University of GuilanJournal of Mathematical Modeling2345-394X9320210901Fractal Kronig-Penney model involving fractal comb potential331345445810.22124/jmm.2020.17537.1510ENAlirezaKhalili GolmankhanehDepartment of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, IranKarminaKamal AliDepartment of Mathematics, Faculty of Science, University of Zakho, IraqJournal Article20200902In this article, we suggest a fractal Kronig-Penny model which includes a fractal lattice, a fractal potential energy comb, and a fractal Bloch's theorem on thin Cantor sets. We solve the fractal Schr\"{o}dinger equation for a given potential, using an exact analytical method. We observe that the allowed band energies and forbidden bands in the fractal lattice are bigger than in the standard lattice. These results show the effect of fractal space-time or their fractal geometry on energy levels.https://jmm.guilan.ac.ir/article_4458_15331da4037abc304165404ab7d73669.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901A block preconditioner for the Gl-LSMR algorithm347359445910.22124/jmm.2020.17687.1525ENAfsanehHasanpourDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, IranMaryamMojarrabDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, IranJournal Article20200915The global least squares minimal residual (Gl-LSMR) method is an efficient solver for linear systems with multiple right-hand sides. To accelerate the convergence of the Gl-LSMR method, we propose a block preconditioner for the global LSMR method which can be used for solving linear systems with a block partitioned coefficient matrix and multiple right-hand sides. Numerical examples and comparing the preconditioned Gl-LSMR method with the Gl-LSMR method validate the effectiveness of the preconditioner. Numerical results confirm that the Block Preconditioned Gl-LSMR (BPGLSMR) method has a better performance in reducing the number of iterations and CPU time.https://jmm.guilan.ac.ir/article_4459_3e9cac74e5523bd0855201c4b20cd5c4.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901Recent advances in the numerical solution of Volterra integral equations361373446110.22124/jmm.2020.17997.1554ENAliAbdiFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20201022Natural Volterra Runge--Kutta methods and general linear methods are two large family of the methods which have recently attracted more attention in the numerical solution of Volterra integral equations. The purpose of the paper is the presentation of some recent advances in these methods. Also, implementation issues for these methods will be discussed.https://jmm.guilan.ac.ir/article_4461_522a9497c7ab9968792f8dd1d29f9d37.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901An efficient conjugate gradient method with strong convergence properties for non-smooth optimization375390447110.22124/jmm.2020.16747.1452ENFahimehAbdollahiDepartment of Mathematics, K. N. Toosi University of Technology, Tehran, IranMasoudFatemiDepartment of Mathematics, K. N. Toosi University of Technology, Tehran, IranJournal Article20200606In this paper, we introduce an efficient conjugate gradient method for solving nonsmooth optimization problems by using the Moreau-Yosida regularization approach. The search directions generated by our proposed procedure satisfy the sufficient descent property, and more importantly, belong to a suitable trust region. Our proposed method is globally convergent under mild assumptions. Our numerical comparative results on a collection of test problems show the efficiency and superiority of our proposed method. We have also examined the ability and the effectiveness of our approach for solving some real-world engineering problems from image processing field. The results confirm better performance of our method.https://jmm.guilan.ac.ir/article_4471_6cf479f380e06f0783bdb615ea168c1e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901Theory and application of the power Ailamujia distribution391413451310.22124/jmm.2020.17547.1512ENFarrukhJamalDepartment of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab, PakistanChristopheChesneauUniversite' de Caen Normandie, LMNO, Campus II, Science 3, Caen, FranceKhaoulaAidiLaboratory of probability and statistics LaPS, University Badji Mokhtar-Annaba, AlgeriaAqibAliDepartment of Computer Science and IT, GLIM institute of modern studies Bahawalpur, Bahawalpur, Punjab, PakistanJournal Article20200903Statistical modeling is constantly in demand for simple and flexible probability distributions. We are helping to meet this demand by proposing a new candidate extending the standard Ailamujia distribution, called the power Ailamujia distribution. The idea is to extend the adaptability of the Ailamujia distribution through the use of the power transform, introducing a new shape parameter in its definition. In particular, the new parameter is able to produce original non-monotonic shapes for the main functions that are desirable for data fitting purposes. Its interest is also shown through results about stochastic orders, quantile function, moments (raw, incomplete and probability weighted), stress-strength parameter and Tsallis entropy. New classes of distributions based on the power Ailamujia distribution are also presented. Then, we investigate the corresponding statistical model to analyze two kinds of data: complete data and data in presence of censorship. In particular, a goodness-of-fit statistical test allowing the processing of right-censored data is developed. The potential of the new model is demonstrated by its application to four data sets, two being related to the Covid-19 pandemic.https://jmm.guilan.ac.ir/article_4513_c22d7a760f28d0ce008d9af3c31fec70.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901Correctness of the free boundary problem for the microscopic in-situ leaching model415423454910.22124/jmm.2021.18402.1581ENAnvarbekMeirmanovNational Research University ``Higher School of Economics'', Moscow, RussiaOlegGaltsevNational Research University ``Belgorod State University'', Belgorod, RussiaVladimirSeldemirovNational Research University ``Higher School of Economics'', Moscow, RussiaJournal Article20201213We consider initial boundary value problem for in-situ leaching process of rare metals at the microscopic level. This physical process describes by the Stokes equations for the liquid component coupled with the Lame's equations for the solid skeleton and the diffusion-convection equations for acid concentration. Due to the dissolution of the solid skeleton, the pore space has an unknown (free) boundary. For formulated initial boundary-value problem we prove existence and uniqueness of the classical solution.https://jmm.guilan.ac.ir/article_4549_846531f1451f137cc3acfbba1d8bd47f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901$d-$Fibonacci and $d-$Lucas polynomials425436458110.22124/jmm.2021.17837.1538ENBoualemSadaouiLESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 AlgeriaAliKrelifaLESI Laboratory,
Faculty of Sciences and Technology,
University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, AlgeriaJournal Article20201002Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called $d-$Fibonacci and $d-$Lucas polynomials (respectively) and provide their properties. Combinatorial identities are obtained for the defined polynomials and by using Riordan method we get factorizations of Pascal matrix involving $d-$Fibonacci polynomials.https://jmm.guilan.ac.ir/article_4581_d5a4d10c1688c9b12ffff9830972967e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901An intrusion detection system with a parallel multi-layer neural network437450460810.22124/jmm.2021.17362.1502ENMohammadHassan Nataj SolhdarShohadaye Hoveizeh University of Technology, Dasht-e Azadegan, Khuzestan, IranMehdiJaninasab SolahdarIslamic Azad University, Mahalat Branch, Mahalat, IranSadeghEskandariDepartment of Computer Science, University of Guilan, Rasht, IranJournal Article20200812Intrusion detection is a very important task that is responsible for supervising and analyzing the incidents that occur in computer networks. We present a new anomaly-based intrusion detection system (IDS) that adopts parallel classifiers using RBF and MLP neural networks. This IDS constitutes different analyzers each responsible for identifying a certain class of intrusions. Each analyzer is trained independently with a small category of related features. The proposed IDS is compared extensively with existing state-of-the-art methods in terms of classification accuracy . Experimental results demonstrate that our IDS achieves a true positive rate (TPR) of 98.60\% on the well-known NSL-KDD dataset and therefore this method can be considered as a new state-of-the-art anomaly-based IDS.https://jmm.guilan.ac.ir/article_4608_6c422be00fed7b4135a706109a9f4fc8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901Mixed fractional differential equation with nonlocal conditions in Banach spaces451463460910.22124/jmm.2021.18439.1582ENAbdellatifBoutiaraLaboratory of Mathematics And Applied Sciences University of Ghardaia, 47000. AlgeriaJournal Article20201219This paper is devoted to study the existence of solution for a class of nonlinear differential equations with nonlocal boundary conditions involving the right Caputo and left Riemann--Liouville fractional derivatives. Our approach is based on Darbo's fixed point theorem associated with the Hausdorff measure of noncompactness. The obtained results generalize and extend some of the results found in the literature. Besides, the reported results concerned in the Banach space's sense. In the end, an example illustrates our acquired results.https://jmm.guilan.ac.ir/article_4609_d62226793e9621e109382e4761d71a46.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901A linear theory of beams with deformable cross section465483461010.22124/jmm.2021.17932.1548ENLucaSabatiniDip. S.B.A.I., University of Rome "La Sapienza", Via Antonio Scarpa 14, 00100 Roma, ItalyJournal Article20201019We present a direct model of beam which takes into consideration the deformation of the section by effect of orthogonal actions. The variation of size and the distortion of the transversal sections are taken into account as well as the usual rigid rotation-torsion-warping. We deduce the equations of motion in terms of the kinematic descriptors. A simple numerical example is also presented to show the consistence of the proposed model.https://jmm.guilan.ac.ir/article_4610_ccea1e91531138ea5fc7c8e36239c13d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901A computational model for texture analysis in images with a reaction-diffusion based filter485500461110.22124/jmm.2021.18289.1569ENHamidLefraichLaboratory (MISI), Faculty of Science and Technology, University Hassan first, Settat 26000, MoroccoHoudaFahimLaboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, MoroccoMariamZirhemLaboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, MoroccoNour EddineAlaaLaboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, MoroccoJournal Article20201128As one of the most important tasks in image processing, texture analysis is related to a class of mathematical models that characterize the spatial variations of an image. In this paper, in order to extract features of interest, we propose a reaction diffusion based model which uses the variational approach. In the first place, we describe the mathematical model, then, aiming to simulate the latter accurately, we suggest an efficient numerical scheme. Thereafter, we compare our method to literature findings. Finally, we conclude our analysis by a number of experimental results showing the robustness and the performance of our algorithm.<br /><br />https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9320210901A computational method based on Legendre wavelets for solving distributed order fractional diffrential equations501516461210.22124/jmm.2021.18634.1596ENParisaRahimkhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranYadollahOrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranJournal Article20210113In the current investigation, the distributed order fractional derivative operational matrix based on the Legendre wavelets (LWs) as the basis functions is derived. This operational matrix is applied together with collocation method for solving distributed order fractional differential equations. Also, convergence analysis of the proposed scheme is given. Finally, numerical examples are presented to show the efficiency and superiority of the mentioned scheme.https://jmm.guilan.ac.ir/article_4612_bf6961ad233fafc467e3c17050a91f51.pdf