The main purpose of this paper is to give a sharper asymptotic formula for the mean square value , where L′(s, χ) denotes the derivative of L (s, χ) with respect to s.
Let f(z) be a transcendental meromorphic function in the plane. Hayman conjectured thatf f' assumes all finite values except possibly zero infinitely many times. In this paper, we solve this conjecture partly.
In the present note the algebraic independence of certain continued fractions is proved. Especially, we prove that the Böhmer-Mahler's series are algebraically independent, where , are some irrational numbers and g1,…,gs are distinct positive integers.
We give a new characterization of the paratingent cone in terms of contingent cones, i.e., the paratingent cone to any open set at a boundary point is the upper limit of the contingent cones at the neighboring points. We use this result to characterize the strict differentiability in terms of the contingent directional derivatives. We also define aP-subderivative for continuous functions and develop a subdifferential calculus with applications to optimality conditions in mathematical programming.
We give a new characterization of the paratingent cone in terms of contingent cones, i.e., the paratingent cone to any open set at a boundary point is the upper limit of the contingent cones at the neighboring points. We use this result to characterize the strict differentiability in terms of the contingent directional derivatives. We also define a P-subderivative for continuous functions and develop a subdifferential calculus with applications to optimality conditions in mathematical programming.
