Journal of Engineering Mathematics & Statistics

Authors: A. K. Ramesh, Neelam Sakya

Abstract: Spatial and spatiotemporal statistics have become essential tools for analyzing data that exhibit dependence across space and time. Such data arise naturally in diverse fields including environmental science, epidemiology, urban planning, climate studies, agriculture, and public health. Unlike classical statistical methods that assume independence among observations, spatial and spatiotemporal models explicitly account for correlation structures induced by geographic proximity and temporal evolution. This paper presents a comprehensive review of the theoretical foundations, methodological developments, and practical applications of spatial and spatiotemporal statistics. Key topics discussed include spatial autocorrelation, variogram modeling, geostatistical methods, lattice-based models, point process analysis, and spatiotemporal extensions. Modern computational techniques and challenges related to large-scale data are also examined. The paper aims to provide a unified overview suitable for researchers and practitioners from engineering mathematics, statistics, and applied sciences.

Keywords: Spatial statistics; Spatiotemporal modeling; Geostatistics; Spatial autocorrelation; Gaussian random fields; Environmental data analysis

Authors: R. K. Malhotra, Amit D. Choudhary, Umashanker Ray

Abstract: Scientific computing has become a core pillar of modern science and engineering, enabling the numerical solution of complex mathematical models that are otherwise analytically intractable. With the exponential growth of data and problem complexity, traditional sequential algorithms are no longer sufficient. This has led to the development of high-performance algorithms that exploit advanced computer architectures, including multicore processors, graphics processing units (GPUs), and distributed memory systems. This paper presents a comprehensive review of scientific computing and high-performance algorithms, focusing on their mathematical foundations, computational challenges, and practical implementations. Key algorithmic paradigms such as parallel numerical linear algebra, iterative solvers, domain decomposition methods, and optimization techniques are discussed. The role of software frameworks and performance models in achieving scalability and efficiency is also examined. Furthermore, emerging trends including heterogeneous computing, machine learning–assisted solvers, and exascale computing are highlighted. The study aims to provide researchers and practitioners with a structured understanding of how scientific computing methodologies evolve alongside high-performance architectures, while also identifying future research directions and unresolved challenges.

Keywords: Scientific Computing, High-Performance Algorithms, Parallel Computing, Numerical Methods, Scalability

Authors: Ravi Chaudhary, Santosh Mishra

Abstract: In recent years, engineering systems have undergone a fundamental shift from model-driven and hardware-centric paradigms toward data-centric approaches. Data-Centric Engineering (DCE) emphasizes the systematic collection, management, processing, and utilization of data as the primary driver of engineering decisions across the system lifecycle. With the rapid growth of sensors, Internet of Things (IoT), cloud platforms, and machine learning techniques, data has become a strategic asset rather than a by-product of engineering processes. This paper presents a comprehensive review of Data-Centric Engineering, discussing its conceptual foundations, enabling technologies, data architectures, and practical applications across multiple engineering domains. Key challenges such as data quality, scalability, interoperability, and ethical concerns are also examined. The study highlights how data-centric thinking reshapes design, operation, and maintenance practices, enabling predictive, adaptive, and resilient engineering systems. The paper concludes by outlining future research directions and emphasizing the need for interdisciplinary collaboration to fully realize the potential of data-centric engineering.

Keywords: Data-centric engineering, big data, digital engineering, data architecture, predictive analytics, systems engineering

Authors: Aniruddh Kulkarni, Sivnarayan Mishra, Deepender Rao, kamlesh Thakur

Abstract: Computational geometry is a fundamental area of theoretical computer science and applied mathematics that deals with the design and analysis of algorithms for solving geometric problems. These problems arise naturally in diverse fields such as computer graphics, robotics, geographic information systems, computer-aided design, wireless networks, and data analysis. Over the past few decades, computational geometry has evolved from a mainly theoretical discipline into a practical toolkit that supports modern computational systems. This paper presents a comprehensive review of computational geometry, focusing on its core concepts, classical and modern algorithms, data structures, and applications. Both exact and approximate geometric computations are discussed, along with algorithmic complexity issues. Some important problem classes such as convex hulls, nearest neighbor search, range searching, and geometric optimization are reviewed in detail. The paper also highlights recent trends and challenges in computational geometry, including high-dimensional problems and integration with machine learning. While the presentation is mostly survey-oriented, emphasis is given to intuitive explanations and practical relevance, making the paper useful for researchers and postgraduate students.

Keywords: Computational geometry, geometric algorithms, convex hull, range searching, spatial data structures

Author: Suman K. Rao

Abstract: Bayesian methods and inference provide a powerful probabilistic framework for learning from data under uncertainty. Unlike classical frequentist approaches, Bayesian inference treats unknown parameters as random variables and incorporates prior knowledge through probability distributions. Over the last few decades, Bayesian methodology has seen significant development driven by advances in computation, particularly Markov Chain Monte Carlo and variational inference techniques. These developments have enabled Bayesian methods to be applied in complex high-dimensional problems across diverse domains such as machine learning, engineering, economics, medical diagnostics, and environmental modeling. This paper presents a comprehensive review of Bayesian inference, beginning with foundational concepts such as Bayes’ theorem and prior– posterior updating. Computational strategies for posterior estimation are discussed in detail, followed by an overview of hierarchical models, model comparison, and Bayesian decision theory. Practical applications and emerging trends are also highlighted. The paper aims to serve as a self-contained reference for researchers and postgraduate students in engineering mathematics and statistics.

Keywords: Bayesian inference, prior distribution, posterior distribution, Markov Chain Monte Carlo, probabilistic modeling, uncertainty quantification

Authors: Umesh Patil, Depesh Deshpande, Ankur. Choudhury

Abstract: Approximation theory forms the mathematical backbone of many numerical and computational methods used to solve real-world problems where exact solutions are difficult or impossible to obtain. In recent decades, meshless (or meshfree) methods have emerged as a powerful alternative to classical mesh-based numerical techniques such as finite difference, finite element, and finite volume methods. These approaches rely heavily on approximation theory, particularly interpolation, regression, and functional approximation using scattered data. This paper presents a comprehensive review of approximation theory and its close connection with meshless methods. Fundamental concepts such as polynomial approximation, radial basis functions, moving least squares, and kernel-based approximations are discussed in detail. Various meshless methods, including the Element-Free Galerkin method, Smoothed Particle Hydrodynamics, and Local Petrov–Galerkin methods, are reviewed with emphasis on their theoretical foundations, advantages, and limitations. Applications in engineering, fluid dynamics, solid mechanics, and computational physics are also highlighted. The paper aims to provide a unified perspective that connects classical approximation theory with modern meshless numerical techniques, while also identifying current challenges and future research directions.

Keywords: Approximation theory, meshless methods, radial basis functions, moving least squares, numerical analysis, scattered data approximation

Author:- Farzana Hussain

Abstract:-A new approach of grid system generation is developed in this study to solve the shallow water equations. A system of straight lines and concentric, uniformly distributed ellipses are considered as the grid lines. Then a stretching along the radial direction is done so that the elliptic arc distant and radial distant between two points is small near the origin which is coarse away from the origin. Using mathematical transformations and appropriate initial/ boundary conditions the transformed shallow wa-ter equations are solved to estimate the water level due to tide and surge associated with some cyclone that hits the coastal region of Bangladesh. This grid system ensures the flexibility of having an optimum shape suitable for representing the coastal and island boundaries by changing the eccentricity of the sys-tem of ellipses and is found to be suitable for incorporation of the bending of the coastline and the isl-and boundaries accurately.

Authors: J.Goldarexy, M.Indhumathi

Abstract: In this paper, we introduce the notion of symmetric bi-multipliers in BCK-algebras. Also, we investigate some of their relative properties. Moreover, we defined kernel and fixed set of BCK-algebras and obtain some properties with illustrations.

Keywords: Cyclone Sidr, Cyclone Aila, Tropical Storms, Surge, Shallow water equations, Transformation of Coordinates, Bay of Bengal.

Authors:-A. Ibrahim, K. JeyaLekshmi

Abstract:-In this paper, we introduce the notion of Type-1fuzzy implicative filter of lattice pseudo-Wajsberg algebra and we obtain some related properties. Further, we introduce Type-2 fuzzy implicative filter of lattice pseudo-Wajsberg algebra, we show that characterization of Type-1and Type-2fuzzyimplicative filters of lattice pseudo Wajsberg algebra.

Authors: J.Subashini, K. Indirani

Abstract: In this paper we introduce a kernelled fuzzy point, boundary kernelled fuzzy point and derived kernelled fuzzy point of a subset A of X, and using these notions to define kernel set of fuzzytopological spaces. Also we introduce fuzzy topological kr space. The investigation enables us topresent some new fuzzy separation axioms between FT_0 and FT_1spaces.

Author: Farzana Hussain

Abstract: Appropriate early warning systems for severe tropical cyclones and response networks are needed to ensure the safety of life and property along the coastal region. In this study a transformed coordinate boundaryfitted shallow water model is developed to predict the associated surge levels. Using appropriate transformations of independent coordinates, the curvilinear physical domain is transformed to a square one and also each island boundary transforms to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain and then the regular explicit finite difference scheme is used to solve the shallow water equations, where the problem domain is divided into 100× 131 grid points. The model is applied to compute the water levels due to astronomical tide and surges associated with Cyclone Phailin (2013) along the East coast of India. The computed results are found in good agreement with the observations.

Authors:-Kokila Ramesh, Anita Chaturvedi, Radha Gupta

Abstract:-Variability in monsoon rainfall is a natural hazard that India faces every year. The total seasonal precipitation in the month of June, July, August and September is generally known as southwest monsoon (SWM) rainfall. While the season recurs annually, the variation about the long term expected value can be as high as 40-50% in some parts of the country. The hazard due to droughts and floods caused by extreme variations can be mitigated to some extent if the rainfall time series can be modeled efficiently for simulation and forecasting. Rainfall data is a strongly non-Gaussian time series exhibiting non-stationarity. Artificial neural network (ANN) models are known to be versatile in handling such complex and unstructured data. In this paper a new ANN model general enough to model the available century long data in several sub regions of India is developed. The model is found to be efficient in explaining nearly 80% of the data variance. One year ahead forecast on a set of data, independent from the training period is also found to perform very well.

Authors: Aniruddh Kale, Ravindra Prasad

Abstract: Dynamical systems and chaos theory form a central part of modern applied mathematics and theoretical science. They provide a unified language to describe systems that evolve with time, ranging from simple mechanical motion to complex biological, economic, and climatic phenomena. This paper presents a comprehensive review of the fundamental concepts of dynamical systems, including continuous and discrete models, linear and nonlinear behavior, stability, and bifurcation theory. Special emphasis is given to chaos theory, which explains how deterministic systems can exhibit unpredictable and seemingly random behavior due to sensitive dependence on initial conditions. Classical models such as the logistic map, Lorenz system, and simple oscillators are discussed to illustrate key ideas. Applications across physics, engineering, biology, and social sciences are also reviewed. The paper aims to provide an accessible yet rigorous overview suitable for postgraduate students and researchers, while maintaining a balance between mathematical formulation and physical interpretation. Some minor inconsistencies in expression are intentionally retained to reflect a natural academic writing style.

Keywords: Dynamical systems, nonlinear dynamics, chaos theory, bifurcation, stability, strange attractors

Autghor: Ankur Deshpande

Abstract: Complex systems arise in a wide range of scientific and engineering domains, including biological networks, socio-economic systems, manufacturing processes, climate systems, and large-scale engineering infrastructures. These systems are characterized by nonlinear interactions, high dimensionality, uncertainty, and emergent behavior, which make their analysis and experimentation particularly challenging. Traditional experimental design techniques, developed primarily for simple and well-controlled systems, are often inadequate when applied to complex systems. This paper presents a comprehensive review of experimental design methodologies tailored for complex systems. The study discusses classical design principles and their limitations, followed by modern approaches such as factorial and fractional factorial designs, response surface methodology, adaptive and sequential designs, simulation-based experimentation, and robust design techniques. Special attention is given to the role of computational tools, uncertainty quantification, and data-driven methods in handling system complexity. Practical challenges, including cost constraints, ethical considerations, and scalability issues, are also highlighted. The paper aims to provide researchers and practitioners with a structured overview of experimental design strategies suitable for complex systems, along with insights into future research directions.

Keywords: Complex systems; Experimental design; Factorial design; Simulationbased experiments; Robust design; Uncertainty analysis

Authors: G. Chinnathambi, Dr. M. Thirumalaisamy

Abstract: In this paper, we introduce the concept of the intuitionistic fuzzy λ – closed set in intuitionistic fuzzy topological spaces and study some of its properties.

Keywords: and Phrases: Intuitionistic fuzzy topology, intuitionistic fuzzy λ – closed set, intuitionistic fuzzy λ – open set, intuitionistic fuzzy λ-irresolute mapping

Author: G. Jothilakshmi

Abstract: A graph has a dominator coloring if it has a proper coloring in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number χd (G) is the minimum number of colors required for a dominator coloring of G. In this paper the dominator chromatic number for Lollipop graph is studied and also the relation between dominator chromatic number, domination number and chromatic number is shown.

Keywords: Coloring, Domination, Dominator Coloring, Lollipop graph Classification number: 05C15, 05C75

Authors: P. Pavithra, P. Solairani 

Abstract: In this paper, the minimum maximal domination energy of a line graph E_DL (G) is introduced. We compute minimum maximal domination energies of some standard graphs and a number of well-known families of graphs. Upper and lower bounds for E_D (G) are established

Keywords: Line graph, Minimum maximal dominating set, minimum maximal domination matrix, minimum maximal eigen values, minimum maximal energy of a line graph.

Authors: Maria Akter, Salma Nasrin

Abstract: A Pseudo-Riemannian manifold whose group of symmetry contains inversion symmetry about every point is called a symmetric space in differential geometry. On the other hand, in Riemannian geometry, a complete, simply connected Riemannian manifold whose curvature tensor is invariant under parallel transport is called a symmetric space. This paper is the study of the formation of symmetric pair from symmetric space. Also, a explanation is given how a symmetric pair can be formed from Lie group.

Authors: D. Sasikala, T.Anitha

Abstract: The notion of this article is to introduce a new type of regular space namely gjregular space in topological spaces. Characterization of the basic properties using these regular spaces have been discussed and studied. 

Author: J. Sathyamalar

Abstract: In this paper we study on solving fuzzy Game problems by using Ranking Technique

Keywords: Fuzzy numbers, Triangular fuzzy number, Ranking of triangular fuzzy number

Authors: Ishrat Zahan, M.A. Alim

Abstract: The study of laminar magnetohydrodynamic (MHD) conjugate natural convection flow on an incompressible, viscous and electrically conducting fluid with heat conducting vertical wall and uniform heat flux is numerically investigated. In the analysis, a two dimensional rectangular enclosure filled with water-Cu nanofluid is used under conjugate convective conduction condition. The left side wall of the enclosure is kept at a constant heat flux which is maintained at ambient air temperature while a constant low temperature is used on the right wall. The horizontal walls are adiabatic. The governing model has been solved by using finite element method with Galerkin weighted residual simulation. The objective of the study is to examine the momentum and energy transport processes in a rectangular enclosure in presence of magnetic field. The outcome are shown in terms of parametric presentations of streamlines and isotherms for the parameter solid fluid thermal conductivity ratio (K_r ) and solid wall thickness (w_1 ) on heat transfer and fluid flow inside the cavity for the range of Hartmann number (Ha) of 0 to 60. Moreover, the implications of the above parameters are depicted on the average Nusselt number (Nu) of the fluid. Finally, it is found that heat transfer and fluid flow can be controlled by the thickness of the solid wall and the thermal conductivity ratio.

Authors: M. Iqbal Jeelani, Fehim Jeelani Wani, S.E.H.Rizvi, Manish Kr Sharma, Anil Bhat, Mansha Gul, Nayeem Sofi

Abstract: Apple is the principle fruit crop of Jammu and Kashmir and accounts for 51 per cent of total area of 2.72 lac hectare under all temperate fruits grown in this state. This paper emphasis on forecasting apple production of Jammu & Kashmir using non-linear approach. Different non-linear growth models viz. Logistic, Gompertz and Monomolecular models have been used for modelling of J&K’s total apple production during the period 1974-75 to 2016-17. It was observed that Monomolecular and Logistic models performed better followed by Gompertz model for this dataset based on various goodness of fit criteria viz. Coefficient of determination (R2), Root mean square Error (RMSE), Mean absolute error (MAE) and Mean absolute percentage error (MAPE). Finally, J&K’ total apple production for 2017-18 to 2019-20 has been forecasted by using the Monomolecular and Logistic models.

Author: Dr. P.K. Mishra

Abstract: In this paper we estimate the number of roots of a random trigonometric polynomial of degree n with independent normally distributed random real coefficients asymptotically crosses the line mx, when m is any real value such that (m2 /n)→0 as n→∞. in our work we have proved that for m > exp (nf) , where f is any function of n such that f(n)→∞, the expected number of level crossings of the above trigonometric polynomial reduces to only one. 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99

Authors: Aarav Kulkarni, Meenakshi Rao, Prithvi Sen, Md Mohsen Alli

Abstract: Pattern recognition and classification form the backbone of modern data-driven systems, enabling machines to identify regularities, assign labels, and make informed decisions based on observed data. These techniques have become central to a wide range of applications, including image analysis, speech recognition, medical diagnosis, bioinformatics, finance, and social network analysis. This paper presents a comprehensive review of pattern recognition and classification methods, covering classical statistical approaches, structural and syntactic methods, and contemporary machine learning and deep learning techniques. Emphasis is placed on feature extraction, similarity measures, learning paradigms, and performance evaluation. The paper also discusses practical challenges such as high dimensionality, noise, class imbalance, and interpretability. By providing an integrated overview of theoretical foundations and applied perspectives, this review aims to serve as a useful reference for researchers and practitioners working in pattern recognition and related fields.

Keywords: Pattern recognition, classification, feature extraction, machine learning, deep learning, supervised learning

Authors: Anirudh Kulkarni, Meera Joshi, R. Venkatesh

Abstract: Optimization and optimal control play a central role in modern science, engineering, and management decision-making. From designing efficient industrial systems to controlling complex dynamical processes, these methodologies aim to identify the best possible solution under given constraints. Optimization focuses on selecting optimal values of decision variables, while optimal control extends these ideas to systems evolving over time. This paper presents a comprehensive review of fundamental concepts, mathematical formulations, classical and modern methods, and real-world applications of optimization and optimal control. Both unconstrained and constrained optimization techniques are discussed, along with optimal control problems governed by differential equations. The paper also highlights numerical approaches, computational challenges, and recent developments in the field. Through examples, tables, and discussions, this review aims to provide a structured understanding suitable for researchers and postgraduate students.

Keywords: Optimization, Optimal Control, Mathematical Programming, Dynamic Systems, Numerical Methods