eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
77
100
10.22052/ijmc.2017.56982.1233
60159
An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures
A. Huber
dr.alfredhuber@gmx.at
1
A-8062 Kumberg, Prottesweg 2a
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. <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.
http://ijmc.kashanu.ac.ir/article_60159_8bd9735c4447d8660bbfdb79d418e5d9.pdf
Nonlinear partial differential equations (nPDEs)
nonlinear ordinary differential equations (nODEs)
Debye-Hückel Theory (DHT)
Poisson-Boltzmann Equation (PBE)
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
101
111
10.22052/ijmc.2018.44232.1153
63235
The irregularity and total irregularity of Eulerian graphs
R. Nasiri
r.nasiri.82@gmail.com
1
H. R. Ellahi
h.r.ellahi@gmail.com
2
A. Gholami
gholami@kashanu.ac.ir
3
G. H. Fath-Tabar
fathtabar@kashanu.ac.ir
4
Department of Mathematics, University of Qom, Qom, I. R. Iran
Department of Mathematics, University of Qom, Qom, I. R. Iran
Department of Mathematics, University of Qom, Qom, I. R. Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, I. R. Iran
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.
http://ijmc.kashanu.ac.ir/article_63235_0809a6de97055b11f063d5835fb9cb61.pdf
Eulerian graphs
irregularity
total irregularity
vertex degree
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
113
120
10.22052/ijmc.2017.96064.1309
63436
Some remarks on the arithmetic-geometric index
J. Palacios
jpalacios@unm.edu
1
The University of New Mexico, Albuquerque, NM 87131, USA
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.
http://ijmc.kashanu.ac.ir/article_63436_8be152ec4953e9f50538a6eca5df34ad.pdf
arithmetic-geometric index
global cyclicity index
majorization
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
121
135
10.22052/ijmc.2017.53844.1200
63437
Novel Atom-Type-Based Topological Descriptors for Simultaneous Prediction of Gas Chromatographic Retention Indices of Saturated Alcohols on Different Stationary Phases
Fariba Safa
safa_f@yahoo.com
1
Department of Chemistry, Rasht Branch, Islamic Azad University, Rasht, Iran
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.
http://ijmc.kashanu.ac.ir/article_63437_9833746c2e140a665215e8505c3dfaa9.pdf
Quantitative structure–retention relationship
Atom-type-based topological indices
Saturated alcohols
Modeling
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
137
147
10.22052/ijmc.2018.98655.1313
63443
A note on the bounds of Laplacian-energy-like-invariant
M. Faghani
m_faghani@pnu.ac.ir
1
E. Pourhadi
epourhadi@alumni.iust.ac.ir
2
payame noor university
Inviting lecturer of Iran university of science and technology
The 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.
http://ijmc.kashanu.ac.ir/article_63443_846253a27afa935b360ad70ebf0d97fb.pdf
Laplacian spectrum
Laplacian-energy-like invariant
Cauchy-Schwarz inequality
Lagrange identity
Spectral radius
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
149
156
10.22052/ijmc.2017.93637.1303
63465
On the eigenvalues of some matrices based on vertex degree
S. Zangi
samanehzangi63@gmail.com
1
M. Ghorbani
mghorbani@sru.ac.ir
2
M. Eslampour
3
Department of Mathematics, Shahid Rajaee Teacher Training University
Department of mathematics, Shahid Rajaee Teacher Training University
Department of Mathematics, Shahid Rajaee Teacher Training University
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.
http://ijmc.kashanu.ac.ir/article_63465_857967802a59a68b050043de1148f170.pdf
Zagreb indices
forgotten index
ISI index
energy of graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-06-01
9
2
157
165
10.22052/ijmc.2018.108515.1327
63466
Further Results on Betweenness Centrality of Graphs
M. Tavakoli
m_tavakoli@um.ac.ir
1
Ferdowsi University of Mashhad, I R Iran
Betweenness 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.
http://ijmc.kashanu.ac.ir/article_63466_ee6eface08eacc351ed6e943da6383b5.pdf
Betweenness centrality
lexicographic product tensor product
strong product