ORIGINAL_ARTICLE
On The Perimeter of an Ellipse
http://msj.iau-arak.ac.ir/article_515387_c42c9a9c1d7fee53576915b34e9022d1.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
1
6
A.
Ansari
ansari.moh@gmail.com
true
1
Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.
Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.
Department of Mathematics, Islamic Azad University, Gachsaran-Branch, Gachsaran, Iran.
LEAD_AUTHOR
[1] Gerard P. Michon, www.numericana.com/answer/ellipse.htm
1
[2] Gerald B. Folland, Real Analysis, Modern Techniques And Their Applications,
2
John Wiley And Sons, Second Edition.
3
[3] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, Third Edition
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[4] George B. Thomas, Ross L. Finney Calculus And Analytic Geometry, Addison-
5
Wesley, Ninth Edition.
6
ORIGINAL_ARTICLE
Redened (anti) fuzzy BM-algebras
http://msj.iau-arak.ac.ir/article_515578_cccce2ca9ff658b7b93bfef7a13fc0e9.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
7
21
A.
Borumand-Saeid
arsham@mail.uk.ac.ir
true
1
Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran.
Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran.
Department of Mathematics, Islamic Azad University, Kerman Branch, Kerman, Iran.
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[1] S. A. Bhatti, M. A. Chaudhry and B. Ahmad, On classication of BCI-algebras,
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Math. Jap. 34 (1989), 865{876.
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[4] Q. P. Hu and X. Li, On BCH-algebras, Math. Seminar Notes 11 (1983), 313{320.
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[5] Q. P. Hu and X. Li, On proper BCH-algebras, Math. Japonica 30 (1985), 659{
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Japonica 23 (1978), 1{26.
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[8] C. B. Kim and H. S. Kim, On BM-algebras, Sci. Math. Japo. Online e-2006
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[9] H. S. Kim, Y. H. Kim and J. Neggers, Coxeters and pre-Coxeter algebras in
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Smarandache setting, Honam Math. J. 26 (2004), 471{481.
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[10] Y. B. Jun, On (; )-fuzzy subalgebras of BCI=BCK-algebras, Bull. Korean
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Math. Soc. 42 (2005), 703{711.
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[11] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Sci. Math. Japonica
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Online 1 (1998), 347{354.
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[12] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa, Co., Seoul, 1994.
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[13] J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), 19{26.
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[14] J. Neggers and H. S. Kim, On B-algebras, Mate. Vesnik 54 (2002), 21{29.
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[15] J. Neggers and H. S. Kim, A fundamental theorem of B-homomorphism for B-
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algebras, Int. Math. J. 2 (2002), 215{219.
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[16] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512-517.
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[17] A. Walendziak, Some axiomatizations of B-algebras, Math. Slovaca 56 (2006),
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Online e-2005 (2005), 49{53.
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[19] L. A. Zadeh, Fuzzy Sets, Inform. Control 8 (1965), 338{353.
28
ORIGINAL_ARTICLE
BMO Space and its relation with wavelet theory
http://msj.iau-arak.ac.ir/article_515579_fdc4230f4e4bf8d6ac2e1c183ec3256f.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
23
28
M.
Ghanbari
m.ghanbari@iau-farahan.ac.ir
true
1
Department of Mathematics, Islamic Azad University, Farahan-Branch, Farahan, Iran.
Department of Mathematics, Islamic Azad University, Farahan-Branch, Farahan, Iran.
Department of Mathematics, Islamic Azad University, Farahan-Branch, Farahan, Iran.
LEAD_AUTHOR
[1] L. Grafakos, Modern Fourier Analysis, Second Edition, Graduate Texts in Math.,
1
No. 250, Springer, New York, 2008.
2
[2] L. Grafakos, L. Liu, D. Yang, Maximal function characterizations of Hardy spaces
3
on RD-spaces and their applications, Sci. China Ser. A 51 (2008), 2253-2284.
4
[3] Dziubanski, G. Garrigos, T. Martnez, J. L. Torrea, J. Zienkiewicz, BMO spaces
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related to Schrodinger operators with potentials satisfying a reverse Holder in-
6
equality, Math. Z. 249 (2005), 329-356.
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[4] E. Hernftndez, G. Weiss, A First Course on wavelet, University Autonoma of
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Madrid, Washington University in St. Louis, 1996
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[5] B. S. Kashin, A. A. Saakyan, Orthogonal Series, Transl. Mth. Monographs, vol
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75, AMS, Providence, 1989
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[6] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and
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Oscillatory Integrals, Princeton University Press, Princeton, New Jersey 1993
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[7] M. T. Lacey, E. Terwilleger, B. D. Wick, Remarks on product VMO, Proc. Amer.
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Math. Soc. 134 (2006), 465-474.
15
[8] O. Blasco, S. Pott, Dyadic BMO on the bidisk, Rev. Mat. Iberoamericana 21
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(2005), , 483-510.
17
ORIGINAL_ARTICLE
Influence of using the strategy of concept maps in learning fractions
http://msj.iau-arak.ac.ir/article_515580_0476ca27afa98b0245d69427757ea874.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
29
37
M.
Haghverdi
m-haghverdi@iau-arak.ac.ir
true
1
Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.
Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.
Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.
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[1] J. D. Novak. Concept maps and vee diagrams: Two meta cognitive tools to
1
facilitate meaningful learning. International Science 19 29-52, (1990).
2
[2] F. Guastello, Concept mapping eects on science content comprehension of low-
3
achieving inner-city seventh grades. Remedial and Special Education 21 (2000),
4
[3] J. M. Kinchin, Using concept maps to reveal understanding: A two-tier analysis.
5
School Science Review 81 (2000), 41-46.
6
[4] S. Rashwan, The eect of using concept maps in teaching biology to high school
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students and their attitudes towards it. Journal of college of education, Zagazig
8
University (), 422-454.
9
[5] S. Gurganus, Math instruction for students with learning problems, Pearson Ed-
10
ucation Inc. Press.
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[6] J. Monagham and E. Bingobali, Concept image revisited, Educational Studies in
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Mathematics 68 (2008), 19-35.
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[7] L. A. Bolte, Using concept maps and interpretive essays for assessment in math-
14
ematics. School Science and Mathematics bf 99 (1999), 19-28.
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[8] C. Chiou, The eect of concept mapping on students' learning achievements
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and interests, Innovations in Education and Teaching Internationa, 45 (2008),
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[9] S. K. Wilcox and M. Sahlo, Another perspective on concept maps: Empovering
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students, Mathematics Teaching in the Middle School 3 (1998), 464-469.
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[10] D. T. Weinhott, Concept mapping by pre service elementary teachers: A case
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[11] P. B. Harton et. al, An investigation of the eectiveness of concept mapping as
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Studies in Mathematics 29 (1995), 45-72.
26
ORIGINAL_ARTICLE
Hybrid model in network DEA
http://msj.iau-arak.ac.ir/article_515581_05b6570ea3cd19ac8d6e902dd67f0a5d.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
39
44
A.
Jahanshahloo
true
1
Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran.
Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran.
LEAD_AUTHOR
[1] Network DEA: A slack - based measure approach by Kaoru Tone, Miki Tsutsui.
1
[2] Data Envelopment Analysis by Dr. Gr. Jahanshahloo, Dr. F. Hosseinzadeh Lot,
2
Dr. H. Nikomaram.
3
ORIGINAL_ARTICLE
Input congestion, technical ineciency and output reduction in fuzzy data envelopment analysis
http://msj.iau-arak.ac.ir/article_515582_603de28b25425e998524b07716bf5d0a.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
45
60
M.
khodabakhshi
mkhbakhshi@yahoo.com
true
1
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
LEAD_AUTHOR
N.
Aryavash
k.aryavash@yahoo.com
true
2
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
Department of Mathematics, Faculty of Science, Lorestan University, Khorram Abad, Iran.
AUTHOR
[1] M. Asgharian, M. Khodabakhshi, L. Neralic, Congestion in stochastic data envelopment
1
analysis: An input relaxation approach, International Journal of
2
statistic and Management System, 5 (2010), 84{106.
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[2] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical
4
and scale ineciencies in data envelopment analysis, Management Science 30
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(1984), 1078{1092.
6
[3] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the eciency of DMUs,
7
European Journal of Operational Research 2 (1978), 429-444.
8
[4] W. W. Cooper, R. G. Thompson, R. M. Thrall, Introduction: Extensions and
9
new developments in DEA, Annals of Operations Research 66 (1996), 3{46.
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[5] W. W. Cooper, L. M. Seiford, J. Zhu, A unied additive model approach for
11
evaluating ineciency and congestion with associated measures in DEA, Socio-
12
Economic Planning Sciences 34 (2000), 1{25.
13
[6] W. W. Cooper, H. Deng, B. Gu, Sh. Li, R. M. Thrall, Using DEA to improve
14
the management of congestion in Chinese industries, Socio-Economic Planning
15
Sciences 35 (2001), 227{242.
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[7] W. W. Cooper, B. Gu, Sh. Li, Comparisons and evaluations of alternative approaches
17
to the treatment of congestion in DEA, European Journal of Operational
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Research 132 (2001), 62{74.
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[8] W. W. Cooper, B. Gu, Sh. Li, Note: Alternative treatments of congestion
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in DEA-A response to the cherchye, Kuosmanen and Post critique, European
21
Journal of Operational Research 132 (2001), 81{87.
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[9] W. W. Cooper , L. M. Seiford, J. Zhu. (2001). Slacks and congestion: Response
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to a comment by R. Fare and S. Grosskopf, Socio-Economic Planning Sciences
24
35 (2001) 205-215.
25
[10] W. W. Cooper, H. Deng, Zh. M. Huang, S. X. Li A one-model approach to
26
congestion in data envelopment analysis, Socio-Economic Planning Sciences 36
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(2002), 231{238.
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[11] R. Fare, L. Svensson, Congestion of factors of production, Econometrica 48
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(1980), 1743{1753.
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tionalokonomie 43 (1983), 257-271.
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[13] R. Fare, S. Groossko, When can slacks be used to identify congestion? An
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answer to W. W. Cooper, L. Seiford and J. Zhu, Socio-Economic Planning
34
Sciences 35 (2001), 217{221.
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[14] G. R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving
36
outputs in DEA with determining input congestion-Considering textile
37
industry of China, Applied Mathematics and Computation 151 (2004), 263{273.
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[15] G. R. Jahanshahloo, M. Khodabakhshi, Determining assurance interval for non-
39
Archimedean element in the improving outputs model in DEA, Applied Mathe-
40
matics and Computation 151 (2004), 501{506.
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[16] M. Khodabakhshi, A one-model approach based on relaxed combinations of
42
inputs for evaluating input congestion in DEA, Journal of Computational and
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Applied mathematics 230 (2009) ,443{450.
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[17] M. Khodabakhshi, Estimating most productive scale size with stochastic data
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in data envelopment analysis, Economic Modelling 26 (2009), 968-973.
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[18] M. Khodabakhshi, M. Asgharian, An input relaxation measure of eciency in
47
stochastic data envelopment analysis, Applied Mathematical Modelling 33 (2009),
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2010-2023.
49
[19] M. S. Saadati, A. Memariani, Reducing weight exibility in fuzzy DEA, Applied
50
Mathematicsand Computation 161 (2005), 611{622.
51
[20] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets System
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1 (1978), 3{28.
53
ORIGINAL_ARTICLE
Some notes concerning the convergence control parameter in homotopy analysis method
http://msj.iau-arak.ac.ir/article_515583_85cc326aea21d955d3d20c6723380d88.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
61
72
M.
Paripour
m paripour@yahoo.com
true
1
Department of Mathematics, Islamic Azad University, Hamedan Branch , Hamedan, 6518118413,
Iran.
Department of Mathematics, Islamic Azad University, Hamedan Branch , Hamedan, 6518118413,
Iran.
Department of Mathematics, Islamic Azad University, Hamedan Branch , Hamedan, 6518118413,
Iran.
LEAD_AUTHOR
J.
Saeidian
true
2
Department of Mathematics and Computer Science, Tarbiat Moallem University, 599 Taleghani
avenue, Tehran 1561836314, Iran.
Department of Mathematics and Computer Science, Tarbiat Moallem University, 599 Taleghani
avenue, Tehran 1561836314, Iran.
Department of Mathematics and Computer Science, Tarbiat Moallem University, 599 Taleghani
avenue, Tehran 1561836314, Iran.
AUTHOR
[1] S. Abbasbandy, Homotopy analysis method for heat radiation equations, Int.
1
Commun. Heat Mass Transf. 34 (2007), 380{387.
2
[2] S. Abbasbandy, The application of the homotopy analysis method to nonlinear
3
equations arising in heat transfer, Phys. Lett. A 360 (2006) 109-113.
4
[3] S. Abbasbandy, F. Samadian Zakaria, Soliton solutions for the 5th-order KdV
5
equation with the homotopy analysis method, Nonlinear Dyn. 51 (2008) 83{87.
6
[4] S. Abbasbandy, Y. Tan and S. J. Liao, Newton-homotopy analysis method for
7
nonlinear equations, Appl. Math. Comput. 188 (2007), 1794{1800.
8
[5] T. Hayat, T. Javed, M. Sajid, Analytic solution for rotating ow and heat transfer
9
analysis of a third-grade uid, Acta Mech 191 (2007), 219{229.
10
[6] T. Hayat, M. Sajid, Homotopy analysis of MHD boundary layer ow of an upper-
11
convected Maxwell uid, Int. J. Eng. Sci. 45 (2007), 393{401.
12
[7] T. Hayat, M. Sajid, Analytic solution for axisymmetric ow and heat transfer
13
of a second grade uid past a stretching sheet, Int. J. Heat Mass Transfer, 50
14
(2007), 75{84.
15
[8] M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann
16
boundary conditions by the homotopy analysis method, Phys. Lett. A 365 (2007),
17
[9] S. J. Liao, Proposed homotopy analysis technique for the solution of nonlinear
18
problems, Ph.D. dissertation, Shanghai Jiao Tong University, 1992.
19
[10] S. J. Liao, A kind of approximate solution technique which does not depend upon
20
small parameters: a special example, Int. J. of Non-Linear Mech. 30 (1995),
21
[11] S. J. Liao, A kind of approximate solution technique which does not depend upon
22
small parameters (II): an application in uid mechanics, Int. J. of Non-Linear
23
Mech. 32 (1997) 815{822.
24
[12] S. J. Liao, A. T. Chwang, Application of homotopy analysis method in nonlinear
25
oscillations, ASME. J. of Appl. Mech. 65 (1998), 914{922.
26
[13] S. J. Liao, Beyond perturbation: An introduction to homotopy analysis method,
27
Chapman Hall/CRC Press, Boca Raton, 2003.
28
[14] S. J. Liao, On the relationship between the homotopy analysis method and Euler
29
transform, Commun. Nonlin. Sci. Num. Simul. 18 (2010), 1421-1431.
30
[15] S. J. Liao, E. Magyari, Exponentially decaying boundary layers as limiting cases
31
of families of algebraically decaying ones, ZAMP 57 (2006), 777{792.
32
[16] S. J. Liao, A new branch of solutions of boundary-layer ows over a permeable
33
stretching plate, Int. J. Non-Linear Mech. 42 (2007), 819{830.
34
[17] S. J. Liao, Notes on the homotopy analysis method: Some denitions and theo-
35
rems, Commun. Nonlin. Sci. Num. Simul. 14 (2009) 983{997.
36
[18] S. J. Liao, An optimal homotopy analysis approach for strongly nonlinear dier-
37
ential equations, Commun. Nonlin. Sci. Num. Simul. 15 (2010), 2003{2016.
38
[19] Y. P. Liu, Z. B. Li, The homotopy analysis method for approximating the solution
39
of the modied Korteweg-de Vries equation, Chaos, Solitons and Fractals, 39
40
(2009), 1{8.
41
[20] M. Paripour, E. Babolian, J. Saeidian, Analytic solutions to diusion equations,
42
Math. Comput. Mod. 51 (2010), 649{657.
43
[21] M. Sajid, T. Hayat, S. Asghar, Comparison between the HAM and HPM solutions
44
of thin lm ows of non-Newtonian uids on a moving belt, Nonlinear Dyn. 50
45
(2007), 27{35.
46
[22] Z. Wang, L. Zou, H. Zhang, Applying homotopy analysis method for solving
47
dierential-dierence equation, Phys. Lett. A 369 (2007), 77{84.
48
[23] S. P. Zhu, An exact and explicit solution for the valuation of American put
49
options, Quantitative Finance 6 (2006), 229{242.
50
[24] S. P. Zhu, A closed-form analytical solution for the valuation of convertible bonds
51
with constant dividend yield, ANZIAM J. 47 (2006), 477{494.
52
[25] L. Zou, Z. Zong, Z. Wang, L. He, Solving the discrete KdV equation with homo-
53
topy analysis method, Phys. Lett. A 370 (2007), 287{294.
54
ORIGINAL_ARTICLE
A numerical solution of Nagumo telegraph equation by Adomian decomposition method
http://msj.iau-arak.ac.ir/article_515584_c55ffcedb0765761611f091dbcfe5f4f.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
73
81
H.
Rouhparvar
rouhparvar59@gmail.com
true
1
Department of Mathematics, Islamic Azad University, Saveh-Branch, Saveh 39187/366, Iran.
Department of Mathematics, Islamic Azad University, Saveh-Branch, Saveh 39187/366, Iran.
Department of Mathematics, Islamic Azad University, Saveh-Branch, Saveh 39187/366, Iran.
LEAD_AUTHOR
[1] T. A. Abassy, Improved Adomian decomposition method, Comput. Math. Appl.
1
9 (2010), 42{54.
2
[2] S. Abbasbandy, Soliton solutions for the Fitzhugh-Nagumo equation with the
3
homotopy analysis method, Appl. Math. Model., 32 (2008), 2706{2714.
4
[3] S. Abbasbandy, A Numerical solution of Blasius equation by Adomian's decom-
5
position method and comparison with homotopy perturbation method, Chaos,
6
Solitons and Fractals, 31 (2007), 257{260.
7
[4] S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by
8
modied Adomian decomposition method, Appl. Math. Comput. 145 (2004),
9
[5] S. Abbasbandy, M.T. Darvish, A numerical solution of Burger's equation by
10
modied Adomian method, Appl. Math. Comput. 163 (2005), 1265{1272.
11
[6] H.A. Abdusalam, E.S. Fahmy, Cross-diusional eect in a telegraph reaction
12
diusion Lotka-Volterra two competitive system, Chaos, Solitons & Fractals, 18
13
(2003), 259{264.
14
[7] H. A. Abdusalam, Analytic and approximate solutions for Nagumo telegraph
15
reaction diusion equation, Appl. Math. Comput. 157 (2004), 515{522.
16
[8] G. Adomain, Solving frontier problems of physics: The decomposition method,
17
Kluwer Academic Publishers, Boston, 1994.
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[10] G. Adomian, A review of the decomposition method in applied mathematics, J.
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Math. Anal. Appl. 135 (1998), 501{544.
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Math. Comput. Model. 18 (1993), 103{106.
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[12] E. Ahmed, H. A. Abdusalam, E. S. Fahmy, On telegraph reaction diusion and
24
coupled map lattice in some biological systems, Int. J. Mod. Phys C, 2 (2001),
25
[13] E. Babolian, J. Biazar, Solution of a system of nonlinear Volterra integral equa-
26
tions by Adomian decomposition method, Far East J. Math. Sci. 2 (2000), 935{
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[14] E. Babolian, Sh. Javadi, H. Sadeghi, Restarted Adomian method for integral
28
equations, Appl. Math. Comput. 153 (2004), 353{359.
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[15] S. A. El-Wakil, M. A. Abdou, New applications of Adomian decomposition
30
method, Chaos, Solitons and Fractals 33 (2007), 513{522.
31
[16] A. C. Metaxas, R. J. Meredith, Industrial microwave, heating, Peter Peregrinus,
32
London, 1993.
33
[17] N. Ngarhasts, B. Some, K. Abbaoui, Y. Cherruault, New numerical study of
34
Adomian method applied to a diusion model, Kybernetes 31 (2002), 61{75.
35
[18] W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh-Nagumo
36
type equations, J. Di. Eq. 2 (2006), 381{410.
37
[19] G. Roussy, J. A. Pearcy, Foundations and industrial applications of microwaves
38
and radio frequency elds, John Wiley, New York, 1995.
39
[20] R. A. Van Gorder, K. Vajravelu, A variational formulation of the Nagumo
40
reaction-diusion equation and the Nagumo telegraph equation, Nonlinear Anal-
41
ysis: Real World Applications 4 (2010), 2957{2962.
42
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43
Math. Comput. 102 (1999), 77{86.
44
[22] A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for non-
45
linear operators, Appl. Math. Comput. 111 (2000), 53{69.
46
ORIGINAL_ARTICLE
On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces
http://msj.iau-arak.ac.ir/article_515585_a7229b983c534504b614af5cecef8fbb.pdf
2010-01-01T11:23:20
2017-09-22T11:23:20
83
91
M.
Salehi
msalehi76@yahoo.com
true
1
Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.
Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.
Department of Mathematics, Islamic Azad University, Savadkooh Branch, Savadkooh, Iran.
LEAD_AUTHOR
V.
Dadashi
vahid.dadashi@iausari.ac.ir
true
2
Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
Department of Mathematics, Islamic Azad University, Sari Branch, Sari, Iran.
AUTHOR
M.
Roohi
mehdi.roohi@gmail.com
true
3
Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.
Department of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, Babolsar, Iran.
AUTHOR
[1] S. Atsushiba and W. Takahashi, Strong convergence theorems for nonexpansive
1
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