eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
339
343
10.22052/ijmc.2017.87093.1290
49788
Borderenergetic graphs of order 12
B. Furtula
furtula@kg.ac.rs
1
I. Gutman
gutman@kg.ac.rs
2
Faculty of Science, University of Kragujevac, Serbia.
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
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_e4fd7626f4f5ccd491b2376fc1ba6d33.pdf
Graph energy
Borderenergetic graph
Spectrum (of graph)
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
345
364
10.22052/ijmc.2017.86494.1289
48032
A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
O. Belhamiti
belhamitio@yahoo.fr
1
B. Absar
belkacem.absar@univ-mosta.dz
2
Department of Mathematics and Computer Science Faculty of Science and Computer Science University of Mostaganem Mostaganem Algeria
Department of Chemical Processes Faculty of Engineering Abdelhamid Ibn Badis University, Mostaganem, Algeria
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_ff48681a45a60de0429bac163d8c4c22.pdf
Reverse osmosis desalination system
Legendre wavelet method
DQL- technique
Caputo fractional derivative
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
365
375
10.22052/ijmc.2017.29095.1109
45351
Solving time-fractional chemical engineering equations by modified variational iteration method as fixed point iteration method
A. Haghbin
ahmadbin@yahoo.com
1
H. Jafari
jafari@umz.ac.ir
2
Islamic Azad University, Gorgan
University of Mazandaran
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_7ad4e59b4cdb4132de2c3a8367a50a90.pdf
Fractional differential equations
Variational iteration method
Fixed point theory
Chemical reactor
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
377
390
10.22052/ijmc.2017.53731.1198
45116
The ratio and product of the multiplicative Zagreb indices
R. Kazemi
r.kazemi@sci.ikiu.ac.ir
1
Imam Khomeini international university
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_bba187473ad5bfb18a6a43340e77aeed.pdf
Molecular graph with tree structure, Multiplicative Zagreb indices
Moments
Doob's supermartingale inequality
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
391
401
10.22052/ijmc.2017.46693.1161
48642
Extermal trees with respect to some versions of Zagreb indices via majorization
M. Eliasi
eliasi@math.iut.ac.ir
1
A. Ghalavand
ali797ghalavand@gmail.com
2
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar Iran
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_8ce4604ddc78e89ae0e39ca4005451db.pdf
Majorization
General first Zagreb index
Multiplicative Zagreb indices
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
403
411
10.22052/ijmc.2016.39228
39228
The uniqueness theorem for inverse nodal problems with a chemical potential
S. Mosazadeh
s.mosazadeh@kashanu.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan
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_810c417f6d7e1c4aec863747b9c351c9.pdf
Boundary Value problem
Inverse Nodal problem
Eigenvalues
Nodal points
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
413
423
10.22052/ijmc.2017.47506.1170
50016
Numerical modeling for nonlinear biochemical reaction networks
Z. A. Zafar
zainzafar@ucp.edu.pk
1
K. Rehan
kkashif.99@gmail.com
2
M. Mushtaq
mmushtaq@uet.edu.pk
3
M. Rafiq
m.rafiq@ucp.edu.pk
4
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
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_11567eff2592ac019bf3417a8b52b650.pdf
Michaelis-Menten model
NSFD Method
RK4 method
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-12-01
8
4
425
437
10.22052/ijmc.2017.54560.1203
50034
Numerical solution of gas solution in a fluid: fractional derivative model
S. Esmaeili
sh.esmaeili@uok.ac.ir
1
Department of Applied Mathematics, University of Kurdistan
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_73a116525fb753b1ccdd521ebf4603c7.pdf
Fractional derivatives
Gas solution
M"{u}ntz polynomials
Gaussian quadrature
Collocation method