In the present paper, we shall establish that IntS( ) = T ( ) for any Fuchsian group uniformizing a compact Riemann surface with nonempty boundary, i.e., for any nitely generated, purely hyperbolic Fuchsian group of the second kind, where S( ) denotes the Schwarzian derivative of all the -equivariant schlicht holomorphic functions and T ( ) is the Teichm uller space of : We also include some r...

1 Kasner, "Algebraic Potential Curves," BuO. Am. Math. Soc., 1901. 2 Kasner, "Conformal Geometry," Proc. Fifth Internat. Cong. of Math., 2, 81 (1912). 3 Kasner, "Geometry of Conformal Symmetry (Schwarzian Reflection)," Ann. Math., 38, 873 (1937). 4 Comenetz, "Conformal Geometry on a Surface," Ibid., 39, 863 (1938). I wish to thank J. De Cicco, Aida Kailish, F. Supnik and C. Vlucay for assistanc...

A relatively simple proof is given for Haimo’s theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo’s criterion, which is now shown to be sharp. It is proved that Haimo’s functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presenc...

Fixed-point theory of one-dimensional maps of R does not completely address the issue of non-hyperbolic fixed points. This paper generalizes the existing tests to completely classify all such fixed points. To do this, a family of operators are exhibited that are analogous to generalizations of the Schwarzian derivative. In addition, a family of functions f are exhibited such that the MacLaurin ...

Cases of acute myocardial infarction (AMI) that occur during pregnancy or postpartum are rarely reported. Ergot derivatives are known to induce the spasmodic contraction of coronary arteries. Administration of ergot derivatives can cause AMI, even in normal healthy people. In several reported cases, ergot derivatives triggered severe AMI during the postpartum period. Here, we report the case of...

We consider the task of filtering the noise from images and other types of inputs which are assumed to be piecewise continuous and piecewise monotone. We show that nonlinear diffusion of the data, a powerful filtering method, is too restrictive for such a case, leading to piecewise constant functions. We claim that the piecewise monotonicity can be enhanced by nonlinear diffusion of first parti...

Pre-mRNA splicing is an essential step of the expression of most metazoan protein-coding genes, which is often regulated in a cell type-specific or developmental manner. We have demonstrated previously that human DNA topoisomerase I, an extensively studied target for anticancer drugs, also has an intrinsic protein kinase activity that specifically phosphorylates proteins involved in splice site...

Based on the local Shannon entropy concept in information theory, a new measure of aromaticity is introduced. This index, which describes the probability of electronic charge distribution between atoms in a given ring, is called Shannon aromaticity (SA). Using B3LYP method and different basis sets (6-31G**, 6-31+G** and 6-311++G**), the SA values of some five-membered heterocycles, C(4)H(4)X, a...