University of GuilanJournal of Mathematical Modeling2345-394X13420251201Generalized distributed-order fractional optimal control problem using Laguerre wavelet method747765874510.22124/jmm.2025.29900.2669ENGunjanDewanganDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, IndiaAkankshaSinghDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, IndiaAnkurKanaujiyaDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, IndiaJournal Article20250220This research presents a novel numerical method for solving a class of complex optimal control problems characterized by distributed-order derivatives. By effectively employing fractional-order Laguerre wavelets, the study transforms the original continuous-time problem into a discrete set of algebraic equations. This transformation is facilitated by the use of Reimann-Liouville distributed-order operational matrices and a carefully chosen set of Newton-Cotes collocation points. The optimized solution is then determined by applying the Lagrange multiplier method to solve the resulting system of equations. The paper rigorously investigates the convergence properties of this approach, establishing error bounds that provide a measure of its accuracy. Finally, the effectiveness of this method is demonstrated through a series of illustrative examples, showcasing its high precision and applicability to a wide range of generalized distributed-order optimal control problems.https://jmm.guilan.ac.ir/article_8745_3a58b590ecb8ada9aa4a844250f4cb5d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Dynamical behavior of a multi-group stochastic SEIR system with symptomatic and asymptomatic individuals767786878210.22124/jmm.2025.30419.2730ENSanazLameiFaculty of Mathematical sciences , University of Guilan, P. O. Box 1914, Rasht, IranJournal Article20250418In this paper, a multigroup stochastic SEIR model dealing with both symptomatic and asymptomatic cases is considered. First, we show there exists a unique global positive solution to the system for any given positive initial value. Next, we provide sufficient criteria for the existence of a unique stationary ergodic distribution of the positive solutions. Finally, sufficient criteria for disease extinction are derived.https://jmm.guilan.ac.ir/article_8782_35602dc76a7d65596767d77210301fd8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201A mixed integer linear programming model for vehicle routing problem for non-complete graphs: Behshahr (Iran) case study787801878410.22124/jmm.2025.29552.2627ENMariaAfshariradDepartment of Mathematics, University of Science and Technology of Mazandaran, P.O. Box: 48518-78195, Behshahr, IranJournal Article20250112We consider Vehicle Routing Problem (VRP) for non-complete graphs. In order to avoid converting all networks to complete graphs, as in travelling salesman problem, we model VRP for non-complete graphs. Subtours are allowed in this model, since they are unavoidable in non-complete structure, while disconnected subtours are not allowed. Since disconnected subtour elimination constraints are time-consuming, we provide a separation problem for these constraints and provide an extended formulation based on this separation problem. This extended formulation turns to be equivalent to the original model. In order to reduce the size of the graph, a blocking procedure is proposed in this paper. In addition, we provide two types of valid inequalities to strengthen the formulation. Finally we test our model on a real case study and compare it to the classical model for complete graphs.https://jmm.guilan.ac.ir/article_8784_427445171842d77c48ee5db9504ca433.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Dimension reduction by identifying and removing redundant variables using copula function803815883710.22124/jmm.2025.28169.2484ENKianoushFathi VajargahDepartment of Statistics, Islamic Azad University, North Tehran Branch, Tehran, IranHamidMottaghi GolshanDepartment of Mathematics, Islamic Azad University, Shahriar Branch, Shahriar, IranFazelBadakhshanDepartment of Statistics, Islamic Azad University, North Tehran Branch, Tehran, IranJournal Article20240816In today's world, rapid developments in science and engineering are increasingly adding up to larger amounts of data; as a result, numerous problems have emerged in the analysis of big data. Hence, data dimensionality reduction can accelerate data analysis and even yield better results without losing any useful data. A copula represents an appropriate model of dependence to compare multivariate distributions and better detect the relationships of data. Therefore, a copula is employed in this study to identify and delete noisy data from the original data. Then, it is compared to the principal component analysis to show its superiority.https://jmm.guilan.ac.ir/article_8837_0c888c51a714133e97ce97d6e8ad0f58.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201A novel leading moving average indicator using ANFIS-Wavelet hybrid method for financial market forecasting817830883810.22124/jmm.2025.30492.2737ENMohammadKazemiDepartment of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranHamedMohammadi PeyhaniDepartment of Information Science, University of Ottago, Dunedin, New ZealandMohsenAkbariDepartment of Business Administration, Faculty of Management and Economics, University of Guilan, Rasht, IranJournal Article20250425Technical analysis aims to identify market trends and forecast future direction to support profitable trading decisions. This paper introduces a novel leading moving average indicator based on a hybrid ANFIS-Wavelet approach. The proposed method consists of two main components. First, a hybrid model combining an Adaptive Network-based Fuzzy Inference System (ANFIS) and Wavelet Transform (WT) is employed to forecast future market prices, with the full wavelet decomposition of the price time series serving as input parameters for ANFIS. Second, a leading moving average is constructed using both historical and forecasted prices. Similar to the other leading indicators, the proposed indicator can serve as a market predictor due to its incorporation of forecasted values. Empirical evaluation on NASDAQ-listed stocks demonstrates that this indicator is effective as a trading decision-support tool in financial markets, such as stock exchanges.https://jmm.guilan.ac.ir/article_8838_c175b155d1c8e754e53dcb850d7b9933.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Application of fixed structure learning automata for designing intrusion detection systems831850883910.22124/jmm.2025.29713.2656ENKayvanAsghariDepartment of Computer Engineering, Tabriz Branch, Islamic Azad University, Tabriz, IranJournal Article20250202Designing an efficient intrusion detection system involves several phases, with feature selection being one of the most important. In this paper, a fixed-structure learning automata has been applied for the feature selection phase. The introduced method includes the exploration and exploitation phases of an optimization method to find the significant features of the network events to detect intrusions. The count of the selected features in the proposed method is a pre-defined number, as the feature selection is a multi-objective problem, and one of its objectives is the feature count. The learning automata-based method uses reward and penalty operators to explore the problem's search space. The proposed method enhances the intrusion detection accuracy rate, another significant objective for a feature selection method. Two well-known intrusion detection datasets called NSL-KDD and UNSW-NB15 have been used in this paper to evaluate the proposed method. The evaluation results indicate the acceptable performance of the proposed method compared with some of the existing ones.https://jmm.guilan.ac.ir/article_8839_2c9ad52e57ac0829961a24a837adda2a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Accelerated DBSCAN via parallel, density-aware multi-objective genetic optimization851864884110.22124/jmm.2025.29702.2648ENHosseinEyvaziDepartment of Computer Science, Tarbiat Modares University, Tehran, IranAliRajaeiDepartment of Computer Science, Tarbiat Modares University, Tehran, IranJournal Article20250129Clustering is a fundamental task in data mining, where the quality of results often hinges on effective parameter selection. DBSCAN is widely used for discovering clusters of arbitrary shapes but is highly sensitive to its input parameters \textit{Eps} and \textit{MinPts}. This paper proposes an enhanced version of the Multi-Objective Genetic Algorithm for DBSCAN, termed \textbf{Enhanced MOGA-DBSCAN}, which introduces a modified objective function based on a density-aware Outlier Index and accelerates the optimization process through parallel computation. We evaluate the proposed method using two benchmark datasets and compare it against the original MOGA-DBSCAN as well as two adaptive variants: AMD-DBSCAN and WOA-DBSCAN. Results show that Enhanced MOGA-DBSCAN consistently achieves superior clustering performance, as measured by Rand Index and Normalized Mutual Information (NMI), while also reducing runtime relative to the original MOGA-DBSCAN. These findings highlight the effectiveness of our enhancements in improving both clustering quality and computational efficiency.https://jmm.guilan.ac.ir/article_8841_5086acd54dd61307fd75520ad389ba20.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Non-standard finite difference scheme for system of singularly perturbed Fredholm integro-differential equations865882886310.22124/jmm.2025.30538.2740ENP. AntonyPrinceDepartment of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, IndiaLoluguGovindaraoDepartment of Mathematics, Amrita School of Physical Science, Coimbatore, Amrita Vishwa Vidyapeetham, IndiaSekarElangoDepartment of Mathematics, Amrita School of Physical Science, Coimbatore,
Amrita Vishwa Vidyapeetham, IndiaJournal Article20250429This article solves computationally a system of reaction-diffusion singularly perturbed Fredholm integro-differential equations. A non-standard finite difference approach applies the derivative components, whereas the composite trapezoidal rule handles the integral components. The proposed computational method for a system of reaction-diffusion singularly perturbed Fredholm integro-differential equations exhibits a convergence rate of order two. An computational example is provided to substantiate the efficacy of the theoretical results.https://jmm.guilan.ac.ir/article_8863_86ab3b720cff00ed218f6e70854ad492.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Optimal third-kind Chebyshev collocation algorithm for solving beam-type micro- and nanoscale BVPs883898887110.22124/jmm.2025.30690.2747ENYoussri HassanYoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptAhmed GamalAttaDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, EgyptJournal Article20250517In this paper, we develop a numerical scheme for solving nonlinear boundary value problems (BVPs) arising in cantilever-type micro-electromechanical (MEMS) and nano-electromechanical (NEMS) systems. The method is based on a novel third-kind Chebyshev collocation approach. We derive an operational matrix of derivatives using shifted third-kind Chebyshev polynomials, which enables efficient spectral approximations of the governing equations. Numerical experiments confirm the accuracy and efficiency of the proposed method in handling the nonlinearities present in MEMS/NEMS actuator models.https://jmm.guilan.ac.ir/article_8871_5590dcc3bb2a985505795664edfb1fbd.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201A prototype model for image authentication, tamper localization and image restoration899916887210.22124/jmm.2025.30185.2704ENSeyed Amir HosseinTabatabaeiDepartment of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranMohammad MatinMirzaeiDepartment of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranSadeghEskandariDepartment of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranAmirhosseinNorouziDepartment of Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranJournal Article20250323In this work, an algorithm and a tool for image authentication and restoration based on DCT coefficients, classic cryptography primitives, and blockchain are presented (Source code appears in https://github.com/capamir/image-authentication). The proposed scheme can verify the authenticity of an image that has been subjected to malicious alteration, localize the modified regions, and restore the original image. However, just the malicious areas (column-wise) will be reconstructed and substituted while the intact parts (columns) are left as are to save unnecessary reconstruction costs. The tool is currently provided as a prototype serving as a web interface that is able to detect the possible maliciously altered columns of the received image precisely and to store the generated hash on a blockchain structure in almost real time. Experimental results together with the analysis of the scheme presenting the performance and security of the approach are provided which enhances the usability and trustworthiness of the scheme in further developments. https://jmm.guilan.ac.ir/article_8872_25f7faf31badba63d6e239747f0c1fc1.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Is evaluation based on accuracy of classification algorithms misleading? An approach to model validation using Bayes error rate917927854910.22124/jmm.2025.28744.2555ENHosseinKazemzadeh GharechopoghFaculty of Mathematics and Computer Science, Amirkabir University of TechnologyAdelMohammadpourFaculty of Mathematics and Computer Science, Amirkabir University of TechnologyJournal Article20241020 Researchers have long regarded model accuracy as the primary metric for evaluating<br /> the performance of classification algorithms. The current evaluation approach, which relies solely<br /> on model accuracy, often leads to inappropriate evaluation of classifiers, regardless of the dataset’s<br /> separability and complexity. This limitation underscores the need for a new and more comprehen<br />sive method. We argue that accuracy-based evaluation can be misleading, even when considering<br /> measures of data separability and complexity. We compare the error rates of well-known classifiers<br /> on Gaussian-generated datasets and show that, paradoxically, many algorithms’ observed errors are<br /> lower than that of the theoretical optimal classifier, leading to an overestimation of their performance.<br /> We consider a model invalid if its error rate is lower than the optimal classifier error, known as the<br /> Bayes error rate. To identify such invalid models, we introduce a procedure and propose an algorithm<br /> for model validation based on the Bayes error rate.https://jmm.guilan.ac.ir/article_8549_01c8cabd7ebe897402c97f19d5aa6604.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Numerical solution of obstacle problem by using the mesh-free radial point interpolation method929942887710.22124/jmm.2025.29905.2671ENAhmedAwad NasserDepartment of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University,
Isfahan, IranMasoudAllameDepartment of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University,
Isfahan, IranHabeebAbed Kadhim Aal-RkhaisDepartment of Mathematics, College of Computer and Mathematics, University of
Thi-Qar, IraqMajidTavassoli-KajaniDepartment of Mathematics, Isfahan (Khorasgan) branch, Islamic Azad University,
Isfahan, IranJournal Article20250307The obstacle problem is a well-known type of elliptic variational inequality that originally arose from contact issues in solid mechanics. The solutions to the obstacle problem often have irregularities along a free boundary, which can be effective in designing an appropriate numerical method for these problems. In this paper, we present a mesh-free method based on the radial point interpolation method for numerically solving an obstacle problem. In the proposed method, the radial point interpolating shape functions are utilized in the global weak form of the obstacle problem, based on the element-free Galerkin method. This approach is combined with an active set strategy to address the obstacle problem. One of the key benefits of the proposed method is its independence from any mesh of the computing domain, along with its straightforward implementation and high numerical stability. To ensure the efficiency of the presented method, we have investigated the convergence of the proposed method. The obtained numerical results confirm the theoretical achievements and demonstrate the method's effectiveness and accuracy.https://jmm.guilan.ac.ir/article_8877_0e8645523f08c816df68dccfae64f1ba.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Layer-resolving mesh method for convection-diffusion delay problems with boundary turning points943966890910.22124/jmm.2025.30347.2724ENYimesgen MehariKebedeDepartment of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.Awoke AndargieTirunehDepartment of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.Endalew GetnetTsegaDepartment of Mathematics, College of Science, Bahir Dar University, Bahir Dar, Ethiopia.Journal Article20250412This paper introduces a numerical scheme designed to solve time-delay singularly perturbed parabolic convection-diffusion problems with turning points. A small parameter induces boundary layers, making standard methods ineffective. To tackle these challenges, we developed a layer-resolving numerical scheme using the Crank-Nicolson method (time) and a central finite difference method on a Shishkin mesh (space). The stability and parameter-uniform convergence analysis show that the error decreases quadratically. Numerical results demonstrate higher accuracy than existing approaches.https://jmm.guilan.ac.ir/article_8909_91aa4c961cf9f4c45d933b5710da27cf.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Modeling and optimization of the number of graduates in a multi-specialization study program967982891410.22124/jmm.2025.29244.2602ENJonathanHoseanaParahyangan Catholic UniversityJournal Article20241214Consider a study program which offers a number of specializations, and requires all students to be enrolled in exactly one specialization at any given time. We construct a continuous mathematical model governing the time evolution of the number of students enrolled in each of the program's specializations. Using the model, we further construct an optimization problem describing the search of an intervention strategy which maximizes the program's total number of graduates, along with a framework for sensitivity analysis. We discretize the constructs accordingly, and employ a coordinate-descent method to solve the optimization problem numerically in two simulated scenarios involving two and four specializations, respectively, describing the results' practical implications.https://jmm.guilan.ac.ir/article_8914_d431303711d29b06a35633d34286d9e1.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13420251201Numerical study of a two-dimensional eco-epidemiological model with diffusion and convex incidence rate: Unconditionally positivity preserving method9831005889610.22124/jmm.2025.29603.2634ENGhasemBarid LoghmaniDepartment of Mathematical Sciences-Yazd University-Yazd-IranMohammad HosseinAkramiDepartment of Mathematics-Yazd University-Yazd-Iran.MohammadHeydariDepartment of Mathematical Sciences, Yazd University, Yazd, Iran.SafiehBagheriDepartment of Mathematical Sciences-Yazd University-Yazd- Iran.Journal Article20250118In this paper, a two-dimensional eco-epidemiological model with diffusion and convex incidence rate is studied, that is, the density of population depends on time and two spatial variables. The main challenge in investigation of population models is finding a numerical method to obtain non-negative solutions. Some numerical methods, for instance Euler's method, based on the standard finite difference formulas are inefficient for solving such models because they are not always able to produce non-negative approximate solutions. On the other hand, the non-standard finite difference schemes can provide non-negative approximations conditionally. In { the} current work, first, the stability of the dynamic proposed eco-epidemiological model is examined. Then, a numerical method that provides unconditional acceptable solutions is introduced. In what follows, the consistency and stability of the numerical method are discussed. Finally, using numerical simulation, the efficiency of this method is compared with the Euler and non-standard methods. Furthermore, we examined the role of initial functions in interpreting species-environment interactions and deliberated on predator-prey behaviors in various scenarios.https://jmm.guilan.ac.ir/article_8896_fad2e4d7b278c7a32a3ff628e460c32d.pdf