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A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimensionApr 11 2018In the present article a semilinear wave equation with scale-invariant damping and mass is considered. The global (in time) existence of radial symmetric solutions in even spatial dimension $n$ is proved using weighted $L^\infty-L^\infty$ estimates, under ... More

Fujita versus Strauss - a never ending storyOct 25 2017In this paper, we obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which the model has a "wave like" behavior. In order to achieve this goal, we perform ... More

Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant caseMay 07 2019This paper is devoted to derive integral representation formulae for the solution of an inhomogeneous linear wave equation with time-dependent damping and mass terms, that are scale-invariant with respect to the so-called hyperbolic scaling. Yagdjian's ... More

Decay estimates for the linear damped wave equation on the Heisenberg groupAug 07 2019This paper is devoted to the derivation of $L^2$ - $L^2$ decay estimates for the solution of the homogeneous linear damped wave equation on the Heisenberg group $\mathbf{H}_n$, for its time derivative and for its horizontal gradient. Moreover, we consider ... More

Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spacesAug 02 2017In this paper we consider the following Cauchy problem for the semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity: \begin{align}\label{CP abstract} \begin{cases} u_{tt}-\Delta u+\dfrac{\mu_1}{1+t} u_t+\dfrac{\mu_2^2}{(1+t)^2}u=|u|^p, ... More

A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order termsDec 17 2018In this note two blow-up results are proved for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms both in the subcritical case and in the critical case, when the damping and the mass terms make both equations ... More

A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative typeMay 27 2019In this note, we prove blow-up results for semilinear wave models with damping and mass in the scale-invariant case and with nonlinear terms of derivative type. We consider the single equation and the weakly coupled system. In the first case we get a ... More

Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear partSep 26 2018In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up result the test ... More

Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg groupMay 14 2019In this paper we consider the semilinear Cauchy problem for the heat equation with power nonlinearity in the Heisenberg group $\mathbf{H}_n$. The heat operator is given in this case by $\partial_t-\Delta_H$, where $\Delta_H$ is the so-called sub-Laplacian ... More

Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear termsJan 13 2019In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear damped wave equations in the scattering case with nonlinearities of mixed type, namely, in one equation a power nonlinearity and in the other a semilinear term ... More

Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearitiesDec 25 2018In this work we study the blow-up of solutions of a weakly coupled system of damped semilinear wave equations in the scattering case with power nonlinearities. We apply an iteration method to study both the subcritical case and the critical case. In the ... More

Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearityMay 17 2018In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper bound for the exponent ... More

Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering caseDec 27 2018In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the corresponding single ... More

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearityAug 08 2019In this paper, we consider the Cauchy problem for the semilinear damped wave equation on the Heisenberg group with power nonlinearity. We prove that the critical exponent is the Fujita exponent $p_{\mathrm{Fuj}}(\mathscr{Q}) = 1+2 / \mathscr{Q}$, where ... More

A Cesàro Average of Hardy-Littlewood numbersJun 01 2012Let $\Lambda$ be the von Mangoldt function and (r_{\textit{HL}}(n) = \sum_{m_1 + m_2^2 = n} \Lambda(m_1),) be the counting function for the Hardy-Littlewood numbers. Let $N$ be a sufficiently large integer. We prove that \sum_{n \le N} r_{\textit{HL}}(n) ... More

On a ternary Diophantine problem with mixed powers of primesJun 01 2012Jul 30 2012Let $1 < k < 33 / 29$. We prove that if $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real numbers, not all of the same sign and that $\lambda_1 / \lambda_2$ is irrational and $\varpi$ is any real number, then for any $\eps > 0$ the inequality ... More

A Diophantine problem with a prime and three squares of primesJun 01 2012We prove that if $\lambda_1$, $\lambda_2$, $\lambda_3$ and $\lambda_4$ are non-zero real numbers, not all of the same sign, $\lambda_1 / \lambda_2$ is irrational, and $\varpi$ is any real number then, for any $\eps > 0$ the inequality $ \bigl|\lambda_1 ... More

Blowdown of hydrocarbons pressure vessel with partial phase separationJan 05 2011We propose a model for the simulation of the blowdown of vessels containing two-phase (gas-liquid) hydrocarbon fluids, considering non equilibrium between phases. Two phases may be present either already at the beginning of the blowdown process (for instance ... More

Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensatesApr 01 2017Oct 18 2017We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schr\"odinger equation at the leading order in the number of particles. The considered system ... More

A Flexible Framework for Accurate Simulation of Cloud In-Memory Data StoresNov 28 2014In-memory (transactional) data stores are recognized as a first-class data management technology for cloud platforms, thanks to their ability to match the elasticity requirements imposed by the pay-as-you-go cost model. On the other hand, defining the ... More

Sums of many primesJan 18 2011Assuming that the Generalized Riemann Hypothesis (GRH) holds, we prove an explicit formula for the number of representations of an integer as a sum of $k\geq 5$ primes. Our error terms in such a formula improve by some logarithmic factors an analogous ... More

A Diophantine problem with prime variablesJun 01 2012We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign, with $\lambda_1 / \lambda_2$ irrational, and $p_1$, ... More

Short intervals asymptotic formulae for binary problems with prime powers, IIOct 26 2018We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_{1}^{\ell_1}+p_{2}^{\ell_2}$ and $n=p^{\ell_1} + m^{\ell_2}$, where $\ell_1, \ell_2\ge 2$ are fixed integers, ... More

A Cesàro Average of Goldbach numbersJun 01 2012Let $\Lambda$ be the von Mangoldt function and (r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2)) be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer. We prove that &\sum_{n \le N} r_G(n) \frac{(1 - n/N)^k}{\Gamma(k ... More

Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$Apr 18 2015Nov 28 2015We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional ... More

Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$Apr 09 2015Nov 28 2015We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional ... More

On the constant in the Mertens product for arithmetic progressions. I. IdentitiesJun 19 2007Sep 26 2008The aim of the paper is the proof of new identities for the constant in the Mertens product for arithmetic progressions. We deal with the problem of the numerical computation of these constants in another paper.

Explicit relations between primes in short intervals and exponential sums over primesDec 22 2012Dec 29 2012Under the assumption of the Riemann Hypothesis (RH), we prove explicit quantitative relations between hypothetical error terms in the asymptotic formulae for truncated mean-square average of exponential sums over primes and in the mean-square of primes ... More

Cesàro average in short intervals for Goldbach numbersJun 02 2016We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.

Effective non-linear spinor dynamics in a spin-1 Bose-Einstein condensateMar 14 2018Sep 03 2018We derive from first principles the experimentally observed effective dynamics of a spinor Bose gas initially prepared as a Bose-Einstein condensate and then left free to expand ballistically. In spinor condensates, which represent one of the recent frontiers ... More

Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressionsJun 11 2009We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\sum\limits_{\substack{p\leq x p\equiv a \bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\sum_{p\equiv ... More

Short intervals asymptotic formulae for binary problems with prime powersJun 14 2018Jun 21 2018We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_{1}^{\ell_1}+p_{2}^{\ell_2}$, with $\ell_1, \ell_2\in\{2,3\}$, $\ell_1+\ell_2\le 5$ are fixed integers, and $n=p^{\ell_1} ... More

Automorphisms of order three on numerical Godeaux surfacesOct 26 2007We prove that a numerical Godeaux surface cannot have an automorphism of order three.

Vanishing lines in generalized Adams spectral sequences are genericJul 02 1999We show that in a generalized Adams spectral sequence, the presence of a vanishing line of fixed slope (at some term of the spectral sequence, with some intercept) is a generic property.

A behavioural approach to obstacle avoidance for mobile manipulators based on distributed sensingFeb 09 2015A reactive obstacle avoidance method for mobile manipulators is presented. The objectives of the developed algorithm are twofold. The first one is to find a trajectory in the configuration space of a mobile manipulator so as to follow a given trajectory ... More

Hodge duality operators on left covariant exterior algebras over two and three dimensional quantum spheresDec 29 2011Jun 04 2012Using non canonical braidings, we first introduce a notion of symmetric tensors and corresponding Hodge operators on a class of left covariant 3d differential calculi over the quantum SU(2) group, then we induce Hodge operators on the left covariant 2d ... More

Free fall and self-force: an historical perspectiveMay 04 2010Free fall has signed the greatest markings in the history of physics through the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The perspectives offered by the capture of stars by supermassive black holes are to be cherished, because ... More

Ground state energy of the low density Hubbard model. An upper boundNov 14 2006May 04 2007We derive an upper bound on the ground state energy of the three-dimensional (3D) repulsive Hubbard model on the cubic lattice agreeing in the low density limit with the known asymptotic expression of the ground state energy of the dilute Fermi gas in ... More

Time-reversal odd distribution functions in chiral models with vector mesonsJan 30 2005The so-called time-reversal odd distribution functions are known to be non-vanishing in QCD due to the presence of the link operator in the definition of these quantities. I show that T-odd distributions can be non-vanishing also in chiral models, if ... More

Models for transverse-momentum distributions and transversityNov 28 2011I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the existence of relations ... More

GLACIER and related R&DJul 05 2011Liquid argon detectors, with mass up to 100 kton, are being actively studied in the context of proton decay searches, neutrino astrophysics and for the next generation of long baseline neutrino oscillation experiments to study the neutrino mass hierarchy ... More

Variational approximations for stationary states of Ising-like modelsJul 25 2013We introduce a new variational approach to the stationary state of kinetic Ising-like models. The approach is based on the cluster expansion of the entropy term appearing in a functional which is minimized by the system history. We rederive a known mean-field ... More

Deriving exact results for Ising-like models from the cluster variation methodSep 24 1999The cluster variation method (CVM) is an approximation technique which generalizes the mean field approximation and has been widely applied in the last decades, mainly for finding accurate phase diagrams of Ising-like lattice models. Here we discuss in ... More

Bubble propagation in a helicoidal molecular chainJul 26 2000We study the propagation of very large amplitude localized excitations in a model of DNA that takes explicitly into account the helicoidal structure. These excitations represent the ``transcription bubble'', where the hydrogen bonds between complementary ... More

On a Rigorous Proof of the Joos-Zeh Formula for Decoherence in a Two-Body ProblemJul 30 2003We consider a simple one dimensional system consisting of two particles interacting with a $\delta$-potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the ... More

A q-Virasoro Algebra at roots of unity, Free Fermions and Temperley Lieb HamiltoniansNov 05 2012In this work we introduce a novel q-deformation of the Virasoro algebra expressed in terms of free fermions, we then realize that this algebra, when the deformation parameter is a root of unity can be realized exactly on the lattice. We then study the ... More

The Nonlocal Involutive Charges of the CFT ${\cal M}_{3,4}$Oct 20 2009Nov 15 2010We consider continuum minimal ${\cal M}_{3,4} $ with central charge $c=1/2$. The eigenvalues of the known local involutive charges are known to be related to spectral zeta functions of suitable one dimensional shroedinger hamiltonians. We investigate ... More

Lattice Integrals of Motion of the Ising Model on the StripNov 12 2012We consider the 2D critical Ising model on a strip with fixed boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable $\csc(4u)$, being $u$ the spectral ... More

Integrals of Motion for Critical Dense Polymers and Symplectic FermionsMar 29 2009Sep 07 2009We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation ... More

Applications of some exponential sums on prime powers: a surveyJun 02 2016A survey paper on some recent results on additive problems with prime powers.

A Formal Framework for Modeling Trust and Reputation in Collective Adaptive SystemsJul 08 2016Trust and reputation models for distributed, collaborative systems have been studied and applied in several domains, in order to stimulate cooperation while preventing selfish and malicious behaviors. Nonetheless, such models have received less attention ... More

Many Haken Heegaard splittingsOct 31 2016We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. ... More

Quantum Dynamics in Classical Spin BathsJun 14 2013A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the evolution of ... More

Non-Hamiltonian Commutators in Quantum MechanicsNov 08 2005The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantum-classical systems are described by a particular realization ... More

Phase space flows for non-Hamiltonian systems with constraintsAug 08 2005In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot ... More

Geometry of non-compact minimal and marginally outer-trapped surfaces in asymptotically flat manifoldsOct 18 2013Apr 07 2014In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped surfaces in ... More

Hilbert++ ManualJun 28 2007Mar 01 2009We present here an installation guide, a hand-on mini-tutorial through examples, and the theoretical foundations of the Hilbert++ code.

Operation and calibration of the Silicon Drift Detectors of the ALICE experiment during the 2008 cosmic ray data taking periodJan 18 2010The calibration and performance of the Silicon Drift Detector of the ALICE experiment during the 2008 cosmic ray run will be presented. In particular the procedures to monitor the running parameters (baselines, noise, drift speed) are detailed. Other ... More

Implications of first LHC resultsJul 06 2011We discuss implications of first LHC results for models motivated by the hierarchy problem: large extra dimensions and supersymmetry. We present bounds, global fits and implications for naturalness.

The fine-tuning price of the early LHCJan 11 2011Jul 26 2011LHC already probed and excluded half of the parameter space of the Constrained Minimal Supersymmetric Standard Model allowed by previous experiments. Only about 0.3% of the CMSSM parameter space survives. This fraction rises to about 0.9% if the bound ... More

Radiatively induced light right-handed stopSep 08 1996Sep 10 1996A right-handed stop not much heavier or even lighter than the Z boson has today desirable phenomenological consequences. We study how it can result within the usual radiative scenario of electroweak symmetry breaking. A restriction on the gaugino mass ... More

Interpreting the 750 GeV digamma excess: a reviewMay 30 2016Aug 05 2016We summarise the main experimental, phenomenological and theoretical issues related to the 750 GeV digamma excess

Accretion ProcessesMar 18 2018In planetary science, accretion is the process in which solids agglomerate to form larger and larger objects and eventually planets are produced. The initial conditions are a disc of gas and microscopic solid particles, with a total mass of about 1% of ... More

Looking at spacetime atoms from within the Lorentz sectorMar 15 2018Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, function of the point $P$ and the vector $v^a$ at $P$, expressing ... More

The world underground scientific facilities. A compendiumDec 07 2007Underground laboratories provide the low radioactive background environment necessary to explore the highest energy scales that cannot be reached with accelerators, by searching for extremely rare phenomena. I have requested to the Directors of the Laboratories ... More

Controllability of bilinear quantum systems in explicit times via explicit control fieldsMay 09 2017Feb 07 2019We consider the bilinear Schroedinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global approximate controllability. ... More

Quaternionic regularity and the dibar-Neumann problem in C^2Dec 04 2006Dec 13 2006Let D be a domain in the quaternionic space H. We prove a differential criterion that characterizes Fueter-regular quaternionic functions f:bD -> H of class C^1. We find differential operators T and N, with complex coefficients, such that a function f ... More

Apolar Ideal and Normal Bundle of Rational CurvesMar 22 2012As in our previous work [1] we address the problem to determine the splitting of the normal bundle of rational curves. With apolarity theory we are able to characterize some particular subvarieties in some Hilbert scheme of rational curves, defined by ... More

On the decomposition numbers of $\mathrm{SO}_8^+(2^f)$Oct 16 2017Let $q=2^f$, and let $G=\mathrm{SO}_8^+(q)$ and $U$ be a Sylow $2$-subgroup of $G$. We first describe the fusion of the conjugacy classes of $U$ in $G$. We then use this information to prove the unitriangularity of the $\ell$-decomposition matrices of ... More

A $K$-theoretical invariant and bifurcation for a parameterized family of functionalsMay 24 2009Jul 24 2013For a family of functionals defined on a Hilbert manifold and smoothly depending on a compact finite dimensional manifold, we give a sufficient condition on the parameter space in such a way the family bifurcate from the trivial branch.

A Jarník-type theorem for a problem of approximation by cubic polynomialsSep 25 2018For a given decreasing positive real function $\psi$, let $\mathcal{A}_n(\psi)$ be the set of real numbers for which there are infinitely many integer polynomials $P$ of degree up to $n$ such that $\left\lvert P(x) \right\rvert \leq \psi(\operatorname{H}(P))$. ... More

A hypothesis on the role of transposonsMay 26 2010"Epigenetic Tracking" is an evo-devo method to generate arbitrary 2d or 3d shapes; as such, it belongs to the field of "artificial embryology". In silico experiments have proved the effectiveness of the method in devo-evolving shapes of any kind and complexity ... More

Review of AdS/CFT Integrability, Chapter VI.2: Yangian AlgebraDec 17 2010Nov 07 2011We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the N=4 vs AdS5xS5 correspondence.

Effective and Big Divisors on a Projective Symmetric VarietyJun 29 2009May 03 2010We describe the effective and the big cones of a projective symmetric variety. Moreover, we give a necessary and sufficient combinatorial criterion for the bigness of a nef divisor on a projective symmetric variety. When the variety is toroidal and the ... More

Geometrical description of smooth projective symmetric varieties with Picard number oneDec 11 2008In a previous paper we have classified the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this work we give a geometrical description of such varieties. In particular, we determine their group of automorphisms. When ... More

An introduction to universality and renormalization group techniquesOct 08 2012Jun 25 2013These lecture notes have been written for a short introductory course on universality and renormalization group techniques given at the VIII Modave School in Mathematical Physics by the author, intended for PhD students and researchers new to these topics. ... More

Universal Enveloping Algebras of PBW TypeAug 26 2010Dec 23 2010We continue our investigation of the general notion of universal enveloping algebra introduced in [A. Ardizzoni, \emph{A Milnor-Moore Type Theorem for Primitively Generated Braided Bialgebras}, J. Algebra \textbf{327} (2011), no. 1, 337--365]. Namely ... More

A Diophantine approximation problem with two primes and one $k$-th power of a primeMay 31 2017Feb 13 2018We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a $k$-th power of a prime which was only proved to hold for $1<k<4/3$. We improve the $k$-range to $1<k\le 3$ by combining Harman's technique ... More

X-ray Resonant Magnetic Scattering : Polarisation Dependence in the non-spherical caseJun 06 2006Jul 24 2006We develop a simple tensorial contraction method to obtain analytical formula for X-ray resonant magnetic scattering. We apply the method considering first electric dipole-dipole and electric quadrupole-quadrupole scattering in the isolated atom approximation ... More

Using Dempster-Shafer Theory in Knowledge RepresentationMar 27 2013In this paper, we suggest marrying Dempster-Shafer (DS) theory with Knowledge Representation (KR). Born out of this marriage is the definition of "Dempster-Shafer Belief Bases", abstract data types representing uncertain knowledge that use DS theory for ... More

Sommerfeld corrections to type-II and III leptogenesisJun 10 2008Oct 09 2008We study thermal leptogenesis from decays of the electroweak triplets that mediate neutrino masses in type-II and type-III see-saw. We find that Sommerfeld corrections reduce the baryon asymmetry by ~30%, and that successful leptogenesis needs triplets ... More

Oscillations of three neutrinos with all Delta m^2 approx 10^{-3} eV^2Apr 06 1999Apr 27 1999Oscillations of three neutrinos with all squared mass splittings around 10^{-3} eV^2 are not firmly excluded by solar neutrino experiments. We carefully verify that they are also perfectly compatible with atmospheric neutrino experiments: due to accidental ... More

Baryogenesis via leptogenesisAug 31 2006We discuss how leptogenesis can explain the observed baryon asymmetry and summarize attempts of testing leptogenesis. We first perform estimates and discuss the main physics, and later outline the techniques that allow to perform precise computations. ... More

A primer on Answer Set ProgrammingAug 23 2005A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.

Percolation on the average and spontaneous magnetization for q-states Potts model on graphJun 06 2003Feb 08 2005We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over all the sites ... More

Contracting elements and random walksDec 12 2011Oct 31 2013We define a new notion of contracting element of a group and we show that contracting elements coincide with hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, rank one isometries in groups acting properly on ... More

Exponential triplesJul 18 2011Using ultrafilter techniques we show that in any partition of $\mathbb{N}$ into 2 cells there is one cell containing infinitely many exponential triples, i.e. triples of the kind $a,b,a^b$ (with $a,b>1$). Also, we will show that any multiplicative $IP^*$ ... More

Review: A Coherent and Comprehensive Model of the Evolution of the Outer Solar SystemOct 29 2010Since the discovery of the first extra-solar planets, we are confronted with the puzzling diversity of planetary systems. Processes like planet radial migration in gas-disks and planetary orbital instabilities, often invoked to explain the exotic orbits ... More

Origin and Dynamical Evolution of Comets and their ReservoirsDec 09 2005This text was originally written to accompany a series of lectures that I gave at the `35th Saas-Fee advanced course' in Switzerland and at the Institute for Astronomy of the University of Hawaii. It reviews my current understanding of the dynamics of ... More

The Polarized Nucleon in Quark ModelsOct 06 1998A brief overview of various problems related to the description of a polarized proton in quark models is presented. Structure functions are discussed both for longitudinal and transverse polarization. A recently introduced quantity, relevant in the study ... More

The ground state construction of the two-dimensional Hubbard model on the honeycomb latticeFeb 18 2011In these lectures I consider the half-filled two-dimensional (2D) Hubbard model on the honeycomb lattice and I review the rigorous construction of its ground state properties by making use of constructive fermionic Renormalization Group methods.

Cluster variation method and disorder varieties of two-dimensional Ising-like modelsSep 24 1999Jun 06 2000I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into ... More

The half-filled Hubbard model in the pair approximation of the Cluster Variation MethodNov 18 1992Nov 20 1992The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions ... More

Transverse-momentum dependent functions in semi-inclusive DISDec 15 2006The cross section for semi-inclusive deep inelastic scattering can be decomposed in terms of 18 structure functions. At low transverse momentum of the detected hadron, the structure functions can be expressed in terms of transverse-momentum-dependent ... More

The Hawking signal in density-density correlations in BECsFeb 11 2011We outline the derivation of the Hawking quanta-partner signal in correlations, and highlight the specific application to detect it in density-density correlations in BECs.

Entropy of gravitating systems: scaling laws versus radial profilesNov 20 2006Apr 17 2007Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which it is no longer ... More

Entropy bounds and field equationsApr 30 2014Aug 13 2015For general metric theories of gravity, we compare the approach that describes-derives the field equations of gravity as a thermodynamic identity with the one which looks at them from entropy bounds. The comparison is made through the consideration of ... More

Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit couplingJun 21 2011Sep 05 2013Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes ... More

Cosmological constraints from Microwave Background Anisotropy and PolarizationNov 25 2003The recent high-quality measurements of the Cosmic Microwave Background anisotropies have presented cosmologists with the possibility of studying the large scale properties of our universe with unprecedented precision. Here I review the current status ... More

CMB and Cosmological Parameters: Current Status and ProspectsApr 01 2002The last years have been an exciting period for the field of the Cosmic Microwave Background (CMB) research. With recent CMB balloon-borne and ground-based experiments we are entering a new era of 'precision' cosmology that enables us to use the CMB anisotropy ... More