DUALITY FOR SOME LARGE SPACES OF ANALYTIC FUNCTIONS

We characterize the duals and biduals of the $L^p$-analogues $\mathcal{N}_\alpha^p$ of the standard Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\ge-1$ and $1\le p\lt \infty$. We adopt the convention to take $\mathcal{N}_{-1}^p$ to be the classical Smirnov class $\mathcal{N}^+$ for $p=1$, and the Hardy-Orlicz space $LH^p$ $(=(\text{Log}^+H)^p)$ for $1\lt p\lt\infty$. Our results generalize and unify earlier characterizations obtained by Eoff for $\alpha=0$ and $\alpha=-1$, and by Yanigahara for the Smirnov class. Each $\mathcal{N}_\alpha^p$ is a complete metrizable topological vector space (in fact, even an algebra); it fails to be locally bounded and locally convex but admits a separating dual. Its bidual will be identified with a specific nuclear power series space of finite type; this turns out to be the ‘Fréchet envelope' of $\mathcal{N}_\alpha^p$ as well. The generating sequence of this power series space is of the form $(n^\theta)_{n\in\mathbb{N}}$ for some $0\lt\theta\lt1$. For example, the $\theta$s in the interval (\smfr12,1) correspond in a bijective fashion to the Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\gt-1$, whereas the $\theta$s in the interval (0,\smfr12) correspond bijectively to the Hardy-Orlicz spaces $LH^p$, $1\lt p\lt \infty$. By the work of Yanagihara, \theta=\smfr12 corresponds to $\mathcal{N}^+$. As in the work by Yanagihara, we derive our results from characterizations of coefficient multipliers from $\mathcal{N}_\alpha^p$ into various smaller classical spaces of analytic functions on $\Delta$. AMS 2000 Mathematics subject classification: Primary 46E10; 46A11; 47B38. Secondary 30D55; 46A45; 46E15\vskip-3p

Remote sensing vegetation index methods to evaluate changes in greenness and evapotranspiration in riparian vegetation in response to the Minute 319 environmental pulse flow to Mexico

During the spring of 2014, 130 million m(3) of water were released from the United States' Morelos Dam on the lower Colorado River to Mexico, allowing water to reach the Gulf of California for the first time in 13 years. Our study assessed the effects of water transfer or ecological environmental flows from one nation to another, using remote sensing. Spatial applications for water resource evaluation are important for binational, integrated water resources management and planning for the Colorado River, which includes seven basin states in the US plus two states in Mexico. Our study examined the effects of the historic binational experiment (the Minute 319 agreement) on vegetative response along the riparian corridor. We used 250 m Moderate Resolution Imaging Spectroradiometer (MODIS), Enhanced Vegetation Index (EVI) and 30 m Landsat 8 satellite imagery to track evapotranspiration (ET) and the normalized difference vegetation index (NDVI). Our analysis showed an overall increase in NDVI and evapotranspiration (ET) in the year following the 2014 pulse, which reversed a decline in those metrics since the last major flood in 2000. NDVI and ET levels decreased in 2015, but were still significantly higher (P < 0.001) than pre-pulse (2013) levels. Preliminary findings show that the decline in 2015 persisted into 2016 and 2017. We continue to analyse results for 2018 in comparison to short-term (2013-2018) and long-term (2000-2018) trends. Our results support the conclusion that these environmental flows from the US to Mexico via the Minute 319 "pulse" had a positive, but short-lived (1 year), impact on vegetation growth in the delta.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Submillimetric spectroscopic observations of volatiles in comet C/2004 Q2 (Machholz)

We aim to determine the production rates of several parent and product volatiles and the 12C/13C isotopic carbon ratio in the long-period comet C/2004 Q2 (Machholz), which is likely to originate from the Oort Cloud. The line emission from several molecules in the coma was measured with high signal-to-noise ratio in January 2005 at heliocentric distance of 1.2 AU by means of high-resolution spectroscopic observations using the Submillimeter Telescope (SMT). We have obtained production rates of several volatiles (CH3OH, HCN, H13CN, HNC, H2CO, CO and CS) by comparing the observed and simulated line-integrated intensities. Furthermore, multiline observations of the CH3OH (7-6) series allow us to estimate the rotational temperature using the rotation diagram technique. We find that the CH3OH population distribution of the levels sampled by these lines can be described by a rotational temperature of 40 \pm 3 K. Derived mixing ratios relative to hydrogen cyanide are CO/CH3OH/H2CO/CS/HNC/H13CN/HCN = 30.9/24.6/4.8/0.57/0.031/0.013/1 assuming a pointing offset of 8" due to the uncertain ephemeris at the time of the observations and the telescope pointing error. The measured relative molecular abundances in C/2004 Q2 (Machholz) are between low- to typical values of those obtained in Oort Cloud comets, suggesting that it has visited the inner solar system previously and undergone thermal processing. The HNC/HCN abundance ratio of ~3.1% is comparable to that found in other comets, accounting for the dependence on the heliocentric distance, and could possibly be explained by ion-molecule chemical processes in the low-temperature atmosphere. From a tentative H13CN detection, the measured value of 97 \pm 30 for the H12CN/H13CN isotopologue pair is consistent with a telluric value.Comment: 14 pages with 11 figures, abridged abstrac

A survey of volatile species in Oort cloud comets C/2001 Q4 (NEAT) and C/2002 T7 (LINEAR) at millimeter wavelengths

The line emission in the coma was measured in the comets C/2001 Q4 (NEAT) and C/2002 T7 (LINEAR), that were observed on five consecutive nights, 7-11 May 2004, at heliocentric distances of 1.0 and 0.7 AU, respectively, by means of high-resolution spectroscopy using the 10-m Submillimeter Telescope (SMT). We present a search for six parent- and product-volatile species (HCN, H2CO, CO, CS, CH3OH, and HNC) in both comets. Multiline observations of the CH3OH J = 5-4 series allow us to estimate the rotational temperature using the rotation diagram technique. We derive rotational temperatures of 54(9) K for C/2001 Q4 (NEAT) and 119(34) K for C/2002 T7 (LINEAR) that are roughly consistent with observations of other comets at similar distances from the Sun. The gas production rates of material are computed using a spherically symmetric molecular excitation code that includes collisions between neutrals and electrons. We find an HCN production rate of 2.96(5)e26 molec.s-1 for comet C/2001 Q4 (NEAT), corresponding to a mixing ratio with respect to H2O of 1.12(2)e-3. The mean HCN production rate during the observing period is 4.54(10)e26 molec.s-1 for comet C/2002 T7 (LINEAR), which gives a Q_HCN/Q_H2O mixing ratio of 1.51(3)e-3. With systematically lower mixing ratios in comet C/2001 Q4 (NEAT), production rate ratios of the observed species with respect to H2O lie within the typical ranges of dynamically new comets in both objects. We find a relative low abundance of CO in C/2001 Q4 (NEAT) compared to the observed range in other comets based on millimeter/submillimeter observations, and a significant upper limit on the CO production in C/2002 T7 (LINEAR) is derived. Depletion of CO suggests partial evaporation from the surface layers during previous visits to the outer Solar System and agrees with previous measurements of dynamically new comets.Comment: 20 pages, 18 figures. Minor changes to match the published versio

Searches for HCl and HF in comets 103P/Hartley 2 and C/2009 P1 (Garradd) with the Herschel space observatory

HCl and HF are expected to be the main reservoirs of fluorine and chlorine wherever hydrogen is predominantly molecular. They are found to be strongly depleted in dense molecular clouds, suggesting freeze-out onto grains in such cold environments. We can then expect that HCl and HF were also the major carriers of Cl and F in the gas and icy phases of the outer solar nebula, and were incorporated into comets. We aimed to measure the HCl and HF abundances in cometary ices as they can provide insights on the halogen chemistry in the early solar nebula. We searched for the J(1-0) lines of HCl and HF at 626 and 1232 GHz, respectively, using the HIFI instrument on board the Herschel Space Observatory. HCl was searched for in comets 103P/Hartley 2 and C/2009 P1 (Garradd), whereas observations of HF were conducted in comet C/2009 P1. In addition, observations of H$_2$O and H$_2^{18}$O lines were performed in C/2009 P1 to measure the H$_2$O production rate. Three lines of CH$_3$OH were serendipitously observed in the HCl receiver setting. HCl is not detected, whereas a marginal (3.6-$\sigma$) detection of HF is obtained. The upper limits for the HCl abundance relative to water are 0.011% and 0.022%, for 103P and C/2009 P1, respectively, showing that HCl is depleted with respect to the solar Cl/O abundance by a factor more than 6$^{+6}_{-3}$ in 103P, where the error is related to the uncertainty in the chlorine solar abundance. The marginal HF detection obtained in C/2009 P1 corresponds to an HF abundance relative to water of (1.8$\pm$0.5) $\times$ 10$^{-4}$, which is approximately consistent with a solar photospheric F/O abundance. The observed depletion of HCl suggests that HCl was not the main reservoir of chlorine in the regions of the solar nebula where these comets formed. HF was possibly the main fluorine compound in the gas phase of the outer solar nebula.Comment: Accepted for publication in Astronomy & Astrophysic

Remote sensing vegetation index methods to evaluate changes in greenness and evapotranspiration in riparian vegetation in response to the Minute 319 environmental pulse flow to Mexico

During the spring of 2014, 130 million&thinsp;m3 of water were released from the United States' Morelos Dam on the lower Colorado River to Mexico, allowing water to reach the Gulf of California for the first time in 13 years. Our study assessed the effects of water transfer or ecological environmental flows from one nation to another, using remote sensing. Spatial applications for water resource evaluation are important for binational, integrated water resources management and planning for the Colorado River, which includes seven basin states in the US plus two states in Mexico. Our study examined the effects of the historic binational experiment (the Minute 319 agreement) on vegetative response along the riparian corridor. We used 250&thinsp;m Moderate Resolution Imaging Spectroradiometer (MODIS), Enhanced Vegetation Index (EVI) and 30&thinsp;m Landsat 8 satellite imagery to track evapotranspiration (ET) and the normalized difference vegetation index (NDVI). Our analysis showed an overall increase in NDVI and evapotranspiration (ET) in the year following the 2014 pulse, which reversed a decline in those metrics since the last major flood in 2000. NDVI and ET levels decreased in 2015, but were still significantly higher (P&thinsp;&lt;&thinsp;0.001) than pre-pulse (2013) levels. Preliminary findings show that the decline in 2015 persisted into 2016 and 2017. We continue to analyse results for 2018 in comparison to short-term (2013–2018) and long-term (2000–2018) trends. Our results support the conclusion that these environmental flows from the US to Mexico via the Minute 319 “pulse” had a positive, but short-lived (1 year), impact on vegetation growth in the delta.</p

HIFI observations of warm gas in DR21: Shock versus radiative heating

The molecular gas in the DR21 massive star formation region is known to be affected by the strong UV field from the central star cluster and by a fast outflow creating a bright shock. The relative contribution of both heating mechanisms is the matter of a long debate. By better sampling the excitation ladder of various tracers we provide a quantitative distinction between the different heating mechanisms. HIFI observations of mid-J transitions of CO and HCO+ isotopes allow us to bridge the gap in excitation energies between observations from the ground, characterizing the cooler gas, and existing ISO LWS spectra, constraining the properties of the hot gas. Comparing the detailed line profiles allows to identify the physical structure of the different components. In spite of the known shock-excitation of H2 and the clearly visible strong outflow, we find that the emission of all lines up to > 2 THz can be explained by purely radiative heating of the material. However, the new Herschel/HIFI observations reveal two types of excitation conditions. We find hot and dense clumps close to the central cluster, probably dynamically affected by the outflow, and a more widespread distribution of cooler, but nevertheless dense, molecular clumps.Comment: Accepted for publication by A&

Three Year Evaluation of Xpert MTB/RIF in a Low Prevalence Tuberculosis Setting

Objectives Xpert MTB/RIF (Cepheid) is a rapid molecular assay shown to be sensitive and specific for pulmonary tuberculosis (TB) diagnosis in highly endemic countries. We evaluated its diagnostic performance in a low TB prevalence setting, examined rifampicin resistance detection and quantitative capabilities predicting graded auramine microscopy and time to positivity (TTP) of culture. Methods Xpert MTB/RIF was used to test respiratory samples over a 3 year period. Samples underwent graded auramine microscopy, solid/ liquid culture, in-house IS6110 real-time PCR, and GenoType MTBDRplus (HAIN Lifescience) to determine rifampicin and/or isoniazid resistance. Results A total of 2103 Xpert MTB/RIF tests were performed. Compared to culture sensitivity was 95.8%, specificity 99.5%, positive predictive value (PPV) 82.1%, and negative predictive value (NPV) 99.9%. A positive correlation was found between auramine microscopy grade and Xpert MTB/RIF assay load. We found a clear reduction in the median TTP as Xpert MTB/RIF assay load increased. Rifampicin resistance was detected. Conclusions Xpert MTB/RIF was rapid and accurate in diagnosing pulmonary TB in a low prevalence area. Rapid results will influence infection prevention and control and treatment measures. The excellent NPV obtained suggests further work should be carried out to assess its role in replacing microscopy

Improving integrability via absolute summability: a general version of Diestel s Theorem

[EN] A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis integrable function gives a Bochner integrable function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the -absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces-including C(K), and Hilbert spaces-and operators-p-summing, (q, p)-summing and p-approximable operators.D. Pellegrino acknowledges with thanks the support of CNPq Grant 401735/2013-3 (Brazil). P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E.A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2012-36740-C02-02.Pellegrino, D.; Rueda, P.; Sánchez Pérez, EA. (2016). Improving integrability via absolute summability: a general version of Diestel s Theorem. Positivity. 20(2):369-383. https://doi.org/10.1007/s11117-015-0361-5S369383202Botelho, G., Pellegrino, D., Rueda, P.: A unified Pietsch domination theorem. J. Math. Anal. Appl. 365(1), 269–276 (2010)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland, Amsterdam (1992)Diestel, J.: An elementary characterization of absolutely summing operators. Math. Ann. 196, 101–105 (1972)Diestel, J., Jarchow, H., Tonge, A.: Absolutely summing operators. Cambridge University Press, Cambridge (1995)Farmer, J., Johnson, W.B.: Lipschitz p-summing operators. Proc. Amer. Math. Soc. 137, 2989–2995 (2009)Jarchow, H.: Localy convex, spaces. Teubner, Stuttgart (1981)López Molina, J.A., Sánchez Pérez, E.A.: Ideales de operadores absolutamente continuos, Ciencias Exactas, Físicas y Naturales, Madrid. Rev. Real Acad. 87, 349–378 (1993)López Molina, J.A., Sánchez Pérez, E.A.: The associated tensor norm to $$(q, p)$$ ( q , p ) -absolutely summing operators on $$C(K)$$ C ( K ) -spaces. Czec. Math. J. 47(4), 627–631 (1997)López, J.A., Molina, Sánchez-Pérez, E.A.: On operator ideals related to $$(p,\sigma )$$ ( p , σ ) -absolutely continuous operator. Studia Math. 131(8), 25–40 (2000)Matter, U.: Absolute continuous operators and super-reflexivity. Math. Nachr. 130, 193–216 (1987)Pellegrino, D., Santos, J.: A general Pietsch domination theorem. J. Math. Anal. Appl. 375(1), 371–374 (2011)Pellegrino, D., Santos, J., Seoane-Sepúlveda, J.B.: Some techniques on nonlinear analysis and applications. Adv. Math. 229, 1235–1265 (2012)Pietsch, A.: Operator Ideals. Deutsch. Verlag Wiss., Berlin, 1978; North-Holland, Amsterdam-London-New York-Tokyo (1980)Pisier, G.: Factorization of operators through $$L_{p\infty }$$ L p ∞ or $$L_{p1}$$ L p 1 and noncommutative generalizations. Math. Ann. 276(1), 105–136 (1986)Rodríguez, J.: Absolutely summing operators and integration of vector-valued functions. J. Math. Anal. Appl. 316(2), 579–600 (2006

Vegetation‐groundwater dynamics at a former uranium mill site following invasion of a biocontrol agent: A time series analysis of Landsat normalized difference vegetation index data

Because groundwater recharge in dry regions is generally low, arid and semiarid environments have been considered well-suited for long-term isolation of hazardous materials (e.g., radioactive waste). In these dry regions, water lost (transpired) by plants and evaporated from the soil surface, collectively termed evapotranspiration (ET), is usually the primary discharge component in the water balance. Therefore, vegetation can potentially affect groundwater flow and contaminant transport at waste disposal sites. We studied vegetation health and ET dynamics at a Uranium Mill Tailings Radiation Control Act (UMTRCA) disposal site in Shiprock, New Mexico, where a floodplain alluvial aquifer was contaminated by mill effluent. Vegetation on the floodplain was predominantly deep-rooted, non-native tamarisk shrubs (Tamarix sp.). After the introduction of the tamarisk beetle (Diorhabda sp.) as a biocontrol agent, the health of the invasive tamarisk on the Shiprock floodplain declined. We used Landsat normalized difference vegetation index (NDVI) data to measure greenness and a remote sensing algorithm to estimate landscape-scale ET along the floodplain of the UMTRCA site in Shiprock prior to (2000-2009) and after (2010-2018) beetle establishment. Using groundwater level data collected from 2011 to 2014, we also assessed the role of ET in explaining seasonal variations in depth to water of the floodplain. Growing season scaled NDVI decreased 30% (p <.001), while ET decreased 26% from the pre- to post-beetle period and seasonal ET estimates were significantly correlated with groundwater levels from 2011 to 2014 (r(2) =.71; p =.009). Tamarisk greenness (a proxy for health) was significantly affected by Diorhabda but has partially recovered since 2012. Despite this, increased ET demand in the summer/fall period might reduce contaminant transport to the San Juan River during this period.Public domain articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]