Iranian Journal of Mathematical Chemistry
Year:2017 | Volume:8 | Issue:2 |Papers Count:8

Born in Rome (Italy) in 1949, Roberto Todeschini graduated in chemistry at the University of Milan (Italy) in 1972 with a thesis in theoretical chemistry. He got married to Marilena in 1973 and soon had a daughter Alessia (1975) and some years later a son Edoardo (1982). In 1975, he was appointed to the position of researcher at the same university in Milano and worked in the field of theoretical chemistry, with special focus on conformational analysis, until the first ‘ 80s. Then, since 1985 his research interests have shifted towards chemometrics, multivariate analysis and applied statistics, QSAR, molecular descriptors, multicriteria decision making, software development, starting to publish on these topics...

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.

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 Schrö dinger 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 are 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.

In the present paper, we develop a modified pseudo spectral 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.

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 Sz(G)= ∑ _e=uv∊ E^n_u(e|G)n_v(e|G), where nu(e|G) is the number of vertices of G closer to u than v and nv(e|G) can be defined in a similar way. Let S be a set of sizen ≥ 8 and V be the set of all subsets of S of size 3. We define three types of intersection graphs with vertex set V. These graphs are denoted by Gi(n), i=0, 1, 2 and we will find their Szeged indices.

The Harary index H(G) of a connected graph Gis defined as H(G) = ∑ _u, v∊ V(G) 1/d_G(u, v), where d_G(u, v) is the distance between vertices u and v of G. The Steiner distance in agraph, 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 S ⊆ V(G), the 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 Katanić introduced the concept of Steiner Harary index and gave its chemical applications...

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 hyper-Wiener, Platt, MinZL is the most appropriate one.

In this paper, Kekulé structures of benzenoid chains are considered. It has been shown that the coefficients of a Bn(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 non-branched catacondensed benzenoid chains and Morgan– Voyce polynomials and between regularly zig− zag non branched catacondensed benzenoid chains and their corresponding caterpillar trees.