.3 mm) and the lowest was recorded in 2014 (854.7 mm). The data analysis of the temperature showed an increase in mean temperatures during recent years, especially after 2015. The period-wise analysis revealed that 2021 – 2025 had the highest average rainfall and 2021 – 2025 had the highest average temperature. The results presented here suggest the increasing climatic variability and the possible effect of climatic change on the hydroclimatic conditions in the region. The observed changes have implications for agriculture, water resources, forest ecosystems and conservation of biodiversity, and planning for climate adaptation in Jharkhand.
Copyright (c) 2026 EPH-International Journal of Mathematics and Statistics
EXISTENCE RESULTS FOR BIGENERAL VECTOREQUILIBRIUM PROBLEM ON BICONVEX SETS: A KKMAPPROACH
In this paper, a general vector equilibrium problem and a general strong vector equilibrium problem are introduced and studied in the Hausdorff topological vector spaces, along with many existing models of vector equilibrium problems and equilibrium problems as special cases. We also consider and introduce some new concepts of general biconvex sets and functions involving an arbitrary function. Applying the KKM theorem yields an existence conclusion for the bi general vector equilibrium problem and the bigeneral strong vector equilibrium problem. There are also a few particular examples and cases displayed.
Avian migration is an awe inspiring phenomenon in the natural world. Traditionally, it was always studied and viewed as a biological mechanism but in due course of time it is validated that it is the profound demonstration of geometric optimization. The journey of a migratory bird is an integrated framework of geometric principles such as formation geometry, navigation geometry and geodesic geometry. This research article studies and applies these geometric principles to administer the migratory journey of Bar-headed Goose (Anser indicus) specifically focusing its winter arrival in Rampur, Uttar Pradesh. At the micro- scale, the geometric arrangement of offsets and angles describes the V - formation. Followers position themselves at approximately one wingspan lateral and half to one wingspan longitudinal separation from the leader, producing a characteristic V- angle of about 53°, which optimizes spatial overlap and reduces energetic cost (Portugal et al., 2014). At the meso scale, the navigational framework is modeled via spherical geometry. We derive the PZS navigational triangle to show how birds leverage the celestial sphere’s axis of rotation to determine true North (Emlen, 1975). Additionally, the role of geomagnetic geometry is evaluated, where the bird utilizes the inclination (dip) angle (I) - defined by the relationship tan (I) = 2 tan(Φ) as a topographic trigger to determine its latitudinal destination in the Indo-Gangetic Plains (Wiltschko & Wiltschko, 2003). Finally, at the macro scale, geodesic geometry is utilized to compare Orthodromes (Great Circle) and Loxodromes (Rhumb Lines). Numerical simulations suggest that for a trajectory from the Tibetan Plateau to Rampur, a Geodesic path optomizes flight distance by approximately 15 km, significantly supressing metabolic cost during high-altitude flight (Alerstam, 2001). This study concludes that the survival of migratory species is fundamentally dependant on their ability to execure real-time geometric computation.
INVENTORY MODEL WITH LINEAR DEMAND, ADVERTISEMENT EFFECT, RELIABILITY AND CONSTANT DETERIORATIONS
In the present competitive market environment, inventory decisions are strongly influenced by demand patterns, product reliability, marketing strategies, and deterioration characteristics. The present study develops a deterministic inventory model incorporating linear time-dependent demand, advertisement-induced demand enhancement, system reliability, and constant rate of deterioration. Product deterioration occurs continuously at a constant rate, while reliability affects the effective availability of inventory over the replenishment cycle. Various relevant costs such as ordering cost, holding cost, deterioration cost, advertisement cost, and reliability-related costs are incorporated into the total cost function. The objective of the model is to determine the optimal replenishment policy and decision variables that minimize the average total cost per unit time. The resulting nonlinear optimization problem is solved analytically, and sufficient conditions for optimality are established. Numerical illustrations and sensitivity analysis demonstrate the effects of key parameters such as deterioration rate, advertisement intensity, reliability level, and demand elasticity on the optimal policy. The proposed model provides valuable managerial insights for firms dealing with perishable or reliability-sensitive products under marketing influence.
Copyright (c) 2025 International Journal of Mathematics and Statistics
INVENTORY MODEL WITH ADVERTISEMENT-DEPENDENT DEMAND
In the present study we develop an inventory model in which demand is influenced by advertisement activities. The advertisement effect is represented by a power function of advertisement cost and its frequency. Demand is assumed to be both inventory-dependent and advertisement-dependent. The system is formulated using a first-order linear differential equation and solved analytically under appropriate boundary conditions. The optimal inventory cycle length is derived by minimizing the average total cost function. Numerical illustrations and sensitivity analysis are presented to demonstrate the applicability of the proposed model. The results indicate that advertisement plays a significant role in accelerating demand and reducing inventory cycle time, although excessive advertisement may increase the total cost. The model provides valuable managerial insights for designing effective inventory and advertisement policies.
MHD CONVECTIVE FLOW THROUGH A POROUS MEDIUM IN A VERTICAL WAVY CHANNEL WITH HALL EFFECT
We have considered heat and mass transfer on the MHD free convection flow of second grade fluid through porous medium bounded by an infinite vertical porous rotating plate taking hall current into account. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration is analysed graphically, and computational results for the skin friction, and Sherwood number are also obtained.
CASSON HYBRID NANOFLUID FLOW AND HEAT TRANSFER PAST AN INFINITE EXPONENTIALLY ACCELERATED VERTICAL POROUS SURFACE WITH CHEMICAL REACTIONS
Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Rotating disks involving chemical reactions find extensive applications in the medical field, particularly in optimizing chemical processes for controlled drug delivery systems, thereby improving precision in therapeutic treatments. In this study, we elucidate the behavior of fluid flow over a rotating disk with Casson ternary hybrid nanofluid with incorporation of chemical reactions. Thus, a similarity transformation approach was employed, converting the boundary layer equations into similarity equations represented as ordinary differential equations. Subsequently, the bvp4c solver in MATLAB is utilized to numerically solve the set of non-linear ordinary differential equations describing the boundary value problem. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters.
MULTIPLE SWITCHING SYNCHRONIZATION: THEORY, METHODS, AND APPLICATIONS
This review synthesizes the state of the art in multiple switching synchronization for chaotic and complex dynamical systems. We formalize the concept, contrast it with single switching and continuous coupling, and survey stability tools including common and multiple Lyapunov functions, average dwell-time, and sliding/adaptive control under switching. Variants such as complete, lag, generalized, projective, intermittent, and fractional-order multiple switching synchronization are compared. We summarize applications in secure communications, power and energy systems, neural dynamics, robotics and multi-agent systems, and outline open problems regarding robustness, implementation, and data-driven switching policies. The article aims to provide a self-contained reference for researchers and practitioners.
A STUDY ON CRYPTOGRAPHIC METHODS FOR ENHANCING CYBERSECURITY
Data security and confidentiality in cryptography depend on mathematical foundations for its implementation. The examination of cryptographic methods throughout this document explains the role of number theory in RSA and elliptic curve algebra in ECC and finite field arithmetic in AES. This research explores two post-quantum cryptographic techniques that employ lattice-based systems and multivariate polynomial systems for their quantum attack defenses. The assessment investigates how statistical and probabilistic techniques operate in cryptanalysis and shows the difficulties of finding an appropriate balance between computational depth and system efficiency. Future studies need to prioritize two aims: establishing quantum-resistant cryptographics along enhancing mathematical security demonstrations while maximizing the efficiency of cryptographic systems.
A TWO-ECHELON SUPPLY CHAIN MODEL FOR TIME DEPEPENDENT DETERIORATING PRODUCTS WITH TIME-DEPENDENT DEMAND, DEMAND-DEPENDENT PRODUCTION RATE AND SHORTAGES WITH FUZZY AND HEXAGONAL FUZZY DEMANDS
In the era of rapidly evolving pedagogical methods, gamification and game-based learning have emerged as innovative strategies to enhance student engagement and academic achievement. This study investigates the effectiveness of card games as a pedagogical tool in improving the learning outcomes of secondary-level students in biology, specifically focusing on the topic "The Fundamental Unit of Life – Cell." A quasi-experimental design was adopted, involving 65 Class IX students from a school in Surat, Gujarat. Pre-test and post-test achievement scores were analyzed using t-test, revealing a statistically significant improvement in the experimental group's performance. Additionally, qualitative data from observation schedules and feedback forms underscored the development of key 21st-century skills such as communication, collaboration, critical thinking, and Conceptual correlation. The card game, composed of 52 cards with pairing mechanisms based on biological terminologies and diagrams, not only facilitated conceptual clarity but also fostered student motivation and curiosity towards science learning. The results suggest that integrating card games into the science curriculum is an effective and enjoyable strategy to reinforce complex biological concepts, promote peer learning, and enhance academic performance. This study highlights the potential of gamified instructional strategies to transform science education and recommends broader implementation for improved student engagement and learning outcomes in STEAM disciplines.
MATHEMATICAL SIMULATION OF THE CONSEQUENCES OF SOCIAL AWARENESS AND VACCINATION ON THE DYNAMICS OF COVID-19 COMMUNICATION
The COVID-19 pandemic has underscored the critical importance of understanding how social awareness and vaccination influence the spread and control of infectious diseases. This study presents a comprehensive mathematical simulation model that investigates the combined effects of social awareness initiatives and vaccination campaigns on the dynamics of COVID-19 transmission. By integrating epidemiological parameters with behavioral factors, the model captures how increased public awareness—through education, media, and policy measures—affects individuals’ preventive behaviors such as social distancing, mask-wearing, and acceptance of vaccination. The simulation explores various scenarios reflecting different levels of social responsiveness and vaccine coverage, analyzing their impact on key outcomes such as infection rates, hospitalization, and mortality over time. Results demonstrate that higher social awareness significantly amplifies the effectiveness of vaccination programs, reducing disease transmission more rapidly and preventing potential resurgence. Moreover, the model highlights critical thresholds for vaccination rates required to achieve herd immunity, especially when combined with sustained public health messaging and adherence to preventive measures. This integrated approach underscores the need for coordinated strategies that simultaneously promote social awareness and maximize vaccination uptake to effectively mitigate the pandemic. The findings offer valuable insights for policymakers and health authorities to optimize intervention strategies, emphasizing that vaccination alone is insufficient without strong public engagement and awareness to control COVID-19’s spread in the community.
OPTIMIZATION TECHNIQUES IN DATA SCIENCE: A MATHEMATICAL PERSPECTIVE
The core function of data science depends on optimization because it provides the base for both algorithmic speed and statistical modeling and decision processes. Research examines optimization methods from a mathematical perspective through evaluations of their theoretical foundations together with their convergence attributes and calculations requirements. The research investigates classical gradient-based approaches Gradient Descent and Newton’s Method with complete convergence analysis and establishes the role of Karush-Kuhn-Tucker (KKT) conditions and Lagrange duality for analyzing convex optimization problems. The discussion focuses on non-convex optimization challenges because traditional methods fall short for these problems yet metaheuristic approaches including Simulated Annealing, Genetic Algorithms, and Particle Swarm Optimization solve complex high-dimensional problems effectively. The study recognizes three main mathematical optimization difficulties: solving large-dimensional optimization issues and finding efficient methods for deep learning while achieving the proper balance between exploration and exploitation. Research proposals outline a strategy to connect classical and heuristic optimization methods by integrating machine learning-based techniques that create adaptive and reliable optimization models. This study produces findings that will impact data science along with artificial intelligence as well as computational mathematics since they create a foundation for upcoming developments in optimization-driven methodologies.
MACHINE LEARNING ALGORITHMS FOR PREDICTIVE ANALYTICS IN FINANCIAL MARKETS
A research examines machine learning algorithm applications for financial data prediction in markets by using synthetic data to minimize reliance on traditional datasets. The study develops a hybrid framework that combines deep learning and reinforcement learning models to enhance forecasting precision. GANs and VAEs work together to generate synthetic financial data through advanced network architectures. The prepared data is improved through logarithmic returns and technical indicator techniques. Transformer-based models deliver better performance than LSTM networks because they decrease prediction errors by 12% compared to LSTM networks. At the same time Deep Q-Networks (DQNs) operating under the reinforcement learning framework generate 23% superior cumulative returns compared to typical trading methods. Research outcomes indicate that artificial intelligence-driven models can improve market predictions and company decision-making functions. The research develops a new synthetic data method that boosts financial prediction while delivering essential information for automated traders and financial establishments.
Copyright (c) 2025 EPH - International Journal of Mathematics and Statistics
A COMPARATIVE ANALYSIS OF MACHINE LEARNING FOR THE EARLY DIAGNOSIS AND IDENTIFICATION OF CARDIOVASCULAR DISEASES
With the advent of advanced digital technologies revolutionizing the healthcare sector through artificial intelligence and machine learning, there is a significant focus on accurate machine learning models to predict chronic heart diseases. The late detection and misdiagnosis of chronic diseases like cardiovascular disease can significantly increase the mortality rate. Therefore, a dependable, accurate, and workable system must identify these illnesses in time for appropriate treatment. Large-scale and sophisticated data processing has been automated using machine learning techniques and algorithms for various medical datasets. Several researchers have recently employed machine-learning techniques to assist the medical community and experts detect heart-related illnesses. The approach assists in predicting chronic diseases like heart failure and effective rehabilitation and timely management. This paper surveys various machine-learning models and compares their accuracy and other parameters in diagnosing heart-related disease. In this paper, we aim to compare various machine-learning models, and a predictive model is proposed for heart disease prediction based on the stacking of various classifiers. This model suggests fostering accurate decision-making. This proposed model will enhance prediction accuracy and eliminate anomalies, thus justifying the selection of the stacking classifier as the most accurate machine-learning model to predict heart failure about 98%.
Copyright (c) 2024 EPH-International Journal of Mathematics and Statistics
Using Advanced Mathematical Method to find Normal Curvature of the Curve on Regular Surfaces
Curvature, being a crucial geometric parameter in many applications of surface analysis, is the amount of deviation of curve from a straight line or plane. This study's objective is to use Matlab to objectively calculate Normal Curvature on Smooth Surfaces. The following article concerns curvature and normal curvature with the focus on two uses: first for the manufacturing of automobile tire’s inner tubes, and second one to identify the ideal choice degree of normal curvature. The aim of the study is finding the normal curvature numerically and using Matlab, which can carry out complex computational tasks with general commands and is relatively more precise and swifter than the standard numerical calculations.
Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman
THE INTERPLAY OF DATA AND ALGORITHMS: BIG DATA INFLUENCE ON ARTIFICIAL INTELLIGENCE
The Interplay of Data and Algorithms: Big Data's Influence on AI" is a research exploration that delves into the dynamic relationship between Big Data and Artificial Intelligence (AI). This paper highlights the pivotal role of Big Data in reshaping AI algorithms and models and the transformative impact this synergy has across various industries. The paper begins by elucidating the fundamental concepts of Big Data and AI, offering insights into how large and diverse datasets empower AI systems to adapt, learn, and improve their decision-making capabilities. Through real-world examples and case studies, it showcases the practical applications of Big Data-driven AI in fields such as healthcare, finance, autonomous vehicles, and natural language processing. Moreover, the paper acknowledges the ethical considerations that accompany the utilization of Big Data in AI. It emphasizes the importance of responsible data handling practices to ensure that the benefits of this convergence are distributed fairly and that individual privacy and societal values are preserved.
MASTERING THE DATA UNIVERSE IN AI: BIG DATA'S POTENTIAL AND CHALLENGES
In the digital age, the exponential growth of data, often referred to as "Big Data," has become a valuable resource for various fields, including Artificial Intelligence (AI). This research paper, titled "Mining the Data Goldmine: Big Data's Impact on AI Algorithms and Models," delves into the profound influence that the abundance of data has on the development and performance of AI algorithms and models. This paper offers a comprehensive overview of the synergistic relationship between Big Data and AI, highlighting the ways in which large-scale datasets have revolutionized AI applications. It explores how Big Data serves as both the fuel and the testing ground for AI algorithms, shaping their accuracy, robustness, and scalability. Moreover, this study investigates the challenges posed by Big Data, such as data quality, privacy, and storage, and how they affect the development of AI models. The research dissects the key mechanisms through which AI algorithms extract insights, learn patterns, and make predictions from massive datasets, emphasizing the pivotal role of data preprocessing, feature engineering, and model selection. The research also delves into advanced techniques, such as deep learning, reinforcement learning, and natural language processing, that leverage Big Data to push the boundaries of AI capabilities.
PARAMETRIZATION OF ALGEBRAIC POINTS OF LOW DEGREES ON THE AFFINE CURVE Y2 = X5 + 1442
In this work, we determine a parametrization of algebraic points of degrees at most 3 over Q on curve C of affine equation y2 = x5 + 20736. This result extends a result of S. Siksek and M. Stoll who described in [4] the set of Q-rational points on this curve.
Planes curves - Degree of algebraic points - Rationals points - Algebraic extensions – Jacobian
Copyright (c) 2021 EPH-International Journal of Mathematics and Statistics http://creativecommons.org/licenses/by-nc-nd/4.0
STATISTICAL ANALYSIS OF GEOMETRIC DISTRIBUTION UNDER CONSTANT-STRESS ACCELERATED LIFE TEST
Firstly, this paper gives the maximum likelihood estimation of the parameter of geometric distribution under fix-group and fix-time censored test, then sets a linear and regression model using the asymptotic normality of MLE and makes statistical analysis of geometric distribution under constant-stress accelerated life test.
BAYESIAN ESTIMATION OF LINEAR REGRESSION MODEL WITH MULTIPLE CHANGE POINTS FOR MISSING DATA
The missing data is filled in by a random way. The complete data likelihood function of linear regression model with multiple change points for missing data is obtained. The full conditional distributions of change-point positions and other unknown parameters are studied. All the parameters are sampled by Gibbs sampler, and the means of Gibbs samples are taken as Bayesian estimations of the parameters. Random simulation results show that the estimations are fairly accurate.
COMPARISON BETWEEN ANALYSIS SOLUTIONS OF VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS OF SECOND KIND
Our goal in this paper is to compare and evaluate the accuracy and efficiency between the Volterra and Fredholm integral equations of the second kind with initial condition. We followed the Adomian Decomposition method and series solution method, and we found that the two methods in terms of accuracy in the solution also we found that the Adomian Decomposition method gave us the more accurate solution than the other method, so the Adomian Decomposition method it’s the best one method.
Volterra and Fredholm integral equations
, Adomian decomposition method series solution method
ON PREOPENNESS PROPERTY IN GRILL TOPOLOGICAL SPACES
The class of a N−preopen sets was introduced by [1] in topological spaces. In this paper we extend the notion of this class into grill topological spaces by giving the concept of GN−preopen sets as a strong form of the class of a N−preopen sets.
Copyright (c) 2020 EPH-International Journal of Mathematics and Statistics http://creativecommons.org/licenses/by-nc-nd/4.0
NEW SOLUTIONS OF LORENTZ TRANSFORMATION II
A simple thought experiment with light clock, which is known in connection with the theory of relativity and its modifications, led me to create the last paper. Paper related to other mathematical solutions of Lorentz transformation. These solutions needed more elaboration and connections. Especially because the mathematical apparatus gains its meaning only when compared to the experiment. The following paper was conceived as a continuation of the previous one, so in this sense the numbering of chapters and, of course, the numbering of equations follows my previous work.
INVERSE DOMINATION IN SOME OPRATIONS ON BIPOLAR FUZZY GRAPHS
In this paper the concept of inverse domintion in some operations on bipolar fuzzy graphs was introduced and investigated the bound of γ8 of some operations on bipolar fuzzy graphs are obtained like union, join,Cartesian product, strong product and composition.
Copyright (c) 2020 International Journal of Mathematics and Statistics http://creativecommons.org/licenses/by-nc-nd/4.0
In this paper we focus on 2- domination number of a fuzzy graph G by using effective edge and is denoted by γ2(G) and we obtain some results on this concept, the relationship between γ2(G) and some other concepts are obtained.
2-dominatic. Classification 2010: 03E72, 05C69, 05C72
SEPARATION AXIOMS AND CONNECTEDNESS FOR βω−OPEN SETS
Our propose in this paper is to introduce the new classes for separation axioms in topo logical spaces by using βω−open sets and Gβω−open sets, called βω−separation axioms and Gβω−separation axioms. Furthermore, we introduce the stronger form of connected spaces.
Copyright (c) 2016 International Journal of Mathematics and Statistics http://creativecommons.org/licenses/by-nc-nd/4.0
The principle purpose of this paper is to introduce and study some new classes of sets in topological spaces which are finer than the classes of open sets and ω−open sets. The continuity via these classes will be introduced and studied.
APPROXIMATE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF HIGHER-ORDER BY THE MODIFIED ADOMAIN DECOMPOSITION METHOD
This paper propose a new modified differential operator for solving third-order boundary value problems into higherorder ordinary differential equation. We found the differential operator for new two inverse operators which can be applied for solving equations at more than one type in different conditions. This paper is given five non-linear examples from a high-order, we got effective and easily approximate solutions to the exact solution.
THE GLOBAL DOMINATION NUMBER IN PRODUCT FUZZY GRAPHS
In this paper we introduced the concepts of global domination number and global domatic number in product fuzzy graph and is denoted by γg(G) and dg(G), respectively we determine the global domination number γg(G) for several classes of product fuzzy graph and obtain Nordhaus-Gaddum type results for this parameter. Further, some bounds of γg(G) and dg(G) are investigated. Also the relations between γg(G)(dg(G)) and other known parameter in Product fuzzy graphs are investigated. Finally we introduce the concept of global full number and some results about this concept in product fuzzy graph are done.
global domatic number and global full number.
INDEPENDENT DOMINATIO N IN BIPOLAR FUZZY GRAPHS
In this paper we introduced and studies the concepts of independent domination of bipolar fuzzy graph G, (γi(G)). And chromatic number χ (G) of bipolar fuzzy graph .We investigated the relationship of γi and χ with the other known parameters. Finally we give γi for same standard bipolar fuzzy graph
Bipolar fuzzy graph independent domination number