University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
Borderenergetic graphs of order 12
339
344
EN
B.
Furtula
0000-0002-5056-6892
Faculty of Science, University of Kragujevac, Serbia.
boris.furtula@pmf.kg.ac.rs
I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/ijmc.2017.87093.1290
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
Graph energy,Borderenergetic graph,Spectrum (of graph)
http://ijmc.kashanu.ac.ir/article_49788.html
http://ijmc.kashanu.ac.ir/article_49788_59c1216a190db25eecedafc58a8b0ef3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
345
364
EN
O.
Belhamiti
Department of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
Algeria
belhamitio@yahoo.fr
B.
Absar
Department of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, Algeria
belkacem.absar@univ-mosta.dz
10.22052/ijmc.2017.86494.1289
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.
Reverse osmosis desalination system,Legendre wavelet method,DQL- technique,Caputo fractional derivative
http://ijmc.kashanu.ac.ir/article_48032.html
http://ijmc.kashanu.ac.ir/article_48032_353840879c192f585d7f14d06d947d30.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method
365
375
EN
A.
Haghbin
Islamic Azad University, Gorgan
ahmadbin@yahoo.com
H.
Jafari
University of Mazandaran
jafari@umz.ac.ir
10.22052/ijmc.2017.29095.1109
The variational iteration method(VIM) was extended to find approximate solutions of<br /> 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.
Fractional differential equations,Variational iteration method,Fixed point theory,Chemical reactor
http://ijmc.kashanu.ac.ir/article_45351.html
http://ijmc.kashanu.ac.ir/article_45351_663180f12cd27ea2d0147431b6a81d9b.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
The ratio and product of the multiplicative Zagreb indices
377
390
EN
R.
Kazemi
Imam Khomeini international university
r.kazemi@sci.ikiu.ac.ir
10.22052/ijmc.2017.53731.1198
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<br /> 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.
Molecular graph with tree structure, Multiplicative Zagreb indices,Moments,Doob's supermartingale inequality
http://ijmc.kashanu.ac.ir/article_45116.html
http://ijmc.kashanu.ac.ir/article_45116_c080bfbf95b3706d865e19550282e4e3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
Extremal trees with respect to some versions of Zagreb indices via majorization
391
401
EN
M.
Eliasi
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar Iran
eliasi@math.iut.ac.ir
A.
Ghalavand
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences,
Khansar Iran
ali797ghalavand@gmail.com
10.22052/ijmc.2017.46693.1161
The aim of this paper is using the majorization technique to identify<br /> the classes of trees with extermal (minimal or maximal) value of some topological<br /> indices, among all trees of order n ≥ 12
majorization,General first Zagreb index,Multiplicative Zagreb indices
http://ijmc.kashanu.ac.ir/article_48642.html
http://ijmc.kashanu.ac.ir/article_48642_64062001663bd96ec4ae467dcd11a0d2.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
The uniqueness theorem for inverse nodal problems with a chemical potential
403
411
EN
S.
Mosazadeh
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan
s.mosazadeh@kashanu.ac.ir
10.22052/ijmc.2016.39228
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.
Boundary value problem,Inverse Nodal problem,Eigenvalues,Nodal points
http://ijmc.kashanu.ac.ir/article_39228.html
http://ijmc.kashanu.ac.ir/article_39228_bffea15fb4cc1335d35422de04f8bfc3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
Numerical modeling for nonlinear biochemical reaction networks
413
423
EN
Z. A.
Zafar
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
zainzafar@ucp.edu.pk
K.
Rehan
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
kkashif.99@gmail.com
M.
Mushtaq
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
mmushtaq@uet.edu.pk
M.
Rafiq
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
m.rafiq@ucp.edu.pk
10.22052/ijmc.2017.47506.1170
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.
Michaelis-Menten model,NSFD Method,RK4 method
http://ijmc.kashanu.ac.ir/article_50016.html
http://ijmc.kashanu.ac.ir/article_50016_3d4b3705afc3725dcaee76c6dbe32ec1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
4
2017
12
01
Numerical solution of gas solution in a fluid: fractional derivative model
425
437
EN
S.
Esmaeili
Department of Applied Mathematics,
University of Kurdistan
sh.esmaeili@uok.ac.ir
10.22052/ijmc.2017.54560.1203
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.
Fractional derivatives,Gas solution,M"{u}ntz polynomials,Gaussian quadrature,Collocation method
http://ijmc.kashanu.ac.ir/article_50034.html
http://ijmc.kashanu.ac.ir/article_50034_b2a8baae1f6d0082a396ac6810ca2c66.pdf