Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
A meshless numerical investigation based on the RBF-QR approach for elasticity problems
1
15
EN
Mostafa
Abbaszadeh
0000-0001-6954-3896
Department of Mathematics and Computer Science, Amirkabir University of Technology
m.abbaszadeh@aut.ac.ir
Mehdi
Dehghan
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
mdehghan@aut.ac.ir
10.22060/ajmc.2019.15990.1019
In the current research work, we present an improvement of meshless<br />boundary element method (MBEM) based on the shape functions of radial<br />basis functions-QR (RBF-QR) for solving the two-dimensional<br />elasticity problems. The MBEM has benefits of the boundary integral<br />equations (BIEs) to reduce the dimension of problem and the<br />meshless attributes of moving least squares (MLS) approximations.<br />Since the MLS shape functions don't have the delta<br />function property, applying boundary conditions is not simple. Here, we<br />propose the MBEM using RBF-QR to increase the accuracy and<br />efficiency of MBEM. To show the performance of the new technique,<br />the two-dimensional elasticity problems have been selected. We solve<br />the mentioned model on several irregular domains and report simulation results.
Boundary element method,RBF-QR approach,Two-dimensional elasticity problems,Meshless Method
https://ajmc.aut.ac.ir/article_3379.html
https://ajmc.aut.ac.ir/article_3379_ffbd2283d5745c4b85031e1eaf021000.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
The bimodal standard normal density and kurtosis
17
25
EN
Javad
Behboodian
Department of Statistics, School of Science, Shiraz University, Shiraz
behboodian@shirazu.ac.ir
Maryam
Sharafi
Department of Statistics, School of Science, Shiraz University, Shiraz
msharafi@shirazu.ac.ir
Zahra
Sajjadnia
Department of Statistics, School of Science, Shiraz University, Shiraz
sajjadnia@shirazu.ac.ir
Mazyar
Zarepour
Department of Mathematics, Islamic Azad University, Shiraz Branch, Shiraz, Iran.
mazyar_z@hotmail.com
10.22060/ajmc.2018.3040
In this article, first a density by the name "The bimodal standard normal density" is introduced and denoted by bΦ(z). Then, a dention for the kurtosis of bimodal densities relative to bΦ(z) is presented. Finally, to illustrate the introduced kurtosis, a few examples<br />are provided and a real data set is studied,too.
normal density,mixed normal density,bimodal standard normal density,kurtosis of a bimodal density
https://ajmc.aut.ac.ir/article_3040.html
https://ajmc.aut.ac.ir/article_3040_cba0b169b1d9096e97113d867cacd623.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
(α,β)-Metrics with killing β of constant length
27
36
EN
Tayebeh
Tabatabaeifar
Amirkabir university
t.tabaee@gmail.com
Behzad
Najafi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
behzad.najafi@aut.ac.ir
10.22060/ajmc.2018.3038
The class of (α,β)-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study (α,β)-metrics with Killing of constant length 1-form β and find a simplified formula for their Ricci curvatures. Then, we<br />show that if F=α+β+bfrac{β^2}{α} is an Einstein Finsler metric, then α is an Einstein Riemann metric.
Finsler metric,(α,β)-metric,Einstein manifold
https://ajmc.aut.ac.ir/article_3038.html
https://ajmc.aut.ac.ir/article_3038_ec3b89402c7338eacb774d68fb1a1cb0.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
On Sobolev spaces and density theorems on Finsler manifolds
37
45
EN
Behrooz
Bidabad
0000-0003-3993-4268
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
bidabad@aut.ac.ir
Alireza
Shahi
Faculty of Mathematics and computer science, Amirkabir University of Technology
alirezashahi@aut.ac.ir
10.22060/ajmc.2018.3039
Here, a natural extension of Sobolev spaces is defined for a Finsler structure $F$ and it is shown that the set of all real $C^{∞}$ functions with compact support on a forward geodesically complete Finsler manifold $(M, F)$, is dense in the extended Sobolev space $H_1^p (M)$.<br />As a consequence, the weak solutions $u$ of the Dirichlet equation $Δu=f$ can be approximated by $C^∞$ functions with compact support on $M$.<br />Moreover, let $W subset M$ be a regular domain with the $C^r$ boundary $partial W$, then the set of all real functions in $C^r (W) cap C^0 (overline W)$ is dense in $H_k^p (W)$, where $k≤r$. Finally, several examples are illustrated and sharpness of the inequality $k≤r$ is shown.
Density theorem,Sobolev spaces,Dirichlet problem,Finsler space
https://ajmc.aut.ac.ir/article_3039.html
https://ajmc.aut.ac.ir/article_3039_ef823186580a9c859620d42c8543c999.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
A simple greedy approximation algorithm for the unit disk cover problem
47
55
EN
Mahdi
Imanparast
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
m.imanparast@aut.ac.ir
Seyed Naser
Hashemi
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
nhashemi@aut.ac.ir
10.22060/ajmc.2018.3044
Given a set P of n points in the plane, the unit disk cover problem, which is known as an NP-hard problem, seeks to find the minimum number of unit disks that can cover all points of P. In this paper, we present a new 4-approximation algorithm with running time O(n log n) for this problem. Our proposed algorithm uses a simple greedy approach and is easy to understand and implement.
computational geometry,approximation algorithms,unit disk cover problem,facility location
https://ajmc.aut.ac.ir/article_3044.html
https://ajmc.aut.ac.ir/article_3044_69fd7125903ed84f45ff4a2b2a419779.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
The complementary odd Weibull power series distribution: properties and applications
57
67
EN
Mehdi
Goldoust
Department of Mathematics, Behbahan Branch, Islamic Azad University, Behbahan, Iran
mehdigoldust@yahoo.com
10.22060/ajmc.2019.15207.1015
In this paper, a new four-parameters model called the complementary odd Weibull power<br />series (COWPS) distribution is defined and its properties are explored. This new distribution exhibits several new and well-known hazard rate shapes such as increasing, decreasing,<br />bathtub-shaped and J-shape hazard rate. Some of its mathematical properties are obtained<br />including moments, quantiles reliability, and moment generating functions. Maximum likelihood estimation method is used to estimate the vector of parameters. A simulation study<br />is presented to investigate the performance of the estimators. Finally, The usefulness of the<br />model has been demonstrated by applying it to a real-life dataset.
Compound distribution,Maximum Likelihood Estimation,Power series distribution,Odd Weibull distribution
https://ajmc.aut.ac.ir/article_3722.html
https://ajmc.aut.ac.ir/article_3722_1be02552deb40e99ef41e3344ca6aa8e.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
A generalization of Marshall-Olkin bivariate Pareto model and its applications in shock and competing risk models
69
87
EN
Shirin
Shoaee
Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.
shirin_shoaee@aut.ac.ir
Esmaeil
Khorram
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
eskhor@aut.ac.ir
10.22060/ajmc.2018.14869.1012
Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by compounding the Pareto Type II and geometric distributions. This new bivariate distribution has natural interpretations and can be applied in fatal shock models or in competing risks models. We call the new proposed model Marshall-Olkin bivariate Pareto-geometric (MOBPG) distribution, and then investigate various properties of the new distribution. This model has five unknown parameters and the maximum likelihood estimators cannot be afforded in explicit structure. We suggest to use the EM algorithm to calculate the maximum likelihood estimators of the unknown parameters, and this structure is quite flexible.<br /> Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes.
Bivariate model,Competing risk model,Expectation-Maximization algorithm,Pareto Type II distribution,Shock model
https://ajmc.aut.ac.ir/article_3125.html
https://ajmc.aut.ac.ir/article_3125_8385d20bf3dcd48513f53a4a97c11981.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
The validity of a Thompson's problem for PSL(4,7)
89
94
EN
Behrooz
Khosravi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
bkhosravi@aut.ac.ir
Cyrus
Kalantarpour
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
siruspoly@gmail.com
10.22060/ajmc.2019.16174.1022
Let $pi_e(G)$ be the set of elements orders of $ G$. Also let $ s_n$ be the number of elements of order $n$ in $G $ and ${rm nse}(G)= lbrace s_nmid nin pi_e(G) rbrace $.<br />In this paper we prove that if $ G$ is a group such that ${rm nse}(G)= {rm nse}(rm PSL(4,7)) $, $19bigvert|G|$ and $19^2nmid|G|$, then $ Gcong rm PSL(4,7)$. As a consequence of this result it follows that Thompson's problem is satisfied for the simple group $rm PSL(4,7)$.
Thompson's problem,Characterization,Number of elements of same order,Projective special linear group
https://ajmc.aut.ac.ir/article_3746.html
https://ajmc.aut.ac.ir/article_3746_c15795a34e3e77400bdbc8563d65144d.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
A real-time decision support system for bridge management based on the rules generalized by CART decision tree and SMO algorithms
95
100
EN
Shadi
Abpeykar
Department of Computer Science
shadi.a@aut.ac.ir
Mehdi
Ghatee
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
ghatee@aut.ac.ir
10.22060/ajmc.2018.3043
Under dynamic conditions on bridges, we need a real-time management. To this end, this paper presents a rule-based decision support system in which the necessary rules are extracted from simulation results made by Aimsun traffic micro-simulation software. Then, these rules are generalized by the aid of fuzzy rule generation algorithms. Then, they are trained by a set of supervised and the unsupervised learning algorithms to get an ability to make decision in real cases. As a pilot case study, Nasr Bridge in Tehran is simulated in Aimsun and WEKA data mining software is used to execute the learning algorithms. Based on this experiment, the accuracy of the supervised algorithms to generalize the rules is greater than 80%. In addition, CART decision tree and sequential minimal optimization (SMO) provides 100% accuracy for normal data and these algorithms are so reliable for crisis management on bridge. This means that, it is possible to use such machine learning methods to manage bridges in the real-time conditions.
Intelligent Transportation Systems,Knowledge Extraction,Learning Algorithms,Traffic Simulators,Fuzzy Rule Generation Algorithm
https://ajmc.aut.ac.ir/article_3043.html
https://ajmc.aut.ac.ir/article_3043_5969ea2b069b3fd8d1e298c8a6383f87.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
Statistical and fuzzy clustering methods and their application to clustering Pprovinces of Iraq based on agricultural products
101
112
EN
Seyed Mahmoud
Taheri
School of Engineering Science, College of Engineering, University of Tehran
sm_taheri@ut.ac.ir
Israa
Atiyah
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran
israa.zad@aut.ac.ir
10.22060/ajmc.2019.14873.1013
The important approaches to statistical and fuzzy clustering are reviewed and compared, and their applications to an agricultural problem based on a real-world data are investigated. The methods employed in this study includes some hierarchical clustering and non-hierarchical clustering methods and fuzzy c-means method. As a case study, these methods are then applied to cluster 15 provinces of Iraq based on some agricultural crops. Finally, a comparative and evaluation study of different statistical and fuzzy clustering methods is performed. The obtained results showed that, based on the Silhouette criterion and Xie-Beni index, fuzzy c-means method is the best one among all reviewed methods.
Hierarchical Clustering,Non-Hierarchical Clustering,Fuzzy C-Means Clustering
https://ajmc.aut.ac.ir/article_3245.html
https://ajmc.aut.ac.ir/article_3245_a255154ebe44780b879781a7e0ee6123.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
Smartphone-based system for driver anger scale estimation using neural network on continuous wavelet transformation
113
124
EN
Hamid Reza
Eftekhari
Department of Computer engineering, Faculty of Engineering, Malayer University, Hamedan, Iran
eftekhari@malayeru.ac.ir
10.22060/ajmc.2019.15327.1016
Monitoring of the driver decreases accidents by reducing the risky behaviors and causes decreases the fuel consumption by preventing aggressive behavior. But this monitoring is costly due to built-in equipment. In this study, we propose a new model to recognize driving behavior by smartphone data without any extra equipment in the vehicles which is an important added value for smartphones. This recognition process is done in this paper based on the continuous wavelet transformation on accelerometer data. Then these patterns are fed to multilayer perceptron neural network to extend the information extracted from the corresponding features. Also the magnetometer sensor is used to detect the maneuvers through the driving period. Results show the accuracy of the proposed system is near 80% for pattern recognition. Driver scale based on a standard questionnaires regarding to driver angry scale (DAS), is also estimated by the proposed multilayer perceptron neural network with 3.7% errors in the average.
Risky behavior,Driver monitoring,smartphone,Wavelet transformation,Multilayer perceptron neural network
https://ajmc.aut.ac.ir/article_3287.html
https://ajmc.aut.ac.ir/article_3287_964f797962c44f02c009a4313255f902.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
1
1
2020
02
01
Adopting GRASP to solve a novel model for bus timetabling problem with minimum transfer and fruitless waiting times
125
134
EN
Javad
Zamani Kafshani
Amirkabir University of Technology
j.zamani@aut.ac.ir
Seyyed Ali
Mirhassani
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
a_mirhassani@aut.ac.ir
Farnaz
Hooshmand
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
f.hooshmand.khaligh@aut.ac.ir
10.22060/ajmc.2019.15497.1018
This paper addresses a variant of bus timetabling problem assuming that travel times changes dynamically over the planning horizon. In addition to minimizing the transfer waiting time, another objective, namely minimizing the fruitless waiting time, is introduced in this paper as a new realistic objective. First, the problem is formulated as a mixed integer linear programming model. Then, since commercial solvers become inefficient to solve moderate and large sized instances of the problem (due to the NP-hardness), a GRASP heuristic algorithm is developed. Computational experiments over a variety of random instances verify the performance of the proposed method.
Bus timetabling,Dynamic travel time,Transfer waiting time,Fruitless waiting time,GRASP
https://ajmc.aut.ac.ir/article_3323.html
https://ajmc.aut.ac.ir/article_3323_85cc256ebddca4a51b227d38698683da.pdf