Let D be a Cd q-convex intersection, d > 2, 0 6 q 6 n − 1, in a complex manifold X of complex dimension n, n > 2, and let E be a holomorphic vector bundle of rank N over X. In this paper, Ck-estimates, k = 2, 3, . . . ,1, for solutions to the -equation with small loss of smoothness are obtained for E-valued (0, s)-forms on D when n − q 6 s 6 n. In addition, we solve the -equation with a support condition in Ck-spaces. More precisely, we prove that for a -closed form f in Ck 0,q(X \ D,E), 1 6 q 6 n − 2, n > 3, with compact support and for " with 0 < " < 1 there exists a form u in Ck−ε 0,q−1(X \ D,E) with compact support such that u = f in X \ D. Applications are given for a separation theorem of Andreotti-Vesentini type in Ck-setting and for the solvability of the -equation for currents., Shaban Khidr, Osama Abdelkader., and Seznam literatury
The effect of β3-adrenoceptor (β3-AR) agonists on adipocytes treated or not tr eated with signaling modulators has not been sufficiently elucidated. Using rat epididymal adipocytes (adipocytes) labeled with [ 32 P]orthophosphate, we found that treatment with the selective β3-AR agonist CL316243 (CL; 1 μ M) induces phosphatidylinositol (PI) 3,4,5-triphosphate (PI[3,4,5]P3) production and that this response is inhibited by adenosine deaminase (ADA, an adenosine -degrading enzyme; 2 U/ml), pertussis toxin (PTX, an inactivator of inhibitory guanine-nucleotide-binding protein; 1 μ g/ml), or wortmannin (WT, a PI -kinase inhibitor; 3 μ M). The results showed that CL induced PI(3,4,5)P 3 production in intact adipocytes and that this production was affected by signaling modulators. Taken together, our findings indicate that CL produces PI(3,4,5)P3 in an ADA-sensitive, PTX-sensitive, or WT-sensitive manner and will advance understanding of the effect of β3-AR agonists on adipocytes., Y. Ohsaka, Y. Nomura., and Obsahuje bibliografii
A Lie algebra $L$ is called 2-step nilpotent if $L$ is not abelian and $[L, L]$ lies in the center of $L$. 2-step nilpotent Lie algebras are useful in the study of some geometric problems, and their classification has been an important problem in Lie theory. In this paper, we give a classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center., Ren Bin, Zhu Lin Sheng., and Obsahuje bibliografii
Let R be a commutative ring with nonzero identity and J(R) the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is defined as the graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface Sn. In this paper, we investigate the genus number of the compact Riemann surface in which JR can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that JR is toroidal., Krishnan Selvakumar, Manoharan Subajini., and Obsahuje seznam literatury