On positive solutions and the Omega limit set for a class of delay differential equations

This paper studies the positive solutions of a class of delay differential equations with two delays. These equations originate from the modeling of hematopoietic cell populations. We give a sufficient condition on the initial function for $t\leq 0$ such that the solution is positive for all time $t>0$. The condition is "optimal". We also discuss the long time behavior of these positive solutions through a dynamical system on the space of continuous functions. We give a characteristic description of the $\omega$ limit set of this dynamical system, which can provide informations about the long time behavior of positive solutions of the delay differential equation.Comment: 15 pages, 2 figure

Postcards from Mars: Insights into Martian Geochemical Processes from the Curiosity Rover

With the successful landing of the Mars Curiosity Rover in August 2012, we now have the most capable geochemical laboratory ever to travel to another planet roving Mars’ Gale crater. The geochemical instrument suite includes the Chemistry Camera (ChemCam), which uses a laser to vaporize geologic targets and performs atomic emission spectroscopy on the vapor from distances of up to 7m. This provides a geochemical surveying capability that enables rapid identification of unique specimens and accumulation of a large set of rock and fines compositions as the rover traverses. The Alpha Particle X-ray Spectrometer (APXS) provides high quality “bulk” elemental analyses for major, minor and a few trace elements through a touch deployment on the surface of a rock or soil, and is an upgraded version of similar instruments previously flown to Mars. The addition of x-ray diffraction through the Chemistry and Mineralogy (CheMin) instrument and volatile, isotope, and organic analyses with the Sample Analysis at Mars (SAM) instrument suite, give Curiosity the capability to assess the geochemical history of the planet more deeply than previously possible. Both CheMin and SAM accept sieved fines from either Curiosity’s scoop or drill. To date, sampling has occurred at the Rocknest aeolian drift deposit and a fine-grained mudstone called John Klein. At Rocknest, CheMin found a mix of primary igneous minerals and amorphous materials. SAM found that Rocknest fines contain significant bound volatiles that can be released upon heating, largely associated with the amorphous material. Because APXS and ChemCam data support the fines being representative of those found at other sites on Mars, Curiosity results show that martian fines are a good source of water, CO2 and other volatiles that could be leveraged by living organisms, including future human explorers. At John Klein, early results are consistent with an ancient aqueous habitable environment. Analyses of isotopes and organics also provide exciting windows into martian habitability and volatile evolution. These early geochemical results will be discussed

Discordant K-Ar and Young Exposure Dates for the Windjana sandstone, Kimberley, Gale Crater, Mars

K-Ar and noble gas surface exposure age measurements were carried out on the Windjana sandstone, Kimberley region, Gale Crater, Mars, by using the Sample Analysis at Mars instrument on the Curiosity rover. The sandstone is unusually rich in sanidine, as determined by CheMin X-ray diffraction, contributing to the high K_2O concentration of 3.09 ± 0.20 wt % measured by Alpha-Particle X-ray Spectrometer analysis. A sandstone aliquot heated to ~915°C yielded a K-Ar age of 627 ± 50 Ma. Reheating this aliquot yielded no additional Ar. A second aliquot heated in the same way yielded a much higher K-Ar age of 1710 ± 110 Ma. These data suggest incomplete Ar extraction from a rock with a K-Ar age older than 1710 Ma. Incomplete extraction at ~900°C is not surprising for a rock with a large fraction of K carried by Ar-retentive K-feldspar. Likely, variability in the exact temperature achieved by the sample from run to run, uncertainties in sample mass estimation, and possible mineral fractionation during transport and storage prior to analysis may contribute to these discrepant data. Cosmic ray exposure ages from ^3He and ^(21)Ne in the two aliquots are minimum values given the possibility of incomplete extraction. However, the general similarity between the ^3He (57 ± 49 and 18 ± 32 Ma, mean 30 Ma) and ^(21)Ne (2 ± 32 and 83 ± 24 Ma, mean 54 Ma) exposure ages provides no evidence for underextraction. The implied erosion rate at the Kimberley location is similar to that reported at the nearby Yellowknife Bay outcrop

A SURVEY FOR ODONTOCETE CETACEANS OFF KAUA‘I AND NI‘IHAU, HAWAI‘I, DURING OCTOBER AND NOVEMBER 2005: EVIDENCE FOR POPULATION STRUCTURE AND SITE FIDELITY

Considerable uncertainty exists regarding population structure and population sizes of most species of odontocetes in the Hawaiian Islands. A small-boat based survey for odontocetes was undertaken off the islands of Kaua‘i and Ni‘ihau in October and November 2005 to photoidentify individuals and collect genetic samples for examining stock structure. Field effort on 24 days covered 2,194 km of trackline. Survey coverage was from shallow coastal waters out to over 3,000 m depth, though almost half (47%) was in waters less than 500 m in depth. There were 56 sightings of five species of odontocetes: spinner dolphins (30 sightings); bottlenose dolphins (14 sightings); short-finned pilot whales (6 sightings); rough-toothed dolphins (5 sightings); and pantropical spotted dolphins (1 sighting). One hundred and five biopsy samples were collected and 14,960 photographs were taken to document morphology and for individual photo-identification. Photographs of distinctive individuals of three species (bottlenose dolphins, 76 identifications; rough-toothed dolphins, 157 identifications; short-finned pilot whales, 68 identifications) were compared to catalogs of these species from a survey off Kaua‘i and Ni‘ihau in 2003, as well as from efforts off O‘ahu, Maui/Lana‘i and the island of Hawai‘i. Within- and between-year matches were found for all three species with individuals previously identified off Kaua‘i and Ni‘ihau, though no matches were found with individuals off any of the other islands. This suggests site fidelity to specific island areas, and population structure among island areas for all three species. Movements of photographically identified bottlenose dolphins were documented between deep water areas off the islands of Kaua‘i and Ni‘ihau, as well as between shallow (\u3c350 m) and deep (\u3e350 m) waters. A lack of sightings or reports of false killer whales off Kaua‘i or Ni‘ihau during our study, combined with documented movements among the other main Hawaiian Islands, suggest that there is no “resident” population of false killer whales that inhabits waters only off Kaua‘i or Ni‘iha

The deuterium-to-oxygen ratio in the interstellar medium

Because the ionization balances for HI, OI, and DI are locked together by charge exchange, D/O is an important tracer for the value of the D/H ratio and for potential spatial variations in the ratio. As the DI and OI column densities are of similar orders of magnitude for a given sight line, comparisons of the two values will generally be less subject to systematic errors than comparisons of DI and HI, which differ by about five orders of magnitude. Moreover, D/O is additionally sensitive to astration, because as stars destroy deuterium, they should produce oxygen. We report here the results of a survey of D/O in the interstellar medium performed with FUSE. We also compare these results with those for D/N. Together with a few results from previous missions, the sample totals 24 lines of sight. The distances range from a few pc to ~2000 pc and log N(DI) from ~13 to ~16 (cm-2). The D/O ratio is constant in the local interstellar medium out to distances of ~150 pc and N(DI) ~ 1x10^15 cm-2, i.e. within the Local Bubble. In this region of the interstellar space, we find D/O = (3.84+/-0.16)x10^-2 (1 sigma in the mean). The homogeneity of the local D/O measurements shows that the spatial variations in the local D/H and O/H must be extremely small, if any. A comparison of the Local Bubble mean value with the few D/O measurements available for low metallicity quasar sight lines shows that the D/O ratio decreases with cosmic evolution, as expected. Beyond the Local Bubble we detected significant spatial variations in the value of D/O. This likely implies a variation in D/H, as O/H is known to not vary significantly over the distances covered in this study. Our dataset suggests a present-epoch deuterium abundance below 1x10^-5, i.e. lower than the value usually assumed, around 1.5x10^-5.Comment: 17 pages, 9 figures, 4 tables, accepted for publication in the Astrophysical Journa

Development of the Potassium-Argon Laser Experiment (KArLE) Instrument for In Situ Geochronology

Absolute dating of planetary samples is an essential tool to establish the chronology of geological events, including crystallization history, magmatic evolution, and alteration. Traditionally, geochronology has only been accomplishable on samples from dedicated sample return missions or meteorites. The capability for in situ geochronology is highly desired, because it will allow one-way planetary missions to perform dating of large numbers of samples. The success of an in situ geochronology package will not only yield data on absolute ages, but can also complement sample return missions by identifying the most interesting rocks to cache and/or return to Earth. In situ dating instruments have been proposed, but none have yet reached TRL 6 because the required high-resolution isotopic measurements are very challenging. Our team is now addressing this challenge by developing the Potassium (K) - Argon Laser Experiment (KArLE) under the NASA Planetary Instrument Definition and Development Program (PIDDP), building on previous work to develop a K-Ar in situ instrument [1]. KArLE uses a combination of several flight-proven components that enable accurate K-Ar isochron dating of planetary rocks. KArLE will ablate a rock sample, determine the K in the plasma state using laser-induced breakdown spectroscopy (LIBS), measure the liberated Ar using quadrupole mass spectrometry (QMS), and relate the two by the volume of the ablated pit using an optical method such as a vertical scanning interferometer (VSI). Our preliminary work indicates that the KArLE instrument will be capable of determining the age of several kinds of planetary samples to +/-100 Myr, sufficient to address a wide range of geochronology problems in planetary science

Glen Torridon Mineralogy and the Sedimentary History of the Clay Mineral Bearing Unit

Clay minerals are common in ancient terrains on Mars and their presence at the surface alludes to aqueous processes in the Noachian to Early Hesperian (>3.5 Ga). Gale crater was selected as Curiositys landing site largely because of the identification of clay mineral rich strata from orbit. On Earth, the types of clay minerals (i.e., smectites) identified in Gale crater are typically juvenile weathering products that ultimately record the interaction between primary igneous minerals with the hydrosphere, atmosphere, and biosphere. Trioctahedral and dioctahedral smectite were identified by Curiosity in units stratigraphically below the Clay Mineral-Bearing Unit (CBU) identified from orbit. Compositional and sedimentological data suggest the smectite formed via authigenesis in a lake environment and may have been altered during early diagenesis. The CBU is stratigraphically equivalent to a hematite-rich unit to the north and stratigraphically underlies sulfate-rich units to the south, suggesting a dynamic environment and evolving history of water in the ancient Gale crater lake. Targeting these clay mineral rich areas on Mars with rover missions provides an opportunity to explore the aqueous and sedimentary history of the planet

Integrated Results from Analysis of the Rocknest Aeolian Deposit by the Curiosity Rover

The Mars Science Laboratory Curiosity rover spent 45 sols (from sol 56-101) at an area called Rocknest (Fig. 1), characterizing local geology and ingesting its aeolian fines into the analytical instruments CheMin and SAM for mineralogical and chemical analysis. Many abstracts at this meeting present the contextual information and detailed data on these first solid samples analyzed in detail by Curiosity at Rocknest. Here, we present an integrated view of the results from Rocknest - the general agreement from discussions among the entire MSL Science Team

Range and primary habitats of Hawaiian insular false killer whales: informing determination of critical habitat

The article of record as published may be found at https://dx.doi.org/10.3354/esr00435For species listed under the US Endangered Species Act, federal agencies must designate 'critical habitat', areas containing features essential to conservation and/or that may require special management considerations. In November 2010, the National Marine Fisheries Service proposed listing a small demographically isolated population of false killer whales Pseudorca crassidens in Hawai'i as endangered but has not yet proposed designating critical habitat. We assessed the population's range and heavily used habitat areas using data from 27 satellite tag deployments. Assessment of independence of individuals with temporally overlapping data indicated that data were from 22 'groups'. Further analyses were restricted to 1 individual per group. Tag data were available for periods of between 13 and 105 d (median = 40.5 d), with 8513 locations (93.4% from July-January). Analyses of photo-identification data indicated that the population is divided into 3 large associations of individuals (social clusters), with tag data from 2 of these clusters. Ranges for these 2 clusters were similar, although one used significantly deeper waters, and their high-use areas differed. A minimum convex polygon range encompassing all locations was ~82800 km2, with individuals ranging from Ni'ihau to Hawai'i Island and up to 122 km offshore. Three high-use areas were identified: (1) off the north half of Hawai'i Island, (2) north of Maui and Moloka'i and (3) southwest of Lana'i. Although this analysis provides information useful for decision-making concerning designation of critical habitat, there are likely other high-use areas that have not yet been identified due to seasonal limitations and availability of data from only 2 of the 3 main social clusters.Fieldwork was primarily funded by grants and contracts to Cascadia Research Collective from the National Marine Fisheries Service Pacific Islands Fisheries Science Center and the US Navy (N45) through the Southwest Fisheries Science Center, Woods Hole Oceano- graphic Institution, and the Naval Postgraduate School. The Wild Whale Research Foundation and Dolphin Quest provided additional support.Funded by Naval Postgraduate School.Office of Naval Research Grant N00014081120

Development of a Linear Ion Trap Mass Spectrometer (LITMS) Investigation for Future Planetary Surface Missions

Future surface missions to Mars and other planetary bodies will benefit from continued advances in miniature sensor and sample handling technologies that enable high-performance chemical analyses of natural samples. Fine-scale (approx.1 mm and below) analyses of rock surfaces and interiors, such as exposed on a drill core, will permit (1) the detection of habitability markers including complex organics in association with their original depositional environment, and (2) the characterization of successive layers and gradients that can reveal the time-evolution of those environments. In particular, if broad-based and highly-sensitive mass spectrometry techniques could be brought to such scales, the resulting planetary science capability would be truly powerful. The Linear Ion Trap Mass Spectrometer (LITMS) investigation is designed to conduct fine-scale organic and inorganic analyses of short (approx.5-10 cm) rock cores such as could be acquired by a planetary lander or rover arm-based drill. LITMS combines both pyrolysis/gas chromatograph mass spectrometry (GCMS) of sub-sampled core fines, and laser desorption mass spectrometry (LDMS) of the intact core surface, using a common mass analyzer, enhanced from the design used in the Mars Organic Molecule Analyzer (MOMA) instrument on the 2018 ExoMars rover. LITMS additionally features developments based on the Sample Analysis at Mars (SAM) investigation on MSL and recent NASA-funded prototype efforts in laser mass spectrometry, pyrolysis, and precision subsampling. LITMS brings these combined capabilities to achieve its four measurement objectives: (1) Organics: Broad Survey Detect organic molecules over a wide range of molecular weight, volatility, electronegativity, concentration, and host mineralogy. (2) Organic: Molecular Structure Characterize internal molecular structure to identify individual compounds, and reveal functionalization and processing. (3) Inorganic Host Environment Assess the local chemical/mineralogical makeup of organic host phases to help determine deposition and preservation factors. (4) Chemical Stratigraphy Analyze the fine spatial distribution and variation of key species with depth