Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
On the rank of the holomorphic solutions of PDE associated to directed graphs
1
9
EN
Hamid
Damadi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
hamid.damadi@aut.ac.ir
Farhad
Rahmati
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
frahmati@aut.ac.ir
10.22060/ajmc.2020.18413.1031
Let G be a directed graph with m vertices and n edges, I(B) the<br />binomial ideal associated to the incidence matrix B of the graph G, and I_L the lattice<br />ideal associated to the columns of the matrix B. Also let B_i be a submatrix of<br />B after removing the ith column. In this paper it is determined that which prime<br />minimal ideals of I(B_i) are Andean or toral. Then we study the rank of the space<br />of solutions of binomial D-module associated to I(B_i) as A-graded ideal, where A is<br />a matrix that, AB_i = 0. Afterwards, we define a maximal cellular cycle and prove<br />that for computing this rank it is enough to consider these components of G. We<br />introduce some bounds for the number of the vertices of the convex hull generated<br />by the columns of the matrix A. Finally an algorthim is introduced by which we can<br />compute the volume of the convex hull corresponded to a cycles with k diagonals, so<br />by Theorem 2.1 the rank of (D / H_A(I(B_i); beta)) can be computed.
Directed graph,Binomial D-module,Lattice basis ideal
https://ajmc.aut.ac.ir/article_4121.html
https://ajmc.aut.ac.ir/article_4121_93e1173b7519f0c5363021779bf5afe9.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
Recognition by degree prime-power graph and order of some characteristically simple group
11
15
EN
Afsane
Bahri
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
afsanebahri@aut.ac.ir
Behrooz
Khosravi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
bkhosravi@aut.ac.ir
Morteza
Baniasad Azad
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
baniasad84@gmail.com
10.22060/ajmc.2020.18418.1033
In this paper, by the order of a group and triviality of $O_p(G)$ for some prime $p$, we give a new characterization for some characteristically simple groups. In fact, we prove that if pϵ{5, 17, 23, 37, 47, 73} and n≤p, where $n$ is a natural number, then $Gcong{{rm PSL}(2,p)}^{n}$ if and only if $ |G|=|{{rm PSL}(2,p)}|^{n}$ and $ O_p(G)=1$.}<br /><br />Recently in [Qin, Yan, Shum and Chen, Comm. Algebra, 2019], the degree prime-power graph of a finite group <br /> have been introduced and it is proved that the Mathieu groups are uniquely determined by their degree prime-power graphs and orders. As a consequence of our results, we show that ${rm PSL}(2,p)^n$, where pϵ{5,17,23,37,47,73} and n≤p are uniquely determined by their degree prime-power graphs and orders.
Degree prime power graph,order,characteristically simple group,Characterization
https://ajmc.aut.ac.ir/article_4122.html
https://ajmc.aut.ac.ir/article_4122_da8bcf27302b7048c4d44272e8b6fb02.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
A class of operator related weighted composition operators between Zygmund space
17
25
EN
Ebrahim
Abbasi
Department of Mathematics&lrm;, &lrm;Mahabad Branch&lrm;, &lrm;Islamic Azad University&lrm;, &lrm;Mahabad&lrm;, &lrm;Iran
ebrahimabbasi81@gmail.com
10.22060/ajmc.2020.18833.1041
Let $mathbb {D}$ be the open unit disk in the complex plane $mathbb{C}$ and $H(mathbb{D})$ be the set of all analytic functions on $mathbb{D}$. Let $u, vin H(mathbb{D})$ and $varphi$ be an analytic self-map of $mathbb{D}$. A class of operator-related weighted composition operators<br />is defined as follow<br />begin{align*}<br />T_{u, v, varphi}f(z) = u(z) f{(varphi(z))}+ v(z) f'(varphi(z)) ,quad fin H(mathbb{D} ), quad zin mathbb{D}.<br />end{align*}<br /><br />In this work, we obtain some new characterizations for boundedness and essential norm of<br /> operator $T_{u, v, varphi}$ between Zygmund space.
boundedness,compactness,essential norm,Zygmund space
https://ajmc.aut.ac.ir/article_4132.html
https://ajmc.aut.ac.ir/article_4132_5f4531b1f76a9ff222c31d2ae30cd504.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
On GDW-Randers metrics on tangent Lie groups
27
36
EN
Mona
Atashafrouz
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
m.atashafrooz@aut.ac.ir
Behzad
Najafi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
behzad.najafi@aut.ac.ir
Akbar
Tayebi
Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran
akbar.tayebi@gmail.com
10.22060/ajmc.2020.18572.1038
Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics.
Left-invariant metric,Douglas metric,Generalized Douglas-Weyl Metrics
https://ajmc.aut.ac.ir/article_4160.html
https://ajmc.aut.ac.ir/article_4160_99ac5fe16a967d7286ca1720956c0a8f.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
Conservation law and Lie symmetry analysis of foam drainage equation
37
44
EN
Mehdi
Nadjafikhah
0000-0002-1354-9786
School of Mathematics, Iran University of Science and Technology
m_nadjafikhah@iust.ac.ir
Omid
Chekini
School of Mathematics, Iran University of Science and Technology
omid_chgini@mathdep.iust.ac.ir
10.22060/ajmc.2020.18460.1036
In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation
Lie group analysis,Conservation law, Optimal system,Foam Drainage equation
https://ajmc.aut.ac.ir/article_4161.html
https://ajmc.aut.ac.ir/article_4161_afc061bca696a62e35f9dcb82217760b.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
An extension of the Cardioid distributions on circle
45
52
EN
Erfan
Salavati
0000-0001-8214-5518
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
erfan.salavati@aut.ac.ir
10.22060/ajmc.2020.18285.1029
A new family of distributions on the circle is introduced which is a generalization of the Cardioid distributions. The elementary properties such as mean, variance, and the characteristic function are computed. The distribution is shown to be either unimodal or bimodal. The modes are computed. The symmetry of the distribution is characterized. The parameters are shown to be canonic (i.e. uniquely determined by the distribution). This implies that the estimation problem is well-defined. We also show that this new family is a subset of distributions whose Fourier series has degree at most 2 and study the implications of this property. Finally, we study the maximum likelihood estimation for this family.
Circular Distributions,Cardioid Distribution,Von Mises Distribution
https://ajmc.aut.ac.ir/article_4209.html
https://ajmc.aut.ac.ir/article_4209_384f506c165ebe2a3d5dda21192cfab2.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
Estimation of the parameter of Levy distribution using ranked set sampling
53
60
EN
Sahar
Dorniani
Department of Statistics, Roudehen
Branch, Islamic Azad University, Tehran, Iran
sdorniani@yahoo.com
Adel
Mohammadpour
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
adelmohammadpour1@gmail.com
Nader
Nematollahi
Department of Statistics, Allameh Tabataba'i
University, Tehran, Iran.
na_nemat@yahoo.com
10.22060/ajmc.2020.18499.1037
Ranked set sampling is a statistical technique for data collection that generally<br />leads to more efficient estimators than competitors based on simple random sampling.<br />In this paper, we consider estimation of scale parameter of Levy distribution<br /> using a ranked set sample. We derive the best linear unbiased estimator<br />and its variance, based on a ranked set sample. Also we compare numerically, variance of this estimator with mean square error of the maximum likelihood, a median based estimator and an estimator based on Laplace transform. It turns out that the best linear unbiased estimator based on ranked set sampling is more efficient than other mentioned estimators.
Best linear unbiased estimator,Levy distribution,Ranked set sampling,Scale parameter
https://ajmc.aut.ac.ir/article_4216.html
https://ajmc.aut.ac.ir/article_4216_661b34a7a906b39e9ebb29c2a6594145.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
Some conformal vector fields and conformal Ricci solitons on N(k)-contact metric manifolds
61
71
EN
Uday
Chand
De
Department of Pure Mathematics, Faculty of Science, University of Calcutta, Kolkata, India
uc_de@yahoo.com
Arpan
Sardar
Department of Mathematics, Faculty of Science, University of Kalyani, West Bengal, India
arpansardar51@gmail.com
Avijit
Sarkar
Department of Mathematics, Faculty of Science, University of Kalyani, West Bengal
avjaj@yahoo.co.in
10.22060/ajmc.2021.19220.1043
Abstract. The target of this paper is to study N(k)-contact metric manifolds<br />with some types of conformal vector fields like φ-holomorphic planar conformal<br />vector fields and Ricci biconformal vector fields. We also characterize N(k)-<br />contact metric manifolds allowing conformal Ricci almost soliton. Obtained results are supported by examples.
N(k)-contact metric manifolds,φ-holomorphic planar conformal vector fields,conformal vector fields and conformal Ricci solitons
https://ajmc.aut.ac.ir/article_4246.html
https://ajmc.aut.ac.ir/article_4246_49abb7a8ca957aa03ddcb0d92035d54f.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
On the reversible geodesics of a Finsler space endowed with a special deformed (α,β)-metric
73
80
EN
Laurian-Ioan
Pişcoran
0000-0003-2269-718X
Department of Mathematics and Computer Science, Victoriei 76, 430122 Baia Mare, Romania
plaurian@yahoo.com
Ali
Akram
0000-0002-6053-3031
Departamento de Matematica-ICE, Universidade Federal de Amazonas-UFAM, 69080-900 Manaus
akramali@ufam.edu.br
Cătălin
Barbu
0000-0002-2094-1938
"Vasile Alecsandri" National College, str. Vasile Alecsandri nr. 37, Bacau, Romania
kafka_mate@yahoo.com
10.22060/ajmc.2021.19522.1048
The scope of this paper is twofold. On the one hand, we will investigate the reversible geodesics of a Finsler space endowed with the deformed newly introduced (α,β)-metric<br /> <br /> begin{equation}<br />F_{ε}(α,β)=frac{β^{2}+α^{2}(a+1)}{α}+εβ<br />end{equation}<br />where ε is a real parameter with |ε|<2√a+1 and ain(¼,∞); and on the other hand, we will investigate the T-tensor for this metric.
Finsler (α,β)-metric,deformation of an (α,β)-metric,T-tensor
https://ajmc.aut.ac.ir/article_4270.html
https://ajmc.aut.ac.ir/article_4270_79017ac55e6d25372a6b270022c5cfae.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
Ensuring software maintainability at software architecture level using architectural patterns
81
102
EN
Mohammad
Tanhaei
Department of Engineering, Ilam University
m.tanhaei@ilam.ac.ir
Zahed
Rahmati
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
zrahmati@aut.ac.ir
10.22060/ajmc.2021.19232.1044
Software architecture is known to be an effective tool with regards to improving software quality attributes. <br />Many quality attributes such as maintainability are architecture dependent, and as such, using an appropriate architecture is essential in providing a sound foundation for the development of highly maintainable software systems. <br />An effective way to produce a well-built architecture is to utilize standard architectural patterns.<br />Although the use of a particular architectural pattern cannot have a preserving effect on software maintainability, the mere conformance of a system to any architecture cannot guarantee the system's high maintainability.<br />The use of an inappropriate architecture can seriously undermine software maintainability at lower levels. <br />In this article, the effect of standard architectural patterns on software maintainability quality attributes is investigated. <br />We develop a quality model for maintainability quality attributes, which is later used to compare various standard architectural patterns.<br />We finish by investigating two real-world experiences regarding the application of a particular pattern to two different existing architectures, exploring the effect of the change in architecture on maintainability quality attributes.
Patterns,Software Architecture,Maintainability
https://ajmc.aut.ac.ir/article_4272.html
https://ajmc.aut.ac.ir/article_4272_ea7523c9c3f0cbd33e998b1518ca6ac7.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
On some aspects of measure and probability logics and a new logical proof for a theorem of Stone
103
108
EN
Alireza
Mofidi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
mofidi@aut.ac.ir
10.22060/ajmc.2021.19318.1045
One of the functions of mathematical logic is studying mathematical objects and notions by logical means. There are several important representation theorems in analysis. Amongst them, there is a well-known classical one which concerns probability algebras. There are quite a few proofs of this result in the literature. This paper pursues two main goals. One is to consider some aspects of measure and probability logics and expose a novel proof for the mentioned representation theorem using ideas from logic and by application of an important result from model theory.<br />The second and even more important goal is to present more connections between two fields of analysis and logic and reveal more the strength of logical methods and tools in analysis. The paper is mostly written for general mathematicians, in particular the people who are active in analysis or logic as the main audience. It is self-contained and includes all prerequisites from logic and analysis.
Integration and probability logics,Representations and measure existence theorems,Compactness in logic
https://ajmc.aut.ac.ir/article_4273.html
https://ajmc.aut.ac.ir/article_4273_b920b2f4d47c144f8ab42c1255b06e16.pdf
Amirkabir University of Technology
AUT Journal of Mathematics and Computing
2
1
2021
02
01
The complexity of cost constrained vehicle scheduling problem
109
115
EN
Malihe
Niksirat
Department of Computer Science, Faculty of Computer and Industrial Engineering, Birjand University of Technology, Birjand, Iran
niksirat@birjandut.ac.ir
Seyed Naser
Hashemi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
nhashemi@aut.ac.ir
10.22060/ajmc.2021.19454.1046
This paper considered the cost constrained vehicle scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a different time processing cost. The goal of this problem is to find a feasible minimum cost schedule for vehicles. A mathematical formulation of the problem is developed and the complexity of the problem when there are more than two depots is investigated. It is proved that in this case, the problem is NP-complete. Also, it is showed that there is not any constant ratio approximation algorithm for the problem, i.e., it is in the complexity class APX.
Vehicle scheduling problem,Fixed job scheduling,NP-complete,Approximation algorithm,APX
https://ajmc.aut.ac.ir/article_4274.html
https://ajmc.aut.ac.ir/article_4274_0c3d0bce2666603bc3ec6491c11a6032.pdf