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Blaschke products with derivative in function spaces

Let $B$ be a Blaschke product with zeros $\{a_n\}$. If $B' \in A^p_{\alpha}$ for certain $p$ and $\alpha$, it is shown that $\sum_n (1 - |a_n|)^{\beta} < \infty$ for appropriate values of $\beta$. Also, if $\{a_n\}$ is uniformly discrete and if $B' \in H^p$ or $B' \in A^{1+p}$ for any $p \in (0,1)$, it is shown that $\sum_n (1 - |a_n|)^{1-p} < \infty$.Comment: Clarified a few points. Accepted for publication in the Kodai Mathematical Journa

An electrostatic interaction between TEA and an introduced pore aromatic drives spring-in-the-door inactivation in Shaker potassium channels

Slow inactivation of Kv1 channels involves conformational changes near the selectivity filter. We examine such changes in Shaker channels lacking fast inactivation by considering the consequences of mutating two residues, T449 just external to the selectivity filter and V438 in the pore helix near the bottom of the selectivity filter. Single mutant T449F channels with the native V438 inactivate very slowly, and the canonical foot-in-the-door effect of extracellular tetraethylammonium (TEA) is not only absent, but the time course of slow inactivation is accelerated by TEA. The V438A mutation dramatically speeds inactivation in T449F channels, and TEA slows inactivation exactly as predicted by the foot-in-the-door model. We propose that TEA has this effect on V438A/T449F channels because the V438A mutation produces allosteric consequences within the selectivity filter and may reorient the aromatic ring at position 449. We investigated the possibility that the blocker promotes the collapse of the outer vestibule (spring-in-the-door) in single mutant T449F channels by an electrostatic attraction between a cationic TEA and the quadrupole moments of the four aromatic rings. To test this idea, we used in vivo nonsense suppression to serially fluorinate the introduced aromatic ring at the 449 position, a manipulation that withdraws electrons from the aromatic face with little effect on the shape, net charge, or hydrophobicity of the aromatic ring. Progressive fluorination causes monotonically enhanced rates of inactivation. In further agreement with our working hypothesis, increasing fluorination of the aromatic gradually transforms the TEA effect from spring-in-the-door to foot-in-the-door. We further substantiate our electrostatic hypothesis by quantum mechanical calculations

Production of Secondary Organic Aerosol During Aging of Biomass Burning Smoke From Fresh Fuels and Its Relationship to VOC Precursors

After smoke from burning biomass is emitted into the atmosphere, chemical and physical processes change the composition and amount of organic aerosol present in the aged, diluted plume. During the fourth Fire Lab at Missoula Experiment, we performed smog-chamber experiments to investigate formation of secondary organic aerosol (SOA) and multiphase oxidation of primary organic aerosol (POA). We simulated atmospheric aging of diluted smoke from a variety of biomass fuels while measuring particle composition using high-resolution aerosol mass spectrometry. We quantified SOA formation using a tracer ion for low-volatility POA as a reference standard (akin to a naturally occurring internal standard). These smoke aging experiments revealed variable organic aerosol (OA) enhancements, even for smoke from similar fuels and aging mechanisms. This variable OA enhancement correlated well with measured differences in the amounts of emitted volatile organic compounds (VOCs) that could subsequently be oxidized to form SOA. For some aging experiments, we were able to predict the SOA production to within a factor of 2 using a fuel-specific VOC emission inventory that was scaled by burn-specific toluene measurements. For fires of coniferous fuels that were dominated by needle burning, volatile biogenic compounds were the dominant precursor class. For wiregrass fires, furans were the dominant SOA precursors. We used a POA tracer ion to calculate the amount of mass lost due to gas-phase oxidation and subsequent volatilization of semivolatile POA. Less than 5% of the POA mass was lost via multiphase oxidation-driven evaporation during up to 2 hr of equivalent atmospheric oxidation

On critical points of Blaschke products

We obtain an upper bound for the derivative of a Blaschke product, whose zeros lie in a certain Stolz-type region. We show that the derivative belongs to the space of analytic functions in the unit disk, introduced recently in \cite{FG}. As an outcome, we obtain a Blaschke-type condition for critical points of such Blaschke products.Comment: 6 pages in LaTe

Electrostatic Contributions of Aromatic Residues in the Local Anesthetic Receptor of Voltage-Gated Sodium Channels

Antiarrhythmics, anticonvulsants, and local anesthetics target voltage-gated sodium channels, decreasing excitability of nerve and muscle cells. Channel inhibition by members of this family of cationic, hydrophobic drugs relies on the presence of highly conserved aromatic residues in the pore-lining S6 segment of the fourth homologous domain of the channel. We tested whether channel inhibition was facilitated by an electrostatic attraction between lidocaine and {pi} electrons of the aromatic rings of these residues, namely a cation-{pi} interaction. To this end, we used the in vivo nonsense suppression method to incorporate a series of unnatural phenylalanine derivatives designed to systematically reduce the negative electrostatic potential on the face of the aromatic ring. In contrast to standard point mutations at the same sites, these subtly altered amino acids preserve the wild-type voltage dependence of channel activation and inactivation. Although these phenylalanine derivatives have no effect on low-affinity tonic inhibition by lidocaine or its permanently charged derivative QX-314 at any of the substituted sites, high-affinity use-dependent inhibition displays substantial cation-{pi} energetics for 1 residue only: Phe1579 in rNaV1.4. Replacement of the aromatic ring of Phe1579 by cyclohexane, for example, strongly reduces use-dependent inhibition and speeds recovery of lidocaine-engaged channels. Channel block by the neutral local anesthetic benzocaine is unaffected by the distribution of {pi} electrons at Phe1579, indicating that our aromatic manipulations expose electrostatic contributions to channel inhibition. These results fine tune our understanding of local anesthetic inhibition of voltage-gated sodium channels and will help the design of safer and more salutary therapeutic agents

Boundary behavior of functions in the de Branges--Rovnyak spaces

This paper deals with the boundary behavior of functions in the de Branges--Rovnyak spaces. First, we give a criterion for the existence of radial limits for the derivatives of functions in the de Branges--Rovnyak spaces. This criterion generalizes a result of Ahern-Clark. Then we prove that the continuity of all functions in a de Branges--Rovnyak space on an open arc $I$ of the boundary is enough to ensure the analyticity of these functions on $I$. We use this property in a question related to Bernstein's inequality