some lie algebra analogues of schur's theorem and its converses are presented. as a result, it is shown that for a capable lie algebra l we always have dim l=z(l)  2(dim(l2))2. we also give give some examples sup- porting our results.

background: breast feeding is subject to social and cultural conditions  of societies.basnef model considered as one of the comprehensive models of behavior study, especially in developing countries. this study was performed to investigate the status of breast feeding during the first two years of infants’ life and its risk factors through basnef model structures. methods: in this cross-section...

A group H is called capable if it is isomorphic to G/Z(G) for some group G. Let H be a capable group. I. M. Isaacs (2001) showed that if H is finite, then the index of the centre is bounded above by some function of |H′|. We show that if |H′| < ∞, then |H : Z(H)| ≤ |H′|c log2 |H′| with some constant c and this bound is essentially best possible. We complete a result of Isaacs, showing that if H...

RESULTS—Both the HF/HS and HF groups similarly developed obesity. EPA treatment strongly suppresses body weight gain and obesity-related hyperglycemia and hyperinsulinemia in HF/ HS-fed mice (HF/HS EPA group), where hepatic triglyceride content and lipogenic enzymes are increased. There is no appreciable effect of EPA on body weight in HF-fed mice (HF EPA group) without enhanced expression of h...

Let G be a finite group with derived subgroup of rank r. We prove that |G : Z2(G)| ≤ |G |. Motivated by the results of I. M. Isaacs in [2] we show that if G is capable then |G : Z(G)| ≤ |G| . This answers a question of L. Pyber. We prove that if G is a capable p-group then the rank of G/Z(G) is bounded above in terms of the rank of G′.

A rat model was used to investigate maternal age-dependent resistance on group B Streptococcus (GBS)-induced mortality of the offspring. Offspring from young (first time) or older (repeat litters) dams were challenged with GBS. There was an approximate log difference in the dose of GBS required to cause identical levels of mortality in the two groups. The sera of the dams from both groups were ...