Abstract. The Leibniz algebras appear as a generalization of the Lie algebras [8]. The classification of naturally graded p-filiform Lie algebras is known [3], [4], [5], [9]. In this work we deal with the classification of 2-filiform Leibniz algebras. The study of p-filiform Leibniz non Lie algebras is solved for p = 0 (trivial) and p = 1 [1]. In this work we get the classification of naturally graded non Lie 2-filiform Leibniz algebras.
In the present article the classification of n-dimensional naturally graded p-filiform (1 ≤ p ≤ n − 4) Leibniz algebras is obtained. A splitting of the set of naturally graded Leibniz algebras into the families of Lie and non Lie Leibniz algebras by means of characteristic sequences (isomorphism invariants) is proved.
Previous studies with different results have suggested that total and bioavailable testosterone levels are modified by physical exercise. Such changes may be related to modifications in cortisol levels and could be reflected in some urine androgens. To determine how weight lifting training may affect serum and urinary androgens, we measured total serum testosterone (T), cortisol, sex hormone binding globulin (SHBG) and urinary testosterone, epitestosterone, androsterone, and etiocholanolone, in a group of 19 elite weight lifters after 20 weeks of training. SHBG increased (from 27.5 +/- 9.5 to 34.7 +/- 8.1 nM, p < 0.05) whereas T/SHBG decreased significantly (from 1.10 +/- 0.4 to 0.85 +/- 0.3, p < 0.05). Serum total testosterone and cortisol did not change significantly. In urine, androsterone and etiocholanolone decreased significantly, whereas testosterone and epitestosterone remained unchanged. Changes in T/SHBG were related positively with changes in urinary androgens (r = 0.680, p < 0.01), and changes in SHBG were negatively related with changes in urinary androgens (r = -0.578, p < 0.01). These results suggest that intense physical activity may have an influence on the elimination of androgenic hormones due mainly to changes in their transporting protein SHBG.
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