951 research outputs found

    Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank

    Get PDF
    With a grading previously introduced by the second-named author, the multiplication maps in the preprojective algebra satisfy a maximal rank property that is similar to the maximal rank property proven by Hochster and Laksov for the multiplication maps in the commutative polynomial ring. The result follows from a more general theorem about the maximal rank property of a minimal almost split morphism, which also yields a quadratic inequality for the dimensions of indecomposable modules involved

    Resolutions of Subsets of Finite Sets of Points in Projective Space

    Get PDF
    Given a finite set, XX, of points in projective space for which the Hilbert function is known, a standard result says that there exists a subset of this finite set whose Hilbert function is ``as big as possible'' inside XX. Given a finite set of points in projective space for which the minimal free resolution of its homogeneous ideal is known, what can be said about possible resolutions of ideals of subsets of this finite set? We first give a maximal rank type description of the most generic possible resolution of a subset. Then we show that this generic resolution is not always achieved, by incorporating an example of Eisenbud and Popescu. However, we show that it {\em is} achieved for sets of points in projective two space: given any finite set of points in projective two space for which the minimal free resolution is known, there must exist a subset having the predicted resolution.Comment: 17 page

    Measuring Star-formation Rate and Far-Infrared Color in High-redshift Galaxies Using the CO (7-6) and [NII] 205 micron Lines

    Get PDF
    To better characterize the global star formation (SF) activity in a galaxy, one needs to know not only the star formation rate (SFR) but also the rest-frame, far-infrared (FIR) color (e.g., the 60-to-100 μ\mum color, C(60/100)C(60/100)] of the dust emission. The latter probes the average intensity of the dust heating radiation field and scales statistically with the effective SFR surface density in star-forming galaxies including (ultra-)luminous infrared galaxies [(U)LIRGs]. To this end, we exploit here a new spectroscopic approach involving only two emission lines: CO\,(7−-6) at 372 μ\mum and [NII] at 205 μ\mum. For local (U)LIRGs, the ratios of the CO (7−-6) luminosity (LCO (7−6)L_{\rm CO\,(7-6)}) to the total infrared luminosity (LIRL_{\rm IR}; 8−-1000 μ\mum) are fairly tightly distributed (to within ∼\sim0.12 dex) and show little dependence on C(60/100)C(60/100). This makes LCO (7−6)L_{\rm CO\,(7-6)} a good SFR tracer, which is less contaminated by active galactic nuclei (AGN) than LIRL_{\rm IR} and may also be much less sensitive to metallicity than LCO (1−0)L_{\rm CO\,(1-0)}. Furthermore, the logarithmic [NII] 205 μ\mum to CO (7−-6) luminosity ratio is fairly steeply (at a slope of ∼\sim−1.4-1.4) correlated with C(60/100)C(60/100), with a modest scatter (∼\sim0.23 dex). This makes it a useful estimator on C(60/100)C(60/100) with an implied uncertainty of ∼\sim0.15 [or ≲\lesssim4 K in the dust temperature (TdustT_{\rm dust}) in the case of a graybody emission with Tdust≳30T_{\rm dust} \gtrsim 30 K and a dust emissivity index β≥1\beta \ge 1]. Our locally calibrated SFR and C(60/100)C(60/100) estimators are shown to be consistent with the published data of (U)LIRGs of zz up to ∼\sim6.5.Comment: 6 pages, 3 figures, 1 table; accepted for publication in the ApJ Lette

    Design of an Integrated Cotton Picking System for Small-Scale Indian Agriculture

    Get PDF
    India, the world's largest producer of cotton, contains more than 4 million cotton farms that are less than 5 acres. These farms are incapable of large-scale mechanization due to small farm size and irregular farm shape. A previous team developed a handheld, roller-based picking device that demonstrated increased performance over similar products. However, a significant improvement in productivity requires increasing picking speed through mechanization as well as increasing worker cotton carrying capacity. We present a system that utilizes the roller-based picking device in tandem with a compressive storage bag and an efficient carrier. Through modeling and initial testing, the system demonstrates a two times (2X) improvement in worker productivity over current methods. This paper characterizes the cotton picking process, details the modules of the integrated system, and suggests further procedural improvements for greater increases in worker productivity

    Ovarian steroid hormones: A long overlooked but critical contributor to brain aging and Alzheimer’s disease

    Get PDF
    Ovarian hormones, particularly 17β-estradiol, are involved in numerous neurophysiological and neurochemical processes, including those subserving cognitive function. Estradiol plays a key role in the neurobiology of aging, in part due to extensive interconnectivity of the neural and endocrine system. This aspect of aging is fundamental for women’s brains as all women experience a drop in circulating estradiol levels in midlife, after menopause. Given the importance of estradiol for brain function, it is not surprising that up to 80% of peri-menopausal and post-menopausal women report neurological symptoms including changes in thermoregulation (vasomotor symptoms), mood, sleep, and cognitive performance. Preclinical evidence for neuroprotective effects of 17β-estradiol also indicate associations between menopause, cognitive aging, and Alzheimer’s disease (AD), the most common cause of dementia affecting nearly twice more women than men. Brain imaging studies demonstrated that middle-aged women exhibit increased indicators of AD endophenotype as compared to men of the same age, with onset in perimenopause. Herein, we take a translational approach to illustrate the contribution of ovarian hormones in maintaining cognition in women, with evidence implicating menopause-related declines in 17β-estradiol in cognitive aging and AD risk. We will review research focused on the role of endogenous and exogenous estrogen exposure as a key underlying mechanism to neuropathological aging in women, with a focus on whether brain structure, function and neurochemistry respond to hormone treatment. While still in development, this research area offers a new sex-based perspective on brain aging and risk of AD, while also highlighting an urgent need for better integration between neurology, psychiatry, and women’s health practices

    Pulmonary cystic disease in HIV positive individuals in the Democratic Republic of Congo: three case reports

    Get PDF
    Pulmonary emphysema and bronchiectasis in HIV seropositive patients has been described in the presence of injection drug use, malnutrition, repeated opportunistic infections, such as Pneumocytis jirovici pneumonia and Mycobacterium tuberculosis infection, and has been linked to the presence of HIV virus in lung tissue. Given the high burden of pulmonary infections and malnutrition among people living with HIV in resource poor settings, these individuals may be at increased risk of developing pulmonary emphysema, potentially reducing the long term benefit of antiretroviral therapy (ART) if initiated late in the course of HIV infection
    • …
    corecore