2021-09-19T03:34:57Z
https://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=756
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
Fractal Kronig-Penney model involving fractal comb potential
Alireza
Khalili Golmankhaneh
Karmina
Kamal Ali
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
2021
09
01
331
345
https://jmm.guilan.ac.ir/article_4458_15331da4037abc304165404ab7d73669.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
A block preconditioner for the Gl-LSMR algorithm
Afsaneh
Hasanpour
Maryam
Mojarrab
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
2021
09
01
347
359
https://jmm.guilan.ac.ir/article_4459_3e9cac74e5523bd0855201c4b20cd5c4.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
Recent advances in the numerical solution of Volterra integral equations
Ali
Abdi
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
2021
09
01
361
373
https://jmm.guilan.ac.ir/article_4461_522a9497c7ab9968792f8dd1d29f9d37.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
An efficient conjugate gradient method with strong convergence properties for non-smooth optimization
Fahimeh
Abdollahi
Masoud
Fatemi
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
2021
09
01
375
390
https://jmm.guilan.ac.ir/article_4471_6cf479f380e06f0783bdb615ea168c1e.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
Theory and application of the power Ailamujia distribution
Farrukh
Jamal
Christophe
Chesneau
Khaoula
Aidi
Aqib
Ali
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
2021
09
01
391
413
https://jmm.guilan.ac.ir/article_4513_c22d7a760f28d0ce008d9af3c31fec70.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
Correctness of the free boundary problem for the microscopic in-situ leaching model
Anvarbek
Meirmanov
Oleg
Galtsev
Vladimir
Seldemirov
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
2021
09
01
415
423
https://jmm.guilan.ac.ir/article_4549_846531f1451f137cc3acfbba1d8bd47f.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
$d-$Fibonacci and $d-$Lucas polynomials
Boualem
Sadaoui
Ali
Krelifa
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
2021
09
01
425
436
https://jmm.guilan.ac.ir/article_4581_d5a4d10c1688c9b12ffff9830972967e.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
An intrusion detection system with a parallel multi-layer neural network
Mohammad
Hassan Nataj Solhdar
Mehdi
Janinasab Solahdar
Sadegh
Eskandari
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
2021
09
01
437
450
https://jmm.guilan.ac.ir/article_4608_6c422be00fed7b4135a706109a9f4fc8.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
Mixed fractional differential equation with nonlocal conditions in Banach spaces
Abdellatif
Boutiara
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
2021
09
01
451
463
https://jmm.guilan.ac.ir/article_4609_d62226793e9621e109382e4761d71a46.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
A linear theory of beams with deformable cross section
Luca
Sabatini
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
2021
09
01
465
483
https://jmm.guilan.ac.ir/article_4610_ccea1e91531138ea5fc7c8e36239c13d.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
A computational model for texture analysis in images with a reaction-diffusion based filter
Hamid
Lefraich
Houda
Fahim
Mariam
Zirhem
Nour Eddine
Alaa
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
2021
09
01
485
500
https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdf
Journal of Mathematical Modeling
J. Math. Model.
2345-394X
2345-394X
2021
9
3
A computational method based on Legendre wavelets for solving distributed order fractional diffrential equations
Parisa
Rahimkhani
Yadollah
Ordokhani
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
2021
09
01
501
516
https://jmm.guilan.ac.ir/article_4612_bf6961ad233fafc467e3c17050a91f51.pdf