Hardy Spaces on Weighted Homogeneous Trees

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space (V, d, μ) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces does not apply in this setting. We construct an atomic Hardy space H1(μ) on (V, d, μ) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H1(μ)

Interpolation Theorems for Self-adjoint Operators

We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator $L$, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where $L$ is a uniformly elliptic operator or a Schr\"odinger operator with electro-magnetic potential.Comment: 8 pages. Submitte

Axial tubule junctions control rapid calcium signaling in atria.

The canonical atrial myocyte (AM) is characterized by sparse transverse tubule (TT) invaginations and slow intracellular Ca2+ propagation but exhibits rapid contractile activation that is susceptible to loss of function during hypertrophic remodeling. Here, we have identified a membrane structure and Ca2+-signaling complex that may enhance the speed of atrial contraction independently of phospholamban regulation. This axial couplon was observed in human and mouse atria and is composed of voluminous axial tubules (ATs) with extensive junctions to the sarcoplasmic reticulum (SR) that include ryanodine receptor 2 (RyR2) clusters. In mouse AM, AT structures triggered Ca2+ release from the SR approximately 2 times faster at the AM center than at the surface. Rapid Ca2+ release correlated with colocalization of highly phosphorylated RyR2 clusters at AT-SR junctions and earlier, more rapid shortening of central sarcomeres. In contrast, mice expressing phosphorylation-incompetent RyR2 displayed depressed AM sarcomere shortening and reduced in vivo atrial contractile function. Moreover, left atrial hypertrophy led to AT proliferation, with a marked increase in the highly phosphorylated RyR2-pS2808 cluster fraction, thereby maintaining cytosolic Ca2+ signaling despite decreases in RyR2 cluster density and RyR2 protein expression. AT couplon "super-hubs" thus underlie faster excitation-contraction coupling in health as well as hypertrophic compensatory adaptation and represent a structural and metabolic mechanism that may contribute to contractile dysfunction and arrhythmias

Potential theory results for a class of PDOs admitting a global fundamental solution

We outline several results of Potential Theory for a class of linear par-tial differential operators L of the second order in divergence form. Under essentially the sole assumption of hypoellipticity, we present a non-invariant homogeneous Harnack inequality for L; under different geometrical assumptions on L (mainly, under global doubling/Poincar\ue9 assumptions), it is described how to obtainan invariant, non-homogeneous Harnack inequality. When L is equipped with a global fundamental solution \u393, further Potential Theory results are available (such as the Strong Maximum Principle). We present some assumptions on L ensuring that such a \u393 exists

Self-healing dyes for super-resolution fluorescence microscopy.

In recent years, optical microscopy techniques have emerged that allow optical imaging at unprecedented resolution beyond the diffraction limit. These techniques exploit photostabilizing buffers to enable photoswitching and/or the enhancement of fluorophore brightness and stability. A major drawback with the use of photostabilizing buffers, however, is that they cannot be used in live cell imaging. In this paper, we tested the performance of self-healing organic fluorophores, which undergo intramolecular photostabilization, in super-resolution microscopy examining both targeted (stimulated emission depletion (STED) microscopy) and stochastic readout (stochastic optical reconstruction microscopy (STORM)). The overall goal of the study was to identify dyes and conditions that lead to improved spatial and temporal resolution of both techniques without the need for mixtures of photostabilizing agents in the imaging buffer. As a result of previously shown superior performance, we identified an ATTO647N-photostabilizer conjugate as a potential candidate for STED microscopy. We have here characterized the photostability and resulting performance of this nitrophenylalanine (NPA) conjugate of ATTO647N on oligonucleotides in STED microscopy. We found that the superior photophysical performance resulted in optimal STED imaging and demonstrated that single-molecule fluorescent transients of individual fluorophores can be obtained with both the excitation-and STED-laser. In similar experiments, we also tested a nitrophenylacetic acid conjugate of STAR635P, another frequently used dye in STED microscopy, and present a characterization of its photophysical properties. Finally, we performed an analysis of the photoswitching kinetics of self-healing Cy5 dyes (containing trolox, cyclooctatetraene and NPA-based stabilizers) in the presence of Tris(2-carboxyethyl) phosphine and cysteamine, which are typically used in STORM microscopy. In line with previous work, we found that intramolecular photostabilization strongly influences photoswitching kinetics and requires careful attention when designing STORM-experiments. In summary, this contribution explores the possibilities and limitations of self-healing dyes in super-resolution microscopy of differing modalities

N-Alkyl-2-pyrrolidones (N-methyl-2-pyrrolidone, N-ethyl-2-pyrrolidone), vapour [Air Monitoring Methods, 2014a]

This analytical method is a validated measurement procedure for the determination of gaseous N‐methyl‐2‐pyrrolidone (NMP) and N‐ethyl‐2‐pyrrolidone (NEP) and for monitoring their Occupational Exposure Limits (OELs) or MAK values at workplaces. Both personal and stationary sampling can be performed for assessment of workplaces. Sampling is performed by drawing air through an ADS‐type silica gel tube using a suitable flow‐regulated pump with a volumetric flow rate of 20 L/h. Gaseous NMP and/or NEP are adsorbed onto the silica gel. For sample preparation the collected NMP and/or NEP are desorbed from the silica gel with a potassium hydroxide solution in methanol. The sample solutions are analysed by gas chromatography using a nitrogen‐selective detector (NPD) with dibutylamine as internal standard. The quantitative determination is based on calibration functions obtained by means of multiple‐point calibrations. The limit of quantification (LOQ) for both, NMP and NEP is 1.6 µg/mL (absolute 1.6 ng), which corresponds to a relative LOQ of 0.1 mg/m3 based on an air sample volume of 40 L