Characterization of Ulrich bundles on Hirzebruch surfaces

In this work we characterize Ulrich bundles of any rank on polarized rational ruled surfaces over $\mathbb{P}^1$. We show that every Ulrich bundle admits a resolution in terms of line bundles. Conversely, given an injective map between suitable totally decomposed vector bundles, we show that its cokernel is Ulrich if it satisfies a vanishing in cohomology. As a consequence we obtain, once we fix a polarization, the existence of Ulrich bundles for any admissible rank and first Chern class. Moreover we show the existence of stable Ulrich bundles for certain pairs $(\textrm{rk}(E),c_1(E))$ and with respect to a family of polarizations. Finally we construct examples of indecomposable Ulrich bundles for several different polarizations and ranks.Comment: 23 pages. Incorporated Section 5 in the other sections. Added Section 6 on existence and moduli space of Ulrich bundles. Final version in Revista Matematica Complutens

Predicting the tau strange branching ratios and implications for V_{us}

Hadronic tau decays provide several ways to extract the Cabbibo-Kobashi-Maskawa (CKM) matrix element V_{us}. The most precise determination involves using inclusive tau decays and requires as input the total branching ratio into strange final states. Recent results from B-factories have led to a discrepancy of about 3.4 sigma from the value of V_{us} implied by CKM unitarity and direct determination from Kaon semi-leptonic modes. In this paper we predict the three leading strange tau branching ratios, using dispersive parameterizations of the hadronic form factors and taking as experimental input the measured Kaon decay rates and the tau -> K pi nu_tau decay spectrum. We then use our results to reevaluate V_{us}, for which we find |V_{us}|=0.2207 \pm 0.0027, in better agreement with CKM unitarity.Comment: 20 pages, 3 figure

Steiner representations of hypersurfaces

Let $X\subseteq{\mathbb P}^{n+1}$ be an integral hypersurface of degree $d$. We show that each locally Cohen-Macaulay instanton sheaf $\mathcal E$ on $X$ with respect to $\mathcal O_X\otimes\mathcal O_{\mathbb P^{n+1}}(1)$ in the sense of Definition 1.3 in arXiv:2205.04767 [math.AG] yields the existence of Steiner bundles $\mathcal G$ and $\mathcal F$ on $\mathbb P^{n+1}$ of the same rank $r$ and a morphism $\varphi\colon \mathcal G(-1)\to\mathcal F^\vee$ such that the form defining $X$ to the power $\mathrm{rk}(\mathcal E)$ is exactly $\det(\varphi)$. We inspect several examples for low values of $d$, $n$ and $\mathrm{rk}(\mathcal E)$. In particular, we show that the form defining a smooth integral surface in $\mathbb P^3$ is the pfaffian of some skew-symmetric morphism $\varphi\colon \mathcal F(-1)\to\mathcal F^\vee$, where $\mathcal F$ is a suitable Steiner bundle on $\mathbb P^3$ of sufficiently large even rank.Comment: 26 page

Even and odd instanton bundles on Fano threefolds

We define non-ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) instanton bundles. We determine a lower bound for the quantum number of a non-ordinary instanton bundle, i.e. the degree of its second Chern class, showing the existence of such bundles for each admissible value of the quantum number when $i_X\ge 2$ or $i_X=1$, $\mathrm{Pic}(X)$ is cyclic and $X$ is ordinary. In these cases we deal with the component inside the moduli spaces of simple bundles containing the vector bundles we construct and we study their restriction to lines. Finally we give a monadic description of non-ordinary instanton bundles on $\mathbb{P}^3$ and the smooth quadric studying their loci of jumping lines, when of the expected codimension.Comment: 34 pages. Minor changes. The final version will appear in The Asian Journal of Mathematic

Problem członkostwa cudzoziemców w partiach politycznych

Foreign participation within political parties is always influenced by the equation: citizenship-political rights-sovereignty, on which is founded the construction of the “modern State”; this is the model on which our legal systems still rely. Increasing the possible participation processes allowed “no-citizens” as well as the extending some political rights to them raises the question of foreign participation in the party system (or party association). Moreover, these changes bring into discussion the traditional role of the political party as a channel of participation in public decisions. With the aim of identifying possible solutions to the problems mentioned above, this essay tries to analysis the experience both at a local and central level. With the developments that characterize the local experience, it is possible to trigger a process of change that might interest the national authorities.La partecipazione degli stranieri ai partiti politici è da sempre condizionata dall’equazione cittadinanza -diritti politici-sovranità sulla quale si è fondata la costruzione dello “stato moderno”, al cui modello ancora oggi è possibile ricondurre i nostri ordinamenti statali.L’incremento dei processi partecipativi e l’estensione di alcuni diritti politici ai “non cittadini” pone il problema della partecipazione dello straniero all’associazione partitica. Questi cambiamenti mettono, altresì, in discussione il tradizionale ruolo del partito politico quale canale di partecipazione alle decisioni pubbliche.Per poter individuare possibili soluzioni ai problemi prospettati il presente studio muove dall’analisi dell’esperienza svolta a livello locale e nelle amministrazioni territoriali. Dalle novità che caratterizzano l’esperienza degli enti locali può scaturire un processo di cambiamento dal basso che potrebbe finire per interessare le istituzioni rappresentative nazionaliProblem członkostwa cudzoziemców w partiach politycznych od zawsze wiąże się z zagadnieniami: obywatestwa, praw politycznych i suwerenności, na których opiera się model „nowoczesnego państwa”, z którego to modelu do dziś czerpią nasze systemy prawne. Wzrost partycypacji oraz rozszerzenie niektórych praw politycznych na „nieobywateli” stawia pytanie, czy uczestnictwo obcokrajowca w partii politycznej powinno być możliwe. Wspomniane zmiany kwestionują bowiem tradycyjną rolę partii politycznej umożliwiającej udział w publicznych procesach decyzyjnych. Autor, w celu odnalezienia możliwych rozwiązań przedstawionych problemów, rozpoczyna niniejszy artykuł od analizy doświadczeń na poziomie lokalnym w administracji terytorialnej. Zmiany, które zaszły na poziomie samorządów lokalnych, mogą bowiem być początkiem oddolnego procesu, który może zainteresować władze krajowe

Problem członkostwa cudzoziemców w partiach politycznych

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On varieties with Ulrich twisted conormal bundles

We study varieties $X \subset P^r$ such that is $N_X^*(k)$ is an Ulrich vector bundle for some integer $k$. We first prove that such an $X$ must be a curve. Then we give several examples of curves with $N_X^*(k)$ an Ulrich vector bundle

MicroRNA-29 family expression and its relation to antiviral immune response and viro-immunological markers in HIV-1-infected patients

Abstract BACKGROUND: Several in vitro studies suggested the microRNA-29 (miRNA-29) family is involved in regulating HIV-1 and modulating the expression of interleukin (IL)-32, an anti-HIV-1 cytokine. METHODS: To investigate the contribution of the miRNA-29 family to HIV-1 infection in vivo, we compared miRNA-29 expression in PBMC collected from 58 HIV-1-infected patients, naïve for antiretroviral therapy, and 21 gender- and age-matched HIV-1 seronegative healthy donors, using RT-Taqman assays. The relation between miRNA-29 levels and HIV-1 viro-immunological markers and the activation rate of antiviral immune response were also evaluated. In addition, we profiled miRNA-29 expression in CD4+ T lymphocytes and CD14+ monocytes collected from 5 antiretroviral treated HIV-1 infected patients. RESULTS: miRNA-29b levels were higher in HIV-1-infected patients than in the control group (p < 0.001). There were no correlations with either HIV-1 RNA levels or CD4+ T count, whereas a significant correlation was found between miRNA-29-a/c levels and integrated HIV-1 DNA (miRNA-29a: p = 0.009, r = -0.448; miRNA-29c: p = 0.029; r = -0.381). When the HIV-1-infected patients were grouped on the basis of their plasma HIV-1 RNA and CD4+ T cell count, we also found that patients expressing the lowest levels of miRNA-29c showed high viraemia, low CD4+ T cell count and high levels of integrated HIV-1 DNA. Moreover, miRNA-29b levels were correlated with those of IL-32nonα (p = 0.028; r = -0.298). Patients expressing higher levels of miRNA-29b showed lower levels of MxA, an interferon-stimulated gene, also induced by IL-32 (p = 0.006 r = -0.397). Lastly, we found that CD4+ T lymphocytes and CD14+ monocytes shared similar miRNA-29a/b/c expression patterns but the amount of miRNA-29a/b/c, IL-32 isoforms and MxA were highly variable in these two cellular subsets. CONCLUSIONS: The miRNA-29 family could influence the clinical progression of HIV-1 infection, the HIV-1 proviral load and the innate immune response against HIV-1