We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.

10aDispersive equations10aEnergy method10aLocal wellposedness10aNLS10aPara-differential calculus10aQuasi-linear PDEs1 aFeola, Roberto1 aIandoli, Felice uhttp://www.sciencedirect.com/science/article/pii/S029414491830042801258nas a2200133 4500008004100000245006300041210006300104260001000167520083800177100002001015700002001035700002101055856004801076 2018 en d00aLocal moduli of semisimple Frobenius coalescent structures0 aLocal moduli of semisimple Frobenius coalescent structures bSISSA3 aThere is a conjectural relation, formulated by the second author, between the enumerative geometry of a wide class of smooth projective varieties and their derived category of coherent sheaves. In particular, there is an increasing interest for an explicit description of certain local invariants, called monodromy data, of semisimple quantum cohomologies in terms of characteristic classes of exceptional collections in the derived categories. Being intentioned to address this problem, which, to our opinion, is still not well understood, we have realized that some issues in the theory of Frobenius manifolds need to be preliminarily clarified, and that an extension of the theory itself is necessary, in view of the fact that quantum cohomologies of certain classes of homogeneous spaces may show a coalescence phenomenon.

1 aCotti, Giordano1 aDubrovin, Boris1 aGuzzetti, Davide uhttp://preprints.sissa.it/handle/1963/3530400583nas a2200145 4500008004100000245008400041210006900125653003700194100002100231700001300252700002100265700002100286700001900307856011100326 2018 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati10aMathematics - Numerical Analysis1 aHess, Martin, W.1 aAlla, A.1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, M. uhttps://www.math.sissa.it/publication/localized-reduced-order-modeling-approach-pdes-bifurcating-solutions00439nas a2200097 4500008004100000245008500041210006900126100001900195700002000214856010700234 2018 eng d00aLong time existence for fully nonlinear NLS with small Cauchy data on the circle0 aLong time existence for fully nonlinear NLS with small Cauchy da1 aRoberto, Feola1 aIandoli, Felice uhttps://www.math.sissa.it/publication/long-time-existence-fully-nonlinear-nls-small-cauchy-data-circle00806nas a2200181 4500008004100000022001400041245009400055210006900149260000800218300001400226490000700240520023200247100002900479700002900508700002300537700001800560856004600578 2018 eng d a1424-066100aLp-Boundedness of Wave Operators for the Three-Dimensional Multi-Centre Point Interaction0 aLpBoundedness of Wave Operators for the ThreeDimensional MultiCe cJan a283–3220 v193 aWe prove that, for arbitrary centres and strengths, the wave operators for three-dimensional Schrödinger operators with multi-centre local point interactions are bounded in Lp(R3)for 1<p<3 and unbounded otherwise.

1 aDell'Antonio, Gianfausto1 aMichelangeli, Alessandro1 aScandone, Raffaele1 aYajima, Kenji uhttps://doi.org/10.1007/s00023-017-0628-400384nas a2200109 4500008004100000245006300041210006000104100002300164700002100187700001800208856004800226 2017 en d00aA Lagrangian approach for scalar multi-d conservation laws0 aLagrangian approach for scalar multid conservation laws1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://preprints.sissa.it/handle/1963/3529001119nas a2200157 4500008004100000245006600041210006600107260004500173300001400218490000700232520056500239100002300804700002100827700001800848856009500866 2017 eng d00aLagrangian representations for linear and nonlinear transport0 aLagrangian representations for linear and nonlinear transport bPeoples' Friendship University of Russia a418–4360 v633 aIn this note we present a unifying approach for two classes of first order partial differential equations: we introduce the notion of Lagrangian representation in the settings of continuity equation and scalar conservation laws. This yields, on the one hand, the uniqueness of weak solutions to transport equation driven by a two dimensional BV nearly incompressible vector field. On the other hand, it is proved that the entropy dissipation measure for scalar conservation laws in one space dimension is concentrated on countably many Lipschitz curves.

1 aBianchini, Stefano1 aBonicatto, Paolo1 aMarconi, Elio uhttp://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cmfd&paperid=327&option_lang=eng01179nas a2200121 4500008004100000245009100041210006900132300001200201490000700213520077600220100002000996856004101016 2017 eng d00aLimit of viscous dynamic processes in delamination as the viscosity and inertia vanish0 aLimit of viscous dynamic processes in delamination as the viscos a593-6250 v233 aWe introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

1 aScala, Riccardo uhttps://doi.org/10.1051/cocv/201600601226nas a2200097 4500008004100000245006100041210006100102520089500163100001901058856005101077 2017 en d00aLinear hyperbolic systems in domains with growing cracks0 aLinear hyperbolic systems in domains with growing cracks3 aWe consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems.1 aCaponi, Maicol uhttp://urania.sissa.it/xmlui/handle/1963/3527101406nas a2200133 4500008004100000245004000041210004000081520101100121100002301132700002101155700002401176700002401200856004801224 2017 en d00aLinearisation of multiwell energies0 aLinearisation of multiwell energies3 aLinear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours.1 aAlicandro, Roberto1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aPalombaro, Mariapia uhttp://preprints.sissa.it/handle/1963/3528800988nas a2200157 4500008004100000245010900041210006900150260001500219300001400234490000700248520038700255100002100642700002200663700001900685856012600704 2017 eng d00aLower semicontinuity of a class of integral functionals on the space of functions of bounded deformation0 aLower semicontinuity of a class of integral functionals on the s bDe Gruyter a183–2070 v103 aWe study the lower semicontinuity of some free discontinuity functionals with linear growth defined on the space of functions with bounded deformation. The volume term is convex and depends only on the Euclidean norm of the symmetrized gradient. We introduce a suitable class of surface terms, which make the functional lower semicontinuous with respect to $L^1$ convergence.

1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttps://www.math.sissa.it/publication/lower-semicontinuity-class-integral-functionals-space-functions-bounded-deformation01104nas a2200145 4500008004100000245009100041210006900132300001200201490000800213520063400221100001800855700002100873700001900894856004500913 2017 en d00aA lower semicontinuity result for a free discontinuity functional with a boundary term0 alower semicontinuity result for a free discontinuity functional a952-9900 v1083 aWe study the lower semicontinuity in $GSBV^{p}(\Omega;\mathbb{R}^{m})$ of a free discontinuity functional $\mathcal{F}(u)$ that can be written as the sum of a crack term, depending only on the jump set $S_{u}$, and of a boundary term, depending on the trace of $u$ on $\partial\Omega$. We give sufficient conditions on the integrands for the lower semicontinuity of $\mathcal{F}$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of $\mathcal{F}$ can be represented by the sum of two integrals on $S_{u}$ and $\partial\Omega$, respectively.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1597901362nas a2200121 4500008004100000245005800041210005800099520096700157100002401124700002101148700002301169856004801192 2016 en d00aLarge KAM tori for perturbations of the dNLS equation0 aLarge KAM tori for perturbations of the dNLS equation3 aWe prove that small, semi-linear Hamiltonian perturbations of the defocusing nonlinear Schr\"odinger (dNLS) equation on the circle have an abundance of invariant tori of any size and (finite) dimension which support quasi-periodic solutions. When compared with previous results the novelty consists in considering perturbations which do not satisfy any symmetry condition (they may depend on x in an arbitrary way) and need not be analytic. The main difficulty is posed by pairs of almost resonant dNLS frequencies. The proof is based on the integrability of the dNLS equation, in particular the fact that the nonlinear part of the Birkhoff coordinates is one smoothing. We implement a Newton-Nash-Moser iteration scheme to construct the invariant tori. The key point is the reduction of linearized operators, coming up in the iteration scheme, to 2×2 block diagonal ones with constant coefficients together with sharp asymptotic estimates of their eigenvalues.1 aBerti, Massimiliano1 aKappeler, Thomas1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3528400522nas a2200133 4500008004100000245008200041210006900123300001100192490000700203100002000210700002200230700001700252856011900269 2016 eng d00aLinearOperator – a generic, high-level expression syntax for linear algebra0 aLinearOperator a generic highlevel expression syntax for linear a1–240 v721 aMaier, Matthias1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/linearoperator-%E2%80%93-generic-high-level-expression-syntax-linear-algebra01765nas a2200217 4500008004100000022001400041245005300055210005300108300001400161490000700175520110000182653002201282653002501304653002801329653003001357653002701387100002201414700001801436700002201454856007101476 2015 eng d a0022-509600aLiquid crystal elastomer strips as soft crawlers0 aLiquid crystal elastomer strips as soft crawlers a254 - 2720 v843 aIn this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

10aCrawling motility10aDirectional surfaces10aFrictional interactions10aLiquid crystal elastomers10aSoft biomimetic robots1 aDeSimone, Antonio1 aGidoni, Paolo1 aNoselli, Giovanni uhttp://www.sciencedirect.com/science/article/pii/S002250961530043001118nas a2200145 4500008004100000245013100041210006900172260001000241520052100251653010200772100002100874700002200895700001900917856003600936 2014 en d00aLaplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length0 aLaplace equation in a domain with a rectilinear crack higher ord bSISSA3 aWe consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

10acracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions1 aDal Maso, Gianni1 aOrlando, Gianluca1 aToader, Rodica uhttp://hdl.handle.net/1963/727100830nas a2200121 4500008004100000245005800041210005800099260003100157520043000188100001700618700002200635856005100657 2014 en d00aLecture notes on gradient flows and optimal transport0 aLecture notes on gradient flows and optimal transport bCambridge University Press3 aWe present a short overview on the strongest variational formulation for gradient flows of geodesically λ-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School "Optimal transportation: Theory and applications" in Grenoble during the week of June 22-26, 2009.1 aDaneri, Sara1 aSavarè, Giuseppe uhttp://urania.sissa.it/xmlui/handle/1963/3509300818nas a2200109 4500008004100000245005900041210005900100260003000159520044600189100002200635856005100657 2014 en d00aLegendre duality on hypersurfaces in Kähler manifolds0 aLegendre duality on hypersurfaces in Kähler manifolds bWalter de Gruyter and Co.3 aWe give a sufficient condition on real strictly Levi-convex hypersurfaces M, embedded in four-dimensional Kähler manifolds V , such that Legendre duality can be performed. We consider the contact form onM whose kernel is the restriction of the holomorphic tangent space of V and show that if there exists a Legendrian Killing vector field v, then the dual form β(̇) := d(v, ̇) is a contact form on M with the same orientation than theta.1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3477701077nas a2200133 4500008004100000245007900041210007000120260001700190300001400207490000700221520058200228100001800810856011500828 2014 eng d00aLinearized plastic plate models as Γ-limits of 3D finite elastoplasticity0 aLinearized plastic plate models as Γlimits of 3D finite elastopl bEDP Sciences a725–7470 v203 aThe subject of this paper is the rigorous derivation of reduced models for a thin plate by means of $\Gamma$-convergence, in the framework of finite plasticity. Denoting by $\epsilon$ the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order $\epsilon^{2 \alpha -2}$, with $\alpha \geq 3$. According to the value of $\alpha$, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/linearized-plastic-plate-models-%CE%B3-limits-3d-finite-elastoplasticity00762nas a2200121 4500008004100000245010000041210006900141260001300210520031900223100002200542700002500564856005100589 2014 en d00aLipschitz continuous viscosity solutions for a class of fully nonlinear equations on lie groups0 aLipschitz continuous viscosity solutions for a class of fully no bSpringer3 aIn this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.1 aMartino, Vittorio1 aMontanari, Annamaria uhttp://urania.sissa.it/xmlui/handle/1963/3469901060nas a2200157 4500008004100000245008400041210006900125260002200194300001400216490000700230520054900237653003500786100002000821700002500841856003600866 2014 en d00aLocal and global minimality results for a nonlocal isoperimetric problem on R^N0 aLocal and global minimality results for a nonlocal isoperimetric bSIAM Publications a2310-23490 v463 aWe consider a nonlocal isoperimetric problem defined in the whole space R^N, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are local minimizers and satisfy a quantitative inequality with respect to the L^1-norm. This criterion provides the existence of a (explicitly determined) critical threshold determining the interval of volumes for which the ball is a local minimizer, and allows to address several global minimality issues.

10aNonlocal isoperimetric problem1 aBonacini, Marco1 aCristoferi, Riccardo uhttp://hdl.handle.net/1963/698400578nas a2200145 4500008004100000245004600041210004500087260001000132520011500142653003000257100002200287700001700309700002500326856008100351 2014 en d00aLocal behavior of fractional p-minimizers0 aLocal behavior of fractional pminimizers bSISSA3 aWe extend the De Giorgi-Nash Moser theory to nonlocal, possibly degerate integro-differential operators

10afractional Sobolev spaces1 aDi Castro, Agnese1 aKuusi, Tuomo1 aPalatucci, Giampiero uhttps://www.math.sissa.it/publication/local-behavior-fractional-p-minimizers00800nas a2200133 4500008004100000245006400041210005600105260003400161520035400195100002200549700002300571700002100594856005100615 2014 en d00aOn the Lp-differentiability of certain classes of functions0 aLpdifferentiability of certain classes of functions bEuropean Mathematical Society3 aWe prove the Lp-differentiability at almost every point for convolution products on ℝd of the form K*μ, where μ is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation.1 aAlberti, Giovanni1 aBianchini, Stefano1 aCrippa, Gianluca uhttp://urania.sissa.it/xmlui/handle/1963/3469501360nas a2200181 4500008004100000022001400041245008900055210006900144260000800213300001400221490000700235520080900242100001701051700002301068700002001091700002101111856004601132 2013 eng d a1559-002X00aLipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces0 aLipschitz Classification of AlmostRiemannian Distances on Compac cJan a438–4550 v233 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot–Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it.

1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttps://doi.org/10.1007/s12220-011-9262-400709nas a2200169 4500008004100000245011000041210006900151260003000220300001200250490000700262520014000269653002500409100002600434700002100460700002200481856003600503 2012 en d00aLinear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions0 aLinear elasticity obtained from finite elasticity by Gammaconver bGauthier-Villars;Elsevier a715-7350 v293 aThe energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/426700646nas a2200133 4500008004100000245005800041210005500099260001300154520025200167653001900419100001600438700002200454856003600476 2012 en d00aOn localization in holomorphic equivariant cohomology0 alocalization in holomorphic equivariant cohomology bSpringer3 aWe prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.10aLie algebroids1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/658400466nas a2200121 4500008004100000022001400041245010500055210006900160300001600229490000700245100001900252856007300271 2012 eng d a0951-771500aOn the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation0 alocation of poles for the AblowitzSegur family of solutions to t a1179–11850 v251 aBertola, Marco uhttp://0-dx.doi.org.mercury.concordia.ca/10.1088/0951-7715/25/4/117901000nas a2200133 4500008004300000245005100043210005100094260002100145520060100166100001800767700002500785700002000810856003600830 2011 en_Ud 00aLarge Time Existence for Thin Vibrating Plates0 aLarge Time Existence for Thin Vibrating Plates bTaylor & Francis3 aWe construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large\\r\\ntimes under appropriate scaling of the initial values such that the limit system as h --> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the\\r\\nlinear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/375500923nas a2200145 4500008004100000245010600041210006900147260001300216520043000229653002300659100002000682700001700702700002200719856003600741 2011 en d00aLinearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations0 aLinearly degenerate Hamiltonian PDEs and a new class of solution bSpringer3 aWe define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete classification of irreducible solutions.10aFrobenius manifold1 aDubrovin, Boris1 aPavlov, M.V.1 aZykov, Sergei, A. uhttp://hdl.handle.net/1963/643000818nas a2200133 4500008004100000245003700041210003300078260001000111520046800121100002000589700002400609700001500633856003600648 2011 en d00aThe Liouville side of the vortex0 aLiouville side of the vortex bSISSA3 aWe analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZhao, Jian uhttp://hdl.handle.net/1963/430400901nas a2200121 4500008004300000245004400043210004300087520054400130100002200674700002200696700002500718856003600743 2010 en_Ud 00aLorentz Covariant k-Minkowski Spacetime0 aLorentz Covariant kMinkowski Spacetime3 aIn recent years, different views on the interpretation of Lorentz covariance of non commuting coordinates were discussed. Here, by a general procedure, we construct the minimal canonical central covariantisation of the k-Minkowski spacetime. We then show that, though the usual k-Minkowski spacetime is covariant under deformed (or twisted) Lorentz action, the resulting framework is equivalent to taking a non covariant restriction of the covariantised model. We conclude with some general comments on the approach of deformed covariance.1 aDabrowski, Ludwik1 aGodlinski, Michal1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/382900554nas a2200145 4500008004100000245010200041210006900143260005400212300001400266490000800280100001700288700002500305700002300330856005500353 2009 eng d00aLow-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners0 aLowFrequency Variations of Force Coefficients on Square Cylinder bAmerican Society of Civil Engineers ({ASCE})cjul a828–8350 v1351 aMola, Andrea1 aBordonaro, Giancarlo1 aHajj, Muhammad, R. uhttps://doi.org/10.1061/(asce)st.1943-541x.000003401845nas a2200133 4500008004300000245006800043210006700111520142200178100001701600700002101617700001701638700002001655856003601675 2008 en_Ud 00aLimit Time Optimal Syntheses for a control-affine system on S²0 aLimit Time Optimal Syntheses for a controlaffine system on S²3 aFor $\\\\alpha \\\\in ]0,\\\\pi/2[$, let $(\\\\Sigma)_\\\\alpha$ be the control system $\\\\dot{x}=(F+uG)x$, where $x$ belongs to the two-dimensional unit sphere $S^2$, $u\\\\in [-1,1]$, and $F,G$ are $3\\\\times3$ skew-symmetric matrices generating rotations with perpendicular axes and of respective norms $\\\\cos(\\\\alpha)$ and $\\\\sin(\\\\alpha)$. In this paper, we study the time optimal synthesis (TOS) from the north pole $(0,0,1)^T$ associated to $(\\\\Sigma)_\\\\alpha$, as the parameter $\\\\alpha$ tends to zero; this problem is motivated by specific issues in the control of quantum systems. We first prove that the TOS is characterized by a \\\"two-snakes\\\" configuration on the whole $S^2$, except for a neighborhood $U_\\\\alpha$ of the south pole $(0,0,-1)^T$ of diameter at most ${\\\\cal O}(\\\\alpha)$. We next show that, inside $U_\\\\alpha$, the TOS depends on the relationship between $r(\\\\alpha):=\\\\pi/2\\\\alpha-[\\\\pi/2\\\\alpha]$ and $\\\\alpha$. More precisely, we characterize three main relationships by considering sequences $(\\\\alpha_k)_{k\\\\geq 0}$ satisfying (a) $r(\\\\alpha_k)=\\\\bar{r}$, (b) $r(\\\\alpha_k)=C\\\\alpha_k$, and (c) $r(\\\\alpha_k)=0$, where $\\\\bar{r}\\\\in (0,1)$ and $C>0$. In each case, we describe the TOS and provide, after a suitable rescaling, the limiting behavior, as $\\\\alpha$ tends to zero, of the corresponding TOS inside $U_\\\\alpha$.1 aMason, Paolo1 aSalmoni, Rebecca1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/186200688nas a2200109 4500008004100000245008400041210006900125260001000194520031700204100002100521856003600542 2008 en d00aOn the Logarithmic Asymptotics of the Sixth Painleve\' Equation (Summer 2007)0 aLogarithmic Asymptotics of the Sixth Painleve Equation Summer 20 bSISSA3 aWe study the solutions of the sixth Painlev\'e equation with a logarithmic\r\nasymptotic behavior at a critical point. We compute the monodromy group\r\nassociated to the solutions by the method of monodromy preserving deformations\r\nand we characterize the asymptotic behavior in terms of the monodromy itself.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652101450nas a2200169 4500008004300000245007300043210006900116520092200185100001801107700001801125700001801143700001901161700001901180700002601199700001901225856003601244 2007 en_Ud 00aLuther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas0 aLutherEmery Phase and AtomicDensity Waves in a Trapped Fermion G3 aThe Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

1 aXianlong, Gao1 aRizzi, Matteo1 aPolini, Marco1 aFazio, Rosario1 aTosi, Mario P.1 aCampo, Vivaldo L. Jr.1 aCapelle, Klaus uhttp://hdl.handle.net/1963/205600940nas a2200109 4500008004300000245005300043210005300096520060900149100001800758700001800776856003600794 2006 en_Ud 00aLarge Parameter Behavior of Equilibrium Measures0 aLarge Parameter Behavior of Equilibrium Measures3 aWe study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).1 aGrava, Tamara1 aTian, Fei-Ran uhttp://hdl.handle.net/1963/178900649nas a2200109 4500008004300000245005600043210005600099520030200155100002400457700002200481856003600503 2006 en_Ud 00aLocal Index Formula on the Equatorial Podles Sphere0 aLocal Index Formula on the Equatorial Podles Sphere3 aWe discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate\\\' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock representation of the Toeplitz algebra and the isopectral one....1 aD'Andrea, Francesco1 aDabrowski, Ludwik uhttp://hdl.handle.net/1963/178200687nas a2200145 4500008004300000245003900043210003300082520027900115100002600394700002200420700002000442700002000462700002300482856003600505 2005 en_Ud 00aThe local index formula for SUq(2)0 alocal index formula for SUq23 aWe discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.1 avan Suijlekom, Walter1 aDabrowski, Ludwik1 aLandi, Giovanni1 aSitarz, Andrzej1 aVarilly, Joseph C. uhttp://hdl.handle.net/1963/171300867nas a2200109 4500008004300000245005900043210005700102260002600159520051500185100002100700856003600721 2003 en_Ud 00aA lemma and a conjecture on the cost of rearrangements0 alemma and a conjecture on the cost of rearrangements bUniversità di Padova3 aConsider a stack of books, containing both white and black books. Suppose that we want to sort them out, putting the white books on the right, and the black books on the left (fig.~1). This will be done by a finite sequence of elementary transpositions. In other words, if we have a stack of all black books of length $a$ followed by a stack of all white books of length $b$, we are allowed to reverse their order at the cost of $a+b$. We are interested in a lower bound on the total cost of the rearrangement.1 aBressan, Alberto uhttp://hdl.handle.net/1963/291400867nas a2200121 4500008004100000245005700041210005000098260001800148520049700166100002500663700002100688856003600709 2003 en d00aOn the local structure of optimal trajectories in R30 alocal structure of optimal trajectories in R3 bSISSA Library3 aWe analyze the structure of a control function u(t) corresponding to an optimal trajectory for the system $\\\\dot q =f(q)+u\\\\, g(q)$ in a three-dimensional manifold, near a point where some nondegeneracy conditions are satisfied. The kind of optimality which is studied includes time-optimality. The control turns out to be the concatenation of some bang and some singular arcs. Studying the index of the second variation of the switching times, the number of such arcs is bounded by four.1 aAgrachev, Andrei, A.1 aSigalotti, Mario uhttp://hdl.handle.net/1963/161200398nas a2200121 4500008004300000245006200043210006100105260001300166100002100179700001800200700002200218856003600240 2002 en_Ud 00aLinearized elasticity as gamma-limit of finite elasticity0 aLinearized elasticity as gammalimit of finite elasticity bSpringer1 aDal Maso, Gianni1 aNegri, Matteo1 aPercivale, Danilo uhttp://hdl.handle.net/1963/305200836nas a2200109 4500008004300000245009200043210006900135260002100204520044000225100002500665856003600690 2002 en_Ud 00aLocal calibrations for minimizers of the Mumford-Shah functional with a triple junction0 aLocal calibrations for minimizers of the MumfordShah functional bWorld Scientific3 aWe prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/305000788nas a2200121 4500008004100000245008600041210006900127260001300196520037700209100002300586700002100609856003600630 2002 en d00aOn a Lyapunov functional relating shortening curves and viscous conservation laws0 aLyapunov functional relating shortening curves and viscous conse bElsevier3 aWe study a nonlinear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the \\\"change of shape\\\" of a BV solution to a scalar conservation law.1 aBianchini, Stefano1 aBressan, Alberto uhttp://hdl.handle.net/1963/133700848nas a2200109 4500008004300000245006600043210006600109260001900175520048700194100002100681856003600702 2001 en_Ud 00aLax representation and Poisson geometry of the Kowalevski top0 aLax representation and Poisson geometry of the Kowalevski top bIOP Publishing3 aWe discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.1 aFalqui, Gregorio uhttp://hdl.handle.net/1963/324400413nas a2200133 4500008004100000022001400041245004300055210004300098300001400141490000700155100001900162700001700181856008100198 2001 eng d a1120-718300aLie triple systems and warped products0 aLie triple systems and warped products a275–2930 v211 aBertola, Marco1 aGouthier, D. uhttps://www.math.sissa.it/publication/lie-triple-systems-and-warped-products00426nas a2200109 4500008004100000245010200041210006900143260001800212100002500230700002500255856003600280 2001 en d00aLocal calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set0 aLocal calibrations for minimizers of the MumfordShah functional bSISSA Library1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/147900462nas a2200121 4500008004100000245010500041210006900146260001800215100002100233700002500254700002500279856003600304 2000 en d00aLocal calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets0 aLocal calibrations for minimizers of the MumfordShah functional bSISSA Library1 aDal Maso, Gianni1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/126101453nas a2200133 4500008004300000245005600043210005500099260001300154520106200167100002101229700001801250700001501268856003601283 1999 en_Ud 00aL-1 stability estimates for n x n conservation laws0 aL1 stability estimates for n x n conservation laws bSpringer3 aLet $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws, each characteristic field being linearly degenerate or genuinely nonlinear. In this paper we explicitly define a functional $\\\\Phi=\\\\Phi(u,v)$, equivalent to the $L^1$ distance, which is `almost decreasing\\\', i.e., $\\\\Phi(u(t),v(t))-\\\\Phi(u(s),v(s))\\\\leq\\\\break O (\\\\epsilon)·(t-s)$ for all $t>s\\\\geq 0$, for every pair of $\\\\epsilon$-approximate solutions $u,v$ with small total variation, generated by a wave-front-tracking algorithm. The small parameter $\\\\epsilon$ here controls the errors in the wave speeds, the maximum size of rarefaction fronts and the total strength of all non-physical waves in $u$ and in $v$. From the above estimate, it follows that front-tracking approximations converge to a unique limit solution, depending Lipschitz continuously on the initial data, in the $L^1$ norm. This provides a new proof of the existence of the standard Riemann semigroup generated by an $n\\\\times n$ system of conservation laws.\\\'\\\'1 aBressan, Alberto1 aLiu, Tai-Ping1 aYang, Tong uhttp://hdl.handle.net/1963/337300817nas a2200133 4500008004100000245009500041210006900136260001000205520036300215100002100578700002700599700002100626856003600647 1999 en d00aA Lipschitz selection from the set of minimizers of a nonconvex functional of the gradient0 aLipschitz selection from the set of minimizers of a nonconvex fu bSISSA3 aA constructive and improved version of the proof that there exist a continuous map that solves the convexified problem is presented. A Lipschitz continuous map is analyzed such that a map vector minimizes the functional at each vector satisfying Cellina\\\'s condition of existence of minimum. This map is explicitly given by a direct constructive algorithm.1 aDal Maso, Gianni1 aGoncharov, Vladimir V.1 aOrnelas, Antonio uhttp://hdl.handle.net/1963/643900455nas a2200133 4500008004100000245007400041210006900115260001000184100002100194700002300215700002300238700002400261856003600285 1998 en d00aLimits of variational problems for Dirichlet forms in varying domains0 aLimits of variational problems for Dirichlet forms in varying do bSISSA1 aDal Maso, Gianni1 aDe Cicco, Virginia1 aNotarantonio, Lino1 aTchou, Nicoletta A. uhttp://hdl.handle.net/1963/644000448nas a2200109 4500008004300000245007400043210006900117260007600186100002100262700001900283856003600302 1994 en_Ud 00aLimits of Dirichlet problems in perforated domains: a new formulation0 aLimits of Dirichlet problems in perforated domains a new formula bUniversità degli Studi di Trieste, Dipartimento di Scienze Matematiche1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/364900424nas a2200133 4500008004100000245005700041210005600098260001800154100002100172700002200193700001900215700002100234856003500255 1989 en d00aLimits of obstacle problems for the area functional.0 aLimits of obstacle problems for the area functional bSISSA Library1 aDal Maso, Gianni1 aCarriero, Michele1 aLeaci, Antonio1 aPascali, Eduardo uhttp://hdl.handle.net/1963/57700693nas a2200121 4500008004100000245006300041210006200104260001800166520030300184100002100487700002800508856003500536 1988 en d00aLimits of nonlinear Dirichlet problems in varying domains.0 aLimits of nonlinear Dirichlet problems in varying domains bSISSA Library3 aWe study the general form of the limit, in the sense of gamma-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boudary conditions. The asymptotic problem is characterized in terms of the limit of suitable nonlinear capacities associated to the domains.1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/53600343nas a2200109 4500008004100000245005000041210004900091260001800140100002000158700002000178856003500198 1987 en d00aLie algebra extensions and abelian monopoles.0 aLie algebra extensions and abelian monopoles bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/50600395nas a2200109 4500008004100000245007300041210006900114260001800183100002100201700002800222856003500250 1987 en d00aLimits of nonlinear Dirichlet problems in varying domains. (Italian)0 aLimits of nonlinear Dirichlet problems in varying domains Italia bSISSA Library1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/486