2013
4
2
2
128
A Diffusion Equation with Exponential Nonlinearity Recant Developments
2
2
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.
1

143
162


A.
HUBER
Austria
Austria
Austria
Nonlinear partial differential equation(s) or (nPDE(s))
Evolution equations
Lie group analysis
Similarity reduction (SR)
Approximate symmetries
Generalized symmetries
nonlinear diffusion
Feature Selection and Classification of Microarray Gene Expression Data of Ovarian Carcinoma Patients using Weighted Voting Support Vector Machine
2
2
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 highdimensional 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 (PLSDA) and support vector machine (SVM) methods have been applied for classification of diminished data. Results show that classification by PLSDA can distinguish two groups somewhat but SVM is more efficient and sufficient classification method.
1

163
175


S.
MASOUM
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran


S.
GHAHERI
University of Kashan, I. R. Iran
University of Kashan, I. R. Iran
I R Iran
Weighted voting algorithm
Support Vector Machine
Tumor classification
Ovarian cancer
Gene Expression data
The Generalized Wiener Polarity Index of some Graph Operations
2
2
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.
1

177
183


Y.
WU
South China Agricultural University, P. R.
China
South China Agricultural University, P. R.
China
P. R. China


F.
WEI
South China Agricultural University, P. R.
China
South China Agricultural University, P. R.
China
P. R. China


Z.
JIA
South China Agricultural University, P. R.
China
South China Agricultural University, P. R.
China
P. R. China
Wiener index
Cartesian product
tensor product
DFT Study of Kinetic and Thermodynamic Parameters of Tautomerism in 4−acyl Pyrazolone
2
2
In the present work, DFT calculations are employed to obtain the optimized structures of 4 acyl pyrazolone tautomers (19 tautomers) using B3LYP/6311++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), NH bond (versus CH 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.
1

185
199


H.
TAVAKOL
Isfahan University of Technology, Iran
Isfahan University of Technology, Iran
I R Iran


H.
MOHAMMADI
Technical Vocational University, Iran
Technical Vocational University, Iran
I R Iran


S.
ASLANZADEH
Technical Vocational University, Iran
Technical Vocational University, Iran
I R Iran
Pyrazolone
DFT
Tautomer
Solvent effect
Implicit Onestep Lstable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems
2
2
In this paper, we introduce the new class of implicit Lstable 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.
1

201
212


A.
SHOKRI
University of Maragheh, Iran
University of Maragheh, Iran
I R Iran


A. A.
SHOKRI
Ahar Branch, Islamic Azad University, Iran
Ahar Branch, Islamic Azad University, Iran
I R Iran
Hybrid method
Initial value problem
Multistep methods
Offstep points
The HyperZagreb Index of Graph Operations
2
2
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 distancebased 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.
1

213
220


G.
SHIRDEL
University of Qom, Iran
University of Qom, Iran
I R Iran


H.
REZAPOUR
University of Qom,
Iran
University of Qom,
Iran
I R Iran


A.
SAYADI
University of Tehran,
Iran
University of Tehran,
Iran
I R Iran
HyperZagreb index
Zagreb index
Graph operation
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
2
2
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.
1

221
230


M.
TAVAKOLI
Ferdowsi University of Mashhad,
Iran
Ferdowsi University of Mashhad,
Iran
I R Iran


F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
Ferdowsi University of Mashhad, Iran
I R Iran
Topological index
Graph operation
Distancebalanced graph
Chemical graph
On the Roots of Hosoya Polynomial of a Graph
2
2
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.
1

231
238


M.
REYHANI
Islamic Azad University, Iran
Islamic Azad University, Iran
I R Iran


S.
ALIKHANI
Yazd University, Yazd, Iran
Yazd University, Yazd, Iran
I R Iran


M.
IRANMANESH
Yazd University, Iran
Yazd University, Iran
I R Iran
Hosoya polynomial
root
Path
Cycle
Wiener Index of Graphs in Terms of Eccentricities
2
2
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 selfcentered graphs.
1

239
248


H.
RAMANE
Karnatak University, India
Karnatak University, India
India


A.
GANAGI
Gogte Institute of Technology, India
Gogte Institute of Technology, India
India


H.
WALIKAR
Karnatak University, India
Karnatak University, India
India
Wiener index
Distance
Eccentricity
radius
diameter
selfcentered graph
Reciprocal Degree Distance of Grassmann Graphs
2
2
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.
1

249
255


L.
POURFARAJ
Islamic Azad University, Central Tehran Branch,
Iran
Islamic Azad University, Central Tehran Branch,
Ir
I R Iran
Grassmann graph
Harary index
Vertex transitive graphs
On the Higher Randić Index
2
2
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 hth 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.
1

257
263


Y.
ALIZADEH
Hakim Sabzevari University, Sabzevar, Iran
Hakim Sabzevari University, Sabzevar, Iran
I R Iran
Randić index
Higher Randić index
Coronene /circumcoronene
On Second AtomBond Connectivity Index
2
2
The atombond 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 atombond connectivity index are computed.
1

265
270


M.
ROSTAMI
Mahallat Branch, Islamic Azad University,
Iran
Mahallat Branch, Islamic Azad University,
Iran
I R Iran


M.
SOHRABIHAGHIGHAT
Arak University, Iran
Arak University, Iran
I R Iran


M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran
Atom–bond connectivity index
Topological index
Star–like graph