A nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules
A.
HUBER
Austria
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
1
20
http://ijmc.kashanu.ac.ir/article_5278_dc16ba1fb594888e241b45da69dbbda2.pdf
dx.doi.org/10.22052/ijmc.2013.5278
On the total version of geometric-arithmetic index
A.
MAHMIANI
Payame Noor University,
Iran
author
O.
KHORMALI
Tarbiat Modares University, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
21
26
http://ijmc.kashanu.ac.ir/article_5279_955312e9f30175aac51452ba1093d89a.pdf
dx.doi.org/10.22052/ijmc.2013.5279
Infinite product representation of solution of indefinite SturmLiouville problem
S.
MOSAZADEH
University of Kashan,
I. R. Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
27
40
http://ijmc.kashanu.ac.ir/article_5280_277e5aafb8e735692c8e11f911d8525b.pdf
dx.doi.org/10.22052/ijmc.2013.5280
Using electrochemical impedance spectroscopy of salicylate anion selective electrode: simulation for behavior of electrode
M.
MAZLOUM-ARDAKANI
Yazd University, I. R. of Iran
author
A.
DEHGHAN MANSHADI
Payame Noor University, I. R. Iran
author
S.
MOZAFFARI
Iranian Research Organization for Science & Technology (IROST),, I. R. Iran
author
H.
AZIZI
Taft Branch, Islamic Azad University, I. R. Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
41
57
http://ijmc.kashanu.ac.ir/article_5281_eb6f01894d0d34a6cfe0ff1030bcabcc.pdf
dx.doi.org/10.22052/ijmc.2013.5281
Wiener numbers of random pentagonal chains
H.
YONG WANG
University of South China, P. R. China
author
J.
QIN
University of South China, P. R. China
author
I.
GUTMAN
University of Kragujevac, Serbia
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
59
76
http://ijmc.kashanu.ac.ir/article_5282_449688029ecc656d9f4df9bdb60bf5d5.pdf
dx.doi.org/10.22052/ijmc.2013.5282
On terminal wiener indices of kenograms and plerograms
I.
GUTMAN
University of Kragujevac, Serbia
author
B.
FURTULA
University of Kragujevac, Serbia
author
J.
TOŠOVIĆ
University of Kragujevac, Serbia
author
M.
ESSALIH
Mohammed V-Agdal University, Morocco
author
M.
MARRAKI
Mohammed V-Agdal University, Morocco
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
77
89
http://ijmc.kashanu.ac.ir/article_5283_671b93611b78e6741260be1dec76b090.pdf
dx.doi.org/10.22052/ijmc.2013.5283
QSAR modeling of antimicrobial activity with some novel 1,2,4 triazole derivatives, comparison with experimental study
Z.
ROSTAMI
Payame Noor University, I. R. Iran
author
A.
AMINI MANESH
Payame Noor University, I. R. Iran
author
L.
SAMIE
Payame Noor University, I. R. Iran
author
text
article
2013
eng
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 .
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
91
109
http://ijmc.kashanu.ac.ir/article_5284_5668c447a5053db6a2b2d4a80d05c9f6.pdf
dx.doi.org/10.22052/ijmc.2013.5284
Counting the number of spanning trees of graphs
M.
GHORBANI
Shahid Rajaee Teacher Training
University,I. R. Iran
author
E.
BANI-ASADI
Shahid Rajaee Teacher Training
University, I. R. Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
111
121
http://ijmc.kashanu.ac.ir/article_5285_483560b3d82294a58ea6be649a695b0d.pdf
dx.doi.org/10.22052/ijmc.2013.5285
Chain hexagonal cacti: extremal with respect to the eccentric connectivity index
Z.
YARAHMADI
Khorramabad Branch, Islamic Azad University, Iran
author
T.
DOŠLIĆ
University of Zagreb,Croatia
author
S.
MORADI
Arak University, Iran
author
text
article
2013
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
123
136
http://ijmc.kashanu.ac.ir/article_5286_580d34e130a03b16b5e1f69fa8081ba0.pdf
dx.doi.org/10.22052/ijmc.2013.5286
Collaborations between the iranian school of mathematical chemistry and the late professor ante graovac
KH.
FATHALIKHANI
University of Kashan, Iran
author
F.
KOOREPAZAN-MOFTAKHAR
University of Kashan, Iran
author
A.
ASHRAFI
University of Kashan, Iran
author
M.
GHORBANI
Shahid Rajaee Teacher Training University, Iran
author
S.
ALIKHANI
Yazd University, Iran
author
M.
IRANMANESH
Yazd University, Iran
author
A.
IRANMANESH
Tarbiat Modares University, Iran
author
text
article
2013
eng
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
4
v.
1
no.
2013
137
142
http://ijmc.kashanu.ac.ir/article_5287_7c996b282064db99200231cc86ab2e97.pdf
dx.doi.org/10.22052/ijmc.2013.5287