1,084 research outputs found
Cyclicity in families of circle maps
In this paper we will study families of circle maps of the form x↦x+2πr+af(x)(mod2π) and investigate how many periodic trajectories maps from this family can have for a ‘typical’ function f provided the parameter a is small
Coarse version of the Banach-Stone theorem
We show that if there exists a Lipschitz homeomorphism between the nets
in the Banach spaces and of continuous real valued functions on
compact spaces and , then the spaces and are homeomorphic
provided . By and we denote the
Lipschitz constants of the maps and . This improves the classical
result of Jarosz and the recent result of Dutrieux and Kalton where the
constant obtained is 17/16. We also estimate the distance of the map from
the isometry of the spaces and
Corrected synonymies: the identities of Strymon bicolor (Philippi, 1859) and Strymon heodes (Druce, 1909) (Lepidoptera: Lycaenidae)
The South American hairstreak species Strymon bicolor (Philippi, 1859) and S. heodes (Druce, 1909) are diagnosed and their synonymies are revised. The distribution of S. bicolor is restricted to the Andean-Patagonian region south of the Atacama Desert and represented now in Argentina and Chile by seven available species group names, considered as subjective synonyms. However, some of these names can most probably be considered as valid taxa. A key to identification is given for distinguishing the superficially most similar Strymon species patterned by orange scaling in the dorsal wing surfaces. It is noted that the Austral S. bicolor group and the Central Peruvian S. heodes appear to belong to a mimicry ring inhabiting the dry areas of the Andes
Banach spaces of universal disposition
In this paper we present a method to obtain Banach spaces of universal and
almost-universal disposition with respect to a given class of
normed spaces. The method produces, among other, the Gurari\u{\i} space
(the only separable Banach space of almost-universal disposition
with respect to the class of finite dimensional spaces), or the
Kubis space (under {\sf CH}, the only Banach space with the
density character the continuum which is of universal disposition with respect
to the class of separable spaces). We moreover show that
is not isomorphic to a subspace of any -space -- which
provides a partial answer to the injective space problem-- and that --under
{\sf CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space.
We study further properties of spaces of universal disposition: separable
injectivity, partially automorphic character and uniqueness properties
Vector-valued optimal Lipschitz extensions
Consider a bounded open set in and a Lipschitz function g from the
boundary of to . Does this function always have a canonical optimal
Lipschitz extension to all of ? We propose a notion of optimal Lipschitz
extension and address existence and uniqueness in some special cases. In the
case , we show that smooth solutions have two phases: in one they are
conformal and in the other they are variants of infinity harmonic functions
called infinity harmonic fans. We also prove existence and uniqueness for the
extension problem on finite graphs.Comment: 24 pages, 10 figure
A stability version of H\"older's inequality
We present a stability version of H\"older's inequality, incorporating an
extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue
2, Pages 842-852. This version differs from the published one in that it
contains a new reference, and a trivial improvement of Corollary 3.2. fo
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