Abstract. We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.
Abstract. For a normalized quasiregular pluriharmonic mapping f of the unit ball B n of C n into C n , we estimate the supremum of numbers R such that some subdomain Ω of the ball is mapped by f diffeomorphically onto some ball of radius R. Our estimates significantly improve earlier estimates, even in the case of harmonic functions in the disc.
Abstract:We report on our examination of pages from the World Wide Web. We have analyzed data collected by the Inktomi Web crawler (this data currently comprises over 2.6 million HTML documents). We have examined many characteristics of these documents, including: document size; number and types of tags, attributes, file extensions, protocols, and ports; the number of in-links; and the ratio of document size to the number of tags and attributes. For a more limited set of documents, we have examined the following: the number and types of syntax errors and readability scores. These data have been aggregated to create a number of ranked lists, e.g., the ten most-used tags, the ten most common HTML errors.
Abstract. We give a necessary and sufficient condition for a composition operator on an α-Bloch space with α ≥ 1 to be bounded below. This extends a known result for the Bloch space due to P. Ghatage,
For compact sets K ⊂ C d , we introduce a subalgebra A D (K) of A(K), which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
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