University of KashanIranian Journal of Mathematical Chemistry2228-64899220180601An Algebraic Calculation Method for Describing Time-dependent Processes in Electrochemistry – Expansion of Existing Procedures771006015910.22052/ijmc.2017.56982.1233ENA.HuberA-8062 Kumberg, Prottesweg 2aJournal Article20160830In 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. <br /> 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.<br /> The important outcome of the present study is twofold meaningful: <br /> (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.https://ijmc.kashanu.ac.ir/article_60159_8bd9735c4447d8660bbfdb79d418e5d9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601The Irregularity and Total Irregularity of Eulerian Graphs1011116323510.22052/ijmc.2018.44232.1153ENR.NasiriDepartment of Mathematics, University of Qom, Qom, I. R. IranH. R.EllahiDepartment of Mathematics, University of Qom, Qom, I. R. IranA.GholamiDepartment of Mathematics, University of Qom, Qom, I. R. IranG. H.Fath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran0000-0003-1105-3020Journal Article20151127For 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.https://ijmc.kashanu.ac.ir/article_63235_0809a6de97055b11f063d5835fb9cb61.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601Some Remarks on the Arithmetic-geometric Index1131206343610.22052/ijmc.2017.96064.1309ENJ.PalaciosThe University of New Mexico, Albuquerque, NM 87131, USAJournal Article20170721Using 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.https://ijmc.kashanu.ac.ir/article_63436_8be152ec4953e9f50538a6eca5df34ad.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601Novel Atom-Type-Based Topological Descriptors for Simultaneous Prediction of Gas Chromatographic Retention Indices of Saturated Alcohols on Different Stationary Phases1211356343710.22052/ijmc.2017.53844.1200ENFaribaSafaDepartment of Chemistry, Rasht Branch, Islamic Azad University, Rasht, IranJournal Article20160511In 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.https://ijmc.kashanu.ac.ir/article_63437_9833746c2e140a665215e8505c3dfaa9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601A Note on the Bounds of Laplacian-energy-like-invariant1371476344310.22052/ijmc.2018.98655.1313ENM.Faghanipayame noor university0000-0002-9415-3934E.PourhadiInviting lecturer of Iran university of science and technologyJournal Article20170918The Laplacian-energy-like of a simple connected graph G is defined as<br /> LEL:=LEL(G)=∑_(i=1)^n√(μ_i ), <br /> 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.https://ijmc.kashanu.ac.ir/article_63443_846253a27afa935b360ad70ebf0d97fb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601On the Eigenvalues of some Matrices based on Vertex Degree1491566346510.22052/ijmc.2017.93637.1303ENS.ZangiDepartment of Mathematics, Shahid Rajaee Teacher Training UniversityM.GhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training University0000-0002-5324-0847M.EslampourDepartment of Mathematics, Shahid Rajaee Teacher Training UniversityJournal Article20170726The 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.https://ijmc.kashanu.ac.ir/article_63465_857967802a59a68b050043de1148f170.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899220180601Further Results on Betweenness Centrality of Graphs1571656346610.22052/ijmc.2018.108515.1327ENM.TavakoliFerdowsi University of Mashhad, I R IranJournal Article20171126Betweenness centrality is a distance-based invariant of graphs. In this paper, we use<br /> lexicographic product to compute betweenness centrality of some important classes of<br /> graphs. Finally, we pose some open problems related to this topic.https://ijmc.kashanu.ac.ir/article_63466_ee6eface08eacc351ed6e943da6383b5.pdf