2020
1
2
0
136
1

Roadside acoustic sensors to support vulnerable pedestrians via their smartphones
https://ajmc.aut.ac.ir/article_3312.html
10.22060/ajmc.2019.15479.1017
1
This paper proposes a smartphonebased warning system to evaluate the risk of a motor vehicle for vulnerable pedestrians (VP). The acoustic sensors are embedded in the roadside to receive vehicle sounds and they are classified into heavy vehicles, light vehicles with low speed, light vehicles with high speed, and no vehicle classes. For this aim, we extract new features by Melfrequency Cepstrum Coefficients (MFCC) and Linear Predictive Coefficients (LPC) algorithms. We use different classification algorithms and show that MLP neural network achieves at least 96.77% accuracy criterion. To install this system, directional microphones are embedded on the roadside and the risk is classified. Then, for every microphone, a danger area is defined and the warning alarms have been sent to every VPs’ smartphones covered in this danger area.
0

135
143


Mehdi
Ghatee
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Iran
ghatee@aut.ac.ir


Masoomeh
Khalili
Department of Computer Science, Amirkabir University of Technology, Tehran, Iran
Iran
mkhalili1228@yahoo.com


Mehdi
Teimouri
Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran
Iran
mehditeimouri@ut.ac.ir


Mohammad Mahdi
Bejani
Department of Computer Science, Amirkabir University of Technology, Tehran, Iran.
Iran
mbejani@aut.ac.ir
Intelligent Transportation Systems
Acoustic signal analysis
smartphone
Road traffic sensors
Road Safety
Risk analysis
Vulnerable pedestrians
[[1] R. SanSegundo, J. M. Montero, R. BarraChicote, F. Fern´andez, J. M. Pardo, Feature extraction from smartphone inertial signals for human activity segmentation, Signal Processing 120 (2016) 359–372.##[2] H. R. Eftekhari, M. Ghatee, An inference engine for smartphones to preprocess data and detect stationary and transportation modes, Transportation Research Part C: Emerging Technologies 69 (2016) 313–327.##[3] R. B. Zadeh, M. Ghatee, H. R. Eftekhari, Threephases smartphonebased warning system to protect vulnerable road users under fuzzy conditions, IEEE Transactions on Intelligent Transportation Systems 19 (7) (2017) 2086–2098.##[4] M. M. Bejani, M. Ghatee, A context aware system for driving style evaluation by an ensemble learning on smartphone sensors data, Transportation Research Part C: Emerging Technologies 89 (2018) 303–320.##[5] H. R. Eftekhari, M. Ghatee, Hybrid of discrete wavelet transform and adaptive neuro fuzzy inference system for overall driving behavior recognition, Transportation research part F: traffic psychology and behaviour 58 (2018) 782–796.##[6] H. R. Eftekhari, M. Ghatee, A similaritybased neurofuzzy modeling for driving behavior recognition applying fusion of smartphone sensors, Journal of Intelligent Transportation Systems 23 (1) (2019) 72–83.##[7] M. M. Bejani, M. Ghatee, Convolutional neural network with adaptive regularization to classify driving styles on smartphones, IEEE Transactions on Intelligent Transportation Systems 21 (2) (2019) 543–552.##[8] N. Desai, K. Dhameliya, V. Desai, Feature extraction and classification techniques for speech recognition: A review, International Journal of Emerging Technology and Advanced Engineering 3 (12) (2013) 367–371.##[9] J. A. G´omezTejedor, J. C. CastroPalacio, J. A. Monsoriu, The acoustic doppler effect applied to the study of linear motions, European Journal of Physics 35 (2) (2014) 025006.##[10] J. Gajda, R. Sroka, M. Stencel, A. Wajda, T. Zeglen, A vehicle classification based on inductive loop detectors, in: IMTC 2001. Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference. Rediscovering Measurement in the Age of Informatics (Cat. No. 01CH 37188), Vol. 1, IEEE, 2001, pp. 460– 464.##[11] J. George, A. Cyril, B. I. Koshy, L. Mary, Exploring sound signature for vehicle detection and classification using ann, International Journal on Soft Computing 4 (2) (2013) 29.##[12] G. Padmavathi, D. Shanmugapriya, M. Kalaivani, et al., A study on vehicle detection and tracking using wireless sensor networks, Wireless Sensor Network 2 (02) (2010) 173.##[13] A. Y. Nooralahiyan, M. Dougherty, D. McKeown, H. R. Kirby, A field trial of acoustic signature analysis for vehicle classification, Transportation Research Part C: Emerging Technologies 5 (34) (1997) 165–177.##[14] A. Averbuch, E. Hulata, V. Zheludev, I. Kozlov, A wavelet packet algorithm for classification and detection of moving vehicles, Multidimensional Systems and Signal Processing 12 (1) (2001) 9–31.##[15] M. V. Ghiurcau, C. Rusu, Vehicle sound classification. application and low pass filtering influence, in: 2009 International Symposium on Signals, Circuits and Systems, IEEE, 2009, pp. 1–4.##[16] A. Dalir, A. A. Beheshti, M. H. Masoom, Classification of vehicles based on audio signals using quadratic discriminant analysis and high energy feature vectors, arXiv preprint arXiv:1804.01212.##[17] M. P. Paulraj, A. H. Adom, S. Sundararaj, N. B. A. Rahim, Moving vehicle recognition and classification based on time domain approach, Procedia Engineering 53 (2013) 405–410.##[18] J. Lee, A. Rakotonirainy, Acoustic hazard detection for pedestrians with obscured hearing, IEEE Transactions on Intelligent Transportation Systems 12 (4) (2011) 1640–1649.##[19] N. Lubbe, E. Ros´en, Pedestrian crossing situations: Quantification of comfort boundaries to guide intervention timing, Accident Analysis & Prevention 71 (2014) 261–266.##[20] X. Jiang, W. Wang, K. Bengler, Intercultural analyses of timetocollision in vehicle–pedestrian conflict on an urban midblock crosswalk, Ieee transactions on intelligent transportation systems 16 (2) (2014) 1048–1053.##[21] E. L. Salomons, P. J. Havinga, A survey on the feasibility of sound classification on wireless sensor nodes, Sensors 15 (4) (2015) 7462–7498.##[22] J. Scholliers, D. Bell, A. Morris, A. B. Garc´ıa Mel´endez, O. M. Perez, Improving safety and mobility of vulnerable road users through its applications, Traffic Safety 4 (2016) 251–269.##[23] T. Williams, P. Alves, G. Lachapelle, C. Basnayake, Evaluation of gpsbased methods of relative positioning for automotive safety applications, Transportation research part C: emerging technologies 23 (2012) 98–108.##[24] G. Korres, A. El Issawi, M. Eid, Tactile glasses (tag) for obstacle avoidance, in: International Conference on Universal Access in HumanComputer Interaction, Springer, 2014, pp. 741–749.##[25] T. Schwarze, M. Lauer, M. Schwaab, M. Romanovas, S. B¨ohm, T. J¨urgensohn, A camerabased mobility aid for visually impaired people, KIK¨unstliche Intelligenz 30 (1) (2016) 29–36.##[26] D. Ni, A. Song, L. Tian, X. Xu, D. Chen, A walking assistant robotic system for the visually impaired based on computer vision and tactile perception, International Journal of Social Robotics 7 (5) (2015) 617–628.##[27] M. Bagheri, M. Siekkinen, J. K. Nurminen, Cellularbased vehicle to pedestrian (v2p) adaptive communication for collision avoidance, in: 2014 international conference on connected vehicles and expo (ICCVE), IEEE, 2014, pp. 450–456.##[28] L. Zhenyu, P. Lin, Z. Konglin, Z. Lin, Design and evaluation of v2x communication system for vehicle and pedestrian safety, The Journal of China Universities of Posts and Telecommunications 22 (6) (2015) 18–26.##[29] N. A. Rahim, M. Paulraj, A. Adom, Adaptive boosting with svm classifier for moving vehicle classification, Procedia Engineering 53 (2013) 411–419.##[30] J. Berdnikova, T. Ruuben, V. Kozevnikov, S. Astapov, Acoustic noise pattern detection and identification method in doppler system, Elektronika ir Elektrotechnika 18 (8) (2012) 65–68.##]
1

Approximation algorithms for multimultiway cut and multicut problems on directed graphs
https://ajmc.aut.ac.ir/article_3810.html
10.22060/ajmc.2018.15109.1014
1
In this paper, we study the directed multicut and directed multimultiway cut problems. The input to the directed multimultiway cut problem is a weighted directed graph G = (V, E) and k sets S1, S2, ..., Sk of vertices. The goal is to find a subset of edges of minimum total weight whose removal will disconnect all the connections between the vertices in each set Si , for 1 ≤ i ≤ k. A special case of this problem is the directed multicut problem whose input consists of a weighted directed graph G = (V, E) and a set of ordered pairs of vertices (s1, t1), ...,(sk, tk). The goal is to find a subset of edges of minimum total weight whose removal will make for any i, 1 ≤ i ≤ k, there is no directed path from si to ti . In this paper, we present two approximation algorithms for these problems. The so called region growing paradigm is modified and used for these two cut problems on directed graphs. using this paradigm, we give an approximation algorithm for each problem such that both algorithms have the approximation factor of O(k) the same as the previous works done on these problems. However, the previous works need to solve k linear programming, whereas our algorithms require only one linear programming. Therefore, our algorithms improve the running time of the previous algorithms.
0

145
152


Ramin
Yarinezhad
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Iran
yarinezhad@aut.ac.ir


Seyed Naser
Hashemi
Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Iran
nhashemi@aut.ac.ir
Approximation algorithm
Complexity
NPhard problems
Directed multimultiway cut
Directed multicut cut
[[1] E. Dahlhaus, D. S. Johnson, C. H. Papadimitriou, P. D. Seymour, M. Yannakakis, The complexity of multiway cuts, In Proceedings of the twentyfourth annual ACM symposium on Theory of computing, (1992) 241251.##[2] G. C˘alinescu, H. Karloff, Y. Rabani, An improved approximation algorithm for multiway cut, In Proceedings of the thirtieth annual ACM symposium on Theory of computing, (1998) pages 4852.##[3] D. R. Karger, P. Klein, C. Stein, M. Thorup, N. E. Young, Rounding algorithms for a geometric embedding of minimum multiway cut, Mathematics of Operations Research, 29(3) (2004) 436461.##[4] N. Garg, V. V. Vazirani, M. Yannakakis, Multiway cuts in directed and node weighted graphs, In International Colloquium on Automata, Languages, and Programming, 487498, Springer, 1994.##[5] J. Naor, L. Zosin, A 2approximation algorithm for the directed multiway cut problem, SIAM Journal on Computing, 31(2) (2001) 477482.##[6] N. Garg, V. V. Vazirani, M. Yannakakis, Approximate maxflow min(multi) cut theorems and their applications, SIAM Journal on Computing, 25(2) (1996) 235251.##[7] J. Chuzhoy, Y. Makarychev, A. Vijayaraghavan, Y. Zhou, Approximation algorithms and hardness of the kroute cut problem, ACM Transactions on Algorithms (TALG), 12(1) (2015) 140.##[8] J. BangJensen, A. Yeo, The complexity of multicut and mixed multicut problems in (di) graphs, Theoretical Computer Science, 520 (2014) 8796.##[9] G. Even, J. S. Naor, S. Rao, B. Schieber, Divideandconquer approximation algorithms via spreading metrics, Journal of the ACM (JACM), 47(4) (2000) 585616.##[10] T. Leighton, S. Rao, An approximate maxflow mincut theorem for uniform multicommodity flow problems with applications to approximation algorithms, Technical report, MASSACHUSETTS INST OF TECH CAMBRIDGE MICROSYSTEMS RESEARCH CENTER, 1989.##[11] G. Even, J. S. Naor, B. Schieber, M. Sudan, Approximating minimum feedback sets and multicuts in directed graphs, Algorithmica, 20(2) (198) 151174.##[12] P. N. Klein, S. A. Plotkin, S. Rao, E. Tardos, Approximation algorithms for steiner and directed multicuts, Journal of Algorithms, 22(2) (1997) 241269.##[13] J. Cheriyan, H. Karloff, Y. Rabani, Approximating directed multicuts, Combinatorica, 25(3) (2005) 251269.##[14] A. Agarwal, N. Alon, M. S. Charikar, Improved approximation for directed cut problems, In Proceedings of the thirtyninth annual ACM symposium on Theory of computing, (2007) 671680.##[15] M. Saks, A. Samorodnitsky, L. Zosin, A lower bound on the integrality gap for minimum multicut in directed networks, Combinatorica, 24(3) (2004) 525530.##[16] A. Avidor, M. Langberg, The multimultiway cut problem, Theoretical Computer Science, 377(13) (2007) 3542.##[17] I. Kanj, G. Lin, T. Liu, W. Tong, G. Xia, J. Xu, B. Yang, F. Zhang, P. Zhang, B. Zhu, Improved parameterized and exact algorithms for cut problems on trees, Theoretical Computer Science, 607 (2015) 455470.##[18] P. Zhang, D. Zhu, J. Luan, An approximation algorithm for the generalized kmulticut problem, Discrete Applied Mathematics, 160(78) (2012) 12401247.##[19] M. Gr¨otschel, L. Lov´asz, A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1(2) (1981) 169197.##]
1

Heuristic artificial bee colony algorithm for solving the Homicidal Chauffeur differential game
https://ajmc.aut.ac.ir/article_3819.html
10.22060/ajmc.2019.16949.1025
1
In this paper, we consider the Homicidal Chauffeur (HC) problem as an interesting and practical differential game. At first, we introduce a bilevel optimal control problem (BOCP) and prove that a saddle point solution for this game exists if and only if this BOCP has an optimal solution in which the optimal value of the objective function is equal to 1. Then, BOCP is discretized and converted to a nonlinear bilevel programming problem. Finally, an Artificial Bee Colony (ABC) algorithm is used for solving this problem, in which the lowerlevel problem will be considered as a constraint and solved by an NLPsolver. Finally, to demonstrate the effectiveness of the presented method, various cases of HC problem are solved and the simulation results are reported.
0

153
163


Zahra
Yazdaniyan
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology,
Tehran, Iran
Iran
z_yazdaniyan64@aut.ac.ir


Mostafa
Shamsi
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Iran
m_shamsi@aut.ac.ir


Maria do Rosario
de Pinho
Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200465, Porto, Portugal
Portugal
mpinho@fe.up.pt


Zahra
Foroozandeh
Department of Electrical and Computer Engineering, SYSTEC, Faculdade de Engenharia, Universidade do Porto, 4200465, Porto, Portugal
Portugal
zahra@fe.up.pt
Differential game
Saddle point solution
Artificial bee colony
Bilevel optimal control
[[1] S. Aslan, H. Badem, D. Karaboga, Improved quick artificial bee colony (iqABC) algorithm for global optimization, Soft Computing, 2019.##[2] T. Ba¸sar, G. Olsder, Dynamic Noncooperative Game Theory, 2nd Edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1998.##[3] J. F. Bard, Practical bilevel optimization: algorithms and applications, volume 30. Springer Science & Business Media, 2013.##[4] J. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Society for Industrial and Applied Mathematics, second edition, 2010.##[5] J. T. Betts, Survey of numerical methods for trajectory optimization, Journal of Guidance, Control, and Dynamics, 21(2) (1998) 193207.##[6] A. E. Bryson, Applied optimal control: optimization, estimation and control, Routledge, 2018.##[7] A. E. Bryson, YC. Ho, Applied optimal control: optimization, estimation and control, Hemisphere, 1975.##[8] B. Colson, P. Marcotte, G. Savard, An overview of bilevel optimization, Annals of Operations Research, 153(1) (2007) 235256.##[9] H. Ehtamo, T. Raivio, On applied nonlinear and bilevel programming or pursuitevasion games, Journal of Optimization Theory and Applications, 108(1) (2001) 6596.##[10] I. Exarchos, P. Tsiotras, M. Pachter, On the suicidal pedestrian differential game, Dynamic Games and Applications, 5(3) (2015) 297317.##[11] I. Exarchos, P. Tsiotras, M. Pachter, UAV collision avoidance based on the solution of the suicidal pedestrian differential game, 2016.##[12] M. Falcone, Numerical methods for differential games based on partial differential equations, International Game Theory Review, 8(2) (2006) 231272.##[13] L. Guo, J. J. Ye, Necessary optimality conditions for optimal control problems with equilibrium constraints, SIAM Journal on Control and Optimization, 54(5) (2016) 27102733.##[14] K. Horie, Collocation with nonlinear programming for twosided flight path optimization, PhD thesis, University of Illinois at UrbanaChampaign, 2002.##[15] K. Horie, B. A. Conway, Genetic algorithm preprocessing for numerical solution of differential games problems, Journal of Guidance, Control, and Dynamics, 27(6) (2004) 10751078.##[16] K. Horie, B. A. Conway, Optimal fighter pursuitevasion maneuvers found via twosided optimization, Journal of Guidance, Control, and Dynamics, 29(1) (2006)105112.##[17] R. Isaacs, Differential games. A mathematical theory with applications to warfare and pursuit, control and optimization, John Wiley & Sons, Inc., New YorkLondonSydney, 1965.##[18] P. A. Johnson, Numerical Solution Methods for Differential Game Problems, PhD thesis, Massachusetts Institute of Technology, 2009.##[19] J. Lewin, J. V. Breakwell, The surveillanceevasion game of degree, Journal of Optimization Theory and Applications, 16(34) (1975) 339353.##[20] V. S. Patsko, V. L. Turova, Families of semipermeable curves in differential games with the homicidal chauffeur dynamics, Automatica, 40(12) (2004) 20592068.##[21] V. S. Patsko, V. L. Turova, Numerical investigation of the value function for the homicidal chauffeur problem with a more agile pursuer, Annals of the International Society of Dynamic Games, 10 (2009) 231258.##[22] V. S. Patsko, V. L. Turova, Homicidal chauffeur game: History and modern studies, Annals of the International Society of Dynamic Games, 11 (2011) 227251.##[23] M. Pontani, Differential games treated by a gradient–restoration approach. In Variational Analysis and Aerospace Engineering, pages 379396. Springer, 2009.##[24] M. Pontani, Numerical solution of orbital combat games involving missiles and spacecraft, Dynamic Games and Applications, 1(4) (2011) 534557.##[25] M. Pontani, B. A. Conway, Numerical solution of the threedimensional orbital pursuitevasion game, Journal of Guidance, Control, and Dynamics, 32(2) (2009) 474487.##[26] S. Sun, Q. Zhang, R. Loxton, B. Li, Numerical solution of a pursuitevasion differential game involving two spacecraft in low earth orbit. Journal of Industrial and Management Optimization, 11(4) (2015) 11271147.##[27] A. W¨achter, L. T. Biegler, On the implementation of an interiorpoint filter linesearch algorithm for largescale nonlinear programming, Math. Program., 106(1, Ser. A) (2006) 2557.##]
1

A new hash function and its use in read mapping on genome
https://ajmc.aut.ac.ir/article_3820.html
10.22060/ajmc.2019.15991.1020
1
Mapping reads onto genomes is an indispensable step in sequencing data analysis. A widely used method to speed up mapping is to index a genome by a hash table, in which genomic positions of kmers are stored in the table. The hash table size increases exponentially with the kmer length and thus the traditional hash function is not appropriate for a kmer as long as a read. We present a hashing mechanism by two functions named score1 and score2 which can hash sequences with the length of reads. The size of hash table is directly proportional to the genome size, which is absolutely lower than that of hash table built by the conventional hash function. We evaluate our hashing system by developing a read mapper and running the mapper on E. coli genome with some simulated data sets. The results show that the high percentage of simulated reads can be mapped to correct locations on the genome.
0

165
170


Farzaneh
Salari
Department of Mathematics and Computer Sciences  Amirkabir University of Technology  Tehran  Iran
Iran
farzsalari@aut.ac.ir


Fatemeh
Zare Mirakabad
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Iran
f.zare@aut.ac.ir


Mehdi
Sadeghi
National Institute of Genetic Engineering and Biotechnology, Tehran, Iran
Iran
sadeghi@nigeb.ac.ir
Read mapping
Referencebased assembly
Hash Function
[[1] A. Ahmadi, A. Behm, N. Honnalli, C. Li, L. Weng, X. Xie, Hobbes: optimized grambased methods for efficient read alignment, Nucleic Acids Research, 40(6) (2011) e41e41.##[2] N. Homer, B. Merriman, S. F. Nelson, BFAST: An alignment tool for lLarge scale genome resequencing. PLoS ONE, 14(11) (2009) 112.##[3] B. Langmead, S. L. Salzberg, Fast gappedread alignment with Bowtie 2. Nature Methods, 9(4) (2012) 357359.##[4] B. Langmead, C. Trapnell, M. Pop, S. L. Salzberg, Ultrafast and memoryefficient alignment of short DNA sequences to the human genome, Genome Biology, 10(3) (2009) R25.##[5] WP. Lee, M. P. Stromberg, A. Ward, C. Stewart, E. P. Garrison, G. T. Marth. Mosaik: A hashbased algorithm for accurate nextgeneration sequencing shortread mapping, PLOS ONE, 9(3) (2014) 111.##[6] H. Li and R. Durbin. Fast and accurate short read alignment with burrowswheeler transform, Bioinformatics, 25(14) (2009) 17541760.##[7] S. M. Rumble, P. Lacroute, A. V. Dalca, M. Fiume, A. Sidow, M. Brudno, Shrimp: Accurate mapping of short colorspace reads, PLOS Computational Biology, 5(5) (2009) 111.##[8] A. D. Smith, WY. Chung, E. Hodges, J. Kendall, G. Hannon, J. Hicks, Z. Xuan, M. Q. Zhang, Updates to the RMAP shortread mapping software, Bioinformatics, 25(21):2841–2842, 2009.##[9] T. F. Smith, M. S. Waterman, Identification of common molecular subsequences, Journal of Molecular Biology, 147(1) (1981) 195197.##[10] H. Zhang, Y. Chan, K. Fan, B. Schmidt, W. Liu, Fast and efficient short read mapping based on a succinct hash index, BMC Bioinformatics, 19(1):92, 2018.##]
1

Counting closed billiard paths
https://ajmc.aut.ac.ir/article_3821.html
10.22060/ajmc.2020.17320.1026
1
Given a pool table enclosing a set of axisaligned rectangles, with a total of n edges, this paper studies closed billiard paths. A closed billiard path is formed by following the ball shooting from a starting point into some direction, such that it doesn’t touch any corner of a rectangle, doesn’t visit any point on the table twice, and stops exactly at the starting position. The signature of a billiard path is the sequence of the labels of edges in the order that are touched by the path, while repeated edge reflections like abab are replaced by ab. We prove that the length of a signature is at most 4.5n−9, and we show that there exists an arrangement of rectangles where the length of the signature is 1.25n+ 2. We also prove that the number of distinct signatures for fixed shooting direction (45◦ ) is at most 1.5n − 6.
0

171
177


Sina
Farahzad
Department of Mathematics and Computer Science, Amirkabir University of Technology
Iran
sinafarahzad@aut.ac.ir


Ali
Rahmati
MalekAshtar University of Technology, Tehran, Iran
Iran
alirahmati@outlook.com


Zahed
Rahmati
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Iran
zrahmati@aut.ac.ir
Billiard Paths
Maximum Path Length
computational geometry
[[1] M. de Berg, O. Cheong, M. V. Kreveld, Mark Overmars. Computational Geometry: Algorithms and Applications. SpringerVerlag TELOS, Santa Clara, CA, 2008.##[2] J. O’Rourke, Open Problems from CCCG 2017, In Proc. of the 30th Canadian Conference on Computational Geometry, (2018) 149154.##]
1

A model transformation approach to perform refactoring on software architecture using refactoring patterns based on stakeholder requirements
https://ajmc.aut.ac.ir/article_3822.html
10.22060/ajmc.2020.17541.1027
1
Software Architecture (SA) generally has a considerable influence on software quality attributes. Coordination of software architecture to the requirements of the stakeholders and avoiding common mistakes and faults in designing SA increases the chance of success of the project and satisfaction of the stakeholders. Making the wrong decisions at the architectural design phase usually proves very costly later on. Refactoring is a method which helps in detecting and avoiding complications, improving the internal characteristics of software, while keeping the external behavior intact. Various problems can undermine the architecture refactoring process. The existence of different requirements in different domains, the diversity of architecture description languages, and the difficulty of describing refactoring patterns lead to the difficulty of performing automatic and semiautomatic refactoring on the SA. In this study, we use model transformation as a way to overcome the above mentioned difficulties. In this regard, the first step is converting the SA to a pivotmodel. Then, based on the refactoring patterns, the refactoring process is performed on the pivotmodel. And finally, the pivotmodel is converted back to the original (source) model. In this paper, the requirements of the stakeholders are taken into account in the refactoring process by modeling them as refactoring goals. These goals show the importance of the quality attributes in the project and the process of refactoring. The applicability of the framework is demonstrated using a case study.
0

179
216


Mohammad
Tanhaei
Karbalaye 5 St., Azadi Bld., Ilam
Tak Apt.
Iran
m.tanhaei@ilam.ac.ir
Refactoring
Software Architecture
Pattern
Model transformation
[[1] A. Abouzahra, J. B´ezivin, M. D. Del Fabro, F. Jouault, A practical approach to bridging domain specific languages with UML profiles, in: Proceedings of the Best Practices for Model Driven Software Development at OOPSLA, Vol. 5, 2005.##[2] J. Adersberger, M. Philippsen, Reflexml: Umlbased architecturetocode traceability and consistency checking, in: Software Architecture, Springer, 2011, pp. 344359.##[3] S. Alshehri, L. Benedicenti, Rankingtherefactoring techniques based on the internal quality attributes, International Journal of Software Engineering & Applications 5 (1) (2014).##[4] A. Amirat, M. Oussalah, et al., Towards an UML profile for the description of software architecture, in: Proceeding of International Conference on Applied Informatics (ICAI’09), 2009, pp. 226232.##[5] L. Apvrille, J. Courtiat, C. Lohr, P. de SaquiSannes, Turtle: a realtime UML profile supported by a formal validation toolkit, IEEE Transactions on Software Engineering, 30 (7) (2004) 473487.##[6] T. Arendt, E. Biermann, S. Jurack, C. Krause, G. Taentzer, Henshin: Advanced concepts and tools for inplace emf model transformations, in: D. Petriu, N. Rouquette, Ø. Haugen (Eds.), Model Driven Engineering Languages and Systems, Vol. 6394 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2010, pp. 121135.##[7] B. W. Boehm, J. R. Brown, M. Lipow, Quantitative evaluation of software quality, in: Proceedings of the 2nd international conference on Software engineering, IEEE Computer Society Press, 1976, pp. 592605.##[8] S. Bosems, A performance analysis of model transformations and tools, Master’s thesis, University of Twente (2011).##[9] S. R. Chidamber, C. F. Kemerer, A metrics suite for object oriented design, IEEE Transactions on Software Engineering, 20 (6) (1994) 476493.##[10] O. Constant, Emf diff merge/patterns.##[11] J. Dietrich, C. Elgar, A formal description of design patterns using owl, in: Software Engineering Conference, 2005. Proceedings. 2005 Australian, IEEE, 2005, pp. 243250.##[12] J. Dong, Y. Sheng, K. Zhang, Visualizing design patterns in their applications and compositions, IEEE Transactions on Software Engineering, 33 (7) (2007) 433453.##[13] R. G. Dromey, A model for software product quality, IEEE Transactions on Software Engineering 21 (2) (1995) 146162.##[14] H. Dubois, F. Lakhal, S. G´erard, The papyrus tool as an eclipse uml2modeling environment for requirements, in: Proceedings of the 2009 Second International Workshop on Managing Requirements Knowledge, MARK ’09, IEEE Computer Society, Washington, DC, USA, 2009, pp. 8588.##[15] A. H. Eden, Precise specification of design patterns and tool support in their application, Ph.D. thesis, Publisher not identified (2000).##[16] P. H. Feiler, B. Lewis, S. Vestal, The sae avionics architecture description language (AADL) standard: A basis for modelbased architecturedriven embedded systems engineering, in: RTAS 2003 Workshop on ModelDriven Embedded Systems, 2003.##[17] M. Fowler, Refactoring: improving the design of existing code, AddisonWesley Professional, 1999.##[18] R. B. France, D.K. Kim, S. Ghosh, E. Song, A UMLbased pattern specification technique, IEEE Transactions on Software Engineering, 30 (3) (2004) 193206.##[19] K. Garc´es, F. Jouault, P. Cointe, J. B´ezivin, A domain specific language for expressing model matching, in: 5`ere Journ´ee sur l’Ing´enierie Dirig´ee par les Mod`eles (IDM09), 2009, pp. 3348.##[20] D. Garlan, R. Monroe, D. Wile, Acme: an architecture description interchange language, in: Centre for Advanced Studies on Collaborative research, IBM Corp., 1997, pp. 722.##[21] G. Giachetti, B. Mar´ın, O. Pastor, Using UML as a domainspecific modeling language: A proposal for automatic generation of UML profiles, in: Advanced Information Systems Engineering, Springer, 2009, pp. 110124.##[22] M. Goul˜ao, F. B. e Abreu, Bridging the gap between Acme and UML 2.0 for CBD, in: Proceedings of Specification and Verification of ComponentBased Systems (SAVSCB’03), workshop at ESEC/FSE 2003, 2003, pp. 7579.##[23] O. M. Group, et al., Query/view/transformation specification version 1.0, formal/20080403, April (2008).##[24] A. Le Guennec, G. Suny´e, J.M. J´ez´equel, Precise modeling of design patterns, in: UML 2000—The Unified Modeling Language, Springer, 2000, pp. 482496.##[25] C. Hofmeister, R. Nord, D. Soni, Applied software architecture, AddisonWesley Professional, 2000.##[26] S. Hussain, Investigating architecture description languages (adls) a systematic literature review, Master’s thesis, Link¨opings universitet (2013).##[27] ISO/IEC, ISO Standard 9126: Software engineering  product quality, parts 1, 2 and 3 (2001 (part 1), 2003 (parts 2 and 3)).##[28] I. Ivkovic, K. Kontogiannis, A framework for software architecture refactoring using model transformations and semantic annotations, in: Software Maintenance and Reengineering, 2006. CSMR 2006. Proceedings of the 10th European Conference on, IEEE, 2006, pp. 1023.##[29] F. Jouault, F. Allilaire, J. B´ezivin, I. Kurtev, Atl: A model transformation tool, Science of computer programming 72 (1) (2008) 3139.##[30] S. H. Kan, Metrics and models in software quality engineering, AddisonWesley Longman Publishing Co., Inc., 2002.##[31] M. M. Kand´e, A. Strohmeier, Towards a UML profile for software architecture descriptions, in: UML 2000— The Unified Modeling Language, Springer, 2000, pp. 513527.##[32] S. Kent, Model driven engineering, in: Integrated formal methods, Springer, 2002, pp. 286298.##[33] R. Khare, M. Guntersdorfer, P. Oreizy, N. Medvidovic, R. N. Taylor, xadl: enabling architecturecentric tool integration with xml, in: System Sciences, 2001. Proceedings of the 34th Annual Hawaii International Conference on, IEEE, 2001, pp. 9pp.##[34] D.K. Kim, Design pattern based model transformation with tool support, Software: Practice and Experience 45 (2013) 473499.##[35] J. P. Kincaid, R. P. Fishburne Jr, R. L. Rogers, B. S. Chissom, Derivation of new readability formulas (automated readability index, fog count and flesch reading ease formula) for navy enlisted personnel, Tech. rep., DTIC Document (1975).##[36] A. G. Kleppe, J. B. Warmer, W. Bast, MDA explained: the model driven architecture: practice and promise, AddisonWesley Professional, 2003.##[37] K. Lano, J. Bicarregui, S. Goldsack, Formalising design patterns, in: RBCSFACS Northern Formal Methods Workshop, 1996.##[38] A. Lauder, S. Kent, Precise visual specification of design patterns, in: ECOOP’98ObjectOriented Programming, Springer, 1998, pp. 114134. [39] I. Malavolta, H. Muccini, P. Pelliccione, D. A. Tamburri, Providing architectural languages and tools interoperability through model transformation technologies, IEEE Transactions on Software Engineering 36 (1) (2010) 119140.##[40] J. A. McCall, P. K. Richards, G. F. Walters, Factors in software quality. volumeiii. preliminary handbook on software quality for an acquisiton manager, Tech. rep., DTIC Document (1977).##[41] T. Mens, P. Van Gorp, A taxonomy of model transformation, Electronic Notes in Theoretical Computer Science 152 (2006) 125142.##[42] T. Mikkonen, Formalizing design patterns, in: Proceedings of the 20th international conference on Software engineering, IEEE Computer Society, 1998, pp. 115124.##[43] N. Moha, V. Mah´e, O. Barais, J.M. J´ez´equel, Generic model refactorings, in: Model driven engineering languages and systems, Springer, 2009, pp. 628643.##[44] E. MurphyHill, C. Parnin, A. P. Black, How we refactor, and how we know it, Software Engineering, IEEE Transactions on 38 (1) (2012) 518.##[45] J. Offutt, A. Abdurazik, S. R. Schach, Quantitatively measuring objectoriented couplings, Software Quality Journal 16 (4) (2008) 489512.##[46] E. Oliva, Interactive graphical maps for infocenter via model to model transformation, EclipseIT 2009 (2009) 104.##[47] W. F. Opdyke, Refactoring objectoriented frameworks, Ph.D. thesis, University of Illinois at UrbanaChampaign (1992).##[48] F. Oquendo, Formally modelling software architectures with the UML 2.0 profile for πadl, ACM SIGSOFT Software Engineering Notes 31 (1) (2006) 113.##[49] I. Porres, A toolkit for model manipulation, Software and Systems Modeling 2 (4) (2003) 262277.##[50] I. Porres, Model refactorings as rulebased update transformations, in: P. Stevens, J. Whittle, G. Booch (Eds.), UML 2003  The Unified Modeling Language. Modeling Languages and Applications, Vol. 2863 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2003, pp. 159174 .##[51] A. Radermacher, Support for design patterns through graph transformation tools, in: Applications of Graph Transformations with Industrial Relevance, Springer, 2000, pp. 111126.##[52] J. Reimann, M. Seifert, U. Aßmann, On the reuse and recommendation of model refactoring specifications, Software & Systems Modeling 12 (3) (2013) 579596.##[53] L. Rose, E. Guerra, J. De Lara, A. Etien, D. Kolovos, R. Paige, Genericity for model management operations, Software & Systems Modeling 12 (1) (2013) 201219.##[54] T. Ruhroth, H. Wehrheim, S. Ziegert, Rel: A generic refactoring language for specification and execution, in: Software Engineering and Advanced Applications (SEAA), 2011 37th EUROMICRO Conference on, 2011, pp. 8390. doi:10.1109/SEAA.2011.22.##[55] T. L. Saaty, What is the analytic hierarchy process?, Springer, 1988.##[56] B. Selic, A systematic approach to domainspecific language design using UML, in: Object and ComponentOriented RealTime Distributed Computing, 2007. ISORC’07. 10th IEEE International Symposium on, IEEE, 2007, pp. 29.##[57] S. Siraj, L. Mikhailov, J. A. Keane, Priest: an interactive decision support tool to estimate priorities from pairwise comparison judgments, International Transactions in Operational Research 22 (2013) 217235.##[58] O. A. Specification, UML 2.0 infrastructure specification.##[59] D. Steinberg, F. Budinsky, E. Merks, M. Paternostro, EMF: eclipse modeling framework, Pearson Education, 2008..##[60] S. Vestal, Metah programmer’s manual (1996).##[61] M. V¨olter, T. Stahl, J. Bettin, A. Haase, S. Helsen, Modeldriven software development: technology, engineering, management, John Wiley & Sons, 2013.##[62] M. Wimmer, S. M. Perez, F. Jouault, J. Cabot, A catalogue of refactorings for modeltomodel transformations., Journal of Object Technology 11 (2) (2012) 140.##[63] R. Yin, Case Study Research: Design and Methods, Applied Social Research Methods, SAGE Publications, 2009.##[64] Y. Yu, J. Mylopoulos, E. Yu, J. C. Leite, L. Liu, E. D’Hollander, Software refactoring guided by multiple softgoals, in: 1st workshop on Refactoring: Achievements, Challenges, and Effects, in conjunction with the 10th WCRE conference 2003, IEEE Computer Society, 2003, pp. 711.##[65] U. Zdun, P. Avgeriou, Modeling architectural patterns using architectural primitives, in: ACM SIGPLAN Notices, Vol. 40, ACM, 2005, pp. 133146.##[66] T. Ziadi, L. H´elou¨et, J.M. J´ez´equel, Towards a UML profile for software product lines, in: Software ProductFamily Engineering, Springer, 2004, pp. 129139.##[67] O. Zimmermann, Architectural refactoring: A taskcentric view on software evolution, IEEE Software (2) (2015) 2629.##]
1

The regularity of binomial edge ideals of graphs
https://ajmc.aut.ac.ir/article_3929.html
10.22060/ajmc.2020.16433.1024
1
In this paper, we study the CastelnuovoMumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph provides an upper bound for the regularity of its binomial edge ideal.
0

217
221


Sara
Saeedi Madani
Mathematics department, Mathematics and Computer Science faculty, Amirkabir University of Technology, Tehran, Iran
Iran
sarasaeedi@aut.ac.ir


Dariush
Kiani
Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)
Iran
dkiani@aut.ac.ir
Binomial edge ideal
CastelnuovoMumford regularity
free cut edge
[[1] J. Herzog, T. Hibi, F. Hreinsdotir, T. Kahle, J. Rauh, Binomial edge ideals and conditional independence statements, Adv. Appl. Math. 45 (2010) 317333.##[2] M. Ohtani, Graphs and ideals generated by some 2minors, Comm. Algebra. 39 (2011) 905917.##[3] A. Dokuyucu, Extremal Betti numbers of some classes of binomial edge ideals, Math. Rep. 17(67) (2015) 359367.##[4] V. Ene, J. Herzog, T. Hibi, CohenMacaulay binomial edge ideals, Nagoya Math. J. 204 (2011) 5768.##[5] V. Ene, A. Zarojanu, On the regularity of binomial edge ideals, Math. Nachr. 288, No. 1 (2015) 1924.##[6] D. Kiani, S. Saeedi Madani, Some CohenMacaulay and unmixed binomial edge ideals, Comm. Algebra. 43 (2015) 54345453.##[7] D. Kiani, S. Saeedi Madani, The CastelnuovoMumford regularity of binomial edge ideals, J. Combin. Theory Ser. A. 139 (2016) 8086.##[8] K. Matsuda, S. Murai, Regularity bounds for binomial edge ideals, Journal of Commutative Algebra. 5(1) (2013) 141149.##[9] F. Mohammadi, L. Sharifan, Hilbert function of binomial edge ideals, Comm. Algebra 42 (2014) 688703.##[10] S. Saeedi Madani, D. Kiani, Binomial edge ideals of graphs, Electron. J. Combin. 19(2) (2012) ] P44.##[11] P. Schenzel, S. Zafar, Algebraic properties of the binomial edge ideal of a complete bipartite graph, An. St. Univ. Ovidius Constanta, Ser. Mat. 22(2) (2014) 217237.##[12] S. Zafar, On approximately CohenMacaulay binomial edge ideal, Bull. Math. Soc. Sci. Math. Roumanie, 55(103) (2012) 429442.##[13] Z. Zahid, S. Zafar, On the Betti numbers of some classes of binomial edge ideals, Electron. J. Combin., 20(4) (2013) ] P37.##[14] S. Saeedi Madani, D. Kiani, On the binomial edge ideal of a pair of graphs, The Electronic Journal of Combinatorics. 20(1) (2013) ] P48.##[15] M. Rouzbahani Malayeri, S. Saeedi Madani, D. Kiani, Regularity of binomial edge ideals of chordal graphs, preprint.##]
1

Lie group analysis for short pulse equation
https://ajmc.aut.ac.ir/article_3997.html
10.22060/ajmc.2020.18416.1032
1
In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [2], and add some further facts, such as an optimal system of Lie symmetry subalgebras and two local symmetries.
0

223
227


Mehdi
Nadjafikhah
School of Mathematics, Iran University of Science and Technology
Iran
m_nadjafikhah@iust.ac.ir
Lie symmetry analysis
General short pulse equation
Invariant solution
Local symmetry
[[1] G. W. Bluman, A. F. Cheviakov, S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, 2010.##[2] H. Liu, J. Li, Lie symmetry analysis and exact solutions for the short pulse equation, Nonlinear Analysis 71 (2009) 21262133.##[3] P. J. Olver, Applications of Lie Groups to Differential equations, Second Edition, GTM, Vol. 107, Springer Verlage, New York, 1993.##[4] P. J. Olver, Equivalence, Invariant and Symmetry, Cambridge University Press, Cambridge University Press, Cambridge 1995.##[5] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.##[6] E. Parkes, Some periodic and solitary travellingwave solutions of the short pulse equation, Chaos, Solitons & Fractals, 38 (2008) 154159.##[7] A. Sakovich, S. Sakovich, Solitary wave solutions of the short pulse equation, J. Phys. A Math. Gen. 39 (2006) L361L367.##[8] T. Schafer, C. E. Wayne, Propagation of ultrashort optical pulses in cubic nonlinear media, Phys. D 196 (2004) 90105.##]
1

On the gradient Finsler Yamabe solitons
https://ajmc.aut.ac.ir/article_3998.html
10.22060/ajmc.2020.18420.1034
1
Here, it is proved that the potential functions of Finsler Yamabe solitons have at most quadratic growth in distance function. Also it is obtained a finite topological type property on complete gradient Finsler Yamabe solitons under suitable scalar curvature assumptions.
0

229
233


Mohamad
Yar Ahmadi
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz
Iran
m.yarahmadi@scu.ac.ir
Finsler metric
gradient Yamabe soliton
finite topological type
[[1] D. Bao, S. S. Chern, Z. Shen, An Introduction to RiemannFinsler Geometry, Graduate Texts in Mathematics, vol. 200, Springer, 2000.##[2] B. Bidabad, A. Shahi, On Sobolev spaces and density theorems on Finsler manifolds, AUT J. Math. Com., 1(1) (2020) 3745.##[3] B. Bidabad, M. Yar Ahmadi, On complete Finslerian Yamabe solitons, Differential Geometry and its Applications, 66 (2019) 5260.##[4] B. Bidabad, M. Yar Ahmadi, On complete Yamabe solitons, Advances in Geometry, 18 (1) (2018) 101104.##[5] B. Bidabad, M. Yar Ahmadi, Complete Ricci solitons on Finsler manifolds, Sci. China Math, 61 (2018) 1825 1832.##[6] B. Bidabad, A. Shahi, M. Yar Ahmadi, Deformation of Cartan curvature on Finsler manifolds, Bull. Korean Math. Soc., 54 (2017) 21192139.##[7] B. Bidabad, M. Yar Ahmadi, On quasiEinstein Finsler spaces, Bull Iranian Math. Soc., 40 (2014) 921930.##[8] F. Q. Fang, J. W. Man, Z .L. Zhang, Complete gradient shrinking Ricci solitons have finite topological type, Comptes Rendus Mathematique 346 (2008) 653656.##[9] R. S. Hamilton, Threemanifolds with positive Ricci curvature, J. Diffl. Geom, 17 (1982) no. 2, 255306.##[10] Z. Shen, On complete manifolds of nonnegative kthRicci curvature, Transactions of the American Mathematical Society, 338(1) (1993) 289310.##[11] J. Y. Wu, On a class of complete noncompact gradient Yamabe solitons, arXiv preprint, arXiv: 1109.0861 (2011).##]
1

Homotopy perturbation transform method for timefractional NewellWhitehead Segel equation containing CaputoPrabhakar fractional derivative
https://ajmc.aut.ac.ir/article_3999.html
10.22060/ajmc.2020.18012.1028
1
The main aim of the current article is to find the solution for Newell WhiteheadSegel equations with constant coefficients containing CaputoPrabhakar fractional derivative using the homotopy perturbation transform method. The convergence analysis of the obtained solution for the proposed fractional order model is presented. Four examples are presented to illustrate the efficiency and applicability and accurateness of the proposed numerical technique
0

235
250


Mohammadhossein
Derakhshan
Faculty of Mathematics, K. N. Toosi University of Technology
Iran
m.h.derakhshan.20@gmail.com


Azim
Aminataei
Faculty of Mathematics, Khajeh Nasir Toosi University of Technology
Iran
ataei@kntu.ac.ir
Nonlinear fractional differential equations
NewellWhiteheadSegel equations
Homotopy perturbation transform method
CaputoPrabhakar fractional derivative
[[1] N. Anjum, J. H. He, Laplace transform: making the variational iteration method easier, Applied Mathematics Letters, 92 (2019) 134138.##[2] L. Beghin, E. Orsingher, Fractional Poisson processes and related planar random motions, Electronic Journal of Probability, 14 (2009) 17901826.##[3] J. An, E. Van Hese, M. Baes, Phasespace consistency of stellar dynamical models determined by separable augmented densities, Monthly Notices of the Royal Astronomical Society, 422(1) (2012) 652664.##[4] V. DaftardarGejji, H. Jafari, An iterative method for solving nonlinear functional equations, Journal of Mathematical Analysis and Applications, 316(2) (2006) 753763.##[5] M. H. Derakhshan, A. Ansari, Fractional SturmLiouville problems for Weber fractional derivatives, International Journal of Computer Mathematics, 96(2) (2019) 217237.##[6] M. H. Derakhshan, A. Ansari, On HyersUlam stability of fractional differential equations with Prabhakar derivatives, Analysis, 38(1), (2018) 3746.##[7] M. H. Derakhshan, A. Ansari, Numerical approximation to Prabhakar fractional SturmLiouville problem, Computational and Applied Mathematics, 38(2) (2019) 7190. https://doi.org/10.1007/s4031401908264.##[8] M. H. Derakhshan, A. Ansari, M. Ahmadi Darani, On asymptotic stability of Weber fractional differential systems, Computational Methods for Differential Equations, 6(1) (2018) 3039.##[9] M. H. Derakhshan, M. Ahmadi Darani, A. Ansari, R. Khoshsiar Ghaziani, On asymptotic stability of Prabhakar fractional differential systems, Computational Methods for Differential Equations, 4(4) (2016) 276284.##[10] M. D’Ovidio, F. Polito, Fractional diffusiontelegraph equations and their associated stochastic solutions, (2013) arXiv preprint arXiv:1307.1696.##[11] B. Dumitru, D. Kai, S. Enrico, Fractional calculus: models and numerical methods (Vol. 3). World Scientific (2012).##[12] A. Giusti, I. Colombaro, Prabhakarlike fractional viscoelasticity, Communications in Nonlinear Science and Numerical Simulation, 56 (2018) 138143.##[13] K. G´orska, A. Horzela, L. Bratek, K. A. Penson, G. Dattoli, The probability density function for the Havriliak Negami relaxation, (2016) arXiv preprint arXiv:1611.06433.##[14] R. Garrappa, F. Mainardi, M. Guido, Models of dielectric relaxation based on completely monotone functions, Fractional Calculus and Applied Analysis, 19(5) (2016) 11051160.##[15] A. Ghorbani, Beyond Adomian polynomials: he polynomials, Chaos, Solitons & Fractals, 39(3) (2009) 1486 1492.##[16] R. Gorenflo, A. A. Kilbas, F. Mainardi, S. V. Rogosin, MittagLeffler functions, related topics and applications (Vol. 2). Berlin: Springer (2014).##[17] R. Garra, R. Gorenflo, F. Polito, Z. Tomovski, HilferPrabhakar derivatives and some applications, Applied ˇ Mathematics and Computation, 242 (2014) 576589.##[18] J. H. He, Homotopy perturbation technique, Computer methods in applied mechanics and engineering, 178(34) (1999) 257262.##[19] M. Hamarsheh, A. I. Ismail, Z. Odibat, An analytic solution for fractional order Riccati equations by using optimal homotopy asymptotic method, Applied Mathematical Sciences, 10(23) (2016) 11311150.##[20] H. Jafari, Iterative methods for solving system of fractional differential equations, Doctoral dissertation, Pune University, Pune, India, (2006).##[21] B. Karaagac, Two step Adams Bashforth method for time fractional Tricomi equation with nonlocal and nonsingular Kernel, Chaos, Solitons & Fractals, 128 (2019) 234241.##[22] P. Karunakar, S. Chakraverty, Solutions of timefractional thirdand fifthorder KortewegdeVries equations using homotopy perturbation transform method. Engineering Computations, 36(7) (2019) 23092326. https://doi.org/10.1108/EC0120190012.##[23] A. A. Kilbas, M. Saigo, R. K. Saxena, Generalized MittagLeffler function and generalized fractional calculus operators, Integral Transforms and Special Functions, 15(1) (2004) 3149.##[24] A. Liemert, T. Sandev, H. Kantz, Generalized Langevin equation with tempered memory kernel, Physica A: Statistical Mechanics and its Applications, 466 (2017) 356369.##[25] P. Miskinis, The HavriliakNegami susceptibility as a nonlinear and nonlocal process, Physica Scripta, 2009(T136) (2009) 014019.##[26] T,.R. Prabhakar, A singular integral equation with a generalized Mittag Leffler function in the kernel, Yokohama Mathematical Journal, 19 (1971) 715.##[27] A. Prakash, M. Goyal, S. Gupta, Fractional variational iteration method for solving timefractional Newell WhiteheadSegel equation, Nonlinear Engineering, 8(1) (2019) 164171.##[28] A. Prakash, H. Kaur, A New Numerical Method for a Fractional Model of NonLinear ZakharovKuznetsov Equations via Sumudu Transform Methods of Mathematical Modelling: Fractional Differential Equations, (2019) 189204.##[29] S. A. Pasha, Y. Nawaz, M. S. Arif, The modified homotopy perturbation method with an auxiliary term for the nonlinear oscillator with discontinuity, Journal of Low Frequency Noise, Vibration and Active Control, 38(34) (2019) 13631373.##[30] I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Vol. 198). Elsevier (1998).##[31] N. A. Pirim, F. Ayaz, A new technique for solving fractional order systems: Hermite collocation method, Applied Mathematics, 7(18) (2016) 23072323.##[32] R. K. Pandey, H. K. Mishra, Homotopy analysis Sumudu transform method for timefractional third order dispersive partial differential equation, Advances in Computational Mathematics, 43(2) (2017) 365383.##[33] H. C. Rosu, O. CornejoP´erez, Supersymmetric pairing of kinks for polynomial nonlinearities, Physical Review E, 71(4) (2005) 046607. doi: 10.1103/PhysRevE.71.046607.##[34] A. Stanislavsky, K. Weron, Atypical case of the dielectric relaxation responses and its fractional kinetic equation, Fractional Calculus and Applied Analysis, 19(1) (2016) 212228.##[35] M. Tatari, M. Dehghan, On the convergence of He’s variational iteration method, Journal of Computational and Applied Mathematics, 207(1) (2007) 121128.##[36] J. Vahidi, The combined Laplacehomotopy analysis method for partial differential equations, J. Math. Comput. Sci.JMCS, 16(1) (2016) 88102.##[37] H. Y´epezMart´ınez, J. F. G´omezAguilar, A new modified definition of CaputoFabrizio fractionalorder derivative and their applications to the Multi Step Homotopy Analysis Method (MHAM), Journal of Computational and Applied Mathematics, 346 (2019) 247260.##[38] D. N. Yu, J. H. He, A. G. Garcıa, Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators, Journal of Low Frequency Noise, Vibration and Active Control, 38(34) (2019) 15401554.##]
1

New directions in general fuzzy automata: a dynamiclogical view
https://ajmc.aut.ac.ir/article_4026.html
10.22060/ajmc.2020.18629.1040
1
In the current study, by a general fuzzy automaton we aim at showing a set of propositions related to a given automaton showing that the truthvalues are depended on thestates, inputs and membership values of active states at time t. This new approach enables us to consider automata from a different point of view which is more close to logical treatment and helps us make estimations about the behavior of automaton particularly in a nondeterministic mode. The logic consists of propositions on the given GFA and its dynamic nature is stated by means of the socalled transition functor. This logic enables us to derive a certain relation on the set of states labeled by inputs. In fact, it is shown that if our set of propositions is large enough, this recovering of the transition relation is possible. Through a synthesis in the theory of systems, this study contributes to construct a general fuzzy automaton which realizes a dynamic process at least partially known to the user, which has been fully achieved in Theorem 3.6. Also, we study the theory of general fuzzy automata by using the concepts of operators. Such operators help us in the algebraic study of general fuzzy automata theory and provide a platform to use fuzzy topological therein. Further, a Galois connection is obtained between the statetransition relation on states and thetransition operators on propositions. To illustrate the proposed approach, the subject matter is more elaborated in detail through examples.
0

251
262


Khadijeh
Abolpour
Dept. of Math., Faculty Member, Islamic Azad University, Shiraz, Iran
Iran
abolpor_kh@yahoo.com


Mohammad mehdi
Zahedi
Dept. of Math., Graduate University of Advanced Technology, Kerman, Iran
Iran
zahedi_mm@kgut.ac.ir


Marzieh
Shamsizadeh
Dept. of Math., Behbahan Khatam Alanbia University of Technology, Behbahan, Iran
Iran
shamsizadeh.m@gmail.com
Dynamic Logic
General Fuzzy Automata
Proposition
Functor
modal
Transition
Active State
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1

A lineartime algorithm to compute total [1, 2]domination number of block graphs
https://ajmc.aut.ac.ir/article_4029.html
10.22060/ajmc.2020.18444.1035
1
Let G = (V, E) be a simple graph without isolated vertices. A set D ⊂ V is a total [1, 2]dominating set if for every vertex v ∈ V , 1 ≤ N(v) ∩ D ≤ 2. The total [1, 2]domination problem is to determine the total [1, 2]domination number γt[1,2](G), which is the minimum cardinality of a total [1, 2]dominating set for a graph G. In this paper, we present a lineartime algorithm to compute γt[1,2](G) for a block graph G.
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Pouyeh
Sharifani
Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
Iran
pouyeh.sharifani@gmail.com


Mohammadreza
Hooshmandasl
Department of Computer Science, University of Mohaghegh Ardabili, Ardabil, Iran.
Iran
hooshmandasl@uma.ac.ir


Saeid
Alikhani
Department of Mathematics, Yazd University, Yazd, Iran.
Iran
alikhani@yazd.ac.ir
Total [1, 2]set
Dominating set
Block graph
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