The mathematical properties of nano molecules are an interesting branch of nanoscience for researches nowadays. The periodic open single wall tubulene is one of the nano molecules which is built up from two caps and a distancing nanotube/neck. We discuss how to automatically construct the graph of this molecule and plot the graph by spring layout algorithm in graphviz and netwrokx packages. The...

Let [Formula: see text] be a commutative Noetherian ring. For finitely generated text]-module text], Northcott introduced the reducibility index of which is number submodules appearing in an irredundant irreducible decomposition submodule text]. On other hand, for Artinian Macdonald proved that sum-irreducible representation does not depend on choice representation. This called sum-reducibility...

background: the sensitivity and specificity of body mass index (bmi) percentiles of centers for disease control 2000 (cdc2000) standard was compared with child actual overweight which was identified by fat mass index (fmi) and overweight status in these children based on bmi and fmi. methods: in this case-control study, elementary school girls (aged 8-10 years) were recruited from schools of is...