University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
Fractal Kronig-Penney model involving fractal comb potential
331
345
EN
Alireza
Khalili Golmankhaneh
0000-0002-5008-0163
Department of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, Iran
alirezakhalili2002@yahoo.co.in
Karmina
Kamal Ali
0000-0002-3815-4457
Department of Mathematics, Faculty of Science, University of Zakho, Iraq
karmina.ali@uoz.edu.krd
10.22124/jmm.2020.17537.1510
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
https://jmm.guilan.ac.ir/article_4458.html
https://jmm.guilan.ac.ir/article_4458_15331da4037abc304165404ab7d73669.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
A block preconditioner for the Gl-LSMR algorithm
347
359
EN
Afsaneh
Hasanpour
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
hasanpour@pgs.usb.ac.ir
Maryam
Mojarrab
0000-0002-9619-211X
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
ma_mojarrab@math.usb.ac.ir
10.22124/jmm.2020.17687.1525
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
https://jmm.guilan.ac.ir/article_4459.html
https://jmm.guilan.ac.ir/article_4459_3e9cac74e5523bd0855201c4b20cd5c4.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
Recent advances in the numerical solution of Volterra integral equations
361
373
EN
Ali
Abdi
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
a_abdi@tabrizu.ac.ir
10.22124/jmm.2020.17997.1554
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
https://jmm.guilan.ac.ir/article_4461.html
https://jmm.guilan.ac.ir/article_4461_522a9497c7ab9968792f8dd1d29f9d37.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
An efficient conjugate gradient method with strong convergence properties for non-smooth optimization
375
390
EN
Fahimeh
Abdollahi
Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
fabdollahi@email.kntu.ac.ir
Masoud
Fatemi
Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
smfatemi@kntu.ac.ir
10.22124/jmm.2020.16747.1452
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
https://jmm.guilan.ac.ir/article_4471.html
https://jmm.guilan.ac.ir/article_4471_6cf479f380e06f0783bdb615ea168c1e.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
Theory and application of the power Ailamujia distribution
391
413
EN
Farrukh
Jamal
Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab, Pakistan
drfarrukh1982@gmail.com
Christophe
Chesneau
Universite' de Caen Normandie, LMNO, Campus II, Science 3, Caen, France
christophe.chesneau@gmail.com
Khaoula
Aidi
Laboratory of probability and statistics LaPS, University Badji Mokhtar-Annaba, Algeria
khaoula.aidi@yahoo.fr
Aqib
Ali
Department of Computer Science and IT, GLIM institute of modern studies Bahawalpur, Bahawalpur, Punjab, Pakistan
aqibcsit@gmail.com
10.22124/jmm.2020.17547.1512
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
https://jmm.guilan.ac.ir/article_4513.html
https://jmm.guilan.ac.ir/article_4513_c22d7a760f28d0ce008d9af3c31fec70.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
Correctness of the free boundary problem for the microscopic in-situ leaching model
415
423
EN
Anvarbek
Meirmanov
0000-0002-8543-3897
National Research University ``Higher School of Economics'', Moscow, Russia
anvarbek47@list.ru
Oleg
Galtsev
0000-0001-7786-4294
National Research University ``Belgorod State University'', Belgorod, Russia
oleg_galtsev@mail.ru
Vladimir
Seldemirov
National Research University ``Higher School of Economics'', Moscow, Russia
utherfjord@gmail.com
10.22124/jmm.2021.18402.1581
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
https://jmm.guilan.ac.ir/article_4549.html
https://jmm.guilan.ac.ir/article_4549_846531f1451f137cc3acfbba1d8bd47f.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
$d-$Fibonacci and $d-$Lucas polynomials
425
436
EN
Boualem
Sadaoui
LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria
sadaouiboualem@gmail.com
Ali
Krelifa
LESI Laboratory,
Faculty of Sciences and Technology,
University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria
a.kerlifa@univ-dbkm.dz
10.22124/jmm.2021.17837.1538
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
https://jmm.guilan.ac.ir/article_4581.html
https://jmm.guilan.ac.ir/article_4581_d5a4d10c1688c9b12ffff9830972967e.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
An intrusion detection system with a parallel multi-layer neural network
437
450
EN
Mohammad
Hassan Nataj Solhdar
Shohadaye Hoveizeh University of Technology, Dasht-e Azadegan, Khuzestan, Iran
nataj.solhdar@gmail.com
Mehdi
Janinasab Solahdar
Islamic Azad University, Mahalat Branch, Mahalat, Iran
mehdi_janinasab@yahoo.com
Sadegh
Eskandari
0000-0002-3007-2369
Department of Computer Science, University of Guilan, Rasht, Iran
eskandari@guilan.ac.ir
10.22124/jmm.2021.17362.1502
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
https://jmm.guilan.ac.ir/article_4608.html
https://jmm.guilan.ac.ir/article_4608_6c422be00fed7b4135a706109a9f4fc8.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
Mixed fractional differential equation with nonlocal conditions in Banach spaces
451
463
EN
Abdellatif
Boutiara
0000-0002-6032-4694
Laboratory of Mathematics And Applied Sciences University of Ghardaia, 47000. Algeria
boutiara_a@yahoo.com
10.22124/jmm.2021.18439.1582
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
https://jmm.guilan.ac.ir/article_4609.html
https://jmm.guilan.ac.ir/article_4609_d62226793e9621e109382e4761d71a46.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
A linear theory of beams with deformable cross section
465
483
EN
Luca
Sabatini
orcid.org/0000-0002-3132-6842
Dip. S.B.A.I., University of Rome "La Sapienza", Via Antonio Scarpa 14, 00100 Roma, Italy
luca.sabatini@sbai.uniroma1.it
10.22124/jmm.2021.17932.1548
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
https://jmm.guilan.ac.ir/article_4610.html
https://jmm.guilan.ac.ir/article_4610_ccea1e91531138ea5fc7c8e36239c13d.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
A computational model for texture analysis in images with a reaction-diffusion based filter
485
500
EN
Hamid
Lefraich
Laboratory (MISI), Faculty of Science and Technology, University Hassan first, Settat 26000, Morocco
lefraichhamid@gmail.com
Houda
Fahim
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
houda.fahim@edu.uca.ma
Mariam
Zirhem
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
mariam.zirhem@gmail.com
Nour Eddine
Alaa
0000-0002-6090-5210
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
n.alaa@uca.ac.ma
10.22124/jmm.2021.18289.1569
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.<br /><br />
Reaction-diffusion system,biomedical images,texture analysis
https://jmm.guilan.ac.ir/article_4611.html
https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
9
3
2021
09
01
A computational method based on Legendre wavelets for solving distributed order fractional diffrential equations
501
516
EN
Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
p.rahimkhani@alzahra.ac.ir
Yadollah
Ordokhani
0000-0002-5167-6874
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
ordokhani@alzahra.ac.ir
10.22124/jmm.2021.18634.1596
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
https://jmm.guilan.ac.ir/article_4612.html
https://jmm.guilan.ac.ir/article_4612_bf6961ad233fafc467e3c17050a91f51.pdf