Journal of Applied Mathematics and Informatics
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Let ζ(V, E) be a simple graph, with |V| = ρ and |E| = ϱ. The degree of a vertex vi ∈ V is the count of edges connected to vi denoted by ςi. The maximum(minimum) vertex and edge degree of a graph is denoted by ∆(δ) and ∆′ (δ′) respectively. A graph ζ is said to be complete if ∆ = δ = ρ − 1 denoted by Kρ. If a vertex set of a graph ζ is partitioned into two sets say |M| = υ and |N | = ν (partite sets) such that every edge meet both M and N then the graph is bipartite graph. If every vertex of M is adjacent to every vertex of N then the graph is complete bipartite graph denoted as Kυ,ν. The graph K1,ρ−1 is called as star graph denoted by Sρ and the graph Kν,ν is called equi-bipartite graph. The complement of a graph ζ denoted by ζ is a graph defined on same vertex set as of ζ such that if two vertices are adjacent in ζ, then they are not adjacent in ζ. For more terminologies refer the following [1].
Copyright (c) 2026 Journal of Applied Mathematics and Informatics https://creativecommons.org/licenses/by-nc-nd/4.0
In graph theory, a set of vertices D ⊆ V (G) in a simple graph G is termed a dominating set if every vertex not in D is adjacent to at least one member of D, formally expressed as N[D] = V (G). This work bridges these two concepts such as domination and topological indices. We establish several bounds for this new graph invariant. The paper concludes by demonstrating potential applications of new dominating energy in the field of chemistry
A NOVEL APPROACH TO PROBABILISTIC INVENTORYMODELING WITH MIXED SHORTAGES AND VARIABLEHOLDING COSTS UNDER BIVARIATE UNCERTAINTY
This study examines a stochastic continuous review inventory model for a single item sourced from one supplier. It introduces a novel approach to varying holding costs and mixed shortages, factoring in the randomness of both demand and lead time. We derived the distribution of lead time demand X in two scenarios: first, when the demand D is a discrete random variable with a continuous lead time L; and second, when both demand and lead time are modeled as continuous random variables. Using the proposed model, we determined the optimal order quantity and reorder point by minimizing the expected annual total cost, leveraging the erived distribution of lead time demand. Finally, a numerical example is presented to demonstrate the applicability and effectiveness of the model.
DUAL-PHASE DEEP LEARNING FRAMEWORK FORSTEGWARE DETECTION USING CNN ANDVAE-CONDITIONED CGAN
The increasing sophistication of stegware—malware concealed within digital images—poses a major challenge to modern cybersecurity. This study develops and compares two novel deep learning frameworks to detect such hidden threats. The first employs a customized Convolutional Neural Network (CNN) that captures minute spatial and statistical distortions within image data to classify clean and infected samples. The second approach utilizes a Conditional Generative Adversarial Network (cGAN), where latent noise features extracted from a Variational Autoencoder (VAE) serve as conditional inputs, enabling improved representation learning and enhanced discrimination between benign and stegwareinfected images. Experiments were conducted on a domain-specific stegware dataset comprising 20,000 images generated using multiple steganographic embedding schemes and realistic payloads. The CNN achieved an accuracy of 94.3%, F1 score of 0.94, and AUC of 0.96, effectively identifying embedded malware patterns. In contrast, the VAE-conditioned cGAN outperformed the CNN, achieving an accuracy of 98.2%, F1 score of 0.98, and AUC of 0.987, particularly excelling under complex embedding conditions. Paired statistical tests confirmed that these improvements were significant (p ¡ 0.005). The comparative results highlight the advantage of combining generative modeling and adversarial learning for stegware detection, offering a robust, adaptive, and interpretable solution for securing image-based communication channels against covert cyber threats.
conditional generative adversarial network
A NUMERICAL SCHEME FOR Q-DIFFERENTIALEQUATIONS
This paper presents the development and application of an innovative numerical technique, the q-Taylor method, for solving q-initial value problems (q-IVPs) arising within the framework of q-calculus. The study begins by extending the classical Taylor series to the q-calculus setting, thereby establishing the theoretical foundation of the proposed method. A comprehensive mathematical analysis is carried out to examine the fundamental properties and convergence behavior of the q-Taylor method. The technique is then applied to two illustrative examples, with MATLAB employed as the computational tool for implementation. Two test problems are used to evaluate the method’s accuracy and efficiency. The results are compared with existing numerical approaches to highlight the strengths and potential limitations of the proposed method
HAAR WAVELET SOLUTION OF NONLINEARBURGERS’ EQUATIONS WITH SMALL KINEMATICVISCOSITY PARAMETER
This article aims to apply an iterative technique to find the numerical solution of the non-linear Burgers’ equation (BE) with small kinematic viscosity parameter based on Haar wavelet collocation method. Two numerical problems are studied with different kinematic viscosity parameters. To show the exactness and capability of the suggested method L∞, L2 error norms are measured and compared with other existing results.
ON A PERTURBED FRACTIONAL SHALLOW-WATERSYSTEM WITH CROSS OPERATORS AND DAMPINGEFFECTS
In this paper, we study a generalized nonlinear shallow water wave system with damping effects and cross operators involving the Khalil derivative, using regular perturbation techniques to investigate its traveling wave solutions. Applying the tanh-method, the system is reduced to a system of perturbed ordinary differential equations. By explicit substitution and algebraic manipulations, we obtain a set of compatibility conditions that govern the coefficients of the solution. A detailed case-by-case study is presented depending on the vanishing or non-vanishing of the parameters. The results provide explicit formulas for wave profiles and derive families of solutions parameterized by wave speed c and shape parameter µ. The approach confirms that the conformable fractional derivative framework is consistent with classical shallow-water solitary waves.
METHODOLOGICAL INSIGHTS INTO SOLVING INITIALVALUE PROBLEMS USING DTM AND SPECIALMULTISTEP TECHNIQUES
The paper explores the application of numerical techniques to solve differential equations, particularly when closed-form solutions are unavailable or difficult to obtain. It focuses on methods like Differential Transform and Multistep approaches to solve differential equations with initial conditions. These techniques have significantly advanced the investigation of differential equations and are extensively used in numerous fields such as fundamental sciences, engineering, technology and economics. Present study highlights the importance of developing more precise and efficient numerical methods, emphasizing convergence stability and in multistep approaches. The results of different techniques are compared to demonstrate their effectiveness. The paper underscores the necessity for ongoing research to enhance numerical methods for solving differential equations, aiming for greater accuracy and efficiency in practical applications.
differential transform method and numerical methods
OPTIMIZING FARM PRODUCTIVITY THROUGHPRIVATIZATION, SUPPORT SERVICES, MISCALIBRATIONSAND LINEAR PROGRAMMING IN AGRICULTURALMANAGEMENT
The study examines the conditional effects of privatization and farm support services on farm production by considering resource calibration and environmental conditions. Several econometric models are used to assess how privatization and resource miscalibration affect farm productivity. Conditional process modeling and linear programming are used to determine the expenditure for reducing greenhouse gas emissions and boosting output from agriculture. The information demonstrate that privatization makes support services more conditional but reduces resource calibration. The linear programming methodology increases farm productivity while reducing environmental impact by eliminating waste of resources and optimizing inputs. The findings emphasize the necessity for ecologically friendly farming that balances rewards with other factors. Our findings used by farm policymakers to inform the development of policies about farm support services, calibration of farm resources, changes to the market, and differentiated policies regarding farm outcomes; these policies will primarily target the oppressed poor farmers in the farm sector.
GENERALIZED CR-SUBMANIFOLDS OF A GOLDENRIEMANNIAN MANIFOLD
In the present paper, we define and study generalized CRsubmanifolds of Riemannian manifold with golden structure. We introduce some properties for generalized CR-submanifolds. Moreover, we obtain many results on totally umbilical generalized CR-submanifolds of a golden Riemannian manifold.
DOMINATION POLYNOMIALS OF SOME NOTABLEGRAPH FAMILIES
A graph polynomial is a graph invariant that evaluates to a polynomial expression. The study of graph polynomials, including their definition and determination, constitutes a fundamental area of research in graph theory. Among these, the domination polynomial stands out, providing valuable insights into the structural properties of a graph. This research contributes to the advancement of domination theory—a branch of graph theory with broad applications—by deriving explicit expressions for the domination polynomials of some significant graphs, namely the path graph Pn, the star graph Sn, the centipede graph CPn, and the corona of the graphs Pn and mK1. The study employs a streamlined and unified methodology based on simultaneous recurrence relations and matrix diagonalisation.
A NEW SUBCLASS OF ANALYTIC AND UNIVALENTFUNCTIONS ASSOCIATED WITH MITTAG-LEFFLERTYPE POISSON DISTRIBUTION OPERATOR
The present work is concerned with the study of a new subclass of analytic functions, T Mm α,ρ,φ(γ), defined in terms of negatively normalized Mittag-Leffler type functions. It establishes conditions under which these functions exhibit significant geometric properties such as starlikeness, convexity, close-to-convexity and boundedness of coefficients within the open unit disc D. The work further explores various function theoretic aspects, including extremal functions, sharp coefficient bounds, integral means inequalities and growth and distortion theorems. In addition, it examines the impact of certain integral operators on the structure of this function class. These results offer a unified framework that encompasses several known subclasses and lays the groundwork for further research in eometric function theory, fractional calculus and operator theory.
EFFECTIVE EVALUATION OF CLUSTERINGAPPROACHES FOR MINING MEDICAL DATASETS
With the explosion of medical data in recent years, there’s a growing need for effective data mining techniques to uncover patterns that can enhance clinical decision-making. Among these techniques, clustering—an unsupervised learning method—has proven especially useful for discovering natural groupings in data without needing pre-labeled outcomes. This study explores and compares the performance of four clustering algorithms—K-Means, Hierarchical Agglomerative Clustering, DBSCAN, and Fuzzy C-Means—across three widely recognized medical datasets: Diabetes, Hepatitis, and Breast Cancer. To assess their effectiveness, both internal validation measures and external metrics are discussed for each algorithm as the performance varies depending on the characteristics of the dataset. For instance, DBSCAN excelled in identifying complex patterns and filtering out noise, particularly in the Breast Cancer dataset. Meanwhile, Fuzzy C-Means showed strength in handling overlapping clusters within the Diabetes dataset. These findings provide useful insights for researchers and healthcare professionals looking to apply the right clustering methods in medical data analysis.
A SMOOTH-GAUSSIAN ENSEMBLE NETWORK FORPARABOLIC TURNING POINT PROBLEMS INSINGULAR PERTURBATION
Singularly perturbed parabolic partial differential equations with turning points pose numerical challenges due to steep gradients and layers dependent on the small parameter ε. Traditional methods require fine or adaptive meshes to accurately resolve these layers. To overcome this, we propose the Smooth-Gaussian Ensemble Network, a novel computational approach that approximates solutions using a weighted sum of two separately trained feedforward neural networks. One network captures the globally smooth behavior, while the other focuses on sharp local features near turning points. Spatially varying Gaussian weights guide the ensemble, concentrating around regions with expected layer behavior. Training utilizes data from known analytical solutions, enabling thorough validation. Numerical experiments demonstrate the method’s ability to maintain high accuracy for small ε values without adaptive meshing. This framework provides an efficient and reliable alternative for handling complex layer dynamics in singular perturbation problems.
Singularly perturbed differential equations
A NUMERICAL GRADIENT DESCENT METHOD FORTHE GENERALIZED CHEEGER PROBLEM ALONGCUBIC SPLINE SHAPE EVOLUTION PATHS
This paper introduces a new evolutionary gradient descent optimization method based on cubic splines for solving the generalized Cheeger problem arising from non-uniform mass and shear strength distributions, relevant to geophysical events such as avalanches and landslides. The goal is to minimize a functional involving surface and boundary integrals to determine the safety factor and collapse domain. The evolving shape is represented using cubic spline interpolation, restricting the search to smooth geometries with minimal bending energy. The gradient of the objective functional is computed using finite differences, and the shape is iteratively updated while preserving topology. Grid refinement confirms the method’s consistency, and the monotonic decay of the gradient norm verifies numerical stability and convergence. Two numerical experiments with different mass and shear strength distributions demonstrate the robustness, efficiency, and physical relevance of the proposed framework, offering an accurate and flexible approach for geometric optimization under complex material distributions.
cubic spline based shape evolution scheme
consistency and stability of numerical method
GENERALIZED η−RICCI SOLITONS ON LP-SASAKIANMANIFOLDS ADMITTING THE GENERAL CONNECTION
We study the properties of LP-Sasakian manifolds endowed with generalized η−Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by constructing a non-trivial example.
A NEW NEUTROSOPHIC ENTROPY MEASURE FORUNCERTAIN DATA IN HEALTHCARE DECISIONSUPPORT SYSTEMS
In this paper, a novel Neutrosophic Entropy measure is proposed to effectively handle the inherent uncertainty, indeterminacy, and inconsistency present in healthcare decision-making data. The proposed entropy measure is grounded in the principles of neutrosophic set theory and is designed to accurately evaluate the significance of decision criteria. To demonstrate the applicability and effectiveness of the proposed entropy, a Multi-Attribute Decision-Making (MADM) framework is developed for the selection of the most suitable healthcare centre. Various attributes such as service quality, cost, accessibility, medical facilities, and patient satisfaction are considered in the evaluation process. The entropy-based weighting is used to assign objective importance to each attribute, and a MADM method is employed to rank the alternatives. A case study is conducted to validate the approach, and the results highlight the robustness and practicality of the proposed method in supporting healthcare decision-making under uncertain environments.
ANALYSIS OF PERISTALTIC TRANSPORT OFTHIRD-GRADE FLUID WITH SUCTION AND INJECTIONUNDER A SINGLE SLIP CONDITION: APPLICATION FORBIOMEDICAL AND INDUSTRIAL SYSTEMS
This study analyzes the peristaltic transport of an incompressible third-grade fluid in a channel with a single slip boundary condition under the assumptions of long wavelength and low Reynolds number. The nonlinear governing equations are simplified and solved analytically using a perturbation method, with numerical validation performed for stronger nonlinear regimes. The influence of key physical parameters including slip coefficient, amplitude ratio, permeability parameter, and nonNewtonian parameter is examined through velocity, pressure difference, frictional force, and streamline patterns. The results show that increasing the non-Newtonian parameter Γ, β enhances the velocity, larger amplitude ratio ϕ promote flow by reducing velocity requirements. In ontrast, increasing permeability parameter k suppresses the velocity and weakens trapping due to cross-wall transport. Pressure drop decreases with increasing β and increases with k and Γ. Skin friction reduces with higher β, ϕ, and k, but increases with Γ. Streamline analysis reveals that bolus trapping becomes stronger for β and ϕ, and weaker for k and Γ
HESITANT TRIANGULAR FUZZY GENERALIZEDGEOMETRIC HERONIAN MEAN:AN ADVANCED MCDM APPROACH
Uncertainty and hesitation are common challenges in real world multi criteria decision making (MCDM) problems, where evaluations often involve vague, imprecise, or incomplete information. This is especially important in areas such as healthcare, supply chain management and sustainability, since there is often uncertainty in the advice offered by experts. Traditional aggregation methods, such as the Generalized Geometric Heronian Mean (GGHM), typically rely on precise numerical data and therefore struggle to represent the ambiguity inherent in expert judgments. To address this limitation, this study introduces a novel aggregation operator, the Hesitant Triangular Fuzzy Generalized Geometric Heronian Mean (HTFGGHM), which integrates hesitant triangular fuzzy sets (HTFs) to better capture uncertainty and hesitation in evaluations. The proposed operator accommodates multiple membership degrees for each input, allowing for a more realistic and flexible aggregation process. The theoretical formulation and essential properties of the HTFGGHM operator are rigorously examined. The numerical example shows that the operator is capable of finding the same best option regardless of the settings. In addition, a sensitivity analysis is performed to evaluate its robustness and stability under different decision making conditions, demonstrating its effectiveness in handling complex and uncertain MCDM scenarios.
Wan Syaidatul Izzati binti Wan Abdul Rahman
ANALYZING LASSA FEVER EPIDEMICSTHROUGH THE SEIR MODEL
Lassa fever is a severe viral illness with an incubation period of 6 to 21 days. Notably, about 80% of those infected show no symptoms, complicating the early detection control of the disease. To explore the transmission dynamics of Lassa fever, a mathematical model was developed that examines the impact of isolating and treating both symptomatic and asymptomatic individuals. This model aims to enhance management strategies and evaluate the feasibility of eradicating the disease. The analysis confirmed that the model’s solutions remain positive and bounded, validating its reliability. Furthermore, an equilibrium analysis identified disease-free and endemic equilibrium points, offering key insights into whether the disease can be controlled or will persist in the population. A critical finding was determining the basic reproduction number, R0, which indicates whether the disease can be eliminated or will continue to spread. If R0 < 1, elimination is possible, but if R0 > 1, the disease remains endemic. These findings provide valuable guidance for designing targeted public health interventions to mitigate the disease’s spread and reduce its impact.
ROBUST WEATHER FORECASTING USING ISLANDPARALLEL HARRIS HAWKS OPTIMIZER WITHCONVOLUTIONAL LONG SHORT TERM MEMORY
Convolutional Long Short-Term Memory (CLSTM) networks and the Island Parallel Harris Hawks Optimizer (IP-HHO) are integrated in this study to improve the precision and effectiveness of weather forecasting. Despite their intricacy, standard Numerical Weather Prediction (NWP) models sometimes fail because of their high processing requirements and sensitivity to beginning circumstances. The IP-HHO, a nature-inspired optimization algorithm, optimizes the hyperparameters of the CLSTM network, significantly improving predictive performance. With a Mean Absolute Error (MAE) of 1.40°C, Root Mean Squared Error (RMSE) of 1.75°C, and Mean Absolute Percentage Error (MAPE) of 4.7%, the IPHHO-CLSTM approach outperformed other models using a dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF). These results mark a substantial improvement over traditional LSTM models. The error distribution centred around zero indicates minimal bias and high consistency in forecasting. The model’s performance varied across weather conditions, excelling in clear conditions while highlighting challenges in extreme weather scenarios. This research has significant implications for agriculture, disaster management, energy, and transportation sectors, offering a robust tool for better decision-making and operational efficiency. The study also contributes to computational meteorology by validating the synergy between advanced optimization algorithms and Deep Learning (DL) techniques, suggesting pathways for future research to further enhance weather forecasting models.
APPROXIMATION BY [r]-BASKAKOV-KANTOROVICHSEQUENCE
This paper modifies the classical Baskakov-Kantorovich sequence by incorporating a positive integer parameter r. The proposed modification aims to enhance the order of approximation and improve numerical accuracy. Initially, the convergence of the modified sequence is analyzed using Korovkin’s theorem. A Voronovskaja-type asymptotic formula is then established, providing a precise framework for estimating convergence and error. Finally, the study presents a numerical example with a test function, to compare the numerical results of the modified sequence to the numerical results of the classical sequence. The results demonstrate that the modified sequence achieves superior numerical accuracy compared to the classical one
FIXED POINT RESULTS VIA NEW GENERALIZEDRATIONAL “α∗-CONTRACTION” IN EXTENDEDb-METRIC SPACES
In this article, we introduce the notion of α–η continuous mappings in the framework of extended b-metric spaces, which reduces to the classical b-metric space as a special case. We further propose a new class of generalized α∗-contractions for multivalued mappings in extended b-metric spaces. Using these newly introduced concepts, we establish a fixed point theorem for multivalued generalized α∗-contractions in the setting of extended b-metric spaces. The obtained results not only extend but also unify several recent fixed point results available in the existing literature. As an application of the main theorem, we prove the existence of a solution to a Fredholm integral equation, thereby demonstrating the effectiveness of the proposed theoretical framework.
SOME APPLICATIONS OF HOMOGENEOUS WEIGHTIN LINEAR CODES OVER Rps,θ
Our contribution to this work is summarized in the following points: We present a few preliminary results for the Frobenius ring Rps,θ, and linear codes over this ring. We define the homogeneous weight and its Gray map. Throughout this study, we carried out a new construction of simplex and MacDonald codes of type α over Rps,θ.Finally, the last construction combines the previous results to construct LCD codes over Rps,θ.