J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.17537.1510 Research Paper Fractal Kronig-Penney model involving fractal comb potential Fractal Kronig-Penney model Khalili Golmankhaneh Alireza Department of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, Iran Kamal Ali Karmina Department of Mathematics, Faculty of Science, University of Zakho, Iraq 01 09 2021 9 3 331 345 02 09 2020 11 12 2020 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4458.html

In 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.

Fractal calculus fractal Schrodinger equation local fractal derivative fractal lattice
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.17687.1525 Research Paper A block preconditioner for the Gl-LSMR algorithm A block preconditioner for the Gl-LSMR algorithm Hasanpour Afsaneh Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran Mojarrab Maryam Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran 01 09 2021 9 3 347 359 15 09 2020 07 11 2020 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4459.html

The 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.

LSMR method Gl-LSMR method preconditioner block partitioned matrices multiple right-hand sides
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.17997.1554 Research Paper Recent advances in the numerical solution of Volterra integral equations Recent advances in the numerical solution of Volterra integral equations Abdi Ali Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran 01 09 2021 9 3 361 373 22 10 2020 25 11 2020 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4461.html

Natural 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.

Volterra integral equations general linear methods natural Volterra Runge--Kutta methods Nordsieck technique implementation issues
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16747.1452 Research Paper An efficient conjugate gradient method with strong convergence properties for non-smooth optimization An Efficient Conjugate Gradient Method with Strong Convergence Properties for Non-smooth Optimization Abdollahi Fahimeh Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran Fatemi Masoud Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran 01 09 2021 9 3 375 390 06 06 2020 23 12 2020 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4471.html

In 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.

Conjugate gradient method nonsmooth optimization Global convergence Image Processing
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.17547.1512 Research Paper Theory and application of the power Ailamujia distribution Theory and application of the power Ailamujia distribution Jamal Farrukh Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab, Pakistan Chesneau Christophe Universite&#039; de Caen Normandie, LMNO, Campus II, Science 3, Caen, France Aidi Khaoula Laboratory of probability and statistics LaPS, University Badji Mokhtar-Annaba, Algeria Ali Aqib Department of Computer Science and IT, GLIM institute of modern studies Bahawalpur, Bahawalpur, Punjab, Pakistan 01 09 2021 9 3 391 413 03 09 2020 30 12 2020 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4513.html

Statistical 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.

Ailamujia distribution power distribution moments stress-strength parameter entropy data analysis Covid-19 pandemic
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.18402.1581 Research Paper Correctness of the free boundary problem for the microscopic in-situ leaching model Microscopic mathematical model for in-situ leaching Meirmanov Anvarbek National Research University ``Higher School of Economics&#039;&#039;, Moscow, Russia Galtsev Oleg National Research University ``Belgorod State University&#039;&#039;, Belgorod, Russia Seldemirov Vladimir National Research University ``Higher School of Economics&#039;&#039;, Moscow, Russia 01 09 2021 9 3 415 423 13 12 2020 12 01 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4549.html

We 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.

mathematical models free boundary problems diffusion-convection
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.17837.1538 Research Paper \$d-\$Fibonacci and \$d-\$Lucas polynomials \$d-\$Fibonacci and \$d-\$Lucas polynomials Sadaoui Boualem LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria Krelifa Ali LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria 01 09 2021 9 3 425 436 02 10 2020 19 01 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4581.html

Riordan 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.

\$d-\$Fibonacci polynomials \$d-\$Lucas polynomials Riordan arrays Pascal matrix \$Q_{d}-\$Fibonacci matrix
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.17362.1502 Research Paper An intrusion detection system with a parallel multi-layer neural network An intrusion detection system with a parallel multi-layer neural network Hassan Nataj Solhdar Mohammad Shohadaye Hoveizeh University of Technology, Dasht-e Azadegan, Khuzestan, Iran Janinasab Solahdar Mehdi Islamic Azad University, Mahalat Branch, Mahalat, Iran Eskandari Sadegh Department of Computer Science, University of Guilan, Rasht, Iran 01 09 2021 9 3 437 450 12 08 2020 21 01 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4608.html

Intrusion 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.

Intrusion detection computer security Neural Network parallel processing
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.18439.1582 Research Paper Mixed fractional differential equation with nonlocal conditions in Banach spaces Mixed fractional differential equation with nonlocal conditions in Banach spaces. Boutiara Abdellatif Laboratory of Mathematics And Applied Sciences University of Ghardaia, 47000. Algeria 01 09 2021 9 3 451 463 19 12 2020 02 02 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4609.html

This 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.

Right Caputo and left Riemann--Liouville fractional derivatives nonlocal boundary conditions existence Banach spaces Darbo's fixed point theorem Hausdorff measure of noncompactness
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.17932.1548 Research Paper A linear theory of beams with deformable cross section A linear theory of beams with deformable cross section Sabatini Luca Dip. S.B.A.I., University of Rome &quot;La Sapienza&quot;, Via Antonio Scarpa 14, 00100 Roma, Italy 01 09 2021 9 3 465 483 19 10 2020 03 02 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4610.html

We 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.

Theory of beams deformation of cross section material anisotropy
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.18289.1569 Research Paper A computational model for texture analysis in images with a reaction-diffusion based filter A computational model for texture analysis in images with a reaction-diffusion based filter Lefraich Hamid Laboratory (MISI), Faculty of Science and Technology, University Hassan first, Settat 26000, Morocco Fahim Houda Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco Zirhem Mariam Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco Alaa Nour Eddine Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco 01 09 2021 9 3 485 500 28 11 2020 07 02 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4611.html

As 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.

Reaction-diffusion system biomedical images texture analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2021.18634.1596 Research Paper A computational method based on Legendre wavelets for solving distributed order fractional diffrential equations A computational method based on Legendre wavelets for solving DOFDEs Rahimkhani Parisa Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Ordokhani Yadollah Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran 01 09 2021 9 3 501 516 13 01 2021 05 02 2021 Copyright © 2021, دانشگاه گیلان. 2021 https://jmm.guilan.ac.ir/article_4612.html

In 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.

Legendre wavelets distributed order fractional diffrential equations numerical method operational matrix