The relative cohomology Hdiff1(K(1|3), osp(2, 3);Dγ,µ(S1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators Dγ,µ(S1|3) acting on tensor densities on S1|3, is calculated in N.Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1-cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1-cocycle s(Xf) = D1D2D3(f)α31/2, Xf \in K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3). In this work we study the supergroup case. We give an explicit construction of 1-cocycles of the group of contactomorphisms K(1|3) on the supercircle S1|3 generating the relative cohomology Hdiff1(K(1|3), PC(2, 3); Dγ,µ(S1|3) with coefficients in Dγ,µ(S1|3). We show that they possess properties similar to those of the super-Schwarzian derivative 1-cocycle S3(Φ) = EΦ-1 (D1(D2),D3)α31/2, Φ ∈ K(1|3) introduced by Radul which is invariant with respect to the conformal group PC(2, 3) of K(1|3). These cocycles are expressed in terms of S3(Φ) and possess its properties., Boujemaa Agrebaoui, Raja Hattab., and Obsahuje seznam literatury
The adrenal glands produce significant amounts of steroid hormones and their metabolites, with various levels of androgenic activities. Until recently, the androgenic potency of these adrenal-derived compounds were not well known, but some recent studies have shown that the production of 11-oxoand 11β-hydroxy-derived testosterone and dihydrotestosterone evidently have high androgenic activity. This fact has clinical importance, for instance, in various types of congenital adrenal hyperplasia with androgenization or polycystic ovarian syndrome, and laboratory determinations of these substances could help to better evaluate the total androgen pressure in patients with these disorders. Another area of concern is the treatment of prostate cancer with androgen deprivation, which loses effectiveness after a certain time. The concurrent blocking of the secretion of adrenal C19-steroids, whether using corticoids or adrenostatics, could increase the effectiveness of androgen-deprivation therapy., Luboslav Stárka, Michaela Dušková, Jana Vítků., and Obsahuje bibliografii