In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters. Dealing with geometrical parameters, especially in the industrial context, this relation may be unknown and not trivial (simulations over hand morphed geometries) or very complex (high number of parameters or many nested morphing techniques). To overcome these scenarios, we propose in this contribution an efficient and complete data-driven framework involving ROM techniques for shape design and optimization, extending the pipeline presented in [7]. By applying the singular value decomposition (SVD) to the points coordinates defining the hull geometry –- assuming the topology is inaltered by the deformation –-, we are able to compute the optimal space which the deformed geometries belong to, hence using the modal coefficients as the new parameters we can reconstruct the parametric formulation of the domain. Finally the output of interest is approximated using the proper orthogonal decomposition with interpolation technique. To conclude, we apply this framework to a naval shape design problem where the bulbous bow is morphed to reduce the total resistance of the ship advancing in calm water.

1 aDemo, Nicola1 aTezzele, Marco1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1905.0598200896nas a2200109 4500008004100000245008200041210006900123260001000192520051200202100001800714856005400732 2019 en d00aA continuous dependence result for a dynamic debonding model in dimension one0 acontinuous dependence result for a dynamic debonding model in di bSISSA3 aIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3532900307nas a2200085 4500008004100000245006200041210006200103100001900165856003700184 2018 eng d00aCanonical Surfaces and Hypersurfaces in Abelian Varieties0 aCanonical Surfaces and Hypersurfaces in Abelian Varieties1 aCesarano, Luca uhttps://arxiv.org/abs/1808.0530200682nas a2200121 4500008004100000245007400041210006600115260001000181520028100191100002100472700001900493856004800512 2018 en d00aOn the Cauchy problem for the wave equation on time-dependent domains0 aCauchy problem for the wave equation on timedependent domains bSISSA3 aWe introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness.1 aDal Maso, Gianni1 aToader, Rodica uhttp://preprints.sissa.it/handle/1963/3531400586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96401398nas a2200121 4500008004100000245014300041210006900184260001000253520092300263100002301186700001901209856004801228 2018 en d00aCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations0 aCharacteristic boundary layers for mixed hyperbolic systems in o bSISSA3 aWe provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.1 aBianchini, Stefano1 aSpinolo, Laura uhttp://preprints.sissa.it/handle/1963/3532501651nas a2200145 4500008004100000245009700041210006900138300001400207490000700221520116600228100001901394700002401413700002201437856004601459 2018 eng d00aCohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue0 aCohesive fracture with irreversibility Quasistatic evolution for a1371-14120 v283 aIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

1 aCrismale, Vito1 aLazzaroni, Giuliano1 aOrlando, Gianluca uhttps://doi.org/10.1142/S021820251850037900587nas a2200133 4500008004100000245012400041210006900165260001300234300001400247100001900261700002400280700002100304856012800325 2018 eng d00aCombined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods0 aCombined parameter and model reduction of cardiovascular problem bSpringer a185–2071 aTezzele, Marco1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/combined-parameter-and-model-reduction-cardiovascular-problems-means-active-subspaces00556nas a2200121 4500008004100000245010600041210006900147260002000216100002200236700002400258700002300282856012900305 2018 eng d00aA Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials0 aComparison Between Active Strain and Active Stress in Transverse bSpringer Nature1 aGiantesio, Giulia1 aMusesti, Alessandro1 aRiccobelli, Davide uhttps://www.math.sissa.it/publication/comparison-between-active-strain-and-active-stress-transversely-isotropic-hyperelastic01813nas a2200205 4500008004100000245005400041210005400095260001400149300000700163520117300170100002601343700001901369700002001388700002101408700002201429700002101451700002601472700002501498856008401523 2018 eng d00aComputational methods in cardiovascular mechanics0 aComputational methods in cardiovascular mechanics bCRC Press a543 aThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

1 aAuricchio, Ferdinando1 aConti, Michele1 aLefieux, Adrian1 aMorganti, Simone1 aReali, Alessandro1 aRozza, Gianluigi1 aVeneziani, Alessandro1 aLabrosse, Michel, F. uhttps://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-500773nas a2200097 4500008004100000245007100041210006000112520043500172100002000607856004800627 2018 en d00aOn the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)0 acontinuity of the trace operator in GSBV Ω and GSBD Ω3 aIn this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.1 aTasso, Emanuele uhttp://preprints.sissa.it/handle/1963/3532402454nas a2200169 4500008004100000020002200041024003400063245010200097210006900199250004300268260002500311490000900336520177800345100001802123700002102141856012202162 2017 eng d a978-3-319-65869-8 aDOI 10.1007/978-3-319-65870-400aCertified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation0 aCerti fied Reduced Basis Method for Affinely Parametric Isogeome aBittencourt, Dumont, Hesthaven. (Eds). aHeildebergbSpringer0 v 1193 aIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization

of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis

(IGA) is a growing research theme in scientic computing and computational mechanics, as well as reduced

basis methods for parametric PDEs. Their combination enhances the solution of some class of problems,

especially the ones characterized by parametrized geometries we introduced in this work. For a general

overview on Reduced Basis (RB) methods we recall [7, 15] and on IGA [3]. This work wants to demonstrate

that it is also possible for some class of problems to deal with ane geometrical parametrization combined

with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other

works dealing with reduced order methods and IGA (set in a non-affine formulation, and using a POD [2]

sampling without certication: see for example for potential flows [12] and for Stokes flows [17]). In this work

we show a certication of accuracy and a complete integration between IGA formulation and parametric

certified greedy RB formulation. Section 2 recalls the abstract setting for parametrized PDEs, Section 3

recalls IGA setting, Section 4 deals with RB formulation, and Section 5 illustrates two numerical examples in heat transfer with different parametrization.

1 aDevaud, Denis1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/certi-fied-reduced-basis-method-affinely-parametric-isogeometric-analysis-nurbs00579nas a2200157 4500008004100000245006200041210005700103300001400160490000700174100001800181700001700199700001700216700002400233700002100257856014300278 2017 eng d00aOn a certified smagorinsky reduced basis turbulence model0 acertified smagorinsky reduced basis turbulence model a3047-30670 v551 aRebollo, T.C.1 aÁvila, E.D.1 aMarmol, M.G.1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c01188nas a2200181 4500008004100000022001400041245007200055210007100127300001600198490000800214520059300222653002900815653001900844653003300863653002100896100001800917856007100935 2017 eng d a0022-039600aClifford Tori and the singularly perturbed Cahn–Hilliard equation0 aClifford Tori and the singularly perturbed Cahn–Hilliard equatio a5306 - 53620 v2623 aIn this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

10aCahn–Hilliard equation10aClifford Torus10aLyapunov–Schmidt reduction10aWillmore surface1 aRizzi, Matteo uhttp://www.sciencedirect.com/science/article/pii/S002203961730053001282nas a2200133 4500008004100000245004800041210004800089520088200137100002001019700002301039700001801062700001701080856005101097 2017 en d00aComplex Friedrichs systems and applications0 aComplex Friedrichs systems and applications3 aWe provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper.1 aAntonić, Nenad1 aBurazin, Krešimir1 aCrnjac, Ivana1 aErceg, Marko uhttp://urania.sissa.it/xmlui/handle/1963/3527002413nas a2200205 4500008004100000245015800041210006900199260001200268300000800280490000800288520159500296653004301891653002501934653002301959653003401982100002102016700002102037700002102058856012802079 2017 eng d00aComputational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology0 aComputational reduction strategies for the detection of steady b c09/2017 a5570 v3443 aWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

We present a novel quasi-Newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena. We perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes. Moreover, we discuss the conditions that, on a theoretical level, guarantee the convergence of this method. At each iterative step, a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess. Discretization performs through cell-centered finite differences. The resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi-grid techniques. The final code achieves three-dimensional, realistic computer experiments comparable to those produced in laboratory settings. This code offers not only new insights into the phenomenology of super-hydrophobicity, but also serves as a reliable predictive tool for the study of hydrophobic surfaces.

10aMultigrid10aPhase field10aQuasi-Newton10aSuper-hydrophobicity1 aFedeli, Livio uhttp://www.sciencedirect.com/science/article/pii/S002199911730356X00871nas a2200109 4500008004100000245005900041210005600100520051100156100001700667700002900684856004800713 2017 en d00aOn contact interactions realised as Friedrichs systems0 acontact interactions realised as Friedrichs systems3 aWe realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems.1 aErceg, Marko1 aMichelangeli, Alessandro uhttp://preprints.sissa.it/handle/1963/3529801069nas a2200181 4500008004100000022001400041245011100055210006900166300001400235490000800249520044900257653001400706653003100720653002700751100002100778700001700799856007100816 2017 eng d a0362-546X00aCurvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators0 aCurvature terms in small time heat kernel expansion for a model a118 - 1340 v1643 aWe consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

10aCurvature10aHypoelliptic heat equation10aSmall time asymptotics1 aBarilari, Davide1 aPaoli, Elisa uhttp://www.sciencedirect.com/science/article/pii/S0362546X1730229800424nas a2200145 4500008004100000245005000041210004700091260002500138300001400163490000700177100001800184700001700202700001300219856004600232 2017 eng d00aCurvature-adapted remeshing of {CAD} surfaces0 aCurvatureadapted remeshing of CAD surfaces bSpringer Naturecdec a565–5760 v341 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1007/s00366-017-0558-200449nas a2200085 4500008004100000245010400041210006900145100002000214856012900234 2016 eng d00aCoalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers0 aCoalescence Phenomenon of Quantum Cohomology of Grassmannians an1 aCotti, Giordano uhttps://www.math.sissa.it/publication/coalescence-phenomenon-quantum-cohomology-grassmannians-and-distribution-prime-numbers00889nas a2200169 4500008004100000022001400041245004700055210004600102260000800148300000800156490000900164520044700173100001600620700001900636700002000655856004400675 2016 eng d a1029-847900aComparing Poisson Sigma Model with A-model0 aComparing Poisson Sigma Model with Amodel cOct a1330 v20163 aWe discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

1 aBonechi, F.1 aCattaneo, A.S.1 aIraso, Riccardo uhttps://doi.org/10.1007/JHEP10(2016)13300926nas a2200205 4500008004100000022001400041245006500055210005800120300000700178490000600185520030900191653001800500653002200518653002200540653003000562653001100592100002300603700001800626856007600644 2016 eng d a1937-163200aOn the concentration of entropy for scalar conservation laws0 aconcentration of entropy for scalar conservation laws a730 v93 aWe prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

10aconcentration10aConservation laws10aentropy solutions10aLagrangian representation10ashocks1 aBianchini, Stefano1 aMarconi, Elio uhttp://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae01304nas a2200133 4500008004100000245008300041210006900124520084400193100002201037700002201059700002001081700001801101856005101119 2016 en d00aConfinement of dislocations inside a crystal with a prescribed external strain0 aConfinement of dislocations inside a crystal with a prescribed e3 aWe study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.1 aLucardesi, Ilaria1 aMorandotti, Marco1 aScala, Riccardo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3524700867nas a2200145 4500008004100000022001400041245006500055210006500120260000800185300001400193490000700207520043700214100002400651856004600675 2016 eng d a1573-869800aConformal Equivalence of 3D Contact Structures on Lie Groups0 aConformal Equivalence of 3D Contact Structures on Lie Groups cApr a251–2830 v223 aIn this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

1 aBoarotto, Francesco uhttps://doi.org/10.1007/s10883-015-9273-801478nas a2200169 4500008004100000022001400041245008500055210006900140260000800209300001200217490000700229520096100236100002301197700002101220700002101241856004601262 2016 eng d a1424-066100aConstruction of Real-Valued Localized Composite Wannier Functions for Insulators0 aConstruction of RealValued Localized Composite Wannier Functions cJan a63–970 v173 aWe consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

1 aFiorenza, Domenico1 aMonaco, Domenico1 aPanati, Gianluca uhttps://doi.org/10.1007/s00023-015-0400-600506nas a2200145 4500008004100000022001400041245011400055210006900169300001200238490000800250100001900258700002000277700001300297856005000310 2016 eng d a0167-278900aCorrelation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$0 aCorrelation functions of the KdV hierarchy and applications to i a30–570 v3271 aBertola, Marco1 aDubrovin, Boris1 aYang, Di uhttp://dx.doi.org/10.1016/j.physd.2016.04.00800358nas a2200097 4500008004100000245008800041210006900129260000700198100001900205856003600224 2016 eng d00aCORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function0 aCORRIGENDUM The dependence on the monodromy data of the isomonod c011 aBertola, Marco uhttp://arxiv.org/abs/1601.0479000357nas a2200085 4500008004100000245006000041210005900101100001800160856009300178 2016 eng d00aCritical points of a perturbed Otha-Kawasaki functional0 aCritical points of a perturbed OthaKawasaki functional1 aRizzi, Matteo uhttps://www.math.sissa.it/publication/critical-points-perturbed-otha-kawasaki-functional01884nas a2200145 4500008004100000245005300041210005300094260003400147300001100181490000700192520140800199100002001607700002501627856008601652 2016 eng d00aCurrents and dislocations at the continuum scale0 aCurrents and dislocations at the continuum scale bInternational Press of Boston a1–340 v233 aA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://www.math.sissa.it/publication/currents-and-dislocations-continuum-scale-001368nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011801020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttps://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations01837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3446901802nas a2200229 4500008004100000245010400041210006900145300001400214490000700228520107100235653001001306653001001316653002901326653001501355653002001370653002501390653001801415100003301433700002001466700002501486856006101511 2015 eng d00aA compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity0 acompatibleincompatible decomposition of symmetric tensors in Lp a5217-52300 v383 aIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

10a35J5810a35Q7410acompatibility conditions10aelasticity10aKorn inequality10astrain decomposition10asubclass74B051 aMaggiani, Giovanni, Battista1 aScala, Riccardo1 aVan Goethem, Nicolas uhttps://onlinelibrary.wiley.com/doi/abs/10.1002/mma.345001202nas a2200133 4500008004100000245004900041210004800090300001200138490000700150520084200157100001300999700001801012856003801030 2015 eng d00aComplexity of Control-Affine Motion Planning0 aComplexity of ControlAffine Motion Planning a816-8440 v533 aIn this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

1 aJean, F.1 aPrandi, Dario uhttps://doi.org/10.1137/13095079301209nas a2200121 4500008004300000245007700043210006900120520072500189100001900914700002500933700002200958856010700980 2015 en_Ud 00aConstrained BV functions on double coverings for Plateau's type problems0 aConstrained BV functions on double coverings for Plateaus type p3 aWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

1 aAmato, Stefano1 aBellettini, Giovanni1 aPaolini, Maurizio uhttps://www.math.sissa.it/publication/constrained-bv-functions-double-coverings-plateaus-type-problems00336nas a2200097 4500008004100000245004100041210004100082100002000123700002300143856007200166 2015 eng d00aConvergence rate of the Glimm scheme0 aConvergence rate of the Glimm scheme1 aModena, Stefano1 aBianchini, Stefano uhttps://www.math.sissa.it/publication/convergence-rate-glimm-scheme01185nas a2200121 4500008004100000245008500041210006900126260001000195520076800205100002100973700001800994856005101012 2015 en d00aConvex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets0 aConvex combinations of low eigenvalues Fraenkel asymmetries and bSISSA3 aWe consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure.1 aMazzoleni, Dario1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514000469nas a2200145 4500008004100000022001400041245007300055210006900128300001400197490000800211100001900219700001700238700002000255856004800275 2014 eng d a0010-361600aCauchy-Laguerre two-matrix model and the Meijer-G random point field0 aCauchyLaguerre twomatrix model and the MeijerG random point fiel a111–1440 v3261 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://dx.doi.org/10.1007/s00220-013-1833-801294nas a2200133 4500008004100000245010400041210006900145260001000214520083900224100002101063700002001084700002001104856003601124 2014 en d00aClassical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents0 aClassical Walgebras and generalized DrinfeldSokolov hierarchies bSISSA3 aWe derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697902162nas a2200133 4500008004100000245009400041210006900135260001300204520170200217100001501919700002201934700002101956856005101977 2014 en d00aComparison between reduced basis and stochastic collocation methods for elliptic problems0 aComparison between reduced basis and stochastic collocation meth bSpringer3 aThe stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.1 aChen, Peng1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3472702011nas a2200241 4500008004100000245013600041210006900177260002200246300000800268490000700276520123100283100002101514700001901535700001901554700001901573700001701592700002701609700002001636700002301656700002101679700001801700856005101718 2014 en d00aComparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics0 aComparison of a Modal Method and a Proper Orthogonal Decompositi bElsevierc09/2014 a2290 v713 aIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

1 aSartori, Alberto1 aBaroli, Davide1 aCammi, Antonio1 aChiesa, Davide1 aLuzzi, Lelio1 aPonciroli, Roberto, R.1 aPrevitali, Ezio1 aRicotti, Marco, E.1 aRozza, Gianluigi1 aSisti, Monica uhttp://urania.sissa.it/xmlui/handle/1963/3503901580nas a2200157 4500008004100000245009300041210006900134260002800203520103900231100001901270700001901289700002101308700002001329700002201349856005101371 2014 en d00aConformal invariants from nodal sets. I. negative eigenvalues and curvature prescription0 aConformal invariants from nodal sets I negative eigenvalues and bOxford University Press3 aIn this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.1 aGover, Rod, R.1 aCanzani, Yaiza1 aJakobson, Dmitry1 aPonge, Raphaël1 aMalchiodi, Andrea uhttp://urania.sissa.it/xmlui/handle/1963/3512801122nas a2200145 4500008004100000245005400041210005100095260001300146520066000159653006000819100002500879700001600904700002000920856003600940 2014 en d00aOn conjugate times of LQ optimal control problems0 aconjugate times of LQ optimal control problems bSpringer3 aMotivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$.10aOptimal control, Lagrange Grassmannian, Conjugate point1 aAgrachev, Andrei, A.1 aRizzi, Luca1 aSilveira, Pavel uhttp://hdl.handle.net/1963/722700720nas a2200109 4500008004100000245007700041210006900118260003100187520031700218100002400535856005100559 2014 en d00aA correction and an extension of Stampacchia's work on the geometric BVP0 acorrection and an extension of Stampacchias work on the geometri bAdvanced Nonlinear Studies3 aG. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results.1 aVidossich, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3502301733nas a2200217 4500008004100000022001400041245003700055210003700092300001200129490000700141520111900148653002901267653001901296653002201315653002501337653002001362100001801382700002201400700002201422856007101444 2014 eng d a0020-746200aCrawling on directional surfaces0 aCrawling on directional surfaces a65 - 730 v613 aIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

10aBio-mimetic micro-robots10aCell migration10aCrawling motility10aDirectional surfaces10aSelf-propulsion1 aGidoni, Paolo1 aNoselli, Giovanni1 aDeSimone, Antonio uhttp://www.sciencedirect.com/science/article/pii/S002074621400021301111nas a2200121 4500008004100000245006400041210006300105260003400168520070800202100002200910700002100932856003600953 2014 en d00aCritical points of the Moser-Trudinger functional on a disk0 aCritical points of the MoserTrudinger functional on a disk bEuropean Mathematical Society3 aOn the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/656001220nas a2200121 4500008004100000245009100041210006900132260001000201520080700211653002801018100001601046856003601062 2014 en d00aThe curvature of optimal control problems with applications to sub-Riemannian geometry0 acurvature of optimal control problems with applications to subRi bSISSA3 aOptimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated.10aSub-Riemannian geometry1 aRizzi, Luca uhttp://hdl.handle.net/1963/732101482nas a2200157 4500008004100000245004800041210004700089260001300136300001400149490000700163520105700170100001801227700001701245700001301262856004901275 2014 en d00aCurvature-adapted remeshing of CAD surfaces0 aCurvatureadapted remeshing of CAD surfaces bElsevier a253–2650 v823 aA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

1 aDassi, Franco1 aMola, Andrea1 aSi, Hang uhttps://doi.org/10.1016/j.proeng.2014.10.38801065nas a2200133 4500008004100000245012700041210006900168260001300237520058400250100002100834700002000855700002000875856003600895 2013 en d00aClassical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras0 aClassical Walgebras and generalized DrinfeldSokolov biHamiltonia bSpringer3 aWe provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/697801890nas a2200145 4500008004100000245011800041210006900159260001300228520137300241653003501614100001801649700002001667700002101687856003601708 2013 en d00aA combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices0 acombination between the reduced basis method and the ANOVA expan bElsevier3 aWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

10aPartial differential equations1 aDevaud, Denis1 aManzoni, Andrea1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/738901565nas a2200169 4500008004100000245010100041210006900142260001000211520092400221100002201145700002401167700002201191700001701213700001901230700002201249856012401271 2013 en d00aCommon dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons.0 aCommon dynamical features of sensory adaptation in photoreceptor bSISSA3 aSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

1 aDe Palo, Giovanna1 aFacchetti, Giuseppe1 aMazzolini, Monica1 aMenini, Anna1 aTorre, Vincent1 aAltafini, Claudio uhttps://www.math.sissa.it/publication/common-dynamical-features-sensory-adaptation-photoreceptors-and-olfactory-sensory01080nas a2200169 4500008004100000022001400041245009400055210006900149300001200218490000800230520048300238653003400721653002000755653004300775100002100818856007100839 2013 eng d a0022-039600aConcentration of solutions for a singularly perturbed mixed problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed mixed prob a30 - 660 v2543 aWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

10aFinite-dimensional reductions10aLocal inversion10aSingularly perturbed elliptic problems1 aDipierro, Serena uhttp://www.sciencedirect.com/science/article/pii/S002203961200331200887nas a2200145 4500008004100000022001400041245006300055210005800118260000800176300001400184490000700198520047000205100002000675856004600695 2013 eng d a1559-002X00aThe Conformal Willmore Functional: A Perturbative Approach0 aConformal Willmore Functional A Perturbative Approach cApr a764–8110 v233 aThe conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

1 aMondino, Andrea uhttps://doi.org/10.1007/s12220-011-9263-300784nas a2200121 4500008004100000245005400041210005300095260001300148520042200161100002100583700002200604856003600626 2013 en d00aConnected Sum Construction for σk-Yamabe Metrics0 aConnected Sum Construction for σkYamabe Metrics bSpringer3 aIn this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation.1 aCatino, Giovanni1 aMazzieri, Lorenzo uhttp://hdl.handle.net/1963/644101071nas a2200145 4500008004100000245006700041210006600108260001300174520054900187100002200736700002400758700002200782700002000804856010100824 2013 en d00aCrawlers in viscous environments: linear vs nonlinear rheology0 aCrawlers in viscous environments linear vs nonlinear rheology bElsevier3 aWe study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.1 aDeSimone, Antonio1 aGuarnieri, Federica1 aNoselli, Giovanni1 aTatone, Amabile uhttps://www.math.sissa.it/publication/crawlers-viscous-environments-linear-vs-nonlinear-rheology01219nas a2200145 4500008004100000245008300041210006900124260001000193520068100203100002000884700001800904700002100922700001800943856011200961 2013 en d00aOn critical behaviour in systems of Hamiltonian partial differential equations0 acritical behaviour in systems of Hamiltonian partial differentia bSISSA3 aWe study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian1 aMoro, Antonio uhttps://www.math.sissa.it/publication/critical-behaviour-systems-hamiltonian-partial-differential-equations01043nas a2200145 4500008004100000245004200041210003700083260001000120520060700130653006200737100002500799700002100824700001600845856003600861 2013 en d00aThe curvature: a variational approach0 acurvature a variational approach bSISSA3 aThe curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.10aCrurvature, subriemannian metric, optimal control problem1 aAgrachev, Andrei, A.1 aBarilari, Davide1 aRizzi, Luca uhttp://hdl.handle.net/1963/722600967nas a2200133 4500008004100000245005000041210004800091260003400139520056900173653001300742100002200755700002000777856003600797 2013 en d00aCurved noncommutative torus and Gauss--Bonnet0 aCurved noncommutative torus and GaussBonnet bAmerican Institute of Physics3 aWe study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.10aGeometry1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/737601113nas a2200145 4500008004100000245009600041210006900137260001300206300001200219490000700231520057100238100002000809700002400829856011400853 2012 en d00aOn a class of vector fields with discontinuity of divide-by-zero type and its applications0 aclass of vector fields with discontinuity of dividebyzero type a bSpringer a135-1580 v183 aWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

1 aGhezzi, Roberta1 aRemizov, Alexey, O. uhttps://www.math.sissa.it/publication/class-vector-fields-discontinuity-divide-zero-type-and-its-applications01113nas a2200121 4500008004100000245008000041210006900121260001000190520071100200100002000911700002400931856003600955 2012 en d00aClassical double, R-operators, and negative flows of integrable hierarchies0 aClassical double Roperators and negative flows of integrable hie bSISSA3 aUsing the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations.1 aDubrovin, Boris1 aSkrypnyk, Taras, V. uhttp://hdl.handle.net/1963/646801152nas a2200145 4500008004100000245009700041210006900138260001000207520067600217100002200893700001500915700002000930700002000950856003600970 2012 en d00aA Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.0 aCodazzilike equation and the singular set for C1 smooth surfaces bSISSA3 aIn this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 11 aMalchiodi, Andrea1 aYang, Paul1 aCheng, Jih-Hsin1 aHwang, JennFang uhttp://hdl.handle.net/1963/655600824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644500854nas a2200157 4500008004100000245012200041210007200163260002100235300001200256490000700268520031300275100002000588700002300608700001900631856004600650 2012 eng d00aConcentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity0 aConcentration on circles for nonlinear Schrödinger–Poisson syste bWorld Scientific a12500090 v143 aThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

1 aBonheure, Denis1 aDi Cosmo, Jonathan1 aMercuri, Carlo uhttps://doi.org/10.1142/S021919971250009501031nas a2200133 4500008004100000245009200041210006900133260002100202300001400223490000700237520058100244100002300825856004900848 2012 eng d00aConservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids0 aConservation of Geometric Structures for NonHomogeneous Inviscid bTaylor & Francis a1553-15950 v373 aIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

1 aFanelli, Francesco uhttps://doi.org/10.1080/03605302.2012.69834300925nas a2200121 4500008004100000245010900041210006900150260001300219520049100232100002500723700001900748856003600767 2012 en d00aConvergence of equilibria of thin elastic plates under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic plates under physical bElsevier3 aThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

1 aMora, Maria Giovanna1 aScardia, Lucia uhttp://hdl.handle.net/1963/346601015nas a2200109 4500008004100000245004300041210004300084260001300127520070800140100002100848856003600869 2012 en d00aConvex pencils of real quadratic forms0 aConvex pencils of real quadratic forms bSpringer3 aWe study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2).1 aLerario, Antonio uhttp://hdl.handle.net/1963/709901915nas a2200121 4500008004100000245008100041210006900122260001300191520151100204100002201715700002001737856003601757 2012 en d00aCrawling motility through the analysis of model locomotors: two case studies0 aCrawling motility through the analysis of model locomotors two c bSpringer3 aWe study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.1 aDeSimone, Antonio1 aTatone, Amabile uhttp://hdl.handle.net/1963/701700864nas a2200121 4500008004100000245008100041210006900122260001000191520046700201100002000668700001800688856003600706 2012 en d00aOn the critical behavior in nonlinear evolutionary PDEs with small viscocity0 acritical behavior in nonlinear evolutionary PDEs with small visc bSISSA3 aWe address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically.1 aDubrovin, Boris1 aElaeva, Maria uhttp://hdl.handle.net/1963/646500981nas a2200121 4500008004100000245006900041210006700110260001300177520058600190100002500776700002200801856003600823 2011 en d00aA class of existence results for the singular Liouville equation0 aclass of existence results for the singular Liouville equation bElsevier3 aWe consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional.1 aCarlotto, Alessandro1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/579300505nas a2200133 4500008004100000245010600041210007000147260004400217300001400261490000700275100001600282700001700298856005600315 2011 eng d00aCluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential0 aCluster solutions for the SchrödingerPoissonSlater problem aroun bReal Sociedad Matemática Españolac01 a253–2710 v271 aRuiz, David1 aVaira, Giusi uhttps://projecteuclid.org:443/euclid.rmi/129682883400613nas a2200097 4500008004100000245003000041210003000071520034600101100002000447856004800467 2011 en d00aCompactness by maximality0 aCompactness by maximality3 aWe derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.1 aZagatti, Sandro uhttp://preprints.sissa.it/handle/1963/3531701286nas a2200145 4500008004100000245007900041210006900120260003300189520078400222653003101006100002401037700002101061700002201082856003601104 2011 en d00aComputing global structural balance in large-scale signed social networks.0 aComputing global structural balance in largescale signed social bNational Academy of Sciences3 aStructural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\"10aCombinatorial optimization1 aFacchetti, Giuseppe1 aIacono, Giovanni1 aAltafini, Claudio uhttp://hdl.handle.net/1963/642600435nas a2200121 4500008004100000245009600041210006900137260001300206300001200219490000700231100002100238856005400259 2011 eng d00aConcentration of solutions for a singularly perturbed Neumann problem in non-smooth domains0 aConcentration of solutions for a singularly perturbed Neumann pr bElsevier a107-1260 v281 aDipierro, Serena uhttp://www.numdam.org/item/AIHPC_2011__28_1_107_001012nas a2200169 4500008004100000245005500041210005400096260006700150520046800217653002100685100002400706700002400730700002000754700001900774700001300793856003600806 2011 en d00aCones of divisors of blow-ups of projective spaces0 aCones of divisors of blowups of projective spaces bUniversità degli Studi di Catania. Dipartimento di matematica3 aWe investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.10aMori dream space1 aLo Giudice, Alessio1 aCacciola, Salvatore1 aDonten-Bury, M.1 aDumitrescu, O.1 aPark, J. uhttp://hdl.handle.net/1963/661300920nas a2200133 4500008004100000245005100041210005100092260007200143520047100215100002100686700002100707700002200728856003600750 2011 en d00aCovered by lines and Conic connected varieties0 aCovered by lines and Conic connected varieties bUniversita\\\' di Catania, Dipartimento di Matematica e Informatica3 aWe study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak.1 aMarchesi, Simone1 aMassarenti, Alex1 aTafazolian, Saeed uhttp://hdl.handle.net/1963/578800974nas a2200121 4500008004300000245009300043210006900136260004800205520051800253100002100771700002400792856003600816 2011 en_Ud 00aCrack growth with non-interpenetration : a simplified proof for the pure Neumann problem0 aCrack growth with noninterpenetration a simplified proof for the bAmerican Institute of Mathematical Sciences3 aWe present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/380100934nas a2200133 4500008004100000245007900041210006900120260001000189520050600199100002200705700001800727700001900745856003600764 2011 en d00aCrepant resolutions of weighted projective spaces and quantum deformations0 aCrepant resolutions of weighted projective spaces and quantum de bSISSA3 aWe compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity.1 aBoissiere, Samuel1 aMann, Etienne1 aPerroni, Fabio uhttp://hdl.handle.net/1963/651400428nas a2200133 4500008004100000245005400041210005300095260001000148653003100158100002600189700002200215700002100237856003600258 2011 en d00aCritical points of the Moser-Trudinger functional0 aCritical points of the MoserTrudinger functional bSISSA10aMoser-Trudinger inequality1 aDe Marchis, Francesca1 aMalchiodi, Andrea1 aMartinazzi, Luca uhttp://hdl.handle.net/1963/459200524nas a2200133 4500008004100000245012600041210006900167260003300236100002000269700002100289700002200310700002200332856003600354 2011 en d00aCytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions0 aCytoskeletal actin networks in motile cells are critically selfo bNational Academy of Sciences1 aCardamone, Luca1 aLaio, Alessandro1 aShahapure, Rajesh1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/435801351nas a2200109 4500008004300000245003600043210003500079520104400114100002501158700002201183856003601205 2010 en_Ud 00aCanonical k-Minkowski Spacetime0 aCanonical kMinkowski Spacetime3 aA complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime.1 aPiacitelli, Gherardo1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/386300422nas a2200145 4500008004100000022001400041245003600055210003600091300001400127490000800141100001900149700001700168700002000185856007100205 2010 eng d a0021-904500aCauchy biorthogonal polynomials0 aCauchy biorthogonal polynomials a832–8670 v1621 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.00801271nas a2200133 4500008004300000245007300043210006800116520083300184100001801017700001901035700002301054700002401077856003601101 2010 en_Ud 00aChern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality0 aChernSimons theory on Lpq lens spaces and GopakumarVafa duality3 aWe consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting.1 aBrini, Andrea1 aGriguolo, Luca1 aSeminara, Domenico1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/293800560nas a2200109 4500008004300000245005000043210004900093520023400142100001600376700002200392856003600414 2010 en_Ud 00aCohomology of Skew-holomorphic lie algebroids0 aCohomology of Skewholomorphic lie algebroids3 aWe introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/385300856nas a2200133 4500008004300000245010300043210006900146520038600215100002600601700002200627700001900649700001800668856003600686 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems. Part I: existence results0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340600912nas a2200133 4500008004300000245011700043210006900160520042800229100002600657700002200683700001900705700001800724856003600742 2010 en_Ud 00aConcentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions0 aConcentration of solutions for some singularly perturbed mixed p3 aIn this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in.1 aGarcia Azorero, Jesus1 aMalchiodi, Andrea1 aMontoro, Luigi1 aPeral, Ireneo uhttp://hdl.handle.net/1963/340900703nas a2200121 4500008004100000245007900041210006900120260001000189520030700199100002500506700001400531856003600545 2010 en d00aContinuity of optimal control costs and its application to weak KAM theory0 aContinuity of optimal control costs and its application to weak bSISSA3 aWe prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/645900908nas a2200109 4500008004300000245010700043210006900150520050000219100001800719700002500737856003600762 2010 en_Ud 00aConvergence of equilibria of thin elastic rods under physical growth conditions for the energy density0 aConvergence of equilibria of thin elastic rods under physical gr3 aThe subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory.1 aDavoli, Elisa1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/408600390nas a2200133 4500008004100000245003400041210003000075300001500105490000800120100001900128700001600147700001900163856007400182 2009 eng d00aThe Cauchy two–matrix model0 aCauchy two–matrix model a983–10140 v2871 aBertola, Marco1 aGekhtman, M1 aSzmigielski, J uhttps://www.math.sissa.it/publication/cauchy-two%E2%80%93matrix-model02219nas a2200157 4500008004300000245014000043210006900183260001900252520163800271100002601909700002101935700002801956700002201984700001902006856003602025 2009 en_Ud 00aCharacterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity0 aCharacterization of the time course of changes of the evoked ele bBioMed Central3 aBACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison.1 aBroccard, Frederic D.1 aPegoraro, Silvia1 aRuaro, Maria Elisabetta1 aAltafini, Claudio1 aTorre, Vincent uhttp://hdl.handle.net/1963/370600578nas a2200133 4500008004100000022001400041245013700055210006900192300001400261490000800275100001900283700001500302856012700317 2009 eng d a0001-870800aCommuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights0 aCommuting difference operators spinor bundles and the asymptotic a154–2180 v2201 aBertola, Marco1 aMo, M., Y. uhttps://www.math.sissa.it/publication/commuting-difference-operators-spinor-bundles-and-asymptotics-orthogonal-polynomials00337nas a2200097 4500008004300000245006000043210005800103100002300161700001900184856003600203 2009 en_Ud 00aA connection between viscous profiles and singular ODEs0 aconnection between viscous profiles and singular ODEs1 aBianchini, Stefano1 aSpinolo, Laura uhttp://hdl.handle.net/1963/255500997nas a2200109 4500008004300000245011900043210006900162260001300231520058500244100002200829856003600851 2009 en_Ud 00aControllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds0 aControllability and simultaneous controllability of isospectral bElsevier3 aFor isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/352301061nas a2200133 4500008004300000245009500043210006900138520060700207100002200814700001700836700002100853700001700874856003600891 2009 en_Ud 00aControllability of the discrete-spectrum Schrodinger equation driven by an external field0 aControllability of the discretespectrum Schrodinger equation dri3 aWe prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials.1 aChambrion, Thomas1 aMason, Paolo1 aSigalotti, Mario1 aBoscain, Ugo uhttp://hdl.handle.net/1963/254700583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/339600806nas a2200121 4500008004300000245007400043210006700117260004800184520037100232100002100603700002400624856003600648 2009 en_Ud 00aOn the convergence of viscous approximations after shock interactions0 aconvergence of viscous approximations after shock interactions bAmerican Institute of Mathematical Sciences3 aWe consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient.1 aBressan, Alberto1 aDonadello, Carlotta uhttp://hdl.handle.net/1963/341200501nas a2200145 4500008004100000022001400041245007700055210006900132300001500201490000700216100001900223700001700242700002000259856007600279 2009 eng d a1751-811300aCubic string boundary value problems and Cauchy biorthogonal polynomials0 aCubic string boundary value problems and Cauchy biorthogonal pol a454006, 130 v421 aBertola, Marco1 aGekhtman, M.1 aSzmigielski, J. uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/45400600787nas a2200145 4500008004100000022001300041245008100054210006900135300001200204490000600216520026300222100002400485700002000509856011200529 2008 eng d a1673345200aCantor families of periodic solutions for completely resonant wave equations0 aCantor families of periodic solutions for completely resonant wa a151-1650 v33 aWe present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-completely-resonant-wave-equations01284nas a2200145 4500008004100000022001300041245008900054210006900143300001400212490000800226520074600234100002400980700002001004856011401024 2008 eng d a0001870800aCantor families of periodic solutions for wave equations via a variational principle0 aCantor families of periodic solutions for wave equations via a v a1671-17270 v2173 aWe prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-variational-principle00827nas a2200145 4500008004100000022001300041245008400054210006900138300001200207490000700219520030000226100002400526700002000550856011100570 2008 eng d a1021972200aCantor families of periodic solutions of wave equations with C k nonlinearities0 aCantor families of periodic solutions of wave equations with C k a247-2760 v153 aWe prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/cantor-families-periodic-solutions-wave-equations-c-k-nonlinearities00588nas a2200097 4500008004300000245007600043210006900119520024400188100002200432856003600454 2008 en_Ud 00aConcentrating solutions of some singularly perturbed elliptic equations0 aConcentrating solutions of some singularly perturbed elliptic eq3 aWe study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/265700915nas a2200145 4500008004100000245009900041210007000140260003700210300001400247490000600261520034300267100002000610700001700630856012200647 2008 eng d00aOn concentration of positive bound states for the Schrödinger-Poisson problem with potentials0 aconcentration of positive bound states for the SchrödingerPoisso bAdvanced Nonlinear Studies, Inc. a573–5950 v83 aWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

1 aIanni, Isabella1 aVaira, Giusi uhttps://www.math.sissa.it/publication/concentration-positive-bound-states-schr%C3%B6dinger-poisson-problem-potentials01160nas a2200109 4500008004300000245007000043210006900113520078700182100002500969700002000994856003601014 2008 en_Ud 00aConvergence of equilibria of three-dimensional thin elastic beams0 aConvergence of equilibria of threedimensional thin elastic beams3 aA convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument.1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/189600899nas a2200109 4500008004300000245006800043210006800111520053400179100002000713700002000733856003600753 2007 en_Ud 00aCanonical structure and symmetries of the Schlesinger equations0 aCanonical structure and symmetries of the Schlesinger equations3 aThe Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/199701185nas a2200121 4500008004100000245004600041210004500087260001000132520079900142653006700941100001901008856003601027 2007 en d00aChen-Ruan cohomology of ADE singularities0 aChenRuan cohomology of ADE singularities bSISSA3 aWe study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.10aChen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence1 aPerroni, Fabio uhttp://hdl.handle.net/1963/650200671nas a2200133 4500008004100000245006700041210005800108260001000166520026600176100002200442700001900464700001800483856003600501 2007 en d00aThe cohomological crepant resolution conjecture for P(1,3,4,4)0 acohomological crepant resolution conjecture for P1344 bSISSA3 aWe prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results.1 aBoissiere, Samuel1 aPerroni, Fabio1 aMann, Etienne uhttp://hdl.handle.net/1963/651302020nas a2200121 4500008004300000245013300043210006900176520155200245100002001797700002301817700002201840856003601862 2007 en_Ud 00aComparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data0 aComparing association network algorithms for reverse engineering3 aMotivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/1 aSoranzo, Nicola1 aBianconi, Ginestra1 aAltafini, Claudio uhttp://hdl.handle.net/1963/202800643nas a2200109 4500008004300000245006200043210005400105520029200159100002200451700002400473856003600497 2007 en_Ud 00aThe complete one-loop spin chain for N=2 Super-Yang-Mills0 acomplete oneloop spin chain for N2 SuperYangMills3 aWe show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap.1 aDi Vecchia, Paolo1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/230901000nas a2200121 4500008004300000245004900043210004800092520063900140100002000779700002400799700001900823856003600842 2007 en_Ud 00aComputing Amplitudes in topological M-theory0 aComputing Amplitudes in topological Mtheory3 aWe define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/190100919nas a2200109 4500008004300000245008500043210006900128520053400197100002000731700002200751856003600773 2007 en_Ud 00aConcentration on minimal submanifolds for a singularly perturbed Neumann problem0 aConcentration on minimal submanifolds for a singularly perturbed3 aWe consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $15. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence.1 aDoubrov, Boris1 aZelenko, Igor uhttp://hdl.handle.net/1963/171201190nas a2200109 4500008004300000245009100043210006900134520079700203100002401000700002001024856003601044 2006 en_Ud 00aCantor families of periodic solutions for completely resonant nonlinear wave equations0 aCantor families of periodic solutions for completely resonant no3 aWe prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity.1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/216100378nas a2200109 4500008004300000245006600043210006400109100001700173700001900190700002300209856003600232 2006 en_Ud 00aClassification of stable time-optimal controls on 2-manifolds0 aClassification of stable timeoptimal controls on 2manifolds1 aBoscain, Ugo1 aNikolaev, Igor1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/219601052nas a2200121 4500008004300000245006900043210006900112520065900181100001700840700001700857700002000874856003600894 2006 en_Ud 00aCommon Polynomial Lyapunov Functions for Linear Switched Systems0 aCommon Polynomial Lyapunov Functions for Linear Switched Systems3 aIn this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given.1 aMason, Paolo1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/218100823nas a2200097 4500008004300000245007000043210006900113520048500182100002200667856003600689 2006 en_Ud 00aCompactness of solutions to some geometric fourth-order equations0 aCompactness of solutions to some geometric fourthorder equations3 aWe prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/212600921nas a2200109 4500008004300000245009700043210006900140520052400209100002000733700002200753856003600775 2006 en_Ud 00aConcentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem0 aConcentration at manifolds of arbitrary dimension for a singular3 aWe consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/217000638nas a2200109 4500008004300000245006800043210006800111520027600179100002100455700001600476856003600492 2006 en_Ud 00aConservative Solutions to a Nonlinear Variational Wave Equation0 aConservative Solutions to a Nonlinear Variational Wave Equation3 aWe establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values.1 aBressan, Alberto1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218401941nas a2200133 4500008004300000245006300043210005900106520150700165100002501672700003001697700002001727700002401747856003601771 2006 en_Ud 00aA cyclic integral on k-Minkowski noncommutative space-time0 acyclic integral on kMinkowski noncommutative spacetime3 aWe examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this ``cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.1 aAgostini, Alessandra1 aAmelino-Camelia, Giovanni1 aArzano, Michele1 aD'Andrea, Francesco uhttp://hdl.handle.net/1963/215801041nas a2200097 4500008004300000245006900043210006900112520070400181100002200885856003600907 2005 en_Ud 00aCommuting multiparty quantum observables and local compatibility0 aCommuting multiparty quantum observables and local compatibility3 aA formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities\\\'\\\'.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222801949nas a2200097 4500008004300000245007900043210006900122520160600191100001801797856003601815 2005 en_Ud 00aComplete systems of invariants for rank 1 curves in Lagrange Grassmannians0 aComplete systems of invariants for rank 1 curves in Lagrange Gra3 aCurves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation.1 aZelenko, Igor uhttp://hdl.handle.net/1963/231000658nas a2200109 4500008004100000245010000041210006900141260001300210520026700223100002200490856003600512 2005 en d00aConcentration at curves for a singularly perturbed Neumann problem in three-dimensional domains0 aConcentration at curves for a singularly perturbed Neumann probl bSpringer3 aWe prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/486600982nas a2200121 4500008004100000245006900041210006900110260001800179520057400197100002800771700002500799856003600824 2005 en d00aConservation laws with time dependent discontinuous coefficients0 aConservation laws with time dependent discontinuous coefficients bSISSA Library3 aWe consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11].1 aCoclite, Giuseppe Maria1 aRisebro, Nils Henrik uhttp://hdl.handle.net/1963/166602094nas a2200121 4500008004300000245013000043210006900173520162100242100002501863700003001888700001801918856003601936 2005 en_Ud 00aOn curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals0 acurvatures and focal points of distributions of dynamical Lagran3 aPairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem.1 aAgrachev, Andrei, A.1 aChtcherbakova, Natalia N.1 aZelenko, Igor uhttp://hdl.handle.net/1963/225400524nas a2200145 4500008004100000245006800041210006800109300001400177490000700191100001800198700001700216700002300233700001900256856010300275 2004 eng d00aCalculation of impulsively started incompressible viscous flows0 aCalculation of impulsively started incompressible viscous flows a877–9020 v461 aMarra, Andrea1 aMola, Andrea1 aQuartapelle, Luigi1 aRiviello, Luca uhttps://www.math.sissa.it/publication/calculation-impulsively-started-incompressible-viscous-flows00910nas a2200109 4500008004100000245008500041210006900126260001300195520053400208100002200742856003600764 2004 en d00aCoarse-grained models of materials with non-convex free-energy: two case studies0 aCoarsegrained models of materials with nonconvex freeenergy two bElsevier3 aBridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response.1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/488400697nas a2200097 4500008004300000245005500043210005500098520038800153100002200541856003600563 2004 en_Ud 00aCoherent control of open quantum dynamical systems0 aCoherent control of open quantum dynamical systems3 aA systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/222701240nas a2200121 4500008004300000245006600043210005900109260001000168520086800178100002101046700001501067856003601082 2004 en_Ud 00aOn the convergence rate of vanishing viscosity approximations0 aconvergence rate of vanishing viscosity approximations bWiley3 aGiven a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves.1 aBressan, Alberto1 aYang, Tong uhttp://hdl.handle.net/1963/291500697nas a2200133 4500008004300000245009100043210006900134260001300203520024900216100002200465700001900487700002100506856003600527 2003 en_Ud 00aThe calibration method for the Mumford-Shah functional and free-discontinuity problems0 acalibration method for the MumfordShah functional and freediscon bSpringer3 aWe present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results.1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/305100362nas a2200109 4500008004100000245005400041210005400095260001000149653002900159100002800188856003600216 2003 en d00aControl Problems for Systems of Conservation Laws0 aControl Problems for Systems of Conservation Laws bSISSA10aAsymptotic Stabilization1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/532500974nas a2200109 4500008004300000245008900043210006900132260003400201520057100235100002200806856003600828 2003 en_Ud 00aControllability properties for finite dimensional quantum Markovian master equations0 aControllability properties for finite dimensional quantum Markov bAmerican Institute of Physics3 aVarious notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/290900668nas a2200109 4500008004300000245008100043210006900124260002200193520028200215100002500497856003600522 2002 en_Ud 00aThe Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps0 aCalibration Method for FreeDiscontinuity Problems on VectorValue bHeldermann Verlag3 aThe calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/304900816nas a2200121 4500008004300000245005800043210005600101260004800157520040900205100002300614700002100637856003600658 2002 en_Ud 00aA center manifold technique for tracing viscous waves0 acenter manifold technique for tracing viscous waves bAmerican Institute of Mathematical Sciences3 aIn this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/307500397nas a2200109 4500008004100000245008300041210006900124260001300193100002400206700002100230856003600251 2002 en d00aChaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems0 aChaotic dynamics for perturbations of infinitedimensional Hamilt bElsevier1 aBerti, Massimiliano1 aCarminati, Carlo uhttp://hdl.handle.net/1963/127900461nas a2200133 4500008004100000022001400041245006600055210005700121300001600178490000700194100002100201700001900222856008600241 2002 eng d a0022-248800aCoherent state realizations of $\rm su(n+1)$ on the $n$-torus0 aCoherent state realizations of rm sun1 on the ntorus a3425–34440 v431 ade Guise, Hubert1 aBertola, Marco uhttps://www.math.sissa.it/publication/coherent-state-realizations-rm-sun1-n-torus00371nas a2200097 4500008004100000245008700041210006900128260001800197100002200215856003600237 2002 en d00aControllability of quantum mechanical systems by root space decomposition of su(N)0 aControllability of quantum mechanical systems by root space deco bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161300727nas a2200121 4500008004300000245006600043210006400109260003400173520032000207100002000527700002200547856003600569 2002 en_Ud 00aCurvature theory of boundary phases: the two-dimensional case0 aCurvature theory of boundary phases the twodimensional case bEuropean Mathematical Society3 aWe describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.1 aBraides, Andrea1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353700359nas a2200109 4500008004300000245004000043210003800083260004800121100002300169700002100192856003600213 2001 en_Ud 00aA case study in vanishing viscosity0 acase study in vanishing viscosity bAmerican Institute of Mathematical Sciences1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/309100661nas a2200121 4500008004300000245006900043210006900112260001300181520027600194100001600470700001700486856003600503 2001 en_Ud 00aComplex Lagrangian embeddings of moduli spaces of vector bundles0 aComplex Lagrangian embeddings of moduli spaces of vector bundles bElsevier3 aBy means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds.1 aBruzzo, Ugo1 aPioli, Fabio uhttp://hdl.handle.net/1963/288500379nas a2200109 4500008004300000245006700043210006700110260001300177100002000190700002300210856003600233 2001 en_Ud 00aControllability for discrete systems with a finite control set0 aControllability for discrete systems with a finite control set bSpringer1 aChitour, Yacine1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/311401123nas a2200121 4500008004100000245011200041210006900153260003100222520054200253653005000795100002100845856013500866 2001 en d00aOn the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painlevé VI Equation0 aCritical Behavior the Connection Problem and the Elliptic Repres bKluwer Academic Publishers3 aIn this paper we find a class of solutions of the sixth Painlevé equation appearing in\r\nthe theory of WDVV equations. This class covers almost all the monodromy data associated to\r\nthe equation, except one point in the space of the data. We describe the critical behavior close to\r\nthe critical points in terms of two parameters and we find the relation among the parameters at\r\nthe different critical points (connection problem). We also study the critical behavior of Painlevé\r\ntranscendents in the elliptic representation.10aPainleve Equations, Isomonodromy deformations1 aGuzzetti, Davide uhttps://www.math.sissa.it/publication/critical-behavior-connection-problem-and-elliptic-representation-painlev%C3%A9-vi-equation-000508nas a2200109 4500008004100000245005900041210005500100260001800155520016800173100002100341856003600362 2000 en d00aThe Calibration Method for Free Discontinuity Problems0 aCalibration Method for Free Discontinuity Problems bSISSA Library3 aThe calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/149600395nas a2200109 4500008004100000245007400041210006700115260001800182100002100200700002800221856003600249 2000 en d00aOn the convergence of Godunov scheme for nonlinear hyperbolic systems0 aconvergence of Godunov scheme for nonlinear hyperbolic systems bSISSA Library1 aBressan, Alberto1 aJenssen, Helge Kristian uhttp://hdl.handle.net/1963/147300703nas a2200133 4500008004100000245005900041210005400100260001300154520030400167100002200471700001900493700002100512856003600533 1999 en d00aThe calibration method for the Mumford-Shah functional0 acalibration method for the MumfordShah functional bElsevier3 aIn this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3).1 aAlberti, Giovanni1 aBouchitte, Guy1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/123500735nas a2200133 4500008004300000245004700043210004700090260001300137520035400150100002200504700001600526700002300542856003600565 1999 en_Ud 00aCategorial mirror symmetry for K3 surfaces0 aCategorial mirror symmetry for K3 surfaces bSpringer3 aWe study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$.1 aBartocci, Claudio1 aBruzzo, Ugo1 aSanguinetti, Guido uhttp://hdl.handle.net/1963/288700568nas a2200157 4500008004100000022001400041245007200055210006900127300001400196490000800210100001900218700002100237700001900258700002300277856011000300 1999 eng d a0370-269300aCorrespondence between Minkowski and de Sitter quantum field theory0 aCorrespondence between Minkowski and de Sitter quantum field the a249–2530 v4621 aBertola, Marco1 aGorini, Vittorio1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://www.math.sissa.it/publication/correspondence-between-minkowski-and-de-sitter-quantum-field-theory00343nas a2200109 4500008004100000245005200041210004500093260001000138653003100148100001800179856003600197 1998 en d00aOn the Cauchy Problem for the Whitham Equations0 aCauchy Problem for the Whitham Equations bSISSA10aKorteweg de Vries equation1 aGrava, Tamara uhttp://hdl.handle.net/1963/555500833nas a2200121 4500008004100000245004300041210004300084260001300127520049300140100002100633700002200654856003500676 1997 en d00aCapacity theory for monotone operators0 aCapacity theory for monotone operators bSpringer3 aIf $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$.1 aDal Maso, Gianni1 aSkrypnik, Igor V. uhttp://hdl.handle.net/1963/91100323nas a2200085 4500008004100000245007000041210006900111100002100180856003600201 1997 it d00aComportamento asintotico delle soluzioni di problemi di Dirichlet0 aComportamento asintotico delle soluzioni di problemi di Dirichle1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/643800411nas a2200109 4500008004100000245009800041210006900139260001800208100002100226700001900247856003500266 1996 en d00aA capacity method for the study of Dirichlet problems for elliptic systems in varying domains0 acapacity method for the study of Dirichlet problems for elliptic bSISSA Library1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/98900323nas a2200097 4500008004100000245005500041210005500096260001800151100002100169856003500190 1995 en d00aCapacity and Dirichlet problems in varying domains0 aCapacity and Dirichlet problems in varying domains bSISSA Library1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/95000328nas a2200097 4500008004100000245005400041210005300095260001800148100002900166856003500195 1995 en d00aClassical solutions for a perturbed N-body system0 aClassical solutions for a perturbed Nbody system bSISSA Library1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/12600404nas a2200121 4500008004100000245006200041210006000103260001800163100002100181700002000202700002500222856003500247 1991 en d00aA class of absolute retracts of dwarf spheroidal galaxies0 aclass of absolute retracts of dwarf spheroidal galaxies bSISSA Library1 aBressan, Alberto1 aCellina, Arrigo1 aFryszkowski, Andrzej uhttp://hdl.handle.net/1963/83700655nas a2200133 4500008004100000245005500041210005400096260001800150520026000168100002000428700002200448700001600470856003500486 1990 en d00aChern-Simons forms on principal superfiber bundles0 aChernSimons forms on principal superfiber bundles bSISSA Library3 aA graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a ``superextension\\\'\\\' of the Dirac monopole is discussed.1 aLandi, Giovanni1 aBartocci, Claudio1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/59000375nas a2200109 4500008004100000245006100041210006100102260001800163100002100181700002800202856003500230 1990 en d00aCorrectors for the homogeneization of monotone operators0 aCorrectors for the homogeneization of monotone operators bSISSA Library1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/81200412nas a2200097 4500008004100000245012700041210006900168260001800237100002400255856003500279 1989 en d00aOn the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version)0 acontinuous dependence of solutions of boundary value problems fo bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/66600394nas a2200097 4500008004100000245010900041210006900150260001800219100002400237856003500261 1989 en d00aOn the continuous dependence of solutions of boundary value problems for ordinary differential equations0 acontinuous dependence of solutions of boundary value problems fo bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/63300377nas a2200109 4500008004100000245006200041210006200103260001800165100002100183700002800204856003500232 1989 en d00aConvergence of unilateral problems for monotone operators0 aConvergence of unilateral problems for monotone operators bSISSA Library1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/72200371nas a2200097 4500008004100000245008900041210006900130260001800199100002100217856003500238 1986 en d00aConvergence of unilateral convex sets. Optimization and related fields (Erice, 1984)0 aConvergence of unilateral convex sets Optimization and related f bSISSA Library1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/35300379nas a2200097 4500008004100000245009400041210006900135260001800204100002400222856003500246 1982 en d00aA criterion for he existence of maximal solutions of strongly nonlinear elliptic problems0 acriterion for he existence of maximal solutions of strongly nonl bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/161