A Diffusion Equation with Exponential Nonlinearity Recant Developments
A.
HUBER
Austria
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
143
162
https://ijmc.kashanu.ac.ir/article_5289_2e007f25037d0d105f2b293110474ea8.pdf
dx.doi.org/10.22052/ijmc.2013.5289
Feature Selection and Classification of Microarray Gene Expression Data of Ovarian Carcinoma Patients using Weighted Voting Support Vector Machine
S.
MASOUM
University of Kashan, I. R. Iran
author
S.
GHAHERI
University of Kashan, I. R. Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
163
175
https://ijmc.kashanu.ac.ir/article_5290_429167f84c969ebf129c9a59185620b1.pdf
dx.doi.org/10.22052/ijmc.2013.5290
The Generalized Wiener Polarity Index of some Graph Operations
Y.
WU
South China Agricultural University, P. R.
China
author
F.
WEI
South China Agricultural University, P. R.
China
author
Z.
JIA
South China Agricultural University, P. R.
China
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
177
183
https://ijmc.kashanu.ac.ir/article_5291_e1096cccf72ca05e59729a62d14028f7.pdf
dx.doi.org/10.22052/ijmc.2013.5291
DFT Study of Kinetic and Thermodynamic Parameters of Tautomerism in 4−acyl Pyrazolone
H.
TAVAKOL
Isfahan University of Technology, Iran
author
H.
MOHAMMADI
Technical Vocational University, Iran
author
S.
ASLANZADEH
Technical Vocational University, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
185
199
https://ijmc.kashanu.ac.ir/article_5292_c138510f74a2bbdb455cb2f330275055.pdf
dx.doi.org/10.22052/ijmc.2013.5292
Implicit One-step L-stable Generalized Hybrid Methods for the Numerical Solution of First Order Initial Value problems
A.
SHOKRI
University of Maragheh, Iran
author
A. A.
SHOKRI
Ahar Branch, Islamic Azad University, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
201
212
https://ijmc.kashanu.ac.ir/article_5293_8028166ae8e7d9a63e3a80b18208adb4.pdf
dx.doi.org/10.22052/ijmc.2013.5293
The Hyper-Zagreb Index of Graph Operations
G.
SHIRDEL
University of Qom, Iran
author
H.
REZAPOUR
University of Qom,
Iran
author
A.
SAYADI
University of Tehran,
Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
213
220
https://ijmc.kashanu.ac.ir/article_5294_fbb55de9f98dd512946bb421b81a8dfe.pdf
dx.doi.org/10.22052/ijmc.2013.5294
Applications of some Graph Operations in Computing some Invariants of Chemical Graphs
M.
TAVAKOLI
Ferdowsi University of Mashhad,
Iran
author
F.
RAHBARNIA
Ferdowsi University of Mashhad, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
221
230
https://ijmc.kashanu.ac.ir/article_5295_d0a3f8a01ff5a70b280c0ea4a94f90f3.pdf
dx.doi.org/10.22052/ijmc.2013.5295
On the Roots of Hosoya Polynomial of a Graph
M.
REYHANI
Islamic Azad University, Iran
author
S.
ALIKHANI
Yazd University, Yazd, Iran
author
M.
IRANMANESH
Yazd University, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
231
238
https://ijmc.kashanu.ac.ir/article_5296_410164e0c444ea9cc736e03dd626520e.pdf
dx.doi.org/10.22052/ijmc.2013.5296
Wiener Index of Graphs in Terms of Eccentricities
H.
RAMANE
Karnatak University, India
author
A.
GANAGI
Gogte Institute of Technology, India
author
H.
WALIKAR
Karnatak University, India
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
239
248
https://ijmc.kashanu.ac.ir/article_5299_e4714d9416dc74cc8611ae33bf9e475e.pdf
dx.doi.org/10.22052/ijmc.2013.5299
Reciprocal Degree Distance of Grassmann Graphs
L.
POURFARAJ
Islamic Azad University, Central Tehran Branch,
Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
249
255
https://ijmc.kashanu.ac.ir/article_5300_292363a7d23f1a685a6e9673fa5fc53f.pdf
dx.doi.org/10.22052/ijmc.2013.5300
On the Higher Randić Index
Y.
ALIZADEH
Hakim Sabzevari University, Sabzevar, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
257
263
https://ijmc.kashanu.ac.ir/article_5301_2937bfe5de90a364cc45426a78b04b0b.pdf
dx.doi.org/10.22052/ijmc.2013.5301
On Second Atom-Bond Connectivity Index
M.
ROSTAMI
Mahallat Branch, Islamic Azad University,
Iran
author
M.
SOHRABI-HAGHIGHAT
Arak University, Iran
author
M.
GHORBANI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
2
no.
2013
265
270
https://ijmc.kashanu.ac.ir/article_5302_88b5b777af28eda3d055d50368c08a18.pdf
dx.doi.org/10.22052/ijmc.2013.5302