We construct the rank-one, singular (point-like) perturbations of the d-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schrödinger operators with regular potentials centred around the perturbation point and shrinking to a delta-like shape. We analyse both possible regimes, the resonance-driven and the resonance-independent limit, depending on the power of the fractional Laplacian and the spatial dimension. To this aim, we also qualify the notion of zero-energy resonance for Schrödinger operators formed by a fractional Laplacian and a regular potential.

1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s11785-019-00927-w01288nas a2200145 4500008004100000245008600041210007000127260004400197490000700241520070800248100001900956700003200975700001801007856011701025 2018 eng d00aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in the Complex Plane0 aPainlevé IV Critical Asymptotics for Orthogonal Polynomials in t bNational Academy of Sciences of Ukraine0 v143 aWe study the asymptotic behaviour of orthogonal polynomials in the complex plane that are associated to a certain normal matrix model. The model depends on a parameter and the asymptotic distribution of the eigenvalues undergoes a transition for a special value of the parameter, where it develops a corner-type singularity. In the double scaling limit near the transition we determine the asymptotic behaviour of the orthogonal polynomials in terms of a solution of the Painlev´e IV equation. We determine the Fredholm determinant associated to such solution and we compute it numerically on the real line, showing also that the corresponding Painlev´e transcendent is pole-free on a semiaxis.

1 aBertola, Marco1 aElias Rebelo, José Gustavo1 aGrava, Tamara uhttps://www.math.sissa.it/publication/painlev%C3%A9-iv-critical-asymptotics-orthogonal-polynomials-complex-plane02205nas a2200253 4500008004100000022001400041245007200055210006900127260001200196490000600208520146100214653002201675653002201697653002501719653002101744653001701765653001601782653002001798653001801818100002501836700002301861700002201884856004501906 2018 eng d a2296-914400aPeristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots0 aPeristaltic Waves as Optimal Gaits in Metameric BioInspired Robo c09/20180 v53 a*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We study the periodic boundary value problem associated with the second order nonlinear equation u''+(λa+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and sublinear growth at infinity. For λ,μ positive and large, we prove the existence of 3^m−1 positive T-periodic solutions when the weight function a(t) has m positive humps separated by m negative ones (in a T-periodicity interval). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics. The proof is based on coincidence degree theory for locally compact operators on open unbounded sets and also applies to Neumann and Dirichlet boundary conditions. Finally, we deal with radially symmetric positive solutions for the Neumann and the Dirichlet problems associated with elliptic PDEs.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526401233nas a2200133 4500008004100000245007600041210006900117300001200186490000700198520080200205100002301007700002301030856004601053 2018 eng d00aPositive subharmonic solutions to nonlinear ODEs with indefinite weight0 aPositive subharmonic solutions to nonlinear ODEs with indefinite a17500210 v203 aWe prove that the superlinear indefinite equation u″ + a(t)up = 0, where p > 1 and a(t) is a T-periodic sign-changing function satisfying the (sharp) mean value condition ∫0Ta(t)dt < 0, has positive subharmonic solutions of order k for any large integer k, thus providing a further contribution to a problem raised by Butler in its pioneering paper [Rapid oscillation, nonextendability, and the existence of periodic solutions to second order nonlinear ordinary differential equations, J. Differential Equations 22 (1976) 467–477]. The proof, which applies to a larger class of indefinite equations, combines coincidence degree theory (yielding a positive harmonic solution) with the Poincaré–Birkhoff fixed point theorem (giving subharmonic solutions oscillating around it).

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo uhttps://doi.org/10.1142/S021919971750021300509nas a2200133 4500008004100000245012700041210006900168300001400237490000600251100002100257700001700278700002200295856005800317 2018 eng d00aPredicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions0 aPredicting and Optimizing Microswimmer Performance from the Hydr a410–4240 v51 aGiuliani, Nicola1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/00402nas a2200133 4500008004100000245004500041210004400086300000800130490000600138100001700144700001900161700002100180856006700201 2018 eng d00aPyDMD: Python Dynamic Mode Decomposition0 aPyDMD Python Dynamic Mode Decomposition a5300 v31 aDemo, Nicola1 aTezzele, Marco1 aRozza, Gianluigi uhttps://joss.theoj.org/papers/734e4326edd5062c6e8ee98d03df9e1d00603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001100961nas a2200133 4500008004100000245014200041210006900183260003100252520042800283100002300711700002300734700001900757856005100776 2016 en d00aPairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case0 aPairs of positive periodic solutions of nonlinear ODEs with inde bCambridge University Press3 aWe study the periodic and Neumann boundary value problems associated with the second order nonlinear differential equation u''+cu'+λa(t)g(u)=0, where g:[0,+∞[→[0,+∞[ is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when ∫a(t)dt 0 is sufficiently large. Our approach is based on Mawhin's coincidence degree theory and index computations.

1 aBoscaggin, Alberto1 aFeltrin, Guglielmo1 aZanolin, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3526200883nas a2200157 4500008004100000245005000041210005000091260001500141300001400156490000600170520040100176100002200577700002300599700001800622856008500640 2016 eng d00aPeriodic perturbations of Hamiltonian systems0 aPeriodic perturbations of Hamiltonian systems bDe Gruyter a367–3820 v53 aWe prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré–Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

1 aFonda, Alessandro1 aGarrione, Maurizio1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/periodic-perturbations-hamiltonian-systems00912nas a2200229 4500008004100000020002200041245004000063210004000103260004400143300001100187520024800198100002100446700002400467700002000491700001800511700002000529700002200549700001900571700002000590700002400610856004800634 2016 eng d a978-3-319-29116-100aPimsner Algebras and Circle Bundles0 aPimsner Algebras and Circle Bundles aChambSpringer International Publishing a1–253 aWe report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with examples of quantum weighted projective and lens spaces and θ-deformations.

1 aArici, Francesca1 aD'Andrea, Francesco1 aLandi, Giovanni1 aAlpay, Daniel1 aCipriani, Fabio1 aColombo, Fabrizio1 aGuido, Daniele1 aSabadini, Irene1 aSauvageot, Jean-Luc uhttps://doi.org/10.1007/978-3-319-29116-1_100454nas a2200145 4500008004100000022001400041245007100055210006900126300001200195490000700207100002100214700001500235700002000250856003800270 2016 eng d a1661-695200aPimsner algebras and Gysin sequences from principal circle actions0 aPimsner algebras and Gysin sequences from principal circle actio a29–640 v101 aArici, Francesca1 aKaad, Jens1 aLandi, Giovanni uhttp://hdl.handle.net/2066/16295102275nas a2200145 4500008004100000245009200041210006900133260006800202520165800270100002101928700001901949700001701968700002101985856012302006 2016 en d00aPOD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations0 aPODGalerkin Method for Finite Volume Approximation of NavierStok bComputer Methods in Applied Mechanics and Engineering, Elsevier3 aNumerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control. In this work, the efforts have been put to develop a ROM for Computational Fluid Dynamics (CFD) application based on Finite Volume approximation, starting from the results available in turbulent Reynold-Averaged Navier Stokes simulations in order to enlarge the application field of Proper Orthogonal Decomposition – Reduced Order Model (POD – ROM) technique to more industrial fields. The approach is tested in the classic benchmark of the numerical simulation of the 2D lid-driven cavity. In particular, two simulations at Re = 103 and Re = 105 have been considered in order to assess both a laminar and turbulent case. Some quantities have been compared with the Full Order Model in order to assess the performance of the proposed ROM procedure i.e., the kinetic energy of the system and the reconstructed quantities of interest (velocity, pressure and turbulent viscosity). In addition, for the laminar case, the comparison between the ROM steady-state solution and the data available in literature has been presented. The results have turned out to be very satisfactory both for the accuracy and the computational times. As a major outcome, the approach turns out not to be affected by the energy blow up issue characterizing the results obtained by classic turbulent POD-Galerkin methods.1 aLorenzi, Stefano1 aCammi, Antonio1 aLuzzi, Lelio1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod-galerkin-method-finite-volume-approximation-navier-stokes-and-rans-equations01502nas a2200121 4500008004100000245010500041210007100146260001000217520097200227100002401199700002101223856013601244 2016 en d00aPOD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems0 aPOD–Galerkin monolithic reduced order models for parametrized fl bWiley3 aIn this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time. We provide a detailed description of the parametrized formulation of the multiphysics problem in its components, together with some insights on how to obtain an offline-online efficient computational procedure through the approximation of parametrized nonlinear tensors. Then, we present the monolithic POD–Galerkin method for the online computation of the global structural displacement, fluid velocity and pressure of the coupled problem. Finally, we show some numerical results to highlight the capabilities of the proposed reduced order method and its computational performances1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/pod%E2%80%93galerkin-monolithic-reduced-order-models-parametrized-fluid-structure-interaction01116nas a2200109 4500008004100000245007800041210006900119520071700188100002900905700002100934856005100955 2016 en d00aOn point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians0 apoint interactions realised as TerMartirosyanSkornyakov Hamilton3 aFor quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the ``Ter-Martirosyan--Skornyakov condition'' gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.1 aMichelangeli, Alessandro1 aOttolini, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3519502865nas a2200121 4500008004100000245007000041210006900111260001000180520240500190653002302595100002302618856010202641 2016 en d00aPositive solutions to indefinite problems: a topological approach0 aPositive solutions to indefinite problems a topological approach bSISSA3 aThe present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.10apositive solutions1 aFeltrin, Guglielmo uhttps://www.math.sissa.it/publication/positive-solutions-indefinite-problems-topological-approach00453nas a2200133 4500008004100000022001400041245008800055210006900143300001500212490000700227100001900234700001300253856005300266 2015 eng d a1751-811300aThe partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy0 apartition function of the extended rreduced KadomtsevPetviashvil a195205, 200 v481 aBertola, Marco1 aYang, Di uhttp://dx.doi.org/10.1088/1751-8113/48/19/19520500827nas a2200193 4500008004100000022001400041245005300055210005100108300001200159490000800171520026300179653002100442653001500463653002000478653002400498100002200522700001800544856007100562 2015 eng d a0362-546X00aA permanence theorem for local dynamical systems0 apermanence theorem for local dynamical systems a73 - 810 v1213 aWe provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka–Volterra predator–prey model with intraspecific competition.

10aLotka–Volterra10apermanence10aPredator–prey10aUniform persistence1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S0362546X1400333200719nas a2200217 4500008004100000245009200041210006900133260003300202100002200235700002400257700001600281700002300297700001500320700001400335700002200349700002600371700002100397700001300418700001900431856005100450 2015 en d00aThe phototransduction machinery in the rod outer segment has a strong efficacy gradient0 aphototransduction machinery in the rod outer segment has a stron bNational Academy of Sciences1 aMazzolini, Monica1 aFacchetti, Giuseppe1 aAndolfi, L.1 aZaccaria, Proietti1 aTuccio, S.1 aTreud, J.1 aAltafini, Claudio1 aDi Fabrizio, Enzo, M.1 aLazzarino, Marco1 aRapp, G.1 aTorre, Vincent uhttp://urania.sissa.it/xmlui/handle/1963/3515700790nas a2200121 4500008004100000245007600041210006900117520031400186100001800500700001900518700002000537856011100557 2015 en d00aPoisson cohomology of scalar multidimensional Dubrovin-Novikov brackets0 aPoisson cohomology of scalar multidimensional DubrovinNovikov br3 aWe compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.1 aCarlet, Guido1 aCasati, Matteo1 aShadrin, Sergey uhttps://www.math.sissa.it/publication/poisson-cohomology-scalar-multidimensional-dubrovin-novikov-brackets01307nas a2200109 4500008004100000245006700041210006600108260001000174520088800184100002101072856010401093 2015 en d00aPrincipal circle bundles, Pimsner algebras and Gysin sequences0 aPrincipal circle bundles Pimsner algebras and Gysin sequences bSISSA3 aPrincipal circle bundles and Gysin sequences play a crucial role in mathematical physics, in particular in Chern-Simons theories and T-duality. This works focuses on the noncommutative topology of principal circle bundles: we investigate the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. At the C*-algebraic level, we start from a self-Morita equivalence bimodule E for a C*-algebra B which we think of as a non commutative line bundle over the `base space’ algebra B. The corresponding Pimsner algebra O_E, is then the total space algebra of an associated circle bundle. A natural six term exact sequence, an analogue of the Gysin sequence for circle bundles, relates the KK-theories of O_E and of the base space B. We illustrate several results with the examples of quantum weighted projective and lens spaces.1 aArici, Francesca uhttps://www.math.sissa.it/publication/principal-circle-bundles-pimsner-algebras-and-gysin-sequences00908nas a2200109 4500008004100000245004700041210004700088260001300135520057900148100002000727856005100747 2014 en d00aPfaffian representations of cubic surfaces0 aPfaffian representations of cubic surfaces bSpringer3 aLet K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x0,x1,x2,x3] and a zero a of F in P3 K and ensures a linear Pfaffian representation of V(F) with entries in K[x0,x1,x2,x3], under mild assumptions on F and a. We use this result to give an explicit construction of (and to prove the existence of) a linear Pfaffian representation of V (F), with entries in K′[x0,x1,x2,x3], being K′ an algebraic extension of K of degree at most six. An explicit example of such a construction is given.

1 aTanturri, Fabio uhttp://urania.sissa.it/xmlui/handle/1963/3468800655nas a2200157 4500008004100000245010000041210006900141260005800210300001400268490000600282100001700288700001700305700002200322700002400344856012900368 2014 eng d00aPotential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures0 aPotential Model for Ship Hydrodynamics Simulations Directly Inte bInternational Society of Offshore and Polar Engineers a815–8220 v41 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/potential-model-ship-hydrodynamics-simulations-directly-interfaced-cad-data-structures00851nas a2200121 4500008004100000245009300041210006900134260001300203520042700216100001900643700001600662856005100678 2014 en d00aPseudo-automorphisms of positive entropy on the blowups of products of projective spaces0 aPseudoautomorphisms of positive entropy on the blowups of produc bSpringer3 aWe use a concise method to construct pseudo-automorphisms fn of the first dynamical degree d1(fn) > 1 on the blowups of the projective n-space for all n ≥ 2 and more generally on the blowups of products of projective spaces. These fn, for n=3 have positive entropy, and for n≥ 4 seem to be the first examples of pseudo-automorphisms with d1(fn) > 1 (and of non-product type) on rational varieties of higher dimensions.1 aPerroni, Fabio1 aZhang, Deqi uhttp://urania.sissa.it/xmlui/handle/1963/3471400555nas a2200133 4500008004100000245009600041210006900137260003700206300001200243490000700255100002300262700001900285856011700304 2013 eng d00aPairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions0 aPairs of nodal solutions for a class of nonlinear problems with bAdvanced Nonlinear Studies, Inc. a13–530 v131 aBoscaggin, Alberto1 aZanolin, Fabio uhttps://www.math.sissa.it/publication/pairs-nodal-solutions-class-nonlinear-problems-one-sided-growth-conditions00503nas a2200133 4500008004100000245006500041210006500106260003700171300001400208490000700222100002200229700001900251856009900270 2013 eng d00aPeriodic bouncing solutions for nonlinear impact oscillators0 aPeriodic bouncing solutions for nonlinear impact oscillators bAdvanced Nonlinear Studies, Inc. a179–1890 v131 aFonda, Alessandro1 aSfecci, Andrea uhttps://www.math.sissa.it/publication/periodic-bouncing-solutions-nonlinear-impact-oscillators01133nas a2200157 4500008004100000022001400041245008000055210007300135260000800208300001400216490000700230520064600237100002300883700002300906856004600929 2013 eng d a1420-900400aPlanar Hamiltonian systems at resonance: the Ahmad–Lazer–Paul condition0 aPlanar Hamiltonian systems at resonance the Ahmad–Lazer–Paul con cJun a825–8430 v203 aWe consider the planar Hamiltonian system\$\$Ju^{\backslashprime} = \backslashnabla F(u) + \backslashnabla_u R(t,u), \backslashquad t \backslashin [0,T], \backslash,u \backslashin \backslashmathbb{R}^2,\$\$with F(u) positive and positively 2-homogeneous and \$\${\backslashnabla_{u}R(t, u)}\$\$sublinear in u. By means of an Ahmad-Lazer-Paul type condition, we prove the existence of a T-periodic solution when the system is at resonance. The proof exploits a symplectic change of coordinates which transforms the problem into a perturbation of a linear one. The relationship with the Landesman–Lazer condition is analyzed, as well.

1 aBoscaggin, Alberto1 aGarrione, Maurizio uhttps://doi.org/10.1007/s00030-012-0181-201215nas a2200193 4500008004100000022001400041245010000055210006900155300001600224490000800240520056000248653002000808653002500828653003200853653002300885100002300908700001900931856007100950 2012 eng d a0022-039600aPairs of positive periodic solutions of second order nonlinear equations with indefinite weight0 aPairs of positive periodic solutions of second order nonlinear e a2900 - 29210 v2523 aWe study the problem of the existence and multiplicity of positive periodic solutions to the scalar ODEu″+λa(t)g(u)=0,λ>0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and a(t) is a T-periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solutions for some classes of nonlinearities g(x) when λ is small. Then, using critical point theory, we prove the existence of at least two positive T-periodic solutions for λ large. Some examples are also provided.

10aCritical points10aNecessary conditions10aPairs of positive solutions10aPeriodic solutions1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100389500499nas a2200133 4500008004100000245010300041210006900144260003300213300001500246490000700261100002200268700001900290856005600309 2012 eng d00aPeriodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces0 aPeriodic solutions of a system of coupled oscillators with onesi bKhayyam Publishing, Inc.c11 a993–10100 v251 aFonda, Alessandro1 aSfecci, Andrea uhttps://projecteuclid.org:443/euclid.die/135601224800752nas a2200133 4500008004100000245006500041210006500106260005100171300001400222490000700236520025200243100002300495856010000518 2012 eng d00aPeriodic solutions to superlinear planar Hamiltonian systems0 aPeriodic solutions to superlinear planar Hamiltonian systems bEuropean Mathematical Society Publishing House a127–1410 v693 aWe prove the existence of infinitely many periodic (harmonic and subharmonic) solutions to planar Hamiltonian systems satisfying a suitable superlinearity condition at infinity. The proof relies on the Poincare-Birkhoff fixed point theorem.

1 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/periodic-solutions-superlinear-planar-hamiltonian-systems00782nas a2200121 4500008004100000245008600041210006900127260001300196520037000209653002400579100002100603856003600624 2012 en d00aPoles Distribution of PVI Transcendents close to a Critical Point (summer 2011)0 aPoles Distribution of PVI Transcendents close to a Critical Poin bElsevier3 aThe distribution of the poles of Painlevé VI transcendents associated to semi-simple Frobenius manifolds is determined close to a critical point. It is shown that the poles accumulate at the critical point,asymptotically along two rays. As an example, the Frobenius manifold given by the quantum cohomology of CP2 is considered. The general PVI is also considered.10aPainleve' equations1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652601126nas a2200193 4500008004100000022001400041245013400055210006900189300001600258490000800274520044900282653002100731653001800752653003200770653001700802100002300819700001900842856007100861 2012 eng d a0022-039600aPositive periodic solutions of second order nonlinear equations with indefinite weight: Multiplicity results and complex dynamics0 aPositive periodic solutions of second order nonlinear equations a2922 - 29500 v2523 aWe prove the existence of a pair of positive T-periodic solutions as well as the existence of positive subharmonic solutions of any order and the presence of chaotic-like dynamics for the scalar second order ODEu″+aλ,μ(t)g(u)=0, where g(x) is a positive function on R+, superlinear at zero and sublinear at infinity, and aλ,μ(t) is a T-periodic and sign indefinite weight of the form λa+(t)−μa−(t), with λ,μ>0 and large.

10aComplex dynamics10aPoincaré map10aPositive periodic solutions10aSubharmonics1 aBoscaggin, Alberto1 aZanolin, Fabio uhttp://www.sciencedirect.com/science/article/pii/S002203961100388302201nas a2200133 4500008004100000245010400041210006900145260001900214520173100233100002401964700002201988700002102010856003602031 2012 en d00aPredicting and characterizing selective multiple drug treatments for metabolic diseases and cancer.0 aPredicting and characterizing selective multiple drug treatments bBioMed Central3 aBackground: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the overall network. Results: Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human metabolism.The results we obtain are consistent with some of the available therapeutic indications and predict some new multiple drug treatments.A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. Conclusion: The in silico prediction of drug synergism can represent an important tool for the repurposing of drug in a realistic perspective which considers also the selectivty of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, also drugs which show a too low efficacy but which have a non-common mechanism of action, can be reconsider as potential ingredients of new multicompound therapeutic indications.Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.1 aFacchetti, Giuseppe1 aAltafini, Claudio1 aZampieri, Mattia uhttp://hdl.handle.net/1963/651500295nas a2200097 4500008004100000245004400041210004100085100001700126700001900143856003500162 2011 eng d00aA planar bi-Lipschitz extension Theorem0 aplanar biLipschitz extension Theorem1 aDaneri, Sara1 aPratelli, Aldo uhttp://arxiv.org/abs/1110.612400420nas a2200109 4500008004300000245009100043210006900134260003400203653001700237100002000254856003600274 2011 en_Ud 00aPlanar loops with prescribed curvature: existence, multiplicity and uniqueness results0 aPlanar loops with prescribed curvature existence multiplicity an bAmerican Mathematical Society10aPlane curves1 aMusina, Roberta uhttp://hdl.handle.net/1963/384200961nas a2200121 4500008004300000245005200043210005100095260001300146520059700159100002200756700002500778856003600803 2011 en_Ud 00aPoincaré covariance and κ-Minkowski spacetime0 aPoincaré covariance and κMinkowski spacetime bElsevier3 aA fully Poincaré covariant model is constructed out of the k-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincaré group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincaré covariance is realised á la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of \\\"Poincaré covariance\\\".1 aDabrowski, Ludwik1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/389301388nas a2200157 4500008004300000245009200043210007000135260002200205300001200227490000800239520088500247100001601132700002201148700002401170856003601194 2011 en_Ud 00aPoincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces0 aPoincaré polynomial of moduli spaces of framed sheaves on stacky bSpringerc06/2011 a395-4090 v3043 aWe perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/373800741nas a2200121 4500008004100000245003700041210003700078260002100115520040400136100002200540700002100562856003600583 2011 en d00aProduct of real spectral triples0 aProduct of real spectral triples bWorld Scientific3 aWe construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.1 aDabrowski, Ludwik1 aDossena, Giacomo uhttp://hdl.handle.net/1963/551000842nas a2200109 4500008004300000245005800043210005600101260001300157520050500170100002100675856003600696 2011 en_Ud 00aA proof of Sudakov theorem with strictly convex norms0 aproof of Sudakov theorem with strictly convex norms bSpringer3 aWe establish a solution to the Monge problem in Rn, with an asymmetric, strictly convex norm cost function, when the initial measure is absolutely continuous. We focus on the strategy, based on disintegration of measures, initially proposed by Sudakov. As known, there is a gap to fill. The missing step is completed when the unit ball is strictly convex, but not necessarily differentiable nor uniformly convex. The key disintegration is achieved following a similar proof for a variational problem.1 aCaravenna, Laura uhttp://hdl.handle.net/1963/296700900nas a2200121 4500008004300000245014000043210007000183260001000253520044500263100001600708700001800724856003600742 2010 en_Ud 00aPainlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small-dispersion limit0 aPainlevé II asymptotics near the leading edge of the oscillatory bWiley3 aIn the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion for the Korteweg-de Vries solution near the leading edge of the oscillatory zone up to second order corrections. This expansion involves the Hastings-McLeod solution of the Painlev\\\\\\\'e II equation. We prove our results using the Riemann-Hilbert approach.1 aClaeys, Tom1 aGrava, Tamara uhttp://hdl.handle.net/1963/379900902nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856011000622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 aWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttps://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena00671nas a2200109 4500008004300000245005300043210005300096520033800149100001600487700002200503856003600525 2010 en_Ud 00aPicard group of hypersurfaces in toric varieties0 aPicard group of hypersurfaces in toric varieties3 aWe show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/410300784nas a2200097 4500008004300000245010500043210006900148520041300217100002000630856003600650 2010 en_Ud 00aPoles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis0 aPoles of Integrale Tritronquee and Anharmonic Oscillators Asympt3 aPoles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.

1 aMasoero, Davide uhttp://hdl.handle.net/1963/384100526nas a2200133 4500008004100000245007800041210007200119260001900191300001400210490000800224100002100232700001700253856012200270 2010 eng d00aPositive solutions for some non-autonomous Schrödinger–Poisson systems0 aPositive solutions for some nonautonomous Schrödinger–Poisson sy bAcademic Press a521–5430 v2481 aCerami, Giovanna1 aVaira, Giusi uhttps://www.math.sissa.it/publication/positive-solutions-some-non-autonomous-schr%C3%B6dinger%E2%80%93poisson-systems01299nas a2200109 4500008004300000245006000043210005600103520095600159100001701115700002101132856003601153 2010 en_Ud 00aProjective Reeds-Shepp car on $S^2$ with quadratic cost0 aProjective ReedsShepp car on S2 with quadratic cost3 aFix two points $x,\\\\bar{x}\\\\in S^2$ and two directions (without orientation) $\\\\eta,\\\\bar\\\\eta$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[\\\\gamma]=\\\\int_0^T g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t))+\\nK^2_{\\\\gamma(t)}g_{\\\\gamma(t)}(\\\\dot\\\\gamma(t),\\\\dot\\\\gamma(t)) ~dt$$ along all smooth curves starting from $x$ with direction $\\\\eta$ and ending in $\\\\bar{x}$ with direction $\\\\bar\\\\eta$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_\\\\gamma$ is the corresponding geodesic curvature.\\nThe interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1).\\nWe compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology.1 aBoscain, Ugo1 aRossi, Francesco uhttp://hdl.handle.net/1963/266800462nas a2200133 4500008004100000022001400041245008300055210007000138300001500208490000700223100001900230700001600249856006300265 2009 eng d a0022-248800aThe partition function of the two-matrix model as an isomonodromic τ function0 apartition function of the twomatrix model as an isomonodromic τ a013529, 170 v501 aBertola, Marco1 aMarchal, O. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1063/1.305486500666nas a2200157 4500008004100000022001300041245006000054210005700114300001200171490000600183520016900189100002400358700001400382700002200396856009000418 2008 eng d a1534039200aOn periodic elliptic equations with gradient dependence0 aperiodic elliptic equations with gradient dependence a601-6150 v73 aWe construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.1 aBerti, Massimiliano1 aMatzeu, M1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/periodic-elliptic-equations-gradient-dependence00618nas a2200133 4500008004100000245011000041210007000151260001300221300001400234490000700248520012200255100001900377856008800396 2008 eng d00aPositive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity0 aPositive solutions of nonlinear SchrödingerPoisson systems with bCiteseer a211–2270 v193 aWe deal with a weighted nonlinear Schr¨odinger-Poisson system, allowing the potentials to vanish at infinity.

1 aMercuri, Carlo uhttp://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.510.3635&rep=rep1&type=pdf00311nas a2200097 4500008004300000245005000043210005000093100001800143700001600161856003600177 2007 en_Ud 00aParametrized curves in Lagrange Grassmannians0 aParametrized curves in Lagrange Grassmannians1 aZelenko, Igor1 aChengbo, Li uhttp://hdl.handle.net/1963/256000408nas a2200097 4500008004100000245011900041210006900160260001000229100002300239856004800262 2007 en d00aPerturbation techniques applied to the real vanishing viscosity approximation of an initial boundary value problem0 aPerturbation techniques applied to the real vanishing viscosity bSISSA1 aBianchini, Stefano uhttp://preprints.sissa.it/handle/1963/3531500673nas a2200109 4500008004300000245005900043210005300102520033100155100002100486700002000507856003600527 2006 en_Ud 00aOn Palais-Smale sequences for H-systems: some examples0 aPalaisSmale sequences for Hsystems some examples3 aWe exhibit a series of examples of Palais-Smale sequences for the Dirichlet problem associated to the mean curvature equation with null boundary condition, and we show that in the case of nonconstant mean curvature functions different kinds of blow up phenomena appear and Palais-Smale sequences may have quite wild behaviour.1 aCaldiroli, Paolo1 aMusina, Roberta uhttp://hdl.handle.net/1963/215700479nas a2200133 4500008004100000022001400041245007300055210006800128300001200196490000600208100001900214700001500233856009700248 2006 eng d a1385-017200aThe PDEs of biorthogonal polynomials arising in the two-matrix model0 aPDEs of biorthogonal polynomials arising in the twomatrix model a23–520 v91 aBertola, Marco1 aEynard, B. uhttps://www.math.sissa.it/publication/pdes-biorthogonal-polynomials-arising-two-matrix-model00834nas a2200145 4500008004100000022001300041245010300054210006900157300001200226490000700238520027500245100001300520700002400533856013100557 2006 eng d a1120633000aPeriodic solutions of nonlinear wave equations for asymptotically full measure sets of frequencies0 aPeriodic solutions of nonlinear wave equations for asymptoticall a257-2770 v173 aWe prove existence and multiplicity of small amplitude periodic solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for asymptotically full measure sets of frequencies, extending the results of [7] to new types of nonlinearities.1 aBaldi, P1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/periodic-solutions-nonlinear-wave-equations-asymptotically-full-measure-sets-frequenci-000415nas a2200109 4500008004100000245008300041210006900124260003500193100002400228700001700252856003600269 2005 en d00aPeriodic solutions of nonlinear wave equations with non-monotone forcing terms0 aPeriodic solutions of nonlinear wave equations with nonmonotone bAccademia Nazionale dei Lincei1 aBerti, Massimiliano1 aBiasco, Luca uhttp://hdl.handle.net/1963/458100942nas a2200109 4500008004300000245005300043210005300096520060100149100002000750700002600770856003600796 2005 en_Ud 00aPrincipal fibrations from noncommutative spheres0 aPrincipal fibrations from noncommutative spheres3 aWe construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.1 aLandi, Giovanni1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/228401171nas a2200133 4500008004300000245008600043210006900129260003700198520070300235100002400938700001700962700002200979856003601001 2004 en_Ud 00aPeriodic orbits close to elliptic tori and applications to the three-body problem0 aPeriodic orbits close to elliptic tori and applications to the t bScuola Normale Superiore di Pisa3 aWe prove, under suitable non-resonance and non-degeneracy ``twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the ``planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.)1 aBerti, Massimiliano1 aBiasco, Luca1 aValdinoci, Enrico uhttp://hdl.handle.net/1963/298500793nas a2200109 4500008004300000245010200043210006900145260001300214520039800227100002200625856003600647 2003 en_Ud 00aParameter differentiation and quantum state decomposition for time varying Schrödinger equations0 aParameter differentiation and quantum state decomposition for ti bElsevier3 aFor the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301700524nas a2200145 4500008004100000022001400041245007400055210006900129300001600198490000700214100001900221700001500240700001500255856010800270 2003 eng d a0305-447000aPartition functions for matrix models and isomonodromic tau functions0 aPartition functions for matrix models and isomonodromic tau func a3067–30830 v361 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/partition-functions-matrix-models-and-isomonodromic-tau-functions00397nas a2200109 4500008004100000245007900041210006900120260001800189100002400207700002000231856003600251 2003 en d00aPeriodic solutions of nonlinear wave equations with general nonlinearities0 aPeriodic solutions of nonlinear wave equations with general nonl bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/164800961nas a2200109 4500008004300000245006400043210006200107260001000169520061500179100002100794856003600815 2003 en_Ud 00aPoisson Pencils, Integrability, and Separation of Variables0 aPoisson Pencils Integrability and Separation of Variables bSISSA3 aIn this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of pencil of Poisson brackets and on the bihamiltonian approach to integrable systems. We will discuss how separability conditions can be intrinsically characterized within such a geometrical set-up, the definition of the separation coordinates being encompassed in the \\\\bih structure itself. We finally discuss these constructions studying in details a particular example, based on a generalization of the classical Toda Lattice.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/302600551nas a2200121 4500008004100000245007300041210006900114260004800183520011800231100002400349700002000373856003600393 2003 en d00aPositive solutions to a class of quasilinear elliptic equations on R0 aPositive solutions to a class of quasilinear elliptic equations bAmerican Institute of Mathematical Sciences3 aWe discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on R.1 aAmbrosetti, Antonio1 aZhi-Qiang, Wang uhttp://hdl.handle.net/1963/162800736nas a2200133 4500008004300000245008800043210006900131260001300200520028300213100002000496700002200516700002800538856003600566 2003 en_Ud 00aPrescribing scalar and boundary mean curvature on the three dimensional half sphere0 aPrescribing scalar and boundary mean curvature on the three dime bSpringer3 aWe consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results.1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/308600481nas a2200121 4500008004300000245011600043210006900159260003000228100002000258700002400278700002100302856003600323 2002 en_Ud 00aThe passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case0 apassage from nonconvex discrete systems to variational problems bMAIK Nauka/Interperiodica1 aBraides, Andrea1 aGelli, Maria Stella1 aSigalotti, Mario uhttp://hdl.handle.net/1963/313000365nas a2200109 4500008004100000245006500041210005500106260001800161100002100179700001900200856003600219 2002 en d00aOn a Poisson reduction for Gel\\\'fand-Zakharevich manifolds0 aPoisson reduction for GelfandZakharevich manifolds bSISSA Library1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/160200461nas a2200121 4500008004100000245010500041210006900146260001800215100002000233700002800253700002200281856003600303 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aAhmedou, Mohameden Ould1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/153900474nas a2200121 4500008004100000245011800041210006900159260001800228100002000246700002200266700002800288856003600316 2002 en d00aPrescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications0 aPrescribing a fourth oder conformal invariant on the standard sp bSISSA Library1 aDjadli, Zindine1 aMalchiodi, Andrea1 aAhmedou, Mohameden Ould uhttp://hdl.handle.net/1963/154001274nas a2200109 4500008004300000245006000043210006000103260001300163520093200176100002001108856003601128 2001 en_Ud 00aPicard and Chazy solutions to the Painlevé VI equation0 aPicard and Chazy solutions to the Painlevé VI equation bSpringer3 aI study the solutions of a particular family of Painlevé VI equations with the parameters $\beta=\gamma=0, \delta=1/2$ and $2\alpha=(2\mu-1)^2$, for $2\mu\in\mathbb{Z}$. I show that the case of half-integer $\mu$ is integrable and that the solutions are of two types: the so-called Picard solutions and the so-called Chazy solutions. I give explicit formulae for them and completely determine their asymptotic behaviour near the singular points $0,1,\infty$ and their nonlinear monodromy. I study the structure of analytic continuation of the solutions to the PVI$\mu$ equation for any $\mu$ such that $2\mu\in\mathbb{Z}$. As an application, I classify all the algebraic solutions. For $\mu$ half-integer, I show that they are in one to one correspondence with regular polygons or star-polygons in the plane. For $\mu$ integer, I show that all algebraic solutions belong to a one-parameter family of rational solutions.

1 aMazzocco, Marta uhttp://hdl.handle.net/1963/311800974nas a2200121 4500008004300000245004200043210004200085260001300127520063300140100002500773700001800798856003600816 2000 en_Ud 00aPrincipal invariants of Jacobi curves0 aPrincipal invariants of Jacobi curves bSpringer3 aJacobi curves are far going generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. Differential geometry of these curves provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. In the present paper we mainly discuss two principal invariants: the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmanian providing the curve with a natural projective structure, and a fundamental form, which is a 4-oder differential on the curve.1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/382500382nas a2200109 4500008004300000020001800043245007200061210007000133260001300203100002000216856003600236 1999 en_Ud a0-387-98888-200aPainlevé transcendents in two-dimensional topological field theory0 aPainlevé transcendents in twodimensional topological field theor bSpringer1 aDubrovin, Boris uhttp://hdl.handle.net/1963/323800698nas a2200133 4500008004300000245010800043210006900151260001300220520022700233100002400460700002600484700001800510856003600528 1999 en_Ud 00aPerturbation of $\Delta u+u^{(N+2)/(N-2)}=0$, the scalar curvature problem in $R^N$, and related topics0 aPerturbation of Delta uu N2N2 0 the scalar curvature problem in bElsevier3 aSome nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

1 aAmbrosetti, Antonio1 aGarcia Azorero, Jesus1 aPeral, Ireneo uhttp://hdl.handle.net/1963/325500367nas a2200109 4500008004100000245006100041210006100102260001800163100001700181700002300198856003600221 1999 en d00aProjection singularities of extremals for planar systems0 aProjection singularities of extremals for planar systems bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/130400407nas a2200121 4500008004100000245006300041210006000104260001800164100002100182700001900203700002800222856003500250 1989 en d00aA pointwise regularity theory for the two-obstacle problem0 apointwise regularity theory for the twoobstacle problem bSISSA Library1 aDal Maso, Gianni1 aMosco, Umberto1 aVivaldi, Maria Agostina uhttp://hdl.handle.net/1963/643