Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

THE SPIRAL WAVE INSTABILITY INDUCED BY A GIANT PLANET. I. PARTICLE STIRRING IN THE INNER REGIONS OF PROTOPLANETARY DISKS

We have recently shown that spiral density waves propagating in accretion disks can undergo a parametric instability by resonantly coupling with and transferring energy into pairs of inertial waves (or inertial-gravity waves when buoyancy is important). In this paper, we perform inviscid three-dimensional global hydrodynamic simulations to examine the growth and consequence of this instability operating on the spiral waves driven by a Jupiter-mass planet in a protoplanetary disk. We find that the spiral waves are destabilized via the spiral wave instability (SWI), generating hydrodynamic turbulence and sustained radially-alternating vertical flows that appear to be associated with long wavelength inertial modes. In the interval $0.3~R_p \leq R \leq 0.7~R_p$, where $R_p$ denotes the semi-major axis of the planetary orbit (assumed to be 5~au), the estimated vertical diffusion rate associated with the turbulence is characterized by $\alpha_{\rm diff} \sim (0.2-1.2) \times 10^{-2}$. For the disk model considered here, the diffusion rate is such that particles with sizes up to several centimeters are vertically mixed within the first pressure scale height. This suggests that the instability of spiral waves launched by a giant planet can significantly disperse solid particles and trace chemical species from the midplane. In planet formation models where the continuous local production of chondrules/pebbles occurs over Myr time scales to provide a feedstock for pebble accretion onto these bodies, this stirring of solid particles may add a time constraint: planetary embryos and large asteroids have to form before a gas giant forms in the outer disk, otherwise the SWI will significantly decrease the chondrule/pebble accretion efficiency.Comment: Accepted for publication in the The Astrophysical Journal, 19 pages, 12 figures, 1 tabl

My Tormented Heart

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Multiple reassortment events in the evolutionary history of H1N1 influenza A virus since 1918

The H1N1 subtype of influenza A virus has caused substantial morbidity and mortality in humans, first documented in the global pandemic of 1918 and continuing to the present day. Despite this disease burden, the evolutionary history of the A/H1N1 virus is not well understood, particularly whether there is a virological basis for several notable epidemics of unusual severity in the 1940s and 1950s. Using a data set of 71 representative complete genome sequences sampled between 1918 and 2006, we show that segmental reassortment has played an important role in the genomic evolution of A/H1N1 since 1918. Specifically, we demonstrate that an A/H1N1 isolate from the 1947 epidemic acquired novel PB2 and HA genes through intra-subtype reassortment, which may explain the abrupt antigenic evolution of this virus. Similarly, the 1951 influenza epidemic may also have been associated with reassortant A/H1N1 viruses. Intra-subtype reassortment therefore appears to be a more important process in the evolution and epidemiology of H1N1 influenza A virus than previously realized

A comparison of host gene expression signatures associated with infection in vitro by the Makona and Ecran (Mayinga) variants of Ebola virus

The Ebola virus (EBOV) variant Makona (which emerged in 2013) was the causative agent of the largest outbreak of Ebola Virus Disease recorded. Differences in virus-host interactions between viral variants have potential consequences for transmission, disease severity and mortality. A detailed profile of the cellular changes induced by the Makona variant compared with other Ebola virus variants was lacking. In this study, A549 cells, a human cell line with a robust innate response, were infected with the Makona variant or with the Ecran variant originating from the 1976 outbreak in Central Africa. The abundance of viral and cellular mRNA transcripts was profiled using RNASeq and differential gene expression analysis performed. Differences in effects of each virus on the expression of interferon-stimulated genes were also investigated in A549 NPro cells where the type 1 interferon response had been attenuated. Cellular transcriptomic changes were compared with those induced by human respiratory syncytial virus (HRSV), a virus with a similar genome organisation and replication strategy to EBOV. Pathway and gene ontology analysis revealed differential expression of functionally important genes; including genes involved in the inflammatory response, cell proliferation, leukocyte extravasation and cholesterol biosynthesis. Whilst there was overlap with HRSV, there was unique commonality to the EBOV variants

Administrative Law - Judicial Control - Appellate Review of Federal Trade Commission Proceedings

During its forty-five year life the Federal Trade Commission has gone through some difficult periods to emerge today as one of the fundamental instrumentalities of government in the regulation of business. Its vast powers and influence, well known to lawyers, will not be explored here. Rather, the purpose of this comment is to appraise the extent of control which the judiciary now exercises over the commission in its adjudicative functions, so as to offer some indication to the practitioner of the probabilities regarding the outcome of judicial review on an appeal beyond the full commission. The approach to be used will be a study of Supreme Court cases involving the commission since 1914 along with a review of Federal Trade Commission cases that have been before the courts of appeals since 1947

Welcome Home

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Pretty Kitty Kelly

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