1,525 research outputs found

    Star configuration points and plane curves

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    Let ℓ 1 , … , ℓ l \ell _1,\ldots ,\ell _l be l l lines in P 2 \mathbb {P}^2 such that no three lines meet in a point. Let X ( l ) \mathbb {X}(l) be the set of points { ℓ i ∩ ℓ j   |   1 ≤ i &gt; j ≤ l } ⊆ P 2 \{\ell _i \cap \ell _j ~|~ 1 \leq i &gt; j \leq l\} \subseteq \mathbb {P}^2 . We call X ( l ) \mathbb {X}(l) a star configuration. We describe all pairs ( d , l ) (d,l) such that the generic degree d d curve in P 2 \mathbb {P}^2 contains an X ( l ) \mathbb {X}(l) . Our proof strategy uses both a theoretical and an explicit algorithmic approach. We also describe how one may extend our algorithmic approach to similar problems.</p

    Angelo de Carlini

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    Botanico: De Carlini, Angelo. Dottore in medicina; nel 1823-1827 assistente di botanica all\u27Università di Pavia, quindi medico provinciale a Cremona e Sondrio. Titolo manoscritto sul recto, dove compaiono anche le note: Dal "Risveglio" Pavia gennaio 1912; + 1911. Immagine ritagliata da pubblicazione 115 x 79 mm. e incollata su carta 119 x 84 mm. 1 stampa fotomeccanica ; 100 x 69 mm. Vai alla scheda bibliografica: https://galileodiscovery.unipd.it/discovery/fulldisplay?context=L&vid=39UPD_INST:VU1&search_scope=MyInst_and_CI&tab=Everything&docid=alma99001566869020604

    Complete intersections on general hypersurfaces

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    We ask when certain complete intersections of codimension r can lie on a generic hypersurface in P^n. We give a complete answer to this question when 2r &lt; n+3 in terms of the degrees of the hypersurfaces and of the degrees of the generators of the complete intersection

    Optically active polymethacrylates with side-chain L-lactic acid residues connected to push-pull azobenzene chromophores

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    Novel optically active methacrylic homopolymers with side-chain l-lactic acid moieties interposed through ester bonds between the main chain and trans-4-azobenzene chromophores bearing in the 4′-position electron withdrawing groups, such as the cyano and nitro residues, have been synthesized and structurally characterized. Investigation by circular dichroism of the chiroptical and conformational properties of the polymers in solution indicates a much higher optical activity of these latter with respect to that of the corresponding low molecular weight model compounds, purposely prepared, due to the presence of dissymmetric conformations of one prevailing handedness. The trans to cis photoisomerization kinetics of the azoaromatic double bond has been measured in solution for polymers and models and the resulting data compared with those of previously reported similar photochromic derivatives. The influence of the nature of the electron withdrawing group in the 4′-position of the azobenzene chromophore on the chiroptical properties of the polymers is also discussed

    Astratto e materico per una matematica inclusiva. Esperienza di ricerca, didattica e museografia

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    Esponiamo l'esperienza di un lungo percorso attraverso didattica universitaria, ricerca, elaborazione di lavori degli studenti, e poi mostre internazionali di divulgazione scientifica, didattica nelle scuole, passeggiate scientifiche in città, tutte attraverso un unico tema. Un percorso le cui tappe si sono certamente nutrite una con l'altra; tutte, vertono attorno al tema della ripetizione di pattern grafici in arabeschi o motivi ornamentali ed al suo trattamento matematico, che ha trovato un assetto completo solo agli inizi del Novecento. Ad accompagnare l'immaginario scientifico, una costante attualizzazione dell'uso e del concetto di patrimonio culturale

    Photoresponsive properties of optically active (meth)acrylic homopolymers with pendant L-lactic acid or L-alanine residues connected to 4-amino-azobenzene

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    The photochromic behaviour and photoisomerization kinetics of optically active homopolymers of trans-(S)-4-N-(2-methacryloyloxypropanoyl)aminoazobenzene and trans-(S)-4-N-(2-acryloyloxypropanoyl)aminoazobenzene were studied by u.v. spectroscopy under irradiation at 366 nm. The resulting data are compared with those obtained for the corresponding low molecular weight structural models trans-(S)-4-N-(2-pivaloyloxypropanoyl)aminoazobenzene and trans-(S)-4-N-(2-isobutyroyloxypropanoyl)aminoazobenzene. The photoresponsive behaviour of the above polymeric systems was also investigated by circular dichroism measurements at various extents of photoisomerization. The results are discussed in terms of the structural requirements of the macromolecules
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