University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
A Diffusion Equation with Exponential Nonlinearity Recant Developments
143
162
EN
A.
HUBER
Austria
10.22052/ijmc.2013.5289
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is therefore the general. We determine the classical Lie point symmetries including algebraic properties whereas similarity solutions are given as well as nonlinear transformations could derived. In addition, we discuss the nonclassical case which seems to be not solvable. Moreover we show how one can deduce approximate symmetries modeling the nonlinear part and we deduce new generalized symmetries of lower symmetry. The analysis allows one to deduce wider classes of solutions either of practical and theoretical usage in different domains of science and engineering.
Nonlinear partial differential equation(s) or (nPDE(s)),Evolution equations,Lie group analysis,Similarity reduction (SR),Approximate symmetries,Generalized symmetries,nonlinear diffusion
http://ijmc.kashanu.ac.ir/article_5289.html
http://ijmc.kashanu.ac.ir/article_5289_2e007f25037d0d105f2b293110474ea8.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
Feature Selection and Classification of Microarray Gene Expression Data of Ovarian Carcinoma Patients using Weighted Voting Support Vector Machine
163
175
EN
S.
MASOUM
University of Kashan, I. R. Iran
S.
GHAHERI
University of Kashan, I. R. Iran
10.22052/ijmc.2013.5290
We can reach by DNA microarray gene expression to such wealth of information with thousands of variables (genes). Analysis of this information can show genetic reasons of disease and tumor differences. In this study we try to reduce high-dimensional data by statistical method to select valuable genes with high impact as biomarkers and then classify ovarian tumor based on gene expression data of two patient groups. One group treated by standard therapies and survived, while another group didn’t be cure and die after some times. In the first step we used weighted voting algorithm (WVA) for selecting impressive genes to reduce dimension, therefore eliminate noisy data and make analysis easier and then partial least square – discriminante analysis (PLS-DA) and support vector machine (SVM) methods have been applied for classification of diminished data. Results show that classification by PLS-DA can distinguish two groups somewhat but SVM is more efficient and sufficient classification method.
Weighted voting algorithm,Support Vector Machine,Tumor classification,Ovarian Cancer,Gene Expression data
http://ijmc.kashanu.ac.ir/article_5290.html
http://ijmc.kashanu.ac.ir/article_5290_429167f84c969ebf129c9a59185620b1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
The Generalized Wiener Polarity Index of some Graph Operations
177
183
EN
Y.
WU
South China Agricultural University, P. R.
China
F.
WEI
South China Agricultural University, P. R.
China
Z.
JIA
South China Agricultural University, P. R.
China
10.22052/ijmc.2013.5291
Let G be a simple connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is k. Some formulas are obtained for computing the generalized polarity Wiener index of the Cartesian product and the tensor product of graphs in this article.
Wiener index,Cartesian product,tensor product
http://ijmc.kashanu.ac.ir/article_5291.html
http://ijmc.kashanu.ac.ir/article_5291_e1096cccf72ca05e59729a62d14028f7.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
DFT Study of Kinetic and Thermodynamic Parameters of Tautomerism in 4−acyl Pyrazolone
185
199
EN
H.
TAVAKOL
Isfahan University of Technology, Iran
H.
MOHAMMADI
Technical Vocational University, Iran
S.
A.
ASLANZADEH
Technical Vocational University, Iran
10.22052/ijmc.2013.5292
In the present work, DFT calculations are employed to obtain the optimized structures of 4- acyl pyrazolone tautomers (19 tautomers) using B3LYP/6-311++G** calculations. In addition, molecular parameters, IR frequencies and relative energies are extracted for all tautomers. The existence of aromatic ring, keto tautomer (versus enol tautomer), N-H bond (versus C-H bond) and C=N double bond (versus N=N double bond) are stabilizing factors in relative stabilities of tautomers. Calculation of vibrational frequencies showed that, in accordance with reported values, intramolecular hydrogen bond (existed in some tautomers) decreased the value of OH frequency. The solvent effects on relative stabilities of tautomers are calculated. The relative stabilities of all the tautomers in acetone, tetrahydrofurane and chloroform (in all solvents, except water) were relatively the same as those in the gas phase. In addition, a nearly good relationship is found between dipole moments of tautomers and their 7Gsolv in chloroform. This relation shows that by increasing the dipole moment, the absolute amount of 7Gsolv in chloroform increases.
Pyrazolone,DFT,Tautomer,Solvent effect
http://ijmc.kashanu.ac.ir/article_5292.html
http://ijmc.kashanu.ac.ir/article_5292_c138510f74a2bbdb455cb2f330275055.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems
201
212
EN
A.
SHOKRI
University of Maragheh, Iran
A. A.
SHOKRI
Ahar Branch, Islamic Azad University, Iran
10.22052/ijmc.2013.5293
In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the numerical solution of stiff first order initial value problems.
Hybrid method,Initial value problem,Multistep methods,Off-step points
http://ijmc.kashanu.ac.ir/article_5293.html
http://ijmc.kashanu.ac.ir/article_5293_8028166ae8e7d9a63e3a80b18208adb4.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
The Hyper-Zagreb Index of Graph Operations
213
220
EN
G.
H.
SHIRDEL
University of Qom, Iran
H.
REZAPOUR
University of Qom,
Iran
A.
M.
SAYADI
University of Tehran,
Iran
10.22052/ijmc.2013.5294
Let G be a simple connected graph. The first and second Zagreb indices have been introduced as vV(G) (v)2 M1(G) degG and M2(G) uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G) (degG(u) degG In this paper, the HyperZagreb index of the Cartesian product, composition, join and disjunction of graphs are computed.
Hyper-Zagreb index,Zagreb index,Graph operation
http://ijmc.kashanu.ac.ir/article_5294.html
http://ijmc.kashanu.ac.ir/article_5294_fbb55de9f98dd512946bb421b81a8dfe.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
221
230
EN
M.
TAVAKOLI
Ferdowsi University of Mashhad,
Iran
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
10.22052/ijmc.2013.5295
In this paper, we first collect the earlier results about some graph operations and then we present applications of these results in working with chemical graphs.
topological index,Graph operation,Distance-balanced graph,Chemical graph
http://ijmc.kashanu.ac.ir/article_5295.html
http://ijmc.kashanu.ac.ir/article_5295_d0a3f8a01ff5a70b280c0ea4a94f90f3.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
On the Roots of Hosoya Polynomial of a Graph
231
238
EN
M.
H.
REYHANI
Islamic Azad University, Iran
S.
ALIKHANI
Yazd University, Yazd, Iran
M.
A.
IRANMANESH
Yazd University, Iran
10.22052/ijmc.2013.5296
Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific graphs.
Hosoya polynomial,root,Path,Cycle
http://ijmc.kashanu.ac.ir/article_5296.html
http://ijmc.kashanu.ac.ir/article_5296_410164e0c444ea9cc736e03dd626520e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
Wiener Index of Graphs in Terms of Eccentricities
239
248
EN
H.
S.
RAMANE
Karnatak University, India
A.
B.
GANAGI
Gogte Institute of Technology, India
H.
B.
WALIKAR
Karnatak University, India
10.22052/ijmc.2013.5299
The Wiener index W(G) of a connected graph G is defined as the sum of the distances between all unordered pairs of vertices of G. The eccentricity of a vertex v in G is the distance to a vertex farthest from v. In this paper we obtain the Wiener index of a graph in terms of eccentricities. Further we extend these results to the self-centered graphs.
Wiener index,Distance,Eccentricity,radius,diameter,self-centered graph
http://ijmc.kashanu.ac.ir/article_5299.html
http://ijmc.kashanu.ac.ir/article_5299_e4714d9416dc74cc8611ae33bf9e475e.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
Reciprocal Degree Distance of Grassmann Graphs
249
255
EN
L.
POURFARAJ
Islamic Azad University, Central Tehran Branch,
Iran
10.22052/ijmc.2013.5300
Recently, Hua et al. defined a new topological index based on degrees and inverse of distances between all pairs of vertices. They named this new graph invariant as reciprocal degree distance as 1 { , } ( ) ( ( ) ( ))[ ( , )] RDD(G) = u v V G d u d v d u v , where the d(u,v) denotes the distance between vertices u and v. In this paper, we compute this topological index for Grassmann graphs.
Grassmann graph,Harary index,Vertex- transitive graphs
http://ijmc.kashanu.ac.ir/article_5300.html
http://ijmc.kashanu.ac.ir/article_5300_292363a7d23f1a685a6e9673fa5fc53f.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
On the Higher Randić Index
257
263
EN
Y.
ALIZADEH
Hakim Sabzevari University, Sabzevar, Iran
10.22052/ijmc.2013.5301
Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih v v v over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher Randic index of a simple graph is presented . Also, the higher Randić index of coronene/circumcoronene is computed.
Randić index,Higher Randić index,Coronene /circumcoronene
http://ijmc.kashanu.ac.ir/article_5301.html
http://ijmc.kashanu.ac.ir/article_5301_2937bfe5de90a364cc45426a78b04b0b.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
2
2013
05
01
On Second Atom-Bond Connectivity Index
265
270
EN
M.
ROSTAMI
Mahallat Branch, Islamic Azad University,
Iran
M.
SOHRABI-HAGHIGHAT
Arak University, Iran
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
10.22052/ijmc.2013.5302
The atom-bond connectivity index of graph is a topological index proposed by Estrada et al. as ABC (G) uvE (G ) (du dv 2) / dudv , where the summation goes over all edges of G, du and dv are the degrees of the terminal vertices u and v of edge uv. In the present paper, some upper bounds for the second type of atom-bond connectivity index are computed.
Atom–bond connectivity index,topological index,Star–like graph
http://ijmc.kashanu.ac.ir/article_5302.html
http://ijmc.kashanu.ac.ir/article_5302_88b5b777af28eda3d055d50368c08a18.pdf