In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

background and aims. a plethora of definitions has been used for periodontitis for epidemiological studies. the aim of this cross-sectional study was to assess the impact of different case definitions on the prevalence of periodontitis and to find the level of agreement among them. materials and methods. periodontal records of 300 subjects were randomly selected from the database of oral health ...

this review deals with studies that have used cdna microarrays and immunohistochemistry to identify a subtype of breast carcinoma recently known as “basal-like” carcinoma. the key breast carcinoma studies are critically discussed to highlight methodological problems in cohort selection, definitions, interpretation of results, and statistical analysis. it concludes that “basal-like” carcinomas d...

Graph transformation systems (GTS) are often used for modeling the behavior of complex systems. A common GTS analysis scenario is the exploration of its state space from an initial state to a state adhering to given goals through a proper trajectory. Guided trajectory exploration uses information from some more abstract analysis of the system as hints to reduce the traversed state space. These ...

A WHO expert consultation addressed the debate about interpretation of recommended body-mass index (BMI) cut-off points for determining overweight and obesity in Asian populations, and considered whether population-specific cut-off points for BMI are necessary. They reviewed scientific evidence that suggests that Asian populations have different associations between BMI, percentage of body fat,...