61 research outputs found

    On the diophantine equation xpx=yqyx^p-x=y^q-y

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    3D printed microchannels for sub-nL NMR spectroscopy

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    Nuclear magnetic resonance (NMR) experiments on subnanoliter (sub-nL) volumes are hindered by the limited sensitivity of the detector and the difficulties in positioning and holding such small samples in proximity of the detector. In this work, we report on NMR experiments on liquid and biological entities immersed in liquids having volumes down to 100 pL. These measurements are enabled by the fabrication of high spatial resolution 3D printed microfluidic structures, specifically conceived to guide and confine sub-nL samples in the sub-nL most sensitive volume of a single-chip integrated NMR probe. The microfluidic structures are fabricated using a two-photon polymerization 3D printing technique having a resolution better than 1 \u3bcm3. The high spatial resolution 3D printing approach adopted here allows to rapidly fabricate complex microfluidic structures tailored to position, hold, and feed biological samples, with a design that maximizes the NMR signals amplitude and minimizes the static magnetic field inhomogeneities. The layer separating the sample from the microcoil, crucial to exploit the volume of maximum sensitivity of the detector, has a thickness of 10 \u3bcm. To demonstrate the potential of this approach, we report NMR experiments on sub-nL intact biological entities in liquid media, specifically ova of the tardigrade Richtersius coronifer and sections of Caenorhabditis elegans nematodes. We show a sensitivity of 2.5x1013spins/ Hz1/2on1H nuclei at 7 T, sufficient to detect 6 pmol of1H nuclei of endogenous compounds in active volumes down to 100 pL and in a measurement time of 3 hours. Spectral resolutions of 0.01 ppm in liquid samples and of 0.1 ppm in the investigated biological entities are also demonstrated. The obtained results may indicate a route for NMR studies at the single unit level of important biological entities having sub-nL volumes, such as living microscopic organisms and eggs of several mammalians, humans included

    The allure of otherness: transnational cult film fandom and the exoticist assumption

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    Academic scholarship addressing transnational cult fandom, particularly Western cult fans forming attachments to films outside their cultures, has frequently addressed the issue of exoticism. Much attention has been paid to how Western fans are problematically drawn to artefacts outside of their own cultures because of exotic qualities, resulting in a shallow and often condescending appreciation of such films. In this article, I critique a number of such articles for merely assuming such processes without proffering sufficient supporting evidence. In fact, I argue that a number of such exotic-oriented critiques of transnational cultism are actually guilty of practising what they preach against: an insufficient contextualization of fandom and a tendency to downplay the messiness of empirical data in favour of generalized abstractions. Further, I argue that the constant critique of fans as avoiding contextualization has not only been overstated but stringently used as a yardstick to denigrate fan engagements with texts as improper. As such, fans are often ‘othered’ within such articles, a process mirroring the ways they are accused of othering distant cultural artefacts

    Non-monogenity of multiquadratic number fields

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    AbstractLet m, n be distinct square-free rational integers and let K=Q(√m, √n). Combining Baker-type inequalities with a suitable version of the Baker-Davenport reduction method we give a computational algorithm for determining all elements with minimal index in such number fields
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