Fourth Order and Fourth Sum Connectivity Indices of Polyphenylene Dendrimers

Fourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers

Fourth-Order Dependency Parsing

We present and implement a fourth-order projective dependency parsing algorithm that effectively utilizes both “grand-sibling” style and “tri-sibling” style interactions of third-order and “grand-tri-sibling” style interactions of forth-order factored parts for performance enhancement. This algorithm requires O(n5) time and O(n4) space. We implement and evaluate the parser on two languages—Engl...

Fourth-order Symplectic Integration*

In this paper we present an explicit fourth-order method for the integration of Hamilton’s Equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it ...

Fourth Order Equations In