2013
4
1
1
142
A nonlinear second order field equation – similarity solutions and relation to a Bellmanntype equation  Applications to Maxwellian Molecules
2
2
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 Bellmantype 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.
1

1
20


A.
HUBER
Austria
Austria
Austria
Classical Lie group formalism
Classes of similarity solutions
Nonlinear partial differential equations (nPDEs)
Maxwellian molecules
Bellmann’s typeequation
On the total version of geometricarithmetic index
2
2
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.
1

21
26


A.
MAHMIANI
Payame Noor University,
Iran
Payame Noor University,
Iran
I R Iran


O.
KHORMALI
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
I R Iran
Geometric–arithmetic index
total graph
vertex degree
Infinite product representation of solution of indefinite SturmLiouville problem
2
2
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. WilckenStoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. Nachr. 229, 5171 (2001)] for a special fundamental system of the solutions of SturmLiouville equation, we obtain the asymptotic behavior of it’s solutions and eigenvalues, then we obtain the infinite product representation of solution of the equation.
1

27
40


S.
MOSAZADEH
University of Kashan,
I. R. Iran
University of Kashan,
I. R. Iran
I R Iran
Singularities
Turning Points
SturmLiouville problem
Nondefinite problem
Infinite products
Hadamard's theorem
Using electrochemical impedance spectroscopy of salicylate anion selective electrode: simulation for behavior of electrode
2
2
In this paper, the behavior of the salicylate anionselective 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 4.010.0. Then "oneimpedance for oneconcentration" 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.
1

41
57


M.
MAZLOUMARDAKANI
Yazd University, I. R. of Iran
Yazd University, I. R. of Iran
I R Iran


A.
DEHGHAN MANSHADI
Payame Noor University, I. R. Iran
Payame Noor University, I. R. Iran
I R Iran


S.
MOZAFFARI
Iranian Research Organization for Science & Technology (IROST),, I. R. Iran
Iranian Research Organization for Science
I R Iran


H.
AZIZI
Taft Branch, Islamic Azad University, I. R. Iran
Taft Branch, Islamic Azad University, I.
I R Iran
Salicylate
Anionselective electrode
Electrochemical impedance spectroscopy
Simulation
Wiener numbers of random pentagonal chains
2
2
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.
1

59
76


H.
YONG WANG
University of South China, P. R. China
University of South China, P. R. China
P. R. China


J.
QIN
University of South China, P. R. China
University of South China, P. R. China
P. R. China


I.
GUTMAN
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia
Wiener index
Pentagonal chain
On terminal wiener indices of kenograms and plerograms
2
2
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.
1

77
89


I.
GUTMAN
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia


B.
FURTULA
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia


J.
TOŠOVIĆ
University of Kragujevac, Serbia
University of Kragujevac, Serbia
Serbia


M.
ESSALIH
Mohammed VAgdal University, Morocco
Mohammed VAgdal University, Morocco
Morocco


M.
MARRAKI
Mohammed VAgdal University, Morocco
Mohammed VAgdal University, Morocco
Morocco
Wiener index
Kenogram
Plerogram
QSAR modeling of antimicrobial activity with some novel 1,2,4 triazole derivatives, comparison with experimental study
2
2
Our study performed upon an extended series of 28 compounds of 1,2,4triazole derivatives that demonstrate substantial in vitro antimicrobial activities by serial plate dilution method, using quantitative structureactivity 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 , 3DMoRSE , Burden eigenvalues and Constitutional descriptors. The obtained multiparametric 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 1,2,4triazole derivatives .
1

91
109


Z.
ROSTAMI
Payame Noor University, I. R. Iran
Payame Noor University, I. R. Iran
I R Iran


A.
AMINI MANESH
Payame Noor University, I. R. Iran
Payame Noor University, I. R. Iran
I R Iran


L.
SAMIE
Payame Noor University, I. R. Iran
Payame Noor University, I. R. Iran
I R Iran
Quantitative structureactivity relationship
Multiple Linear Regression
Antimicrobial activity
1
2
4triazole derivatives
Counting the number of spanning trees of graphs
2
2
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.
1

111
121


M.
GHORBANI
Shahid Rajaee Teacher Training
University,I. R. Iran
Shahid Rajaee Teacher Training
University,I.
I R Iran


E.
BANIASADI
Shahid Rajaee Teacher Training
University, I. R. Iran
Shahid Rajaee Teacher Training
University,
I R Iran
Spanning tree
Laplacian eigenvalue
Fullerene
Chain hexagonal cacti: extremal with respect to the eccentric connectivity index
2
2
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.
1

123
136


Z.
YARAHMADI
Khorramabad Branch, Islamic Azad University, Iran
Khorramabad Branch, Islamic Azad University,
I R Iran


T.
DOŠLIĆ
University of Zagreb,Croatia
University of Zagreb,Croatia
Croatia


S.
MORADI
Arak University, Iran
Arak University, Iran
I R Iran
Chain hexagonal cactus
eccentric connectivity index
Collaborations between the iranian school of mathematical chemistry and the late professor ante graovac
2
2
1

137
142


KH.
FATHALIKHANI
University of Kashan, Iran
University of Kashan, Iran
I R Iran


F.
KOOREPAZANMOFTAKHAR
University of Kashan, Iran
University of Kashan, Iran
I R Iran


A.
ASHRAFI
University of Kashan, Iran
University of Kashan, Iran
I R Iran


M.
GHORBANI
Shahid Rajaee Teacher Training University, Iran
Shahid Rajaee Teacher Training University,
I R Iran


S.
ALIKHANI
Yazd University, Iran
Yazd University, Iran
I R Iran


M.
IRANMANESH
Yazd University, Iran
Yazd University, Iran
I R Iran


A.
IRANMANESH
Tarbiat Modares University, Iran
Tarbiat Modares University, Iran
I R Iran