ORIGINAL_ARTICLE
Fractal Kronig-Penney model involving fractal comb potential
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.
https://jmm.guilan.ac.ir/article_4458_15331da4037abc304165404ab7d73669.pdf
2021-09-01
331
345
10.22124/jmm.2020.17537.1510
Fractal calculus
fractal Schrodinger equation
local fractal derivative
fractal lattice
Alireza
Khalili Golmankhaneh
alirezakhalili2002@yahoo.co.in
1
Department of Physics, Urmia Branch Islamic Azad University, Urmia, PO Box 969, Iran
LEAD_AUTHOR
Karmina
Kamal Ali
karmina.ali@uoz.edu.krd
2
Department of Mathematics, Faculty of Science, University of Zakho, Iraq
AUTHOR
ORIGINAL_ARTICLE
A block preconditioner for the Gl-LSMR algorithm
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.
https://jmm.guilan.ac.ir/article_4459_3e9cac74e5523bd0855201c4b20cd5c4.pdf
2021-09-01
347
359
10.22124/jmm.2020.17687.1525
LSMR method
Gl-LSMR method
preconditioner
block partitioned matrices
multiple right-hand sides
Afsaneh
Hasanpour
hasanpour@pgs.usb.ac.ir
1
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
AUTHOR
Maryam
Mojarrab
ma_mojarrab@math.usb.ac.ir
2
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Recent advances in the numerical solution of Volterra integral equations
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.
https://jmm.guilan.ac.ir/article_4461_522a9497c7ab9968792f8dd1d29f9d37.pdf
2021-09-01
361
373
10.22124/jmm.2020.17997.1554
Volterra integral equations
general linear methods
natural Volterra Runge--Kutta methods
Nordsieck technique
implementation issues
Ali
Abdi
a_abdi@tabrizu.ac.ir
1
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
An efficient conjugate gradient method with strong convergence properties for non-smooth optimization
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.
https://jmm.guilan.ac.ir/article_4471_6cf479f380e06f0783bdb615ea168c1e.pdf
2021-09-01
375
390
10.22124/jmm.2020.16747.1452
Conjugate gradient method
nonsmooth optimization
Global convergence
Image Processing
Fahimeh
Abdollahi
fabdollahi@email.kntu.ac.ir
1
Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
AUTHOR
Masoud
Fatemi
smfatemi@kntu.ac.ir
2
Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Theory and application of the power Ailamujia distribution
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.
https://jmm.guilan.ac.ir/article_4513_c22d7a760f28d0ce008d9af3c31fec70.pdf
2021-09-01
391
413
10.22124/jmm.2020.17547.1512
Ailamujia distribution
power distribution
moments
stress-strength parameter
entropy
data analysis
Covid-19 pandemic
Farrukh
Jamal
drfarrukh1982@gmail.com
1
Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab, Pakistan
AUTHOR
Christophe
Chesneau
christophe.chesneau@gmail.com
2
Universite' de Caen Normandie, LMNO, Campus II, Science 3, Caen, France
LEAD_AUTHOR
Khaoula
Aidi
khaoula.aidi@yahoo.fr
3
Laboratory of probability and statistics LaPS, University Badji Mokhtar-Annaba, Algeria
AUTHOR
Aqib
Ali
aqibcsit@gmail.com
4
Department of Computer Science and IT, GLIM institute of modern studies Bahawalpur, Bahawalpur, Punjab, Pakistan
AUTHOR
ORIGINAL_ARTICLE
Correctness of the free boundary problem for the microscopic in-situ leaching model
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.
https://jmm.guilan.ac.ir/article_4549_846531f1451f137cc3acfbba1d8bd47f.pdf
2021-09-01
415
423
10.22124/jmm.2021.18402.1581
mathematical models
free boundary problems
diffusion-convection
Anvarbek
Meirmanov
anvarbek47@list.ru
1
National Research University ``Higher School of Economics'', Moscow, Russia
AUTHOR
Oleg
Galtsev
oleg_galtsev@mail.ru
2
National Research University ``Belgorod State University'', Belgorod, Russia
LEAD_AUTHOR
Vladimir
Seldemirov
utherfjord@gmail.com
3
National Research University ``Higher School of Economics'', Moscow, Russia
AUTHOR
ORIGINAL_ARTICLE
$d-$Fibonacci and $d-$Lucas polynomials
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.
https://jmm.guilan.ac.ir/article_4581_d5a4d10c1688c9b12ffff9830972967e.pdf
2021-09-01
425
436
10.22124/jmm.2021.17837.1538
$d-$Fibonacci polynomials
$d-$Lucas polynomials
Riordan arrays
Pascal matrix
$Q_{d}-$Fibonacci matrix
Boualem
Sadaoui
sadaouiboualem@gmail.com
1
LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana, 44225 Algeria
AUTHOR
Ali
Krelifa
a.kerlifa@univ-dbkm.dz
2
LESI Laboratory, Faculty of Sciences and Technology, University of Khemis Miliana, Road of Theniet El-Had, Khemis Miliana 44225, Algeria
LEAD_AUTHOR
ORIGINAL_ARTICLE
An intrusion detection system with a parallel multi-layer neural network
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.
https://jmm.guilan.ac.ir/article_4608_6c422be00fed7b4135a706109a9f4fc8.pdf
2021-09-01
437
450
10.22124/jmm.2021.17362.1502
Intrusion detection
computer security
Neural Network
parallel processing
Mohammad
Hassan Nataj Solhdar
nataj.solhdar@gmail.com
1
Shohadaye Hoveizeh University of Technology, Dasht-e Azadegan, Khuzestan, Iran
AUTHOR
Mehdi
Janinasab Solahdar
mehdi_janinasab@yahoo.com
2
Islamic Azad University, Mahalat Branch, Mahalat, Iran
AUTHOR
Sadegh
Eskandari
eskandari@guilan.ac.ir
3
Department of Computer Science, University of Guilan, Rasht, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Mixed fractional differential equation with nonlocal conditions in Banach spaces
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.
https://jmm.guilan.ac.ir/article_4609_d62226793e9621e109382e4761d71a46.pdf
2021-09-01
451
463
10.22124/jmm.2021.18439.1582
Right Caputo and left Riemann--Liouville fractional derivatives
nonlocal boundary conditions
existence
Banach spaces
Darbo's fixed point theorem
Hausdorff measure of noncompactness
Abdellatif
Boutiara
boutiara_a@yahoo.com
1
Laboratory of Mathematics And Applied Sciences University of Ghardaia, 47000. Algeria
LEAD_AUTHOR
ORIGINAL_ARTICLE
A linear theory of beams with deformable cross section
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.
https://jmm.guilan.ac.ir/article_4610_ccea1e91531138ea5fc7c8e36239c13d.pdf
2021-09-01
465
483
10.22124/jmm.2021.17932.1548
Theory of beams
deformation of cross section
material anisotropy
Luca
Sabatini
luca.sabatini@sbai.uniroma1.it
1
Dip. S.B.A.I., University of Rome "La Sapienza", Via Antonio Scarpa 14, 00100 Roma, Italy
LEAD_AUTHOR
ORIGINAL_ARTICLE
A computational model for texture analysis in images with a reaction-diffusion based filter
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.
https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdf
2021-09-01
485
500
10.22124/jmm.2021.18289.1569
Reaction-diffusion system
biomedical images
texture analysis
Hamid
Lefraich
lefraichhamid@gmail.com
1
Laboratory (MISI), Faculty of Science and Technology, University Hassan first, Settat 26000, Morocco
AUTHOR
Houda
Fahim
houda.fahim@edu.uca.ma
2
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
AUTHOR
Mariam
Zirhem
mariam.zirhem@gmail.com
3
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
AUTHOR
Nour Eddine
Alaa
n.alaa@uca.ac.ma
4
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Morocco
LEAD_AUTHOR
ORIGINAL_ARTICLE
A computational method based on Legendre wavelets for solving distributed order fractional diffrential equations
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.
https://jmm.guilan.ac.ir/article_4612_bf6961ad233fafc467e3c17050a91f51.pdf
2021-09-01
501
516
10.22124/jmm.2021.18634.1596
Legendre wavelets
distributed order fractional diffrential equations
numerical method
operational matrix
Parisa
Rahimkhani
p.rahimkhani@alzahra.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
AUTHOR
Yadollah
Ordokhani
ordokhani@alzahra.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
LEAD_AUTHOR