Multiplicity one for LL-functions and applications

We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients satisfy a partial Ramanujan bound and do not differ by too much. Additionally, we prove a number of multiplicity one type results for the number-theoretic objects attached to $L$-functions. These results follow from our main result about $L$-functions

Characterizations of the Saito-Kurokawa lifting: a survey

There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts

Deep Equatorial Pacific Ocean Oxygenation and Atmospheric CO\u3csub\u3e2\u3c/sub\u3e Over the Last Ice Age

Ventilation of carbon stored in the deep ocean is thought to play an important role in atmospheric CO2 increases associated with Pleistocene deglaciations. The presence of this respired carbon has been recorded by an array of paleoceanographic proxies from various locations across the global ocean. Here we present a new sediment core from the Eastern Equatorial Pacific (EEP) Ocean spanning the last 180,000 years and reconstruct high-resolution 230Th-derived fluxes of 232Th and excess barium, along with redox-sensitive uranium concentrations to examine past variations in dust delivery, export productivity, and bottom-water oxygenation, respectively. Our bottom-water oxygenation record is compared to other similar high-resolution records from across the Pacific and in the Southern Ocean. We suggest that the deep Pacific is a site of respired carbon storage associated with periods of decreased global atmospheric CO2 concentration during the LGM, confirming the conclusions from a wealth of previous studies. However, our study is the first to show a similar relationship beyond the last glacial, extending to at least 70,000 years

Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space-time

Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics (orbits) in the outer region of a Kerr Black Hole, representing the space time created by a bigger object. In our paper we study the entire class of orbits, both of constant radius (spherical orbits), as well as non-null eccentricity orbits, showing a number of properties on the physical parameters and trajectories. The main result is the determination of the geometrical locus of all the orbits in the space of physical parameters in Kerr space-time. This becomes a powerful tool to know if different orbits can be connected by a continuous change of their physical parameters. A discussion on the influence of different values of the angular momentum of the hole is given. Main results have been obtained by analytical methods.Comment: 26 pages, 12 figure

Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field

The future LISA detector will constitute the prime instrument for high-precision gravitational wave observations.LISA is expected to provide information for the properties of spacetime in the vicinity of massive black holes which reside in galactic nuclei.Such black holes can capture stellar-mass compact objects, which afterwards slowly inspiral,radiating gravitational waves.The body's orbital motion and the associated waveform carry information about the spacetime metric of the massive black hole,and it is possible to extract this information and experimentally identify (or not!) a Kerr black hole.In this paper we lay the foundations for a practical `spacetime-mapping' framework. Our work is based on the assumption that the massive body is not necessarily a Kerr black hole, and that the vacuum exterior spacetime is stationary axisymmetric,described by a metric which deviates slightly from the Kerr metric. We first provide a simple recipe for building such a `quasi-Kerr' metric by adding to the Kerr metric the deviation in the value of the quadrupole moment. We then study geodesic motion in this metric,focusing on equatorial orbits. We proceed by computing `kludge' waveforms which we compare with their Kerr counterparts. We find that a modest deviation from the Kerr metric is sufficient for producing a significant mismatch between the waveforms, provided we fix the orbital parameters. This result suggests that an attempt to use Kerr waveform templates for studying EMRIs around a non-Kerr object might result in serious loss of signal-to-noise ratio and total number of detected events. The waveform comparisons also unveil a `confusion' problem, that is the possibility of matching a true non-Kerr waveform with a Kerr template of different orbital parameters.Comment: 19 pages, 6 figure

Effect of hydrocarbon adsorption on the wettability of rare earth oxide ceramics

Vapor condensation is routinely used as an effective means of transferring heat, with dropwise condensation exhibiting a 5 − 7x heat transfer improvement compared to filmwise condensation. However, state-of-the-art techniques to promote dropwise condensation rely on functional hydrophobic coatings, which are often not robust and therefore undesirable for industrial implementation. Natural surface contamination due to hydrocarbon adsorption, particularly on noble metals, has been explored as an alternative approach to realize stable dropwise condensing surfaces. While noble metals are prohibitively expensive, the recent discovery of robust rare earth oxide (REO) hydrophobicity has generated interest for dropwise condensation applications due to material costs approaching 1% of gold; however, the underlying mechanism of REO hydrophobicity remains under debate. In this work, we show through careful experiments and modeling that REO hydrophobicity occurs due to the same hydrocarbon adsorption mechanism seen previously on noble metals. To investigate adsorption dynamics, we studied holmia and ceria REOs, along with control samples of gold and silica, via X-Ray photoelectron spectroscopy (XPS) and dynamic time-resolved contact angle measurements. The contact angle and surface carbon percent started at ≈0 on in-situ argon-plasma-cleaned samples and increased asymptotically over time after exposure to laboratory air, with the rare earth oxides displaying hydrophobic (>90°) advancing contact angle behavior at long times (>4 days). The results indicate that REOs are in fact hydrophilic when clean and become hydrophobic due to hydrocarbon adsorption. Furthermore, this study provides insight into how REOs can be used to promote stable dropwise condensation, which is important for the development of enhanced phase change surfaces.United States. Office of Naval ResearchUnited States. Dept. of Energy (MIT S3TEC Energy Research Frontier Center, Award No. DE- FG02-09ER46577)National Science Foundation (U.S.) (Graduate research fellowship)National Science Foundation (U.S.) (Graduate Research Fellowship Program, Grant No. 1122374)Irish Research Council for Science, Engineering, and Technology (Marie Curie Actions under FP7

TID Tolerance of Popular CubeSat Components

In this paper we report total dose test results of COTS components commonly used on CubeSats. We investigate a variety of analog integrated circuits, a popular microcontroller (PIC24) as well as SD memory card

An Asymmetric Double-Degenerate Type Ia Supernova Explosion with a Surviving Companion Star

We present nebular spectroscopy of SN 2020hvf, a Type Ia supernova (SN Ia) with an early bump in its light curve. SN 2020hvf shares many spectroscopic and photometric similarities to the carbon-rich high-luminosity "03fg-like" SNe Ia. At $>$240 days after peak brightness, we detect unambiguous emission from [Ca II] $\lambda\lambda$7291, 7324 which is never observed in normal-SNe Ia and only seen in peculiar subclasses. SN 2020hvf displays "saw-tooth" emission profiles near 7300 A that cannot be explained with single symmetric velocity components of [Fe II], [Ni II], and [Ca II], indicating an asymmetric explosion. The broad [Ca II] emission is best modeled by two velocity components offset by 1,220 km s$^{-1}$, which could be caused by ejecta associated with each star in the progenitor system, separated by their orbital velocity. For the first time in a SN Ia, we identify narrow (${\rm FWHM} = 180\pm40$ km s$^{-1}$) [Ca II] emission, which we associate with a wind from a surviving, puffed-up companion star. Few published spectra have sufficient resolution and signal-to-noise ratio necessary to detect similar narrow [Ca II] emission, however, we have detected similar line profiles in other 03fg-like SNe Ia. The extremely narrow velocity width of [Ca II] has only otherwise been observed in SNe Iax at late times. Since this event likely had a double-degenerate "super-Chandrasekhar" mass progenitor system, we suggest that a single white dwarf (WD) was fully disrupted and a wind from a surviving companion WD is producing the observed narrow emission. It is unclear if this unique progenitor and explosion scenario can explain the diversity of 03fg-like SNe Ia, potentially indicating that multiple progenitor channels contribute to this subclass.Comment: 18 pages, 10 figures, Published in Ap