the main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. this is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the ::::union:::: of the eigenvalues of the healed submodels result in the eigenvalues of the ent...

shape and movement features of sperms are important parameters for infertility study and treatment. in this article, a new method is introduced for characterizing sperms in microscopic videos. in this method, first a hypothesis framework is defined to distinguish sperms from other particles in captured video. then decision about each hypothesis is done in following steps: selecting some primary...

In graph theory, lattices are used when some structural part of the repeats itself finitely or infinitely many times. They have applications in complex analysis and geometry mathematics, also natural chemical theory. As a lattice can be taken as graph, it is possible to use them study large networks. Recently, topological indices pentagonal chains studied here, we double similarly that work. We...

The notion of a polygraph was introduced in chemical graph theory as a formalization of the chemical notion of polymers.’ Fasciagraphs and rotagraphs form an important class of polygraphs. In the language of graph theory they describe polymers with open ends and polymers that are closed upon themselves, respectively. They are highly structured, and this structure makes it possible to design eff...

the zagreb indices are the oldest graph invariants used in mathematical chemistry to predictthe chemical phenomena. in this paper we define the multiple versions of zagreb indicesbased on degrees of vertices in a given graph and then we compute the first and secondextremal graphs for them.

The Wiener index of a graph is defined as the sum of distances between all pairs of vertices in a connected graph. Wiener index correlates well with many physio chemical properties of organic compounds and as such has been well studied over the last quarter of a century. In this paper we prove some general results on Wiener Index for graphs using degree sequence.

Anti-Kekulé problem is a concept of chemical graph theory precluding the Kekulé structure of molecules. Matching preclusion and conditional matching preclusion were proposed as measures of robustness in the event of edge failure in interconnection networks. It is known that matching preclusion problem on bipartite graphs is NP-complete. In this paper, we mainly prove that anti-Kekulé problem on...

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.

This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the ...