Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces

In 1994, H. Bart and V. É. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (SC) coincide, leaving only the implication EAE/MC => SC open. Despite several affirmative results, in this paper we show that the answer in general is no. This follows from a complete description of EAE and SC for the case that the operators act on essentially incomparable Banach spaces, which also leads to a new characterisation of the notion of essential incomparability. Concretely, the forward shift operators $U$ on $\ell$$^p$ and $V$ on $\ell$$^p$, for $1 ≤ p, q ≤ \infty, p ≠ q$, are EAE but not SC. As a corollary, SC is not transitive. Under mild assumptions, given $U$ and $V$ that are Atkinson or generalised invertible and EAE, we give a concrete operator $W$ that is SC to both $U$ and $V$, even if $U$ and $V$ are not SC themselves. Some further affirmative results for the case where the Banach spaces are isomorphic are also obtained

Vegetation Type and Decomposition Priming Mediate Brackish Marsh Carbon Accumulation Under Interacting Facets of Global Change

Coastal wetland carbon pools are globally important, but their response to interacting facets of global change remain unclear. Numerical models neglect species-specific vegetation responses to sea level rise (SLR) and elevated CO2 (eCO2) that are observed in field experiments, while field experiments cannot address the long-term feedbacks between flooding and soil growth that models show are important. Here, we present a novel numerical model of marsh carbon accumulation parameterized with empirical observations from a long-running eCO2 experiment in an organic rich, brackish marsh. Model results indicate that eCO2 and SLR interact synergistically to increase soil carbon burial, driven by shifts in plant community composition and soil volume expansion. However, newly parameterized interactions between plant biomass and decomposition (i.e. soil priming) reduce the impact of eCO2 on marsh survival, and by inference, the impact of eCO2 on soil carbon accumulation

Toward accurate CO_2 and CH_4 observations from GOSAT

The column-average dry air mole fractions of atmospheric carbon dioxide and methane (X_(CO_2) and X_(CH_4)) are inferred from observations of backscattered sunlight conducted by the Greenhouse gases Observing SATellite (GOSAT). Comparing the first year of GOSAT retrievals over land with colocated ground-based observations of the Total Carbon Column Observing Network (TCCON), we find an average difference (bias) of −0.05% and −0.30% for X_(CO_2) and X_(CH_4) with a station-to-station variability (standard deviation of the bias) of 0.37% and 0.26% among the 6 considered TCCON sites. The root-mean square deviation of the bias-corrected satellite retrievals from colocated TCCON observations amounts to 2.8 ppm for X_(CO_2) and 0.015 ppm for X_(CH_4). Without any data averaging, the GOSAT records reproduce general source/sink patterns such as the seasonal cycle of X_(CO_2) suggesting the use of the satellite retrievals for constraining surface fluxes

Radiation enhancement and "temperature" in the collapse regime of gravitational scattering

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $\sqrt{s}\gg m_P$ and finite scattering angles $\Theta_s$, so as to approach the collapse regime of impact parameters $b \simeq b_c \sim R\equiv 2G\sqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $\Theta_s\ll 1$ but, for sizeable angles $\Theta_s(b)\leq \Theta_c = O(1)$ acquires an exponential cutoff of the large $\omega R$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $b\to b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $\langle N \rangle\sim Gs \gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $\sqrt{s}$.Comment: 5 pages, 2 figures, talk presented at the European Physical Society Conference on High Energy Physics, 5-12 July, Venice, Ital

Confidentiality and public protection: ethical dilemmas in qualitative research with adult male sex offenders

This paper considers the ethical tensions present when engaging in in-depth interviews with convicted sex offenders. Many of the issues described below are similar to those found in other sensitive areas of research. However, confidentiality and public protection are matters that require detailed consideration when the desire to know more about men who have committed serious and harmful offences is set against the possibility of a researcher not disclosing previously unknown sensitive information that relates to the risk of someone being harmed.</p

Imaging Molecular Structure through Femtosecond Photoelectron Diffraction on Aligned and Oriented Gas-Phase Molecules

This paper gives an account of our progress towards performing femtosecond time-resolved photoelectron diffraction on gas-phase molecules in a pump-probe setup combining optical lasers and an X-ray Free-Electron Laser. We present results of two experiments aimed at measuring photoelectron angular distributions of laser-aligned 1-ethynyl-4-fluorobenzene (C8H5F) and dissociating, laseraligned 1,4-dibromobenzene (C6H4Br2) molecules and discuss them in the larger context of photoelectron diffraction on gas-phase molecules. We also show how the strong nanosecond laser pulse used for adiabatically laser-aligning the molecules influences the measured electron and ion spectra and angular distributions, and discuss how this may affect the outcome of future time-resolved photoelectron diffraction experiments.Comment: 24 pages, 10 figures, Faraday Discussions 17