The database of molecular motions, MolMovDB (http://molmovdb.org), has been in existence for the past decade. It classifies macromolecular motions and provides tools to interpolate between two conformations (the Morph Server) and predict possible motions in a single structure. In 2005, we expanded the services offered on MolMovDB. In particular, we further developed the Morph Server to produce ...

The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.

Data are presented on an old and familiar Gestalt demonstration--perceiving wheel-generated motions--in which the perceived motions of a rolling wheel are shown not to be obviously derived from the motions of the parts. The history of study of this phenomenon is presented, and contradictions in the literature are noted. The focus for experimentation is on the contrasting approaches found in Joh...

background :falls have been strongly associated with decreased physical activity and impaired mobility. reduced range of motion, as a consequence of muscle stiffness, has been indicated to assume a positive relationship to fall incidence. also clinical observations suggest that maintaining the normal spinal curves is associated with the prevention of spinal, knee and hip disorders. thus, the ai...

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

ASCE 7-16 has provided a comprehensive platform for the performance-based design of tall buildings. The core of the procedure is based on nonlinear response history analysis of the structure subjected to recorded or simulated ground motions. This study investigates consistency in the ASCE 7-16 requirements regarding the use of different types of ground motions. For this purpose performance of a...

We expand on the known result that Carroll algebra in $2+1$ dimensions admits two non-trivial central extensions by computing associated Lie group, which we call extended group. The symplectic geometry to this group is then computed describe motion of planar elementary particles, free case, when coupled an electromagnetic field, and a gravitational field. compare motions particles $3+1$ same co...

Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

the hosoya index and the merrifield-simmons index are two types of graph invariants used in mathematical chemistry. in this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. furthermore, we obtain exact formulas of hosoya and merrifield-simmons indices for the set of bicyclic graphs, caterpillars and dual star.

Many researches have been currently conducted on the effects of fault distance on structures revealing that their seismic response can differ according to their distance from the fault. Suspension bridges due to their long period and high flexibility can be more sensitive to this phenomenon, especially in vertical vibration. Since the engineers tend to use longer spans, the length factor should...