University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Autobiography of Roberto Todeschini931054309510.22052/ijmc.2017.43095ENR.TodeschiniMilano Chemometrics and QSAR Research GroupJournal Article20160902University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601A novel topological descriptor based on the expanded wiener index: Applications to QSPR/QSAR studies1071354411510.22052/ijmc.2017.27307.1101ENA.MohajeriShiraz UniversityP.ManshourPersian Gulf UniversityM.MousaeeShiraz UniversityJournal Article20150406In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601A 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 solutions1371594449210.22052/ijmc.2017.62671.1243ENA.ShokriDepartment of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.M.TahmourasiDepartment of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.Journal Article20161002A 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.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Optimal control of switched systems by a modified pseudo spectral method1611734471810.22052/ijmc.2017.44718ENH. R.TabrizidoozDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of KashanM.PourbabaeeDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of KashanM.HedayatiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of KashanJournal Article20160118In 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.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Computing Szeged index of graphs on triples1751804472410.22052/ijmc.2017.80007.1275ENM. R.DarafshehSchool of Mathematics, College of Science, University of TehranR.ModaberniaDepartment of Mathematics, Shahid Chamran University of AhvazM.NamdariDepartment of Mathematics, Shahid Chamran University of AhvazJournal Article20161020ABSTRACT 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).<br /> 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.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Nordhaus-Gaddum type results for the Harary index of graphs1811984475910.22052/ijmc.2017.67735.1254ENZ.WangBeijing Normal UnviersityY.MaoQinghai Normal UnviersityX.WangQinghai Normal UniversityC.WangQinghai Normal UnviersityJournal Article20161116The 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 $d_G(u,v)$<br /> is the distance between vertices $u$ and $v$ of $G$. The<br /> Steiner distance in a graph, introduced by Chartrand et al. in<br /> 1989, is a natural generalization of the concept of classical graph<br /> distance. For a connected graph $G$ of order at least $2$ and<br /> $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the<br /> vertices of $S$ is the minimum size of a connected subgraph whose<br /> vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept<br /> of Steiner Harary index and gave its chemical applications. The emph{$k$-center Steiner Harary index} $SH_k(G)$ of $G$ is<br /> defined by $SH_k(G)=sum_{Ssubseteq V(G),|S|=k}frac{1}{d_G(S)}$.<br /> In this paper, we get the sharp upper and lower<br /> bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot<br /> SH_k(overline{G})$, valid for any connected graph $G$ whose<br /> complement $overline {G}$ is also connected.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Determination of critical properties of Alkanes derivatives using multiple linear regression1992204491110.22052/ijmc.2017.58461.1225ENE.MohammadinasabIslamic Azad University of Arak BranchJournal Article20160727This 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.University of KashanIranian Journal of Mathematical Chemistry2228-64898220170601Some relations between Kekule structure and Morgan-Voyce polynomials2212294491210.22052/ijmc.2017.49481.1177ENI.GultekinAtaturk UniversityB.Sahinbayburt universityJournal Article20160302In 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.