On the determinant bundles of abelian schemes

Let \pi:\CA\ra S be an abelian scheme over a scheme $S$ which is quasi-projective over an affine noetherian scheme and let \CL be a symmetric, rigidified, relatively ample line bundle on \CA. We show that there is an isomorphism \det(\pi_*\CL)^{\o times 24}\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o times 12d} of line bundles on $S$, where $d$ is the rank of the (locally free) sheaf \pi_*\CL. We also show that the numbers 24 and $12d$ are sharp in the following sense: if $N>1$ is a common divisor of 12 and 24, then there are data as above such that \det(\pi_*\CL)^{\o times (24/N)}\not\simeq\big(\pi_*\omega_{\CA}^{\vee}\big)^{\o times (12d/N)}.Comment: 8 page

On a canonical class of Green currents for the unit sections of abelian schemes

We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar\partial$-exact differential forms. This current generalizes the Siegel functions defined on elliptic curves. We prove generalizations of classical properties of Siegel functions, like distribution relations, limit formulae and reciprocity laws.Comment: 42 page

Formes automorphes et theoremes de Riemann-Roch arithmetiques

Nous construisons trois familles de formes automorphes au moyen du theoreme de Riemann-Roch arithmetique et de la formule de Lefschetz arithmetique. Deux de ces familles ont deja ete construites par Yoshikawa et notre construction met en lumiere leur origine arithmetique. ----- We construct three families of automorphic forms following the arithmetic Riemann-Roch theorem and the arithmetic Lefschetz formula. Two of these families were already constructed by Yoshikawa and our construction illuminates their arithmetic origin.Comment: 16 pages, in Frenc

Information Flow in Secret Sharing Protocols

The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes

A comparison of mean winds and gravity wave activity in the northern and southern polar MLT

Mean winds and waves observed in the mesosphere and lower thermosphere with MF radars located at Davis (69°S, 78°E) and Poker Flat (65°N, 147°W) are compared. Measurements covering the period from 1999 to mid 2000 show differences in the strength of the horizontal wind fields. In the southern hemisphere the zonal and meridional winds reach their maximum values near the summer solstice, but are delayed by 2–3 weeks in the northern hemisphere. Gravity wave variances also show significant differences, as do the strength of vertical velocities.Andrew Dowdy and Robert A. Vincent, Kiyoshi Igarashi and Yasuhiro Murayama, Damian J. Murph

The Molloy Student Literary Magazine Volume 12

The Molloy Student Literary Magazine, sponsored by Molloy College’s Office of Student Affairs, is devoted to publishing the best previously unpublished works of prose, poetry, drama, literary review, criticism, and other literary genres, that the Molloy student community has to offer. The journal welcomes submissions, for possible publication, from currently enrolled Molloy students at all levels. All submitted work will undergo a review process initiated by the Managing Editor prior to a decision being made regarding publication of said work. Given sufficient content, The Molloy Student Literary Magazine is published twice annually in Spring and Fall. Interested contributors from the currently enrolled Molloy student community should send work via e-mail attachment and brief cover letter (including a two-sentence biographical statement) to: Dr. Damian Ward Hey, Managing Editor, The Molloy Student Literary Magazine: [email protected]. Enrolled students who are interested in becoming members of The Molloy Student Literary Magazine staff may e-mail letters of inquiry. Excelsior!https://digitalcommons.molloy.edu/eng_litmag/1004/thumbnail.jp

The Molloy Student Literary Magazine Volume 14

The Molloy Student Literary Magazine, sponsored by Molloy College’s Office of Student Affairs, is devoted to publishing the best previously unpublished works of prose, poetry, drama, literary review, criticism, and other literary genres, that the Molloy student community has to offer. The journal welcomes submissions, for possible publication, from currently enrolled Molloy students at all levels. All submitted work will undergo a review process initiated by the Managing Editor prior to a decision being made regarding publication of said work. Given sufficient content, The Molloy Student Literary Magazine is published twice annually in Spring and Fall.https://digitalcommons.molloy.edu/eng_litmag/1006/thumbnail.jp

Modeling noise experiments performed at AKR-2 and CROCUS zero-power reactors

CORTEX is a EU H2020 project (2017-2021) devoted to the analysis of ’reactor neutron noise’ in nuclear reactors, i.e. the small fluctuations occurring around the stationary state due to external or internal disturbances in the core. One important aspect of CORTEX is the development of neutron noise simulation codes capable of modeling the spatial variations of the noise distribution in a reactor. In this paper we illustrate the validation activities concerning the comparison of the simulation results obtained by several noise simulation codes with respect to experimental data produced at the zero-power reactors AKR-2 (operated at TUD, Germany) and CROCUS (operated at EPFL, Switzerland). Both research reactors are modeled in the time and frequency domains, using transport or diffusion theory. Overall, the noise simulators managed to capture the main features of the neutron noise behavior observed in the experimental campaigns carried out in CROCUS and AKR-2, even though computational biases exist close to the region where the noise-inducing mechanical vibration was located (the so-called ”noise source”). In some of the experiments, it was possible to observe the spatial variation of the relative neutron noise, even relatively far from the noise source. This was achieved through reduced uncertainties using long measurements, the installation of numerous, robust and efficient detectors at a variety of positions in the near vicinity or inside the core, as well as new post-processing methods. For the numerical simulation tools, modeling the spatial variations of the neutron noise behavior in zero-power research reactors is an extremely challenging problem, because of the small magnitude of the noise field; and because deviations from a point-kinetics behavior are most visible in portions of the core that are especially difficult to be precisely represented by simulation codes, such as experimental channels. Nonetheless the limitations of the simulation tools reported in the paper were not an issue for the CORTEX project, as most of the computational biases are found close to the noise source

Structure, variability, and mean-flow interactions of the January 2015 quasi-two-day wave at middle and high southern latitudes

The structure, variability, and mean-flow interactions of the quasi-2-day wave (Q2DW) in the mesosphere and lower thermosphere during January 2015 were studied employing meteor and medium-frequency radar winds at eight sites from 23 degrees S to 76 degrees S and Microwave Limb Sounder (MLS) temperature and geopotential height measurements from 30 degrees S to 80 degrees S. The event had a duration of 20-25 days, dominant periods of 44-52 hr, temperature amplitudes as large as 16 K, and zonal and meridional wind amplitudes as high as 40 and 80 m/s, respectively, at middle and lower latitudes. MLS measurements enabled definition of balance winds that agreed well with radar wind amplitudes and phases at middle latitudes where amplitudes were large and quantification of the various Q2DW modes contributing to the full wave field. The Q2DW event was composed primarily of the westward zonal wavenumber 3 (W3) mode but also had measurable amplitudes in other westward modes W1, W2, and W4; eastward modes E1 and E2; and stationary mode S0. Of the secondary modes, W1, W2, and E2 had the larger amplitudes. Inferred MLS balance winds enabled estimates of the Eliassen-Palm fluxes for each mode, and cumulative zonal accelerations that were found to be in reasonable agreement with radar estimates from 35 degrees S to 70 degrees S at the lower altitudes at which radar winds were available