University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
A nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules
1
20
EN
A.
HUBER
Austria
10.22052/ijmc.2013.5278
In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian elliptic functions. By using a special transformation the first derivative of the equation can be transformed off leading to a further nPDE. The latter equation is also studied as well as algebraic properties and group invariant solutions could be derived. This new classes of solutions obtained are closely related to solutions of the kinetic model and so far, expressions for a generating function considering normalized moments are also deduced. Finally, the connection to Painlevé’s first equation is shown whereby these classes of solutions are solutions due to the invariant properties too. For practical use in numerical calculations some series representations are given explicitly. In view of the point of novelty it is further shown how to derive a Bellman-type equation to the first time and asymptotic classes of solutions result by appropriate transformations. The importance of the present paper is the relation to the Boltzmann Equation which describes the one particle distribution function in a gas of particles interacting only through binary collisions. Since transformations remain an equation invariant, solutions of the new transformed equation also generates solutions of physical relevance. Normalized moments are discussed finally.
Classical Lie group formalism,Classes of similarity solutions,Nonlinear partial differential equations (nPDEs),Maxwellian molecules,Bellmann’s typeequation
http://ijmc.kashanu.ac.ir/article_5278.html
http://ijmc.kashanu.ac.ir/article_5278_dc16ba1fb594888e241b45da69dbbda2.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
On the total version of geometric-arithmetic index
21
26
EN
A.
MAHMIANI
Payame Noor University,
Iran
O.
KHORMALI
Tarbiat Modares University, Iran
10.22052/ijmc.2013.5279
The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.
Geometric–arithmetic index,total graph,vertex degree
http://ijmc.kashanu.ac.ir/article_5279.html
http://ijmc.kashanu.ac.ir/article_5279_955312e9f30175aac51452ba1093d89a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Infinite product representation of solution of indefinite SturmLiouville problem
27
40
EN
S.
MOSAZADEH
University of Kashan,
I. R. Iran
10.22052/ijmc.2013.5280
In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. Nachr. 229, 51-71 (2001)] for a special fundamental system of the solutions of Sturm-Liouville equation, we obtain the asymptotic behavior of it’s solutions and eigenvalues, then we obtain the infinite product representation of solution of the equation.
Singularities,Turning Points,Sturm-Liouville problem,Non-definite problem,Infinite products,Hadamard's theorem
http://ijmc.kashanu.ac.ir/article_5280.html
http://ijmc.kashanu.ac.ir/article_5280_277e5aafb8e735692c8e11f911d8525b.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Using electrochemical impedance spectroscopy of salicylate anion selective electrode: simulation for behavior of electrode
41
57
EN
M.
MAZLOUM-ARDAKANI
Yazd University, I. R. of Iran
A.
DEHGHAN MANSHADI
Payame Noor University, I. R. Iran
S.
MOZAFFARI
Iranian Research Organization for Science & Technology (IROST),, I. R. Iran
H.
AZIZI
Taft Branch, Islamic Azad University, I. R. Iran
10.22052/ijmc.2013.5281
In this paper, the behavior of the salicylate anion-selective electrode was studied using the electrochemical impedance spectroscopy technique. Considering the diagram of the charge transfer resistance and -logarithm of the double layer capacitance versus -logarithm of the concentration, linear range concentration increased to 1.0×10^{-8}-1.0×10^{-1} M and 1.0×10^{-9}-1.0×10^{-1} M, respectively. Among the other characteristics of this study, it can be pointed out a wide pH range of 4.0-10.0. Then "one-impedance for one-concentration" method was used to measure the salicylate ion at the linear range of 1.0×10^{-8}-1.0×10^{-1} M. Finally, the impedance spectra of this electrode were simulated in which the obtained results of this simulation indicate proximity of experimental and simulation data.
Salicylate,Anion-selective electrode,electrochemical impedance spectroscopy,Simulation
http://ijmc.kashanu.ac.ir/article_5281.html
http://ijmc.kashanu.ac.ir/article_5281_eb6f01894d0d34a6cfe0ff1030bcabcc.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Wiener numbers of random pentagonal chains
59
76
EN
H.
YONG WANG
University of South China, P. R. China
J.
QIN
University of South China, P. R. China
I.
GUTMAN
University of Kragujevac, Serbia
10.22052/ijmc.2013.5282
The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.
Wiener index,Pentagonal chain
http://ijmc.kashanu.ac.ir/article_5282.html
http://ijmc.kashanu.ac.ir/article_5282_449688029ecc656d9f4df9bdb60bf5d5.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
On terminal wiener indices of kenograms and plerograms
77
89
EN
I.
GUTMAN
University of Kragujevac, Serbia
B.
FURTULA
University of Kragujevac, Serbia
J.
TOŠOVIĆ
University of Kragujevac, Serbia
M.
ESSALIH
Mohammed V-Agdal University, Morocco
M.
EL
MARRAKI
Mohammed V-Agdal University, Morocco
10.22052/ijmc.2013.5283
Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices of kenograms and plerograms.
Wiener index,Kenogram,Plerogram
http://ijmc.kashanu.ac.ir/article_5283.html
http://ijmc.kashanu.ac.ir/article_5283_671b93611b78e6741260be1dec76b090.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
QSAR modeling of antimicrobial activity with some novel 1,2,4 triazole derivatives, comparison with experimental study
91
109
EN
Z.
ROSTAMI
Payame Noor University, I. R. Iran
A.
AMINI MANESH
Payame Noor University, I. R. Iran
L.
SAMIE
Payame Noor University, I. R. Iran
10.22052/ijmc.2013.5284
Our study performed upon an extended series of 28 compounds of 1,2,4-triazole derivatives that demonstrate substantial in vitro antimicrobial activities by serial plate dilution method, using quantitative structure-activity relationship (QSAR) methods that imply analysis of correlations and multiple linear regression (MLR); a significant collection of molecular descriptors was used e.g., Edge adjacency indices, GETAWAY , 3D-MoRSE , Burden eigenvalues and Constitutional descriptors. The obtained multi-parametric models when a different class of molecular descriptors was used led to three correlation coefficients closed to 0.900, 0.896 and 0.901 respectively. Results indicated this is no significant statistical differences between calculated activities of these compounds with laboratory methods thus, the obtained models allowed us to predict antimicrobial activity of substituted 1,2,4-triazole derivatives .
Quantitative structure-activity relationship,Multiple linear regression,Antimicrobial activity,1,2,4-triazole derivatives
http://ijmc.kashanu.ac.ir/article_5284.html
http://ijmc.kashanu.ac.ir/article_5284_5668c447a5053db6a2b2d4a80d05c9f6.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Counting the number of spanning trees of graphs
111
121
EN
M.
GHORBANI
Shahid Rajaee Teacher Training
University,I. R. Iran
E.
BANI-ASADI
Shahid Rajaee Teacher Training
University, I. R. Iran
10.22052/ijmc.2013.5285
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
Spanning tree,Laplacian eigenvalue,Fullerene
http://ijmc.kashanu.ac.ir/article_5285.html
http://ijmc.kashanu.ac.ir/article_5285_483560b3d82294a58ea6be649a695b0d.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Chain hexagonal cacti: extremal with respect to the eccentric connectivity index
123
136
EN
Z.
YARAHMADI
Khorramabad Branch, Islamic Azad University, Iran
T.
DOŠLIĆ
University of Zagreb,Croatia
S.
MORADI
Arak University, Iran
10.22052/ijmc.2013.5286
In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.
Chain hexagonal cactus,eccentric connectivity index
http://ijmc.kashanu.ac.ir/article_5286.html
http://ijmc.kashanu.ac.ir/article_5286_580d34e130a03b16b5e1f69fa8081ba0.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
4
1
2013
03
01
Collaborations between the iranian school of mathematical chemistry and the late professor ante graovac
137
142
EN
KH.
FATHALIKHANI
University of Kashan, Iran
F.
KOOREPAZAN-MOFTAKHAR
University of Kashan, Iran
A.
R.
ASHRAFI
University of Kashan, Iran
M.
GHORBANI
Shahid Rajaee Teacher Training University, Iran
S.
ALIKHANI
Yazd University, Iran
M.
A.
IRANMANESH
Yazd University, Iran
A.
IRANMANESH
Tarbiat Modares University, Iran
10.22052/ijmc.2013.5287
http://ijmc.kashanu.ac.ir/article_5287.html
http://ijmc.kashanu.ac.ir/article_5287_7c996b282064db99200231cc86ab2e97.pdf