ORIGINAL_ARTICLE
Borderenergetic graphs of order 12
A graph G of order n is said to be borderenergetic if its energy is equal to 2n-2 and if G differs from the complete graph Kn. The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order n was determined for n
http://ijmc.kashanu.ac.ir/article_49788_59c1216a190db25eecedafc58a8b0ef3.pdf
2017-12-01T11:23:20
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339
344
10.22052/ijmc.2017.87093.1290
Graph energy
Borderenergetic graph
Spectrum (of graph)
B.
Furtula
boris.furtula@pmf.kg.ac.rs
true
1
Faculty of Science, University of Kragujevac, Serbia.
Faculty of Science, University of Kragujevac, Serbia.
Faculty of Science, University of Kragujevac, Serbia.
AUTHOR
I.
Gutman
gutman@kg.ac.rs
true
2
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
LEAD_AUTHOR
1. D. Cvetković, P. Rowlinson, S. Simić, An Introduction to the Theory of Graph
1
Spectra, Cambridge Univ. Press, Cambridge, 2010.
2
2. X. Li, Y. Shi, I. Gutman, Graph Energy, Springer, New York, 2012.
3
3. I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry,
4
Springer, Berlin, 1986.
5
4. B. J. McClelland, Properties of the latent roots of a matrix: The estimation of π-
6
electron energies, J. Chem. Phys. 54 (1971) 640−643.
7
5. I. Gutman, Total π-electron energy of benzenoid hydrocarbons, Topics Curr.
8
Chem. 162 (1992) 29−63.
9
6. I. Gutman, T. Soldatović, (n,m)-Type approximations for total π-electron energy of
10
benzenoid hydrocarbons, MATCH Commun. Math. Comput. Chem. 44 (2001)
11
169−182.
12
7. I. Gutman, McClelland-type lower bound for total π-electron energy, J. Chem. Soc.
13
Faraday Trans. 86 (1990) 3373−3375.
14
8. D. Cvetković, I. Gutman, The computer system GRAPH: A useful tool in chemical
15
graph theory, J. Comput. Chem. 7 (1986) 640−644.
16
9. H. B. Walikar, H. S. Ramane, P. R. Hampiholi, On the energy of a graph, in: R.
17
Balakrishnan, H. M. Mulder, A. Vijayakumar (Eds.), Graph Connections, Allied
18
Publishers, New Delhi, 1999, pp. 120−123.
19
10. I. Gutman, Hyperenergetic molecular graphs, J. Serb. Chem. Soc. 64 (1999)
20
199−205.
21
11. I. Gutman, Hyperenergetic and hypoenergetic graphs, in: D. Cvetković, I. Gutman
22
(Eds.), Selected Topics on Applications of Graph Spectra, Math. Inst., Belgrade,
23
2011, pp. 113−135.
24
12. V. Nikiforov, Graphs and matrices with maximal energy, J. Math. Anal. Appl. 327
25
(2007) 735−738.
26
13. S. Gong, X. Li, G. Xu, I. Gutman, B. Furtula, Borderenergetic graphs, MATCH
27
Commun. Math. Comput. Chem.74 (2015) 321−332.
28
14. Y. Hou, I. Gutman, Hyperenergetic line graphs, MATCH Commun. Math. Comput.
29
Chem. 43 (2001) 29−39.
30
15. X. Li, M. Wei, S. Gong, A computer search for the borderenergetic graphs of order
31
10, MATCH Commun. Math. Comput. Chem. 74 (2015) 333−342.
32
16. B. Deng, X. Li, I. Gutman, More on borderenergetic graphs, Lin. Algebra Appl.
33
497 (2016) 199−208.
34
17. Y. Hou, Q. Tao, Borderenergetic threshold graphs, MATCH Commun. Math.
35
Comput. Chem. 75 (2016) 253−262.
36
18. Z. Shao, F. Deng, Correcting the number of borderenergetic graphs of order 10,
37
MATCH Commun. Math. Comput. Chem. 75 (2016) 263−265.
38
19. X. Li, M. Wei, X. Zhu, Borderenergetic graphs with small maximum or large
39
minimum degrees, MATCH Commun. Math. Comput. Chem. 77 (2017) 25−36.
40
20. B. D. McKay, A. Piperno, Practical graph isomorphism II, J. Symb. Comput. 60
41
(2013) 94−112.
42
ORIGINAL_ARTICLE
A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential technique and to highlight the broad applicability and the efficiency of this method. The fractional derivative is described in the Caputo sense.
http://ijmc.kashanu.ac.ir/article_48032_353840879c192f585d7f14d06d947d30.pdf
2017-12-01T11:23:20
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345
364
10.22052/ijmc.2017.86494.1289
Reverse osmosis desalination system
Legendre wavelet method
DQL- technique
Caputo fractional derivative
O.
Belhamiti
belhamitio@yahoo.fr
true
1
Department of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
Algeria
Department of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
Algeria
Department of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
Algeria
LEAD_AUTHOR
B.
Absar
belkacem.absar@univ-mosta.dz
true
2
Department of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, Algeria
Department of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, Algeria
Department of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, Algeria
AUTHOR
[1] A. Abbas, Model predictive control of a reverse osmosis desalination unit, Desalin.
1
194 (2006) 268−280.
2
[2] B. Absar and O. Belhamiti, Modeling and computer simulation of a reverse osmosis
3
desalination plant-case study of Bousfer plant-Algeria, Desalin. Water Treat. 51 (2013)
4
5942−5953.
5
[3] B. Absar, S. E. M. L. Kadi and O. Belhamiti, Reverse osmosis modeling with the
6
orthogonal collocation on finite element method, Desalin. Water Treat. 21 (2010)
7
23−32.
8
[4] M. G. Marcovecchio, P. A. Aguirre and N. J. Scenna, Global optimal design of reverse
9
osmosis networks for seawater desalination: modeling and algorithm, Desalin. 184
10
(2005) 259−271.
11
[5] H. J. Oh, T. M. Hwang and S. Lee, A simplified simulation model of RO systems for
12
seawater desalination, Desalin. 238 (2009) 128−139.
13
[6] N. Ablaoui-Lahmar and O. Belhamiti, Numerical study of convection-reactiondiffusion
14
equation by the Legendre wavelet finite difference method. Adv. Nonlinear
15
Var. Inequal. 19 (2016) (2) 94−112.
16
[7] H. Ali Merina and O. Belhamiti, Simulation Study of Nonlinear Reverse Osmosis
17
Desalination System Using Third and Fourth Chebyshev Wavelet Methods. MATCH
18
Commun. Math. Comput. Chem. 75 (2016) 629−652.
19
[8] A. Atangana and A. A. Secer, Note on fractional order derivatives and table of
20
fractional derivatives of some special functions, Abstr. Appl. Anal. 2013 (2013) 1−8.
21
[9] O. Belhamiti, A new approach to solve a set of nonlinear split boundary value
22
problems, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 555−565.
23
[10] M. Caputo, Linear model of dissipation whose Q is almost frequency independent − II,
24
Geophys. J. R. Astron. Soc. 13 (1967), 529−539.
25
[11] M. Du, Z. Wang and H. Hu, Measuring memory with the order of fractional
26
derivative, Sci. Rep. 3 (2013) 1−3.
27
[12] K. Diethelm, A fractional calculus based model for the simulation of an outbreak of
28
dengue fever, Nonlinear Dyn. 71 (2013) 613−619.
29
[13] F. Gorenflo and F. Mainardi, Fractional Calculus: Integral and Differential Equations
30
of Fractional Order, in Fractals and Fractional Calculus in Continuum Mechanics,
31
Series CISM Courses and Lecture Notes, Springer Verlag, Wien, 378 (1997), 223−276.
32
[14] M. Hamou Maamar and O. Belhamiti, New (0,2) Jacobi multi-wavelets adaptive
33
method for numerical simulation of gas separations using hollow fiber membranes,
34
Commun. Appl. Nonlinear Anal. 22 (2015) 3, 61−81.
35
[15] H. A. Jalab and R. W. Ibrahim, Texture enhancement for medical images based on
36
fractional differential masks, Discrete Dyn. Nat. Soc. 2013, Article ID 618536, (2013),
37
[16] H. A. Jalab and R. W. Ibrahim, Texture enhancement based on the Savitzky-Golay
38
fractional, differential operator, Math. Probl. Eng. 2013, Article ID 149289, (2013), 8
39
[17] A. A. Kilbas and S. A. Marzan, Nonlinear differential equation with the caputo
40
fraction derivative in the space of continuously differentiable functions, Differ. Equ. 41
41
(2005) 84−89.
42
[18] J. Klafter, S. C. Lim and R. Metzler, Fractional Dynamics. Recent Advances, World
43
Scientific, Singapore, (2011).
44
[19] A. D. Khawajia, I. K. Kutubkhanaha and J. M. Wieb, Advances in seawater
45
desalination technologies. Desalin. 221 (2008) 47−69.
46
[20] K. Hakiki and O. Belhamiti, A dynamical study of fractional order obesity model by a
47
combined Legendre wavelet method, submited, (2016).
48
[21] V. Lakshmikantham and A. S. Vatsala, Basic theory of fractional differential
49
equations, Nonlinear Anal. (2008), 2677−2682.
50
[22] Y. Q. Liu and J. H. Ma, Exact solutions of a generalized multi-fractional nonlinear
51
diffusion equation in radical symmetry, Commun. Theor. Phys. 52 (2009) 857−861.
52
[23] J. Lu and G. A. Chen, Note on the fractional-order Chen system, Chaos, Solitons and
53
Fractals 27 (2006) 685−688.
54
[24] C. Qing−li, H. Guo and Z. A. Xiu−qiong, Fractional differential approach to low
55
contrast image enhancement, Int. J. Knowledge Lang. Proces. 3 (2012) 20−29.
56
[25] M. Rehman and R. A. Khan, The Legendre wavelet method for solving fractional
57
differential equations, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 4163−4173.
58
[26] M. Razzaghi and S. Yousefi, Legendre wavelets direct method for variational
59
problems, Math. Comput. Simul. 53 (2000) 185−192.
60
[27] C. H. Wang, On the generalization of Block Pulse Operational matrices for fractional
61
and operational calculus, J. Frankin Inst. 315 (1983) 91−102.
62
[28] C. S. Slater, Development of a simulation model predicting performance of reverse
63
osmosis batch systems, Separa. Sci. Techno. 27 (1992) 1361−1388.
64
[29] C. S. Slater, J. M. Zielinski, R. G. Wendel and C. G. Uchrin, Modeling of small scale
65
reverse osmosis systems, Desalin. 52 (1985) 267−284.
66
[30] V. M. Starov, J. Smart and D. R. Lloyd, Performance optimization of hollow fiber
67
reverse osmosis membranes, Part I. Development of theory, J. Membrane Sci. 103
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(1995) 257−270.
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[31] J. Smart, V. M. Starov and D.R. Lloyd, Performance optimization of hollow fiber
70
reverse osmosis membranes. Part II. Comparative study of flow configurations, J.
71
Membrane Sci. 119 (1996) 117−128.
72
ORIGINAL_ARTICLE
Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method
The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.
http://ijmc.kashanu.ac.ir/article_45351_663180f12cd27ea2d0147431b6a81d9b.pdf
2017-12-01T11:23:20
2020-02-17T11:23:20
365
375
10.22052/ijmc.2017.29095.1109
Fractional differential equations
Variational iteration method
Fixed point theory
Chemical reactor
A.
Haghbin
ahmadbin@yahoo.com
true
1
Islamic Azad University, Gorgan
Islamic Azad University, Gorgan
Islamic Azad University, Gorgan
LEAD_AUTHOR
H.
Jafari
jafari@umz.ac.ir
true
2
University of Mazandaran
University of Mazandaran
University of Mazandaran
AUTHOR
1. D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and
1
Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World
2
Scientific, 2012.
3
2. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional
4
differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science
5
B.V., Amsterdam, 2006.
6
3. V. Kiryakova, Generalized Fractional Calculus and Applications, Longman and
7
John Wiley, Harlow−New York, 1994.
8
4. F. Mainardi, An historical perspective on fractional calculus in linear
9
viscoelasticity, Frac. Calc. Appl. Anal. 15(4) (2012), 712−718.
10
5. A. B. Malinowska, D. F. M. Torres, Fractional calculus of variations for a
11
combined Caputo derivative, Frac. Calc. Appl. Anal. 14 (4) (2011), 523−538.
12
6. K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York
13
and London, 1974.
14
7. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
15
8. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives:
16
Theory and Applications, Gordon and Breach, Yverdon, 1993.
17
9. J. H. He, Variational iteration method some recent result and new interpretations,
18
J. Comput. Appl. Math. 207 (2007) 3−17.
19
10. H. Jafari, M. Zabihi, E. Salehpor, Application of variational iteration method for
20
modified Camassa−Holm and Degasperis−Procesi equations, Numer. Meth. Part.
21
D. E. 26 (5) (2010) 1033−1039.
22
11. H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Solutions of the fractional Davey−
23
Stewartson equations with variational iteration method, Rom. Rep. Phys. 64 (2)
24
(2012) 337−346.
25
12. S. Momani, Z. Odibat, Numerical comparison of methods for solving linear
26
differential equations of fractional order, Chaos Soliton. Fract. 31 (2007)
27
1248−1255.
28
13. A. M. Wazwaz, A comparison between the variational iteration method and
29
Adomian decomposition method, J. Comput. Appl. Math. 207 (2007) 129−136.
30
14. V. Daftardar−Gejji, H. Jafari, Adomian decomposition: A tool for solving a system
31
of fractional differential equations, J. Math. Anal. Appl. 2 (2005) 508−518.
32
15. S. Momani, N. Shawagfeh, Decomposition method for solving fractional Riccati
33
differential equations, Appl. Math. Comput. 182 (2006) 1083−1092.
34
16. H. Jafari, A comparison between the variational iteration method and the
35
successive approximations method, App. Math. Letters 32 (2014) 1−5.
36
17. A. S. Khuri, A. Sayfy, Variational iteration method: Green's functions and fixed
37
point iterations perspective, Appl. Math. Letters 32 (2014) 28−34.
38
18. K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional
39
Differential Equations, John Wiley and Sons, New York, 1993.
40
19. K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York,
41
20. M. Caputo, Linear models of dissipation whose Q is almost frequency
42
independent. Part II, J. Roy. Astr. Soc. (1967) 529−539.
43
21. M. Inokuti, H. Sekine, T. Mura, General use of the Lagrange multiplier in
44
nonlinear mathematical physics, in: S. Nemat-Nasser (Ed.), Variational Method in
45
Mechanics of Solids, Pergamon Press, Oxford, 1978, pp. 156−162.
46
22. D. D. Ganji, M. Nourollahi, E. Mohseni, Application of He's method to nonlinear
47
chemistry problems, Comp. Math. Appl. 54 (2007) 1122−1132.
48
23. N. Alam Khan, A. Ara, A. Mahmood, Approximate solution of time-fractional
49
chemical engineering equations: A comparative study, Int. J. Chem. Reactor Eng. 8
50
(2010) Article A19.
51
ORIGINAL_ARTICLE
The ratio and product of the multiplicative Zagreb indices
The first multiplicative Zagreb index $\Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $\Pi_2(G)$ is equal to the product of the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $\Pi_3(G)$ is equal to the product of the sums of the degree of pairs of adjacent vertices of $G$. In this paper, we introduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all above indices in a randomly chosen molecular graph with tree structure of order $n$. Also, a supermartingale is introduced by Doob's supermartingale inequality.
http://ijmc.kashanu.ac.ir/article_45116_c080bfbf95b3706d865e19550282e4e3.pdf
2017-12-01T11:23:20
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377
390
10.22052/ijmc.2017.53731.1198
Molecular graph with tree structure, Multiplicative Zagreb indices
Moments
Doob's supermartingale inequality
R.
Kazemi
r.kazemi@sci.ikiu.ac.ir
true
1
Imam Khomeini international university
Imam Khomeini international university
Imam Khomeini international university
LEAD_AUTHOR
1. R. B. Ash, C. A. Doléans-Dade, Probability and Measure Theory, Second Edition,
1
Academic Press, 2000.
2
2. M. Eliasi, A. Iranmanesh, and I. Gutman, Multiplicative versions of first Zagreb
3
index, MATCH Commun. Math. Comput. Chem. 68 (2012) 217−230.
4
3. M. Ghorbani, M. Songhori, Computing Multiplicative Zagreb Indices with respect
5
to Chromatic and Clique Numbers, Iranian J. Math. Chem. 5 (1) (2012) 11−18.
6
4. M. Ghorbani, N. Azami, Note on multiple Zagreb indices, Iranian J. Math. Chem. 3
7
(2) (2012) 137−143.
8
5. I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (4) (2013)
9
351−361.
10
6. I. Gutman, Multiplicative Zagreb indices of trees, Bull. Internat. Math. Virt. Inst. 1
11
(2011) 13−19.
12
7. A. Iranmanesh, M. A. Hosseinzadeh, and I. Gutman, On multiplicative Zagreb
13
indices of graphs, Iranian J. Math. Chem.3(2) (2012), 145−154.
14
8. R. Kazemi, Probabilistic analysis of the first Zagreb index, Trans. Comb. 2 (2)
15
(2013) 35−40.
16
9. R. Kazemi, The eccentric connectivity index of bucket recursive trees, Iranian J.
17
Math. Chem. 5 (2) (2014) 77−83.
18
10. R. Kazemi, The second Zagreb index of molecular graphs with tree structure,
19
MATCH Commun. Math. Comput. Chem. 72 (2014) 753−760.
20
11. R. Kazemi, Note on the multiplicative Zagreb indices, Discrete Appl. Math. 198 (1)
21
(2016) 147−154.
22
12. R. Kazemi, A. Fallah, Analysis on some degree-based topological indices, J. of Sci.
23
Math. Issue 25 (98.2) (2016) 15−24.
24
13. J. Liu, Q. Zhang, Sharp upper bounds for multiplicative Zagreb indices, MATCH
25
Commun. Math. Comput. Chem. 68 (2012), 231−240.
26
14. T. Réti, I. Gutman, Relations between ordinary and multiplicative Zagreb indices,
27
Bull. Internat. Math. Virt. Inst. 2 (2012) 133−140.
28
15. R. Todeschini, D. Ballabio, and V. Consonni, Novel molecular descriptors based on
29
functions of new vertex degrees, in: I. Gutman, B. Furtula (Eds.), Novel Molecular
30
Structure Descriptors Theory and Applications I, Univ. Kragujevac, Kragujevac,
31
(2010) 72−100.
32
16. R. Todeschini, V. Consonni, New local vertex invariants and molecular descriptors
33
based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem.
34
64 (2010) 359−372.
35
17. S. Wang, B. Wei, Multiplicative Zagreb indices of k-trees, Discrete Appl. Math.
36
180 (2015) 168−175.
37
18. K. Xu, H. Hua, A unified approach to extremal multiplicative Zagreb indices for
38
trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68
39
(2012) 241−256.
40
ORIGINAL_ARTICLE
Extremal trees with respect to some versions of Zagreb indices via majorization
The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12
http://ijmc.kashanu.ac.ir/article_48642_64062001663bd96ec4ae467dcd11a0d2.pdf
2017-12-01T11:23:20
2020-02-17T11:23:20
391
401
10.22052/ijmc.2017.46693.1161
majorization
General first Zagreb index
Multiplicative Zagreb indices
M.
Eliasi
eliasi@math.iut.ac.ir
true
1
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar Iran
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar Iran
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar Iran
LEAD_AUTHOR
A.
Ghalavand
ali797ghalavand@gmail.com
true
2
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences,
Khansar Iran
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences,
Khansar Iran
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences,
Khansar Iran
AUTHOR
1. A. T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, Topological indices for
1
structure activity correlations, Topics Curr. Chem.114 (1983) 21–55.
2
2. C. Bey, An upper bound on the sum of squares of degrees in a hypergraph, Discrete
3
Math. 269 (2003) 259–263.
4
3. K. C. Das, Sharp bounds for the sum of the squares of the degrees of a graph,
5
Kragujevac J. Math. 25 (2003) 31–49.
6
4. K. C. Das, A. Yurttas, M. Togan, A. S. Cevik and I. N. Cangu, The multiplicative
7
Zagreb indices of graph operations, J. Inequal. Appl. 90 (2013) 1–14.
8
5. D. de Caen, An upper bound on the sum of squares of degrees in a graph, Discrete
9
Math. 185 (1998) 245–248.
10
6. J. Devillers and A. T. Balaban, Topological Indices and Related Descriptors in
11
QSAR and QSPR, Gordon and Breach Science Publishers (1999).
12
7. M. Eliasi, A simple approach to orther the multiplicative Zagreb indices of
13
connectedgraphs, Trans. Comb. 1 (2012) 17–24.
14
8. M. Eliasi, A. Iranmanesh and I. Gutman, Multiplicative versions of first Zagreb
15
index, MATCH Commun. Math. Comput. Chem. 68 (2012) 217–230.
16
9. M. Eliasi and D. Vukicević, Comparing the multiplicative Zagreb indices, MATCH
17
Commun. Math. Comput. Chem. 69 (2013) 765–773.
18
10. M. Eliasi and A. Ghalavand, Ordering of trees by multiplicative second Zagreb
19
index, Trans. Comb. 5 (1) (2016) 49–55.
20
11. I. Gutman, Multiplicative Zagreb indices of trees, Bull. Int. Math. Virt. Inst. 1
21
(2011) 13–19.
22
12. I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun.
23
Math. Comput. Chem. 50 (2004) 83–92.
24
13. I. Gutman, Graphs with smallest sum of squares of vertex degree, Kragujevac J.
25
Math. 25 (2003) 51–54.
26
14. I. Gutman and N. Trinajstić, Graph theory and molecular orbital.Total φ-electron
27
energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
28
15. M. Karelson, Molecular Descriptors in QSAR/QSPR, Wiley, New York (2000).
29
16. X. Li and J. Zheng, A unified approach to the extremal trees for different indices,
30
MATCH Commun. Math. Comput. Chem. 54 (2005) 195–208.
31
17. X. Li and H. Zhao, Trees with the first three smallest and largest generalized
32
topological indices, MATCH Commun. Math. Comput. Chem. 50 (2004) 57–62.
33
18. M. Liu and B. Liu, Some properties of the first general Zagreb index, Australas. J.
34
Combin. 47 (2010) 285–294.
35
19. J. Liu and Q. Zhang, Sharp upper bounds for multiplicative Zagreb indices,
36
MATCH Commun. Math. Comput. Chem. 68 (2012) 231–240.
37
20. S. Nikolić, G. Kovacević, A. Miličević and N. Trinajstić, The Zagreb indices 30
38
years after, Croat. Chem. Acta 76 (2003) 113–124.
39
21. T. Rseti and I. Gutman, Relation between ordinary and multiplicative Zagreb
40
indices, Bull. Int. Math. Virt. Inst. 2 (2012) 133–140.
41
22. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley–VCH
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23. R. Todeschini and V. Consonni, New local vertex invariants and molecular
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descriptors based on functions of the vertex degrees, MATCH Commun. Math.
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Comput. Chem. 64 (2010) 359–372.
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24. K. Xu and H. Hua, A unified approach to extremal multiplicative Zagreb indices
46
for trees, unicyclic and bicyclic raphs, MATCH Commun. Math. Comput. Chem. 68
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(2012) 241–256.
48
ORIGINAL_ARTICLE
The uniqueness theorem for inverse nodal problems with a chemical potential
In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.
http://ijmc.kashanu.ac.ir/article_39228_bffea15fb4cc1335d35422de04f8bfc3.pdf
2017-12-01T11:23:20
2020-02-17T11:23:20
403
411
10.22052/ijmc.2016.39228
Boundary value problem
Inverse Nodal problem
Eigenvalues
Nodal points
S.
Mosazadeh
s.mosazadeh@kashanu.ac.ir
true
1
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan
LEAD_AUTHOR
1. R. Kh. Amirov, On system of Dirac differential equations with discontinuity
1
conditions inside an interval, Ukrainian Math. J. 57 (2005) 712–727.
2
2. R. Amirov and N. Topsakal, On inverse problem for singular Sturm-Liouville
3
operator with discontinuity conditions, Bull. Iranian Math. Soc. 40 (2014) 585–
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3. W. O. Amrein, A. M. Hinz and D. B. Pearson, SturmLiouville Theory: Past and
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Present, Birkhäuser Verlag, Basel, 2005.
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Cambridge, 1980.
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with several singular points and turning points, Math. Nachr. 229 (2001) 51–71.
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singularity, Bull. Iranian Math. Soc. 41 (2015) 1061–1070.
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56
ORIGINAL_ARTICLE
Numerical modeling for nonlinear biochemical reaction networks
Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A NSFD model has been constructed for the biochemical reaction problem and numerical experiments are performed for different values of discretization parameter ‘h’. The results are compared with the well-known numerical scheme, i.e. RK4. Unlike RK4 which fails for large time steps, the developed scheme gives results that converge to true steady states for any time step used.
http://ijmc.kashanu.ac.ir/article_50016_3d4b3705afc3725dcaee76c6dbe32ec1.pdf
2017-12-01T11:23:20
2020-02-17T11:23:20
413
423
10.22052/ijmc.2017.47506.1170
Michaelis-Menten model
NSFD Method
RK4 method
Z. A.
Zafar
zainzafar@ucp.edu.pk
true
1
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
LEAD_AUTHOR
K.
Rehan
kkashif.99@gmail.com
true
2
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
AUTHOR
M.
Mushtaq
mmushtaq@uet.edu.pk
true
3
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
AUTHOR
M.
Rafiq
m.rafiq@ucp.edu.pk
true
4
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
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3
behavior of a model biochemical reaction, J Math Anal Appl. 131 (1988) 232–245.
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3. P. Pongsumpun, Mathematical model of Dengue disease with incubation period of
5
virus, World Acad. Sci. Eng. Technol. 44 (2008) 328–332.
6
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7
Difference Methods for One Dimensional Burgers Equation for Irrotational
8
Incompressible Flow Problem, Pak. J. Engg. & Appl. Sci. 9 (2011) 13–16.
9
5. Z. Zafar, M. O. Ahmad, A. Pervaiz and M. Rafiq, Fourth Order Compact Method
10
for One Dimensional Inhomogeneous Telegraph Equation with (ℎ, ), Pak. J.
11
Engg. & Appl. Sci. 14 (2014) 96–101.
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laws: NSFD METHODS, Biological Dynamics 1 (2007) 427–436.
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Non–standard finite difference schemes for differential equations, J. Differ. Equ.
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analysis method to the transient behavior of a biochemical reaction model, Inf. Sci.
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Lett. 3 (2014) 29–33.
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9. S. O. Edeki, E. A. Owoloko, A. S. Osheku, A. A. Opanuga, H. I. Okagbue and G.
21
O. Akinlabi, Numerical solutions of nonlinear biochemical model using a hybrid
22
numerical – analytical technique, Int. J. Math. Anal. 9 (2015) 403–416.
23
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Epidemology, Springer–Verlag, 2012.
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perturbation method applied to non–linear biochemical reaction model, Chaos
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28
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29
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30
ORIGINAL_ARTICLE
Numerical solution of gas solution in a fluid: fractional derivative model
A computational technique for solution of mathematical model of gas solution in a fluid is presented. This model describes the change of mass of the gas volume due to diffusion through the contact surface. An appropriate representation of the solution based on the M"{u}ntz polynomials reduces its numerical treatment to the solution of a linear system of algebraic equations. Numerical examples are given and discussed to illustrate the effectiveness of the proposed approach.
http://ijmc.kashanu.ac.ir/article_50034_b2a8baae1f6d0082a396ac6810ca2c66.pdf
2017-12-01T11:23:20
2020-02-17T11:23:20
425
437
10.22052/ijmc.2017.54560.1203
Fractional derivatives
Gas solution
M"{u}ntz polynomials
Gaussian quadrature
Collocation method
S.
Esmaeili
sh.esmaeili@uok.ac.ir
true
1
Department of Applied Mathematics,
University of Kurdistan
Department of Applied Mathematics,
University of Kurdistan
Department of Applied Mathematics,
University of Kurdistan
LEAD_AUTHOR
1. A. Ansari and M. Ahmadi Darani, On the generalized mass transfer with a chemical
1
reaction: Fractional derivative model, Iranian J. Math. Chem. 7 (2016) 77–88
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2. Y. I. Babenko, Heat and Mass Transfer: The Method of Calculation for the Heat and
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Diffusion Flows (in Russian), Khimiya, Leningrad, 1986.
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3. Y. I. Babenko, The Method of Fractional Differentiation in Applied Problems of Heat
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and Mass Transfer Theory (in Russian), NPO Professional Publ, St Petersburg, 2009.
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Numerical Methods 2nd ed., World Scientific, Singapore, 2016.
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Appl. 62 (2011) 918–929.
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Application in Fluid Mechanics, Heat and Mass Transfer, Academic Press, New York,
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Philadelphia, 2016.
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to Mathematical Models, Imperial College Press, London, 2010.
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Orthogonal Polynomials, Birkhäuser, Basel 131 (1999) 179–194.
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39
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51