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...

djendjen river is one of the largest rivers in the region of jijel (algeria). human activities such as urban discharges, industrial, agricultural, and livestock have significant effects on the quality of water. the present study attempts to evaluate the quality of water along the banks of the djendjen river at different sampling sites, using physico-chemical and bacteriological methods. the col...

the harary index h can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. a generalization of the harary index, denoted by hk, is achieved by employing the steiner-type distance between k-tuples of atoms. we show that the linear c...

in this survey article a brief account on the development of padmakar-ivan (pi) index in thatapplications of padmakar-ivan (pi) index in the fascinating field of nano-technology arediscussed.

in this paper, at first we introduce a new index with the name co-pi index and obtain someproperties related this new index. then we compute this new index for tuc4c8(r) nanotubes.