eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
143
162
10.22052/ijmc.2013.5289
5289
A Diffusion Equation with Exponential Nonlinearity Recant Developments
A. HUBER
1
Austria
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.
http://ijmc.kashanu.ac.ir/article_5289_2e007f25037d0d105f2b293110474ea8.pdf
Nonlinear partial differential equation(s) or (nPDE(s))
Evolution equations
Lie group analysis
Similarity reduction (SR)
Approximate symmetries
Generalized symmetries
nonlinear diffusion
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
163
175
10.22052/ijmc.2013.5290
5290
Feature Selection and Classification of Microarray Gene Expression Data of Ovarian Carcinoma Patients using Weighted Voting Support Vector Machine
S. MASOUM
1
S. GHAHERI
2
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5290_429167f84c969ebf129c9a59185620b1.pdf
Weighted voting algorithm
support vector machine
Tumor classification
Ovarian cancer
Gene Expression data
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
177
183
10.22052/ijmc.2013.5291
5291
The Generalized Wiener Polarity Index of some Graph Operations
Y. WU
1
F. WEI
2
Z. JIA
3
South China Agricultural University, P. R. China
South China Agricultural University, P. R. China
South China Agricultural University, P. R. China
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.
http://ijmc.kashanu.ac.ir/article_5291_e1096cccf72ca05e59729a62d14028f7.pdf
Wiener index
Cartesian product
tensor product
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
185
199
10.22052/ijmc.2013.5292
5292
DFT Study of Kinetic and Thermodynamic Parameters of Tautomerism in 4−acyl Pyrazolone
H. TAVAKOL
1
H. MOHAMMADI
2
S. ASLANZADEH
3
Isfahan University of Technology, Iran
Technical Vocational University, Iran
Technical Vocational University, Iran
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.
http://ijmc.kashanu.ac.ir/article_5292_c138510f74a2bbdb455cb2f330275055.pdf
Pyrazolone
DFT
Tautomer
Solvent effect
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
201
212
10.22052/ijmc.2013.5293
5293
Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems
A. SHOKRI
1
A. A. SHOKRI
2
University of Maragheh, Iran
Ahar Branch, Islamic Azad University, Iran
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.
http://ijmc.kashanu.ac.ir/article_5293_8028166ae8e7d9a63e3a80b18208adb4.pdf
Hybrid method
Initial value problem
Multistep methods
Off-step points
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
213
220
10.22052/ijmc.2013.5294
5294
The Hyper-Zagreb Index of Graph Operations
G. SHIRDEL
1
H. REZAPOUR
2
A. SAYADI
3
University of Qom, Iran
University of Qom, Iran
University of Tehran, Iran
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.
http://ijmc.kashanu.ac.ir/article_5294_fbb55de9f98dd512946bb421b81a8dfe.pdf
Hyper-Zagreb index
Zagreb index
Graph operation
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
221
230
10.22052/ijmc.2013.5295
5295
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
M. TAVAKOLI
1
F. RAHBARNIA
2
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
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.
http://ijmc.kashanu.ac.ir/article_5295_d0a3f8a01ff5a70b280c0ea4a94f90f3.pdf
Topological index
Graph operation
Distance-balanced graph
Chemical graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
231
238
10.22052/ijmc.2013.5296
5296
On the Roots of Hosoya Polynomial of a Graph
M. REYHANI
1
S. ALIKHANI
2
M. IRANMANESH
3
Islamic Azad University, Iran
Yazd University, Yazd, Iran
Yazd University, Iran
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.
http://ijmc.kashanu.ac.ir/article_5296_410164e0c444ea9cc736e03dd626520e.pdf
Hosoya polynomial
root
Path
Cycle
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
239
248
10.22052/ijmc.2013.5299
5299
Wiener Index of Graphs in Terms of Eccentricities
H. RAMANE
1
A. GANAGI
2
H. WALIKAR
3
Karnatak University, India
Gogte Institute of Technology, India
Karnatak University, India
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.
http://ijmc.kashanu.ac.ir/article_5299_e4714d9416dc74cc8611ae33bf9e475e.pdf
Wiener index
distance
Eccentricity
radius
diameter
self-centered graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
249
255
10.22052/ijmc.2013.5300
5300
Reciprocal Degree Distance of Grassmann Graphs
L. POURFARAJ
1
Islamic Azad University, Central Tehran Branch, Iran
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.
http://ijmc.kashanu.ac.ir/article_5300_292363a7d23f1a685a6e9673fa5fc53f.pdf
Grassmann graph
Harary index
Vertex- transitive graphs
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
257
263
10.22052/ijmc.2013.5301
5301
On the Higher Randić Index
Y. ALIZADEH
1
Hakim Sabzevari University, Sabzevar, Iran
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.
http://ijmc.kashanu.ac.ir/article_5301_2937bfe5de90a364cc45426a78b04b0b.pdf
Randić index
Higher Randić index
Coronene /circumcoronene
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2013-05-01
4
2
265
270
10.22052/ijmc.2013.5302
5302
On Second Atom-Bond Connectivity Index
M. ROSTAMI
1
M. SOHRABI-HAGHIGHAT
2
M. GHORBANI
3
Mahallat Branch, Islamic Azad University, Iran
Arak University, Iran
Shahid Rajaee Teacher Training University, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_5302_88b5b777af28eda3d055d50368c08a18.pdf
Atom–bond connectivity index
Topological index
Star–like graph