Essential dimension and the second serre conjecture for exceptional groups

We study the essential dimension of exceptional connected simply connected algebraic groups over algebraically closed fields. In the present paper, we find upper estimates for the essential dimensions of the groupsF ₄ ,E ₆ , andE ₇ . For the groupF ₄ , the upper estimate, thus obtained coincides with the known lower estimate. We also prove the second Serre conjecture for the groupE ₆ and for a function field. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 539–547, October, 2000.     

The Characterization of the Derivatives for Linear Combinations of Post–Widder Operators inLp

The aim of the paper is to characterize the global rate of approximation of derivativesf^(l)through corresponding derivatives of linear combinations of Post–Widder operators in an appropriate weightedL_p-metric using a weighted Ditzian and Totik modulus of smoothness, and also to characterize derivatives of these operators in Besov spaces of Ditzian–Totik type.