On some problems of optimal recovery of analytic and harmonic functions from inaccurate data

AbstractWe consider some problems of optimal recovery of holomorphic and harmonic functions in the unit disc. We obtain extensions of Schwartz's Lemma and optimal formulas for numerical differentiation

The n-width of the unit ball of Hq

AbstractLet E be a compact subset of the open unit disc Δ and let Hq be the Hardy space of analytic functions f on Δ for which stf¦q has a harmonic majorant. We determine the value of the Kolmogorov, Gel'fand, and linear n-widths in Lp(E, μ) of the restriction to E of the unit ball of Hq when p ⩽ q or when 1 ⩽ q < p < ∞ and E is “small”

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Molecular, Enzymatic, and Cellular Characterization of Soluble Adenylyl Cyclase From Aquatic Animals.

The enzyme soluble adenylyl cyclase (sAC) is the most recently identified source of the messenger molecule cyclic adenosine monophosphate. sAC is evolutionarily conserved from cyanobacteria to human, is directly stimulated by [Formula: see text] ions, and can act as a sensor of environmental and metabolic CO2, pH, and [Formula: see text] levels. sAC genes tend to have multiple alternative promoters, undergo extensive alternative splicing, be translated into low mRNA levels, and the numerous sAC protein isoforms may be present in various subcellular localizations. In aquatic organisms, sAC has been shown to mediate various functions including intracellular pH regulation in coral, blood acid/base regulation in shark, heart beat rate in hagfish, and NaCl absorption in fish intestine. Furthermore, sAC is present in multiple other species and tissues, and sAC protein and enzymatic activity have been reported in the cytoplasm, the nucleus, and other subcellular compartments, suggesting even more diverse physiological roles. Although the methods and experimental tools used to study sAC are conventional, the complexity of sAC genes and proteins requires special considerations that are discussed in this chapter

Calcium-sensing soluble adenylyl cyclase mediates TNF signal transduction in human neutrophils

Through chemical screening, we identified a pyrazolone that reversibly blocked the activation of phagocyte oxidase (phox) in human neutrophils in response to tumor necrosis factor (TNF) or formylated peptide. The pyrazolone spared activation of phox by phorbol ester or bacteria, bacterial killing, TNF-induced granule exocytosis and phox assembly, and endothelial transmigration. We traced the pyrazolone's mechanism of action to inhibition of TNF-induced intracellular Ca2+ elevations, and identified a nontransmembrane (“soluble”) adenylyl cyclase (sAC) in neutrophils as a Ca2+-sensing source of cAMP. A sAC inhibitor mimicked the pyrazolone's effect on phox. Both compounds blocked TNF-induced activation of Rap1A, a phox-associated guanosine triphosphatase that is regulated by cAMP. Thus, TNF turns on phox through a Ca2+-triggered, sAC-dependent process that may involve activation of Rap1A. This pathway may offer opportunities to suppress oxidative damage during inflammation without blocking antimicrobial function

Potential alternative treatment approach for pediatric patient with diffusely infiltrative primary rhabdomyosarcoma of the liver

Primary hepatic rhabdomyosarcoma is rare, making decisions regarding locoregional management with resection and/or conventional radiation difficult. We present a novel treatment approach for a pediatric patient diagnosed with rhabdomyosarcoma diffusely involving the liver. This patient underwent treatment with yttrium-90 (Y-90) microspheres followed by external beam radiation therapy (EBRT) to residual disease, interdigitated with systemic chemotherapy. Initial post-radiation imaging showed significant response to treatment, and she experienced minimal acute toxicities and no long-term toxicities. She developed recurrent PET-avid disease 23 months after Y-90 treatment, necessitating further local and continued systemic therapies. We report on the tumor control following Y-90 and EBRT treatment