Iranian Journal of Mathematical Chemistry
Volume:11 Issue: 3, Summer 2020

In this paper we continue to study the chaotic properties of the following lattice dynamical system: bji+1= a1 g(bji)+ a2 g(bj-1i)+ a3 g(bj+1i), where i is discrete time index, j is lattice side index with system size L, g is a selfmap on [0, 1] and a1+a2+a3 ∊ [0, 1] with a1+a2+a3=1 are coupling constants. In particular, it is shown that if g is turbulent (resp. erratic) then so is the above system, and that if there exists a g-connected family G with respect to disjointed compact subsets D1, D2, …, Dm, then there is a compact invariant set K'⊆D' such that F |K' is semi-conjugate to m-shift for any coupling constants a1+a2+a3 ∊ [0, 1] with  a1+a2+a3=1, where D' ⊆ IL is nonempty and compact. Moreover, an example and two problems are given.

The Symmetric division deg (SDD) index is a well-established valuable index in the analysis of quantitative structure-property and structure-activity relationships for molecular graphs. In this paper, we study the range of SDD-index for special classes of trees and unicyclic graphs. We present the first four lower bounds for SDD-index of trees and unicyclic graphs, which admit a perfect matching and find the subclasses of graphs that attain these bounds. Further, we also compute the upper bounds of SDD-index for the collection of molecular graphs, namely the trees and unicyclic graphs, each having maximum degree four and that admit a perfect matching.

The non-uniform hypergraph is the general hypergraph in which an edge can join any number of vertices. This makes them more applicable data structure than the uniform hypergraph and also, on the other hand, mathematical relations of the nonuniform hypergraph are usually complicated. In this paper, we study the non-uniform hypergraph more precisely and then analyze some of its spectral properties and compare them with those of the uniform hypergraph.

In this study, six molecular descriptors were selected from a pool of variables using stepwise regression to built a QSAR model for a series of 2-benzyloxy benzamide derivatives as an SMS2 inhibitor to reduce atherosclerosis. Simple multiple linear regression (MLR) and a nonlinear method, artificial neural network (ANN), were used to modeling the bioactivities of the compounds. Modeling was carried out in total with 34 compounds of 2-benzyl oxybenzamide derivatives. PCA was used to divide the compounds into two groups of two training series and tests. The model was constructed with 27 combinations as training set, then the validity and predictive ability of the model were evaluated with the remaining 7 combinations. While the MLR provides an acceptable model for predictions, the ANN-based model significantly improves the predictive ability. In ANN model the average relative error (RE%) of prediction set is lower than 1% and square correlation coefficient (R2) is 0.9912.

For a connected graph G, the Wiener index W(G) of G is the sum of the distances of all pairs of vertices, the Kirchhoff index Kf(G) of G is the sum of the resistance distances of all pairs of vertices. A k-polygonal cactus is a connected graph in which the length of every cycle is k and any two cycles have at most one common vertex. In this paper, we give the maximum and minimum values of the Wiener index and the Kirchhoff index for all k-polygonal cacti with n cycles and determine the corresponding extremal graphs, generalize results of spiro hexagonal chains with n hexagons.