Linear maps on k^I, and homomorphic images of infinite direct product algebras

Let k be an infinite field, I an infinite set, V a k-vector-space, and g:k^I\to V a k-linear map. It is shown that if dim_k(V) is not too large (under various hypotheses on card(k) and card(I), if it is finite, respectively countable, respectively < card(k)), then ker(g) must contain elements (u_i)_{i\in I} with all but finitely many components u_i nonzero. These results are used to prove that any homomorphism from a direct product \prod_I A_i of not-necessarily-associative algebras A_i onto an algebra B, where dim_k(B) is not too large (in the same senses) must factor through the projection of \prod_I A_i onto the product of finitely many of the A_i, modulo a map into the subalgebra \{b\in B | bB=Bb=\{0\}\}\subseteq B. Detailed consequences are noted in the case where the A_i are Lie algebras.Comment: 14 pages. Lemma 6 has been strengthened, with resulting strengthening of other results. Some typos etc. have been correcte

Geometry Diagnostics of a Stellar Flare from Fluorescent X-rays

We present evidence of Fe fluorescent emission in the Chandra HETGS spectrum of the single G-type giant HR 9024 during a large flare. In analogy to solar X-ray observations, we interpret the observed Fe K$\alpha$ line as being produced by illumination of the photosphere by ionizing coronal X-rays, in which case, for a given Fe photospheric abundance, its intensity depends on the height of the X-ray source. The HETGS observations, together with 3D Monte Carlo calculations to model the fluorescence emission, are used to obtain a direct geometric constraint on the scale height of the flaring coronal plasma. We compute the Fe fluorescent emission induced by the emission of a single flaring coronal loop which well reproduces the observed X-ray temporal and spectral properties according to a detailed hydrodynamic modeling. The predicted Fe fluorescent emission is in good agreement with the observed value within observational uncertainties, pointing to a scale height $\lesssim 0.3$\rstar. Comparison of the HR 9024 flare with that recently observed on II Peg by Swift indicates the latter is consistent with excitation by X-ray photoionization.Comment: accepted for publication on the Astrophysical Journal Letter

The use of high frequency oscillations to guide neocortical resections in children with medically-intractable epilepsy: How do we ethically apply surgical innovations to patient care?

AbstractPurposeResective surgical strategies are increasingly applied to treat medically-intractable epilepsy in children as uncontrolled seizures are associated with poor cognitive, developmental and behavioral outcomes. Innovative surgical strategies are, however, needed to improve outcomes and minimize the morbidity of such procedures.MethodThe current article utilizes an axiological approach to explore and highlight ethical issues in the use of high frequency oscillations (HFOs) to guide surgical resections in children with medically-intractable epilepsy. We frame our discussion in the context of the broader challenges in the application of surgical innovation to patient care.ResultsDespite a paucity of knowledge regarding their pathogenesis, limited evidence suggests the use of HFOs as biomarkers of epileptogenicity in resective procedures can improve seizure outcome. Clinicians must therefore weigh deficiencies in knowledge against the limited evidence supporting the utility of HFOs and make ethical decisions for the treatment of individual patients. Important ethical considerations for clinicians include the extent of deviation from established practice, the extent of evidence required to establish clinical validity, and the impact of technique implementation on equitable distribution of healthcare.ConclusionThe use of HFO signatures to guide neocortical resections represents a novel approach for the treatment of epilepsy. It is hoped that the issues discussed herein will contribute to and advance meaningful dialog on the ethical application of this surgical innovation to the treatment of a very vulnerable patient population

Photosynthesis Under Field Conditions. XB. Origins of Short-Time CO2 Fluctuations in a Cornfield

Studies of the vertical distributions of CO? fluctuation in a cornfield were made in the 4-to 0.25-cycle/min frequency range. Amplitude of fluctuations decreased with height above the ground. Frequency in this range appeared rather constant, however. Sources and sinks for CO? within the cornfield contribute to the fluctuations; however, eddy structure originating inside and/or outside the cornfield plays an important role too

Modeling the Low State Spectrum of the X-Ray Nova XTE J1118+480

Based on recent multiwavelength observations of the new X-ray nova XTE J1118+480, we can place strong constraints on the geometry of the accretion flow in which a low/hard state spectrum, characteristic of an accreting black hole binary, is produced. We argue that the absence of any soft blackbody-like component in the X-ray band implies the existence of an extended hot optically-thin region, with the optically-thick cool disk truncated at some radius R_{tr} > 55 R_{Schw}. We show that such a model can indeed reproduce the main features of the observed spectrum: the relatively high optical to X-ray ratio, the sharp downturn in the far UV band and the hard X-ray spectrum. The absence of the disk blackbody component also underscores the requirement that the seed photons for thermal Comptonization be produced locally in the hot flow, e.g. via synchrotron radiation. We attribute the observed spectral break at 2 keV to absorption in a warm, partially ionized gas.Comment: 6 pages, including 1 figure; LaTeX (emulateapj5.sty), to appear in Ap

Solar Magnetic Field Studies Using the 12-Micron Emission Lines. IV. Observations of a Delta-Region Solar Flare

We have recently developed the capability to make solar vector (Stokes IQUV) magnetograms using the infrared line of MgI at 12.32 microns. On 24 April 2001, we obtained a vector magnetic map of solar active region NOAA 9433, fortuitously just prior to the occurrence of an M2 flare. Examination of a sequence of SOHO/MDI magnetograms, and comparison with ground-based H-alpha images, shows that the flare was produced by the cancellation of newly emergent magnetic flux outside of the main sunspot. The very high Zeeman-sensitivity of the 12-micron data allowed us to measure field strengths on a spatial scale which was not directly resolvable. At the flare trigger site, opposite polarity fields of 2700 and 1000 Gauss occurred within a single 2 arc-sec resolution element, as revealed by two resolved Zeeman splittings in a single spectrum. Our results imply an extremely high horizontal field strength gradient (5 G/km) prior to the flare, significantly greater than seen in previous studies. We also find that the magnetic energy of the cancelling fields was more than sufficient to account for the flare's X-ray luminosity.Comment: 14 pages, 5 figures, accepted for Ap.

Prospects for precision measurements of atomic helium using direct frequency comb spectroscopy

We analyze several possibilities for precisely measuring electronic transitions in atomic helium by the direct use of phase-stabilized femtosecond frequency combs. Because the comb is self-calibrating and can be shifted into the ultraviolet spectral region via harmonic generation, it offers the prospect of greatly improved accuracy for UV and far-UV transitions. To take advantage of this accuracy an ultracold helium sample is needed. For measurements of the triplet spectrum a magneto-optical trap (MOT) can be used to cool and trap metastable 2^3S state atoms. We analyze schemes for measuring the two-photon $2^3S \to 4^3S$ interval, and for resonant two-photon excitation to high Rydberg states, $2^3S \to 3^3P \to n^3S,D$. We also analyze experiments on the singlet-state spectrum. To accomplish this we propose schemes for producing and trapping ultracold helium in the 1^1S or 2^1S state via intercombination transitions. A particularly intriguing scenario is the possibility of measuring the $1^1S \to 2^1S$ transition with extremely high accuracy by use of two-photon excitation in a magic wavelength trap that operates identically for both states. We predict a ``triple magic wavelength'' at 412 nm that could facilitate numerous experiments on trapped helium atoms, because here the polarizabilities of the 1^1S, 2^1S and 2^3S states are all similar, small, and positive.Comment: Shortened slightly and reformatted for Eur. Phys. J.

Exploring the Optical Transient Sky with the Palomar Transient Factory

The Palomar Transient Factory (PTF) is a wide-field experiment designed to investigate the optical transient and variable sky on time scales from minutes to years. PTF uses the CFH12k mosaic camera, with a field of view of 7.9 deg^2 and a plate scale of 1 asec/pixel, mounted on the the Palomar Observatory 48-inch Samuel Oschin Telescope. The PTF operation strategy is devised to probe the existing gaps in the transient phase space and to search for theoretically predicted, but not yet detected, phenomena, such as fallback supernovae, macronovae, .Ia supernovae and the orphan afterglows of gamma-ray bursts. PTF will also discover many new members of known source classes, from cataclysmic variables in their various avatars to supernovae and active galactic nuclei, and will provide important insights into understanding galactic dynamics (through RR Lyrae stars) and the Solar system (asteroids and near-Earth objects). The lessons that can be learned from PTF will be essential for the preparation of future large synoptic sky surveys like the Large Synoptic Survey Telescope. In this paper we present the scientific motivation for PTF and describe in detail the goals and expectations for this experiment.Comment: 15 pages, 6 figures, submitted to PAS

Disentangling the influence of earthworms in sugarcane rhizosphere

For the last 150 years many studies have shown the importance of earthworms for plant growth, but the exact mechanisms involved in the process are still poorly understood. Many important functions required for plant growth can be performed by soil microbes in the rhizosphere. To investigate earthworm influence on the rhizosphere microbial community, we performed a macrocosm experiment with and without Pontoscolex corethrurus (EW+ and EW−, respectively) and followed various soil and rhizosphere processes for 217 days with sugarcane. In EW+ treatments, N2O concentrations belowground (15 cm depth) and relative abundances of nitrous oxide genes (nosZ) were higher in bulk soil and rhizosphere, suggesting that soil microbes were able to consume earthworm-induced N2O. Shotgun sequencing (total DNA) revealed that around 70 microbial functions in bulk soil and rhizosphere differed between EW+ and EW− treatments. Overall, genes indicative of biosynthetic pathways and cell proliferation processes were enriched in EW+ treatments, suggesting a positive influence of worms. In EW+ rhizosphere, functions associated with plant-microbe symbiosis were enriched relative to EW− rhizosphere. Ecological networks inferred from the datasets revealed decreased niche diversification and increased keystone functions as an earthworm-derived effect. Plant biomass was improved in EW+ and worm population proliferated.São Paulo Research Foundation (FAPESP)/13/22845-2São Paulo Research Foundation (FAPESP)/15/11120-2).FAPESP/15/08564-6CNPq fellowshi

Disentangling the influence of earthworms in sugarcane rhizosphere

For the last 150 years many studies have shown the importance of earthworms for plant growth, but the exact mechanisms involved in the process are still poorly understood. Many important functions required for plant growth can be performed by soil microbes in the rhizosphere. To investigate earthworm influence on the rhizosphere microbial community, we performed a macrocosm experiment with and without Pontoscolex corethrurus (EW+ and EW−, respectively) and followed various soil and rhizosphere processes for 217 days with sugarcane. In EW+ treatments, N2O concentrations belowground (15 cm depth) and relative abundances of nitrous oxide genes (nosZ) were higher in bulk soil and rhizosphere, suggesting that soil microbes were able to consume earthworm-induced N2O. Shotgun sequencing (total DNA) revealed that around 70 microbial functions in bulk soil and rhizosphere differed between EW+ and EW− treatments. Overall, genes indicative of biosynthetic pathways and cell proliferation processes were enriched in EW+ treatments, suggesting a positive influence of worms. In EW+ rhizosphere, functions associated with plant-microbe symbiosis were enriched relative to EW− rhizosphere. Ecological networks inferred from the datasets revealed decreased niche diversification and increased keystone functions as an earthworm-derived effect. Plant biomass was improved in EW+ and worm population proliferated.São Paulo Research Foundation (FAPESP)/13/22845-2São Paulo Research Foundation (FAPESP)/15/11120-2).FAPESP/15/08564-6CNPq fellowshi