eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
107
135
10.22052/ijmc.2017.27307.1101
44115
A novel topological descriptor based on the expanded wiener index: Applications to QSPR/QSAR studies
A. Mohajeri
mohajeriaf@gmail.com
1
P. Manshour
2
M. Mousaee
mahboub.mousaee@gmail.com
3
Shiraz University
Persian Gulf University
Shiraz University
In this paper, a novel topological index, named M-index, is introduced based on expanded form of the Wiener matrix. For constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. The usefulness of the M-index is demonstrated by several QSPR/QSAR models for different physico-chemical properties and biological activities of a large number of diversified compounds. Moreover, the applicability of the proposed index has been checked among isomeric compounds. In each case the stability of the obtained model is confirmed by the cross validation test. The results of present study indicate that the M-index provides a promising route for developing highly correlated QSPR/QSAR models. On the other hand, the M-index is easy to generate and the developed QSPR/QSAR models based on this index are linearly correlated. This is an interesting feature of the M-index when compared with quantum chemical descriptors which require vast computational cost and exhibit limitations for large sized molecules.
http://ijmc.kashanu.ac.ir/article_44115_ed97ba1d6515eb34503dd2b4475fc58f.pdf
Topological index
Graph theory
Expanded Wiener index
QSPR
QSAR
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
137
159
10.22052/ijmc.2017.62671.1243
44492
A new two-step Obrechkoff method with vanished phase-lag and some of its derivatives for the numerical solution of radial Schrodinger equation and related IVPs with oscillating solutions
A. Shokri
shokri2090@gmail.com
1
M. Tahmourasi
mortazatahmoras@gmail.com
2
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phase-lag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.
http://ijmc.kashanu.ac.ir/article_44492_8e01a67f4fc6b7019d50bca3ab4de5e4.pdf
Schrodinger equation
Phase-lag
Ordinary differential equations
Symmetric multistep methods
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
161
173
10.22052/ijmc.2017.44718
44718
Optimal control of switched systems by a modified pseudo spectral method
H. Tabrizidooz
htabrizidooz@kashanu.ac.ir
1
M. Pourbabaee
m.pourbabaee@kashanu.ac.ir
2
M. Hedayati
mehr-hedayati@yahoo.com
3
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching times appear as unknown parameters. Using the Legendre-Gauss-Lobatto quadrature and the corresponding differentiation matrix, the alternative problem is discretized to a nonlinear programming problem. At last, we examine three examples in order to illustrate the efficiency of the proposed method.
http://ijmc.kashanu.ac.ir/article_44718_1e87a1ff18ab935c6f732d0c3ec9c742.pdf
Optimal control
switched systems
Legendre pseudospectral method
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
175
180
10.22052/ijmc.2017.80007.1275
44724
Computing Szeged index of graphs on triples
M. Darafsheh
darafsheh@ut.ac.ir
1
R. Modabernia
r.modabber@yahoo.com
2
M. Namdari
namdari@ipm.ir
3
School of Mathematics, College of Science, University of Tehran
Department of Mathematics, Shahid Chamran University of Ahvaz
Department of Mathematics, Shahid Chamran University of Ahvaz
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define three types of intersection graphs with vertex set V. These graphs are denoted by and we will find their Szeged indices.
http://ijmc.kashanu.ac.ir/article_44724_d35b9b76bc3595501f731bbd75dc4af7.pdf
Szeged index
Intersection graph
Automorphism of graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
181
198
10.22052/ijmc.2017.67735.1254
44759
Nordhaus-Gaddum type results for the Harary index of graphs
Z. Wang
wangzhao580@yahoo.com
1
Y. Mao
maoyaping@ymail.com
2
X. Wang
wangxiaia@163.com
3
C. Wang
wangchunxiaia@163.com
4
Beijing Normal Unviersity
Qinghai Normal Unviersity
Qinghai Normal University
Qinghai Normal Unviersity
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept of Steiner Harary index and gave its chemical applications. The emph{$k$-center Steiner Harary index} $SH_k(G)$ of $G$ is defined by $SH_k(G)=sum_{Ssubseteq V(G),|S|=k}frac{1}{d_G(S)}$. In this paper, we get the sharp upper and lower bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot SH_k(overline{G})$, valid for any connected graph $G$ whose complement $overline {G}$ is also connected.
http://ijmc.kashanu.ac.ir/article_44759_1d786c099348a391085f5f29d56acc39.pdf
Distance
Steiner distance
Harary index
K-center Steiner Harary index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
199
220
10.22052/ijmc.2017.58461.1225
44911
Determination of critical properties of Alkanes derivatives using multiple linear regression
E. Mohammadinasab
esmohammadinasab@gmail.com
1
Islamic Azad University of Arak Branch
This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.
http://ijmc.kashanu.ac.ir/article_44911_fb51b07421247e66c784b0b7270c8254.pdf
Alkanes
MLR
Critical Properties
QSPR
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-06-01
8
2
221
229
10.22052/ijmc.2017.49481.1177
44912
Some relations between Kekule structure and Morgan-Voyce polynomials
I. Gultekin
igultekin@atauni.edu.tr
1
B. Sahin
bsahin@bayburt.edu.tr
2
Ataturk University
bayburt university
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.
http://ijmc.kashanu.ac.ir/article_44912_fea8dc821c1e063ed5c0cf85f2a9e709.pdf
Kekule structure
Hosoya Index
Morgan-Voyce polynomial
Caterpillar Tree