REMARKS ON THE HARDY INEQUALITY

Remarks on the hardy inequality

Let be an open subset of with finite Lebesgue -measure, let be Antenna Splitter the distance from to the boundary of , and let.We give a simple direct proof that if satisfies the plumpness condition of Martio and Väisälä [10], then the inequality of Hardy type, holds whenever.We also show that the plumpness condition may be replaced

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Cryptic genera, cryptic species: phylogeny of the genus Philopteroides Mey, 2004, sensu lato, with descriptions of two new genera and one new species

Closely related chewing lice in the Philopterus-complex are typically morphologically homogeneous, with the most significant differences often being in the male genitalia.However, in many groups within this complex the male genitalia are reduced and lacking one or more element, with the remaining components often at least partially fused.This is no

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Antimicrobial geopolymer paints based on modified natural zeolite

Many antimicrobial coatings deliver a peak release of antimicrobial agent at an early age, after which they lost antimicrobial activity over time.In the present study a novel geopolymer paints with long term antimicrobial activity were developed based on natural zeolite modified with silver and Shape Sorter copper ions.The obtained geopolymer paint

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Control of lateral root initiation by DA3 in Arabidopsis

Summary: Lateral root (LR) initiation is controlled by the pericycle and the neighboring endodermis in Arabidopsis.Here, we demonstrate that UBIQUITIN-SPECIFIC PROTEASE14/DA3 regulates LR initiation by modulating auxin signaling in the pericycle and endodermis.DA3 negatively affects the mRNA and protein levels of AUXIN RESPONSE FACTOR7 (ARF7) and A

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