1,721,021 research outputs found
Lang-Vojta Conjecture over function fields for surfaces dominating
Full text linkWe prove the nonsplit case of the Lang-Vojta conjecture over function fields for surfaces of log general type that are ramified covers of . This extends results of Corvaja and Zannier, who proved the conjecture in the split case, and results of Corvaja and Zannier and the second author that were obtained in the case of the complement of a degree four and three component divisor in . We follow the strategy developed by Corvaja and Zannier and make explicit all the constants involved
Unlikely Intersections and applications to Diophantine Geometry
Full text linkThis thesis concerns problems of "Unlikely Intersections", i.e. about varieties who are not expected to intersect unless there is a special geometric relation between them. In literature, there are many problems from very different settings that can be viewed in this perspective, starting from the celebrated Mordell conjecture (also known as Faltings' theorem) and the common formulation of these problems in this language gives common strategies to deal with them. The most general conjecture in this setting is the so called "Zilber-Pink Conjecture", raised in somewhat different form independently by Bombieri, Masser and Zannier and by Zilber in the case of tori and by Pink in the more general context of mixed Shimura varieties. This conjecture includes several famous statements, as Mordell-Lang and Manin-Mumford conjecture for semiabelian varieties and as André-Oort conjecture for Shimura varieties.
With the aim of studying some particular cases of the conjecture, in this thesis we are going to apply the so called "Pila-Zannier strategy" to two particular cases: the first one in the setting of multiplicative
groups, and the second new one in a special family of split semiabelian varieties over a curve. To tackle this problems, we use different ingredients coming from o-minimality, theory of heights of algebraic numbers and deeper results of Diophantine geometry
Lang–Vojta conjecture over function fields for surfaces dominating Gm2
Full text linkWe prove the nonsplit case of the Lang–Vojta conjecture over function fields for surfaces of log general type that are ramified covers of Gm2. This extends the results of Corvaja and Zannier (J Differ Geom 93(3):355–377, 2013), where the conjecture was proved in the split case, and the results of Corvaja and Zannier (J Algebr Geom 17(2):295–333, 2008), Turchet (Trans Amer Math Soc 369(12):8537–8558, 2017) that were obtained in the case of the complement of a degree four and three component divisor in P2. We follow the strategy developed by Corvaja and Zannier and make explicit all the constants involved
Betti maps, Pell equations in polynomials and almost-Belyi maps
Full text linkWe study the Betti map of a particular (but relevant) section of the family of Jacobians of hyperelliptic curves using the polynomial Pell equation A(2) - DB2 = 1, with A, B, D is an element of C[t] and certain ramified covers P-1 -> P-1 arising from such equation and having heavy constrains on their ramification. In particular, we obtain a special case of a result of Andre, Corvaja and Zannier on the submersivity of the Betti map by studying the locus of the polynomials D that fit in a Pell equation inside the space of polynomials of fixed even degree. Moreover, Riemann existence theorem associates to the abovementioned covers certain permutation representations: We are able to characterize the representations corresponding to 'primitive' solutions of the Pell equation or to powers of solutions of lower degree and give a combinatorial description of these representations when D has degree 4. In turn, this characterization gives back some precise information about the rational values of the Betti map
Innovazione tecnologica nelle coperture: l’impiego di materiali compositi,in atti del convegno “Architettura e tecnica delle coperture” , Ancona 10-11 marzo 2006, marzo 2006
No full textOn periodicity of p-adic Browkin continued fractions
No full textThe classical theory of continued fractions has been widely studied for centuries for its important properties of good approximation, and more recently it has been generalized to p-adic numbers where it presents many differences with respect to the real case. In this paper we investigate periodicity for the p-adic continued fractions introduced by Browkin. We give some necessary and sufficient conditions for periodicity in general, although a full characterization of p-adic numbers having purely periodic Browkin continued fraction expansion is still missing. In the second part of the paper, we describe a general procedure to construct square roots of integers having periodic Browkin p-adic continued fraction expansion of prescribed even period length. As a consequence, we prove that, for every n = 1, there exist infinitely many vm ? Q(p) with periodic Browkin expansion of period 2(n), extending a previous result of Bedocchi obtained for n = 1
A note on cyclotomic polynomials and Linear Feedback Shift Registers
No full textLinear Feedback Shift Registers (LFSR) are tools commonly used in cryptography in many contexts, for example as pseudo-random numbers generators. In this paper we characterize LFSR with certain symmetry properties. Related to this question we also classify polynomials f satisfying the property that if α is a root of f then f (α deg f) = 0. The classification heavily depends on the choice of the fields of coefficients of the polynomial; we consider the cases (Figure presented.) and K = Q
Fisiologia e metodi di misura della produzione di ossido nitrico nell’uomo
No full textNitric oxide (NO) is a simple molecule, highly conserved across species with important effects on several physiological mechanisms. In the cardiovascular system, NO is tonically released by the endothelial cells in response to shear stress to maintain vascular tone. This effect is due to the relaxation of the vascular smooth muscle cells in the medium layer (tunica media) of the arterial wall. However, NO is also involved in the regulation of synaptic neurotransmission, platelet aggregation, inflammation, appetite, peristalsis, renal metabolism, respiratory function, lipid metabolism and glucose metabolism. Therefore, an abnormal production of NO (over- or under-production) has multi-systemic effects. Metabolic disorders like hypertension, obesity or dyslipidaemia are associated with a reduction of NO production. The mechanisms responsible for a decreased NO synthesis are partially known but oxidative stress, overproduction of endogenous inhibitors of the Nitric Oxide Synthase (NOS) such as asymmetric dimethylarginine (ADMA) and genetic factors may be implicated. The half-life of NO is extremely short in biological samples (t1/2 < or = 0.2 sec) and its in vivo measurement is very difficult. Therefore, indirect methods have been developed to measure the end products of NO metabolism in biological samples. Some of these methods have used stable isotopes to trace the metabolic fate of the precursor of NO (Arginine) and measure the appearance of stable isotopes in the end products [nitrate (NO3), nitrite (NO2), citrulline]. However, the existing methods are expensive, invasive and require complex analytical laboratory techniques
Unlikely intersections in families of abelian varieties and the polynomial Pell equation
Full text linkLet be a smooth irreducible curve defined over a number field and consider an abelian scheme over and a curve inside , both defined over . In previous works, we proved that, when is a fibered product of elliptic schemes, if is not contained in a proper subgroup scheme of , then it contains at most finitely many points that belong to a flat subgroup scheme of codimension at least 2. In this article, we continue our investigation and settle the crucial case of powers of simple abelian schemes of relative dimension . This, combined with the above mentioned result and work by Habegger and Pila, gives the statement for general abelian schemes which has applications in the study of solvability of almost-Pell equations in polynomials
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