Abstract. In this note we study the Schwarz lemma and inequalities for some holomorphic functions on the unit disc. Also, we obtain the inequality of the derivative of holomorphic maps at a boundary point of the unit disc and find a holomorphic map to satisfy the equality.
Abstract. In this note we study the Schwarz lemma and its various versions. We find a condition for a holomorphic map to have fixed points only on the boundary of the unit disc and compare its derivatives at fixed points to get some relations among them.
Abstract. In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate n-connected planar domain Ω, where n > 1 is representable as Ω = {|f | < 1} with a suitable rational function f of degree n. This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.
In this paper, we determine the homotopy type of the coefficient body of Bell representations of non-degenerate n-connected planar domains with n 3. Also, by considering the isomorphism classes of rational functions, we get the precise number of those corresponding to Bell representations with same set of critical values. Further, the case of those with the same set of critical points is discussed.
Information Technology influenced on classroom to change the teaching and learning method. Recently, flipped learning method became a hot issue in education by using Information Technology. Learning management system that is introduced in our university in the spring semester 2015, made it possible to apply flipped learning method. So, we used the flipped learning method in a calculus course. In this paper, we found that flipped learning in Calculus we was a little bit affirmative in the aspect of motivation and active learning from students' response on flipped learning method. We analyzed the reason that students were not so positive in continuing flipped learning even though they liked flipped learning a little bit better than traditional learning. We suggest what we pay attention to for applying the flipped learning method effectively.
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