Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2017.56982.1233 Computational Chemistry An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures Huber A. A-8062 Kumberg, Prottesweg 2a 01 06 2018 9 2 77 100 30 08 2016 15 02 2017 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_60159.html

In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads to a reformulation of the meaning of the nonlinear Poisson-Boltzmann Equation (PBE). If a concentration and/or flux gradient of particles is considered the original structure of the PBE will be modified leading to a nonlinear partial differential equation (nPDE) of the third order. It is shown how one can derive classes of solutions for the potential function analytically by application of pure algebraic steps. The benefit of the mathematical tools used here is the fact that closed-form solutions can be calculated and thus, numerical methods are not necessary. The important outcome of the present study is twofold meaningful: (i) The model equation allows the description of time dependent problems in the theory of ions, and (ii) the mathematical procedure can be used to derive classes of solutions of arbitrary nPDEs, especially those of higher order.

Nonlinear partial differential equations (nPDEs) nonlinear ordinary differential equations (nODEs) Debye-Hückel Theory (DHT) Poisson-Boltzmann Equation (PBE)
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2018.44232.1153 Chemical Graph Theory The irregularity and total irregularity of Eulerian graphs The irregularity and total irregularity of Eulerian graphs Nasiri R. Department of Mathematics, University of Qom, Qom, I. R. Iran Ellahi H. R. Department of Mathematics, University of Qom, Qom, I. R. Iran Gholami A. Department of Mathematics, University of Qom, Qom, I. R. Iran Fath-Tabar G. H. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran 01 06 2018 9 2 101 111 27 11 2015 11 01 2016 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63235.html

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

Eulerian graphs irregularity total irregularity vertex degree
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2017.96064.1309 Chemical Graph Theory Some remarks on the arithmetic-geometric index Some remarks on the arithmetic-geometric index Palacios J. The University of New Mexico, Albuquerque, NM 87131, USA 01 06 2018 9 2 113 120 21 07 2017 30 08 2017 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63436.html

Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

arithmetic-geometric index global cyclicity index majorization
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2017.53844.1200 Chemometrics Novel Atom-Type-Based Topological Descriptors for Simultaneous Prediction of Gas Chromatographic Retention Indices of Saturated Alcohols on Different Stationary Phases Novel Atom-Type-Based Topological Descriptors for Simultaneous Prediction of Gas Chromatographic Retention Indices of Saturated Alcohols on Different Stationary Phases Safa Fariba Department of Chemistry, Rasht Branch, Islamic Azad University, Rasht, Iran 01 06 2018 9 2 121 135 11 05 2016 12 03 2017 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63437.html

In this work, novel atom-type-based topological indices, named AT indices, were presented as descriptors to encode structural information of a molecule at the atomic level. The descriptors were successfully used for simultaneous quantitative structure-retention relationship (QSRR) modeling of saturated alcohols on different stationary phases (SE-30, OV-3, OV-7, OV-11, OV-17 and OV-25). At first, multiple linear regression models for Kovats retention index (RI) of alcohols on each stationary phase were separately developed using AT and Randic’s first-order molecular connectivity (1χ) indices. Adjusted correlation coefficient (R2adj) and standard error (SE) for the models were in the range of 0.994-0.999 and 4.40-8.90, respectively. Statistical validity of the models were verified by leave-one-out cross validation (R2cv > 0.99). In the next step, whole RI values on the stationary phases were combined to generate a new data set. Then, a unified model, added McReynolds polarity term as a descriptor, was developed for the new data set and the results were satisfactory (R2adj=0.995 and SE=8.55). External validation of the model resulted in the average values of 8.29 and 8.69 for standard errors of calibration and prediction, respectively. The topological indices well covered the molecular properties known to be relevant for retention indices of the model compounds.

Quantitative structure–retention relationship Atom-type-based topological indices Saturated alcohols Modeling
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2018.98655.1313 Spectral Graph Theory A note on the bounds of Laplacian-energy-like-invariant A note on the bounds of Laplacian-energy-like-invariant Faghani M. payame noor university Pourhadi E. Inviting lecturer of Iran university of science and technology 01 06 2018 9 2 137 147 18 09 2017 28 01 2018 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63443.html

The Laplacian-energy-like of a simple connected graph G is defined as LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), Where μ_1 (G)≥μ_2 (G)≥⋯≥μ_n (G)=0 are the Laplacian eigenvalues of the graph G. Some upper and lower bounds for LEL are presented in this note. Moreover, throughout this work, some results related to lower bound of spectral radius of graph are obtained using the term of ΔG as the number of triangles in graph.

Laplacian spectrum Laplacian-energy-like invariant Cauchy-Schwarz inequality Lagrange identity Spectral radius
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2017.93637.1303 Spectral Graph Theory On the eigenvalues of some matrices based on vertex degree On the eigenvalues of some matrices based on vertex degree Zangi S. Department of Mathematics, Shahid Rajaee Teacher Training University Ghorbani M. Department of mathematics, Shahid Rajaee Teacher Training University Eslampour M. Department of Mathematics, Shahid Rajaee Teacher Training University 01 06 2018 9 2 149 156 26 07 2017 25 09 2017 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63465.html

The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.

Zagreb indices forgotten index ISI index energy of graph
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Iranian J. Math. Chem. University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 University of Kashan 70 10.22052/ijmc.2018.108515.1327 Combinatorics Further Results on Betweenness Centrality of Graphs Further Results on Betweenness Centrality of Graphs Tavakoli M. Ferdowsi University of Mashhad, I R Iran 01 06 2018 9 2 157 165 26 11 2017 06 05 2018 Copyright © 2018, University of Kashan. 2018 http://ijmc.kashanu.ac.ir/article_63466.html

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

Betweenness centrality lexicographic product tensor product strong product
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