00946nas a2200109 4500008004100000245009800041210006900139520046800208100001800676700001900694856012300713 2023 eng d00aA general splitting principle on RCD spaces and applications to spaces with positive spectrum0 ageneral splitting principle on RCD spaces and applications to sp3 a

In this paper we develop a general `analytic' splitting principle for RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about RCD spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.

1 aGigli, Nicola1 aMarconi, Fabio uhttps://www.math.sissa.it/publication/general-splitting-principle-rcd-spaces-and-applications-spaces-positive-spectrum01171nas a2200121 4500008004100000020001400041245007800055210006900133260001500202520075800217100002700975856004701002 2022 eng d a1573-869800aA Gradient Flow Equation for Optimal Control Problems With End-point Cost0 aGradient Flow Equation for Optimal Control Problems With Endpoin c2022/07/073 aIn this paper, we consider a control system of the form $\dot x = F(x)u$, linear in the control variable u. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an end-point cost and the squared 2-norm of the control. This functional induces a gradient flow on the Hilbert space of admissible controls, and we prove a convergence result by means of the Lojasiewicz-Simon inequality. Finally, we show that, if we let the weight of the end-point cost tend to infinity, the resulting family of functionals is Γ-convergent, and it turns out that the limiting problem consists in joining the starting point and a minimizer of the end-point cost with a horizontal length-minimizer path.1 aScagliotti, Alessandro uhttps://doi.org/10.1007/s10883-022-09604-200996nas a2200121 4500008004100000245004100041210003400082260001200116520067500128100001400803700002000817856003700837 2020 eng d00aOn the gauge group of Galois objects0 agauge group of Galois objects c03/20203 aWe study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the classical gauge groupoid of a principal bundle. When the base algebra is in the centre of the total space algebra, the gauge group of the noncommutative principal bundle is isomorphic to the group of bisections of the bialgebroid. In particular we consider Galois objects (non-trivial noncommutative bundles over a point in a sense) for which the bialgebroid is a Hopf algebra. For these we give a crossed module structure for the bisections and the automorphisms of the bialgebroid. Examples include Galois objects of group Hopf algebras and of Taft algebras.1 aHan, Xiao1 aLandi, Giovanni uhttps://arxiv.org/abs/2002.0609700522nas a2200157 4500008004100000245004600041210004600087260000600133100002000139700002200159700002900181700002600210700002300236700002400259856008100283 2020 eng d00aGauge theories on compact toric manifolds0 aGauge theories on compact toric manifolds c71 aBonelli, Giulio1 aFucito, Francesco1 aMorales, Jose, Francisco1 aRonzani, Massimiliano1 aSysoeva, Ekaterina1 aTanzini, Alessandro uhttps://www.math.sissa.it/publication/gauge-theories-compact-toric-manifolds01292nas a2200145 4500008004100000245004900041210004900090300001200139490000700151520086800158100002901026700002101055700002401076856004601100 2019 eng d00aGround state energy of mixture of Bose gases0 aGround state energy of mixture of Bose gases a19500050 v313 a

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number N becomes large. In the dilute regime, when the interaction potentials have the length scale of order O(N−1), we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is O(1), we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

1 aMichelangeli, Alessandro1 aNam, Phan, Thanh1 aOlgiati, Alessandro uhttps://doi.org/10.1142/S0129055X1950005300800nas a2200121 4500008004100000245006300041210005900104520039700163100002000560700002900580700002100609856004800630 2018 en d00aOn Geometric Quantum Confinement in Grushin-Like Manifolds0 aGeometric Quantum Confinement in GrushinLike Manifolds3 aWe study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.1 aGallone, Matteo1 aMichelangeli, Alessandro1 aPozzoli, Eugenio uhttp://preprints.sissa.it/handle/1963/3532201283nas a2200169 4500008004100000022001400041245010100055210006900156260000800225300000700233490000700240520074700247100002100994700002901015700002301044856004601067 2018 eng d a1420-903900aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed cMar a460 v693 a

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele uhttps://doi.org/10.1007/s00033-018-0938-500391nas a2200097 4500008004100000245006800041210006800109260003900177100001800216856005900234 2018 eng d00aGround states and spectral properties in quantum field theories0 aGround states and spectral properties in quantum field theories bFriedrich-Schiller-University Jena1 aLange, Markus uhttps://www.db-thueringen.de/receive/dbt_mods_0003519601393nas a2200145 4500008004100000245005300041210005100094260001000145520095500155100002201110700002101132700001901153700002701172856004801199 2017 en d00aGamma-Convergence of Free-discontinuity problems0 aGammaConvergence of Freediscontinuity problems bSISSA3 aWe study the Gamma-convergence of sequences of free-discontinuity functionals depending on vector-valued functions u which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of our result is that we work under very general assumptions on the integrands which, in particular, are not required to be periodic in the space variable. Further, we consider the case of surface integrands which are not bounded from below by the amplitude of the jump of u. We obtain three main results: compactness with respect to Gamma-convergence, representation of the Gamma-limit in an integral form and identification of its integrands, and homogenisation formulas without periodicity assumptions. In particular, the classical case of periodic homogenisation follows as a by-product of our analysis. Moreover, our result covers also the case of stochastic homogenisation, as we will show in a forthcoming paper.1 aCagnetti, Filippo1 aDal Maso, Gianni1 aScardia, Lucia1 aZeppieri, Caterina Ida uhttp://preprints.sissa.it/handle/1963/3527601348nas a2200241 4500008004100000022001400041245010800055210006900163300001200232490000800244520055100252653000800803653002500811653002900836653002900865653001800894653003000912100002300942700002000965700002600985700002401011856007101035 2017 eng d a0393-044000aGauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants0 aGauge theories on compact toric surfaces conformal field theorie a40 - 500 v1183 a

We show that equivariant Donaldson polynomials of compact toric surfaces can be calculated as residues of suitable combinations of Virasoro conformal blocks, by building on AGT correspondence between $\mathcal{N}=2$ supersymmetric gauge theories and two-dimensional conformal field theory. Talk presented by A.T. at the conference Interactions between Geometry and Physics — in honor of Ugo Bruzzo’s 60th birthday 17–22 August 2015, Guarujá, São Paulo, Brazil, mostly based on Bawane et al. (0000) and Bershtein et al. (0000).

10aAGT10aDonaldson invariants10aEquivariant localization10aExact partition function10aSupersymmetry10aVirasoro conformal blocks1 aBershtein, Mikhail1 aBonelli, Giulio1 aRonzani, Massimiliano1 aTanzini, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S039304401730016500448nas a2200121 4500008004100000245007100041210006400112300001400176490000700190100001700197700001600214856009600230 2017 eng d00aOn the generalized Cheeger problem and an application to 2d strips0 ageneralized Cheeger problem and an application to 2d strips a219–2370 v331 aPratelli, A.1 aSaracco, G. uhttps://www.math.sissa.it/publication/generalized-cheeger-problem-and-application-2d-strips01320nas a2200133 4500008004100000245008300041210006900124300001400193490000700207520089100214100001801105700002201123856004101145 2017 eng d00aOn the genesis of directional friction through bristle-like mediating elements0 agenesis of directional friction through bristlelike mediating el a1023-10460 v233 a

We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

1 aGidoni, Paolo1 aDeSimone, Antonio uhttps://doi.org/10.1051/cocv/201703001385nas a2200145 4500008004100000022001400041245009300055210006900148260000800217300001400225490000800239520092700247100001901174856004601193 2017 eng d a1618-189100aGlobally stable quasistatic evolution for strain gradient plasticity coupled with damage0 aGlobally stable quasistatic evolution for strain gradient plasti cApr a641–6850 v1963 a

We consider evolutions for a material model which couples scalar damage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin–Anand formulation (J Mech Phys Solids 53:1624–1649, 2005). The aim of the present model is to account for different phenomena: On the one hand, the elastic stiffness reduces and the plastic yield surface shrinks due to material's degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so-called energetic formulation). Furthermore, we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic damage model studied in Crismale (ESAIM Control Optim Calc Var 22:883-912, 2016).

1 aCrismale, Vito uhttps://doi.org/10.1007/s10231-016-0590-701947nas a2200145 4500008004100000245007100041210006800112260002100180300001200201490000700213520147800220100002901698700002401727856005001751 2017 eng d00aGross-Pitaevskii non-linear dynamics for pseudo-spinor condensates0 aGrossPitaevskii nonlinear dynamics for pseudospinor condensates bTaylor & Francis a426-4640 v243 a

We derive the equations for the non-linear effective dynamics of a so called pseudo-spinor Bose-Einstein condensate, which emerges from the linear many-body Schrödinger equation at the leading order in the number of particles. The considered system is a three-dimensional diluted gas of identical bosons with spin, possibly confined in space, and coupled with an external time-dependent magnetic field; particles also interact among themselves through a short-scale repulsive interaction. The limit of infinitely many particles is monitored in the physically relevant Gross-Pitaevskii scaling. In our main theorem, if at time zero the system is in a phase of complete condensation (at the level of the reduced one-body marginal) and with energy per particle fixed by the Gross-Pitaevskii functional, then such conditions persist also at later times, with the one-body orbital of the condensate evolving according to a system of non-linear cubic Schrödinger equations coupled among themselves through linear (Rabi) terms. The proof relies on an adaptation to the spinor setting of Pickl’s projection counting method developed for the scalar case. Quantitative rates of convergence are available, but not made explicit because evidently non-optimal. In order to substantiate the formalism and the assumptions made in the main theorem, in an introductory section we review the mathematical formalisation of modern typical experiments with pseudo-spinor condensates.

1 aMichelangeli, Alessandro1 aOlgiati, Alessandro uhttps://doi.org/10.1080/14029251.2017.134634800945nas a2200157 4500008004100000022001400041245007900055210007200134260000800206300001600214490000800230520046300238100002200701700001800723856004600741 2016 eng d a1618-189100aGeneralizing the Poincaré–Miranda theorem: the avoiding cones condition0 aGeneralizing the Poincaré–Miranda theorem the avoiding cones con cAug a1347–13710 v1953 a

After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\$±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

1 aFonda, Alessandro1 aGidoni, Paolo uhttps://doi.org/10.1007/s10231-015-0519-600947nas a2200133 4500008004100000245008500041210006900126260001700195300001400212490000700226520047700233100001900710856008400729 2016 eng d00aGlobally stable quasistatic evolution for a coupled elastoplastic–damage model0 aGlobally stable quasistatic evolution for a coupled elastoplasti bEDP Sciences a883–9120 v223 a

We show the existence of globally stable quasistatic evolutions for a rate-independent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.

1 aCrismale, Vito uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/03/cocv150037/cocv150037.html01057nas a2200145 4500008004100000245004700041210004300088300001600131490000600147520062100153100002100774700001700795700002000812856007900832 2016 eng d00aThe Gysin sequence for quantum lens spaces0 aGysin sequence for quantum lens spaces a1077–11110 v93 a

We define quantum lens spaces as ‘direct sums of line bundles’ and exhibit them as ‘total spaces’ of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence in K-theory. We use the sequence to compute the K-theory of the quantum lens spaces, in particular to give explicit geometric representatives of their K-theory classes. These representatives are interpreted as ‘line bundles’ over quantum lens spaces and generically define ‘torsion classes’. We work out explicit examples of these classes.

1 aArici, Francesca1 aBrain, Simon1 aLandi, Giovanni uhttps://www.math.sissa.it/publication/gysin-sequence-quantum-lens-spaces-001381nas a2200205 4500008004100000022001400041245007100055210006900126300001400195490000800209520074400217653001900961653002200980653002401002100002001026700002001046700002201066700001601088856007101104 2015 eng d a0001-870800aA general existence result for the Toda system on compact surfaces0 ageneral existence result for the Toda system on compact surfaces a937 - 9790 v2853 a

In this paper we consider the following Toda system of equations on a compact surface:−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−Δu1=−4π∑j=1mα1,j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−Δu2=−4π∑j=1mα2,j(δpj−1), which is motivated by the study of models in non-abelian Chern–Simons theory. Here h1,h2 are smooth positive functions, ρ1,ρ2 two positive parameters, pi points of the surface and α1,i,α2,j non-negative numbers. We prove a general existence result using variational methods. The same analysis applies to the following mean field equation−Δu=ρ1(heu∫ΣheudVg−1)−ρ2(he−u∫Σhe−udVg−1), which arises in fluid dynamics."

10aGeometric PDEs10aMin–max schemes10aVariational methods1 aBattaglia, Luca1 aJevnikar, Aleks1 aMalchiodi, Andrea1 aRuiz, David uhttp://www.sciencedirect.com/science/article/pii/S000187081500307201188nas a2200157 4500008004100000245005800041210005700099260003700156300001600193490000700209520065100216100002500867700002400892700002100916856009300937 2015 eng d00aGeodesics and horizontal-path spaces in Carnot groups0 aGeodesics and horizontalpath spaces in Carnot groups bMathematical Sciences Publishers a1569–16300 v193 a

We study properties of the space of horizontal paths joining the origin with a vertical point on a generic two-step Carnot group. The energy is a Morse-Bott functional on paths and its critical points (sub-Riemannian geodesics) appear in families (compact critical manifolds) with controlled topology. We study the asymptotic of the number of critical manifolds as the energy grows. The topology of the horizontal-path space is also investigated, and we find asymptotic results for the total Betti number of the sublevels of the energy as it goes to infinity. We interpret these results as local invariants of the sub-Riemannian structure.

1 aAgrachev, Andrei, A.1 aGentile, Alessandro1 aLerario, Antonio uhttps://www.math.sissa.it/publication/geodesics-and-horizontal-path-spaces-carnot-groups02043nas a2200121 4500008004100000245006000041210006000101260001000161520154600171653008801717100002101805856009501826 2015 en d00aGeometric phases in graphene and topological insulators0 aGeometric phases in graphene and topological insulators bSISSA3 aThis thesis collects three of the publications that the candidate produced during his Ph.D. studies. They all focus on geometric phases in solid state physics. We first study topological phases of 2-dimensional periodic quantum systems, in absence of a spectral gap, like e.g. (multilayer) graphene. A topological invariant n_v in Z, baptized eigenspace vorticity, is attached to any intersection of the energy bands, and characterizes the local topology of the eigenprojectors around that intersection. With the help of explicit models, each associated to a value of n_v in Z, we are able to extract the decay at infinity of the single-band Wannier function w in mono- and bilayer graphene, obtaining |w(x)| <= const |x|^{-2} as |x| tends to infinity. Next, we investigate gapped periodic quantum systems, in presence of time-reversal symmetry. When the time-reversal operator Theta is of bosonic type, i.e. it satisfies Theta^2 = 1, we provide an explicit algorithm to construct a frame of smooth, periodic and time-reversal symmetric (quasi-)Bloch functions, or equivalently a frame of almost-exponentially localized, real-valued (composite) Wannier functions, in dimension d <= 3. In the case instead of a fermionic time-reversal operator, satisfying Theta^2 = -1, we show that the existence of such a Bloch frame is in general topologically obstructed in dimension d=2 and d=3. This obstruction is encoded in Z_2-valued topological invariants, which agree with the ones proposed in the solid state literature by Fu, Kane and Mele.10aGeometric phases, graphene, topological insulators, Wannier functions, Bloch frames1 aMonaco, Domenico uhttps://www.math.sissa.it/publication/geometric-phases-graphene-and-topological-insulators01836nas a2200121 4500008004100000245006000041210005800101260001000159520139100169653003901560100002001599856009501619 2015 en d00aGibbs-Markov-Young Structures and Decay of Correlations0 aGibbsMarkovYoung Structures and Decay of Correlations bSISSA3 aIn this work we study mixing properties of discrete dynamical systems and related to them geometric structure. In the first chapter we show that the direct product of maps with Young towers admits a Young tower whose return times decay at a rate which is bounded above by the slowest of the rates of decay of the return times of the component maps. An application of this result, together with other results in the literature, yields various statistical properties for the direct product of various classes of systems, including Lorenz-like maps, multimodal maps, piecewise $C^2$ interval maps with critical points and singularities, H\'enon maps and partially hyperbolic systems. The second chapter is dedicated to the problem of decay of correlations for continuous observables. First we show that if the underlying system admits Young tower then the rate of decay of correlations for continuous observables can be estimated in terms of modulus of continuity and the decay rate of tail of Young tower. In the rest of the second chapter we study the relations between the rates of decay of correlations for smooth observables and continuous observables. We show that if the rates of decay of correlations is known for $C^r,$ observables ($r\ge 1$) then it is possible to obtain decay of correlations for continuous observables in terms of modulus of continuity.10aDecay of Correlations, GMY-towers1 aRuziboev, Marks uhttps://www.math.sissa.it/publication/gibbs-markov-young-structures-and-decay-correlations00332nas a2200085 4500008004100000245007900041210006900120100001900189856003800208 2015 eng d00aGli abachi: antichi strumenti precursori delle moderne macchine da calcolo0 aGli abachi antichi strumenti precursori delle moderne macchine d1 aKlun, Giuliano uhttp://hdl.handle.net/10077/1088400723nas a2200109 4500008004100000245009500041210006900136260001000205520031800215100002900533856005100562 2015 en d00aGlobal well-posedness of the magnetic Hartree equation with non-Strichartz external fields0 aGlobal wellposedness of the magnetic Hartree equation with nonSt bSISSA3 aWe study the magnetic Hartree equation with external fields to which magnetic Strichartz estimates are not necessarily applicable. We characterise the appropriate notion of energy space and in such a space we prove the global well-posedness of the associated initial value problem by means of energy methods only.1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444001517nas a2200121 4500008004100000245010200041210006900143260001000212520108600222653001901308100001801327856005001345 2014 en d00aGeometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution0 aGeometry and analysis of controlaffine systems motion planning h bSISSA3 aThis thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. In order to do this, we also prove a result in the same spirit as the Ball-Box theorem for sub-Riemannian systems, in the context of control-affine systems equipped with the L1 cost. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the diffusion dynamics. More precisely, we study whether solutions to the heat and Schrödinger equations associated with this Laplace-Beltrami operator are able to cross this singularity, and how its the presence affects the spectral properties of the operator, in particular under a magnetic Aharonov–Bohm-type perturbation.10acontrol theory1 aPrandi, Dario uhttp://urania.sissa.it/xmlui/handle/1963/747401332nas a2200121 4500008004100000245014300041210006900184260002100253520085000274100002301124700001201147856005101159 2014 en d00aGlobal Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension0 aGlobal Structure of Admissible BV Solutions to Piecewise Genuine bTaylor & Francis3 a

The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points Θ and a countable family of Lipschitz curves T{script} such that outside T{script} ∪ Θ the solution is continuous, and for all points in T{script}{set minus}Θ the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems.

1 aBianchini, Stefano1 aYu, Lei uhttp://urania.sissa.it/xmlui/handle/1963/3469400476nas a2200121 4500008004100000245011700041210006900158300001200227490000700239100001900246700002000265856006900285 2013 eng d00aThe gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation0 agap probabilities of the tacnode Pearcey and Airy point processe a13500030 v021 aBertola, Marco1 aCafasso, Mattia uhttp://www.worldscientific.com/doi/abs/10.1142/S201032631350003201258nas a2200145 4500008004100000245010200041210006900143260008500212300001400297490000700311520069200318100002201010700002301032856005701055 2013 eng d00aGeneralized Sturm-Liouville boundary conditions for first order differential systems in the plane0 aGeneralized SturmLiouville boundary conditions for first order d bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a293–3250 v423 a

We study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

1 aFonda, Alessandro1 aGarrione, Maurizio uhttps://projecteuclid.org:443/euclid.tmna/146124898101314nas a2200181 4500008004100000245006100041210006100102260001000163520076900173653001800942653002400960653002700984653002301011100002301034700002001057700001901077856003601096 2013 en d00aGenus stabilization for moduli of curves with symmetries0 aGenus stabilization for moduli of curves with symmetries bSISSA3 aIn a previous paper, arXiv:1206.5498, we introduced a new homological\r\ninvariant $\\e$ for the faithful action of a finite group G on an algebraic\r\ncurve.\r\n We show here that the moduli space of curves admitting a faithful action of a\r\nfinite group G with a fixed homological invariant $\\e$, if the genus g\' of the\r\nquotient curve is sufficiently large, is irreducible (and non empty iff the\r\nclass satisfies the condition which we define as \'admissibility\'). In the\r\nunramified case, a similar result had been proven by Dunfield and Thurston\r\nusing the classical invariant in the second homology group of G, H_2(G, \\ZZ).\r\n We achieve our result showing that the stable classes are in bijection with\r\nthe set of admissible classes $\\e$.10agroup actions10amapping class group10aModuli space of curves10aTeichmüller space1 aCatanese, Fabrizio1 aLönne, Michael1 aPerroni, Fabio uhttp://hdl.handle.net/1963/650900456nas a2200133 4500008004100000245006900041210006700110260001300177653003000190100001800220700002100238700002700259856003600286 2012 en d00aGamma-convergence and H-convergence of linear elliptic operators0 aGammaconvergence and Hconvergence of linear elliptic operators bElsevier10aLinear elliptic operators1 aAnsini, Nadia1 aDal Maso, Gianni1 aZeppieri, Caterina Ida uhttp://hdl.handle.net/1963/587800922nas a2200133 4500008004100000245007400041210006900115260001000184520049000194100002000684700002400704700002400728856003600752 2012 en d00aGauge Theories on ALE Space and Super Liouville Correlation Functions0 aGauge Theories on ALE Space and Super Liouville Correlation Func bSISSA3 aWe present a relation between N=2 quiver gauge theories on the ALE space O_{P^1}(-2) and correlators of N=1 super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the N=2^* instanton partition function is given by the product of the character of \\\\hat{SU}(2)_2 times the super Virasoro conformal block on the torus with one puncture.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/430501004nas a2200169 4500008004100000022001400041245009800055210006900153300001600222490000800238520043000246653002300676653002300699100002200722700001900744856007100763 2012 eng d a0022-039600aA general method for the existence of periodic solutions of differential systems in the plane0 ageneral method for the existence of periodic solutions of differ a1369 - 13910 v2523 a

We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems “at resonance” are also considered, provided a Landesman–Lazer type of condition is assumed.

10aNonlinear dynamics10aPeriodic solutions1 aFonda, Alessandro1 aSfecci, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002203961100319601643nas a2200157 4500008004100000245012600041210006900167260001300236520109700249653002201346100001801368700002001386700002201406700002101428856003601449 2012 en d00aGeneralized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs0 aGeneralized reduced basis methods and nwidth estimates for the a bSpringer3 aThe set of solutions of a parameter-dependent linear partial di fferential equation with smooth coe fficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affi ne parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions. In the case that the parameter-dependent operator has a dominant term in its affi ne expansion, one can prove the existence of exponentially convergent uniform approximation spaces for the entire solution manifold. These spaces can be constructed without any assumptions on the parametric regularity of the manifold \\r\\nonly spatial regularity of the solutions is required. The exponential convergence rate is then inherited by the generalized reduced basis method. We provide a numerical example related to parametrized elliptic\\r\\nequations con rming the predicted convergence rates.10asolution manifold1 aLassila, Toni1 aManzoni, Andrea1 aQuarteroni, Alfio1 aRozza, Gianluigi uhttp://hdl.handle.net/1963/634000982nas a2200133 4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812 2012 en d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin uhttp://hdl.handle.net/1963/646400898nas a2200145 4500008004100000245008300041210006900124260001300193490000800206520043400214653002000648100002600668700002200694856003600716 2011 en d00aGamma-convergence of energies for nematic elastomers in the small strain limit0 aGammaconvergence of energies for nematic elastomers in the small bSpringer0 v 233 a

We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

10aLiquid crystals1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/414101081nas a2200121 4500008004100000245004900041210004900090260001000139520061100149653014200760100002100902856003600923 2011 en d00aGeneralised functions of bounded deformation0 aGeneralised functions of bounded deformation bSISSA3 a

We introduce the space GBD of generalized functions of bounded deformation and study the structure properties of these functions: the rectifiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for GBD, which leads to a compactness result for the space GSBD of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational problems arising in fracture mechanics in the framework of linearized elasticity.

10afree discontinuity problems, special functions of bounded deformation, jump set, rec- tifiability, slicing, approximate differentiability1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/637401134nas a2200145 4500008004100000245006700041210006700108260001000175520068000185100002000865700002400885700002400909700001900933856003600952 2011 en d00aGeneralized matrix models and AGT correspondence at all genera0 aGeneralized matrix models and AGT correspondence at all genera bSISSA3 aWe study generalized matrix models corresponding to n-point Virasoro\r\nconformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT\r\ncorrespondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge\r\ntheories with generalized quiver diagrams. We obtain the generalized matrix\r\nmodels from the perturbative evaluation of the Liouville correlation functions\r\nand verify the consistency of the description with respect to degenerations of\r\nthe Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2\r\ngauge theory as the spectral curve of the generalized matrix model, thus\r\nproviding a check of AGT correspondence at all genera.1 aBonelli, Giulio1 aMaruyoshi, Kazunobu1 aTanzini, Alessandro1 aYagib, Futoshi uhttp://hdl.handle.net/1963/656800398nas a2200109 4500008004100000245009300041210006900134260001000203100002500213700001400238856003600252 2011 en d00aGeneralized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds0 aGeneralized Ricci Curvature Bounds for Three Dimensional Contact bSISSA1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/650700442nas a2200109 4500008004100000245003800041210003400079520013500113100002500248700002300273856003600296 2011 en d00aThe geometry of Maximum Principle0 ageometry of Maximum Principle3 aAn invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.1 aAgrachev, Andrei, A.1 aGamkrelidze, Revaz uhttp://hdl.handle.net/1963/645600792nas a2200109 4500008004300000245004300043210004200086260005400128520044800182100001600630856003600646 2010 en_Ud 00aGauge theory: from physics to geometry0 aGauge theory from physics to geometry bIstituto di matematica. Universita\\\' di Trieste3 aMaxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/410502590nas a2200265 4500008004100000245013200041210006900173260001000242520175000252100001702002700002402019700002002043700001902063700002102082700001802103700003002121700001802151700001702169700001702186700002002203700002202223700002402245700001902269856003602288 2010 en d00aGene expression analysis of the emergence of epileptiform activity after focal injection of kainic acid into mouse hippocampus.0 aGene expression analysis of the emergence of epileptiform activi bWiley3 a

We report gene profiling data on genomic processes underlying the progression towards recurrent seizures after injection of kainic acid (KA) into the mouse hippocampus. Focal injection enabled us to separate the effects of proepileptic stimuli initiated by KA injection. Both the injected and contralateral hippocampus participated in the status epilepticus. However, neuronal death induced by KA treatment was restricted to the injected hippocampus, although there was some contralateral axonal degeneration. We profiled gene expression changes in dorsal and ventral regions of both the injected and contralateral hippocampus. Changes were detected in the expression of 1526 transcripts in samples from three time-points: (i) during the KA-induced status epilepticus, (ii) at 2 weeks, before recurrent seizures emerged, and (iii) at 6 months after seizures emerged. Grouping genes with similar spatio-temporal changes revealed an early transcriptional response, strong immune, cell death and growth responses at 2 weeks and an activation of immune and extracellular matrix genes persisting at 6 months. Immunostaining for proteins coded by genes identified from array studies provided evidence for gliogenesis and suggested that the proteoglycan biglycan is synthesized by astrocytes and contributes to a glial scar. Gene changes at 6 months after KA injection were largely restricted to tissue from the injection site. This suggests that either recurrent seizures might depend on maintained processes including immune responses and changes in extracellular matrix proteins near the injection site or alternatively might result from processes, such as growth, distant from the injection site and terminated while seizures are maintained.

1 aMotti, Dario1 aLe Duigou, Caroline1 aChemaly, Nicole1 aWittner, Lucia1 aLazarevic, Dejan1 aKrmac, Helena1 aMarstrand, Troels, Torben1 aValen, Eivind1 aSanges, Remo1 aStupka, Elia1 aSandelin, Albin1 aCherubini, Enrico1 aGustincich, Stefano1 aMiles, Richard uhttp://hdl.handle.net/1963/448000947nas a2200181 4500008004100000022001400041245007300055210006900128300001600197490000800213520035200221653002500573653002000598653002300618653002700641100002600668856007100694 2010 eng d a0022-123600aGeneric multiplicity for a scalar field equation on compact surfaces0 aGeneric multiplicity for a scalar field equation on compact surf a2165 - 21920 v2593 a

We prove generic multiplicity of solutions for a scalar field equation on compact surfaces via Morse inequalities. In particular our result improves significantly the multiplicity estimate which can be deduced from the degree-counting formula in Chen and Lin (2003) [12]. Related results are derived for the prescribed Q-curvature equation.

10aGeneric multiplicity10aGeometric PDE's10aMorse inequalities10aScalar field equations1 aDe Marchis, Francesca uhttp://www.sciencedirect.com/science/article/pii/S002212361000269700807nas a2200157 4500008004300000245008900043210006900132260002800201520027900229100002200508700002100530700002100551700002200572700001900594856003600613 2010 en_Ud 00aOn the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system0 ageometric origin of the biHamiltonian structure of the CalogeroM bOxford University Press3 aWe show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.1 aBartocci, Claudio1 aFalqui, Gregorio1 aMencattini, Igor1 aOrtenzi, Giovanni1 aPedroni, Marco uhttp://hdl.handle.net/1963/380001140nas a2200109 4500008004300000245006600043210006200109520077800171100002400949700002100973856003600994 2010 en_Ud 00aThe geometry emerging from the symmetries of a quantum system0 ageometry emerging from the symmetries of a quantum system3 aWe investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of \\\"continuous sections\\\" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne\\\'s thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.1 aDe Nittis, Giuseppe1 aPanati, Gianluca uhttp://hdl.handle.net/1963/383400848nas a2200133 4500008004100000245008600041210006900127300001400196490000700210520038600217100001900603700001900622856007300641 2010 eng d00aA global compactness result for the p-Laplacian involving critical nonlinearities0 aglobal compactness result for the pLaplacian involving critical  a469–4930 v283 a
We prove a representation theorem for Palais-Smale sequences involving the p-Laplacian and critical nonlinearities. Applications are given to a critical problem.

 

1 aMercuri, Carlo1 aWillem, Michel uhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=509700873nas a2200133 4500008004300000245004600043210004600089260001300135520049300148100002000641700001800661700002400679856003600703 2009 en_Ud 00aGauged Laplacians on quantum Hopf bundles0 aGauged Laplacians on quantum Hopf bundles bSpringer3 aWe study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum sphere\\\' in the field of a magnetic monopole. The energies are not invariant under the exchange monopole/antimonopole, that is under inverting the direction of the magnetic field. There are potential applications to models of quantum Hall effect.1 aLandi, Giovanni1 aReina, Cesare1 aZampini, Alessandro uhttp://hdl.handle.net/1963/354001551nas a2200121 4500008004300000245007900043210006900122520113900191100002501330700001701355700002101372856003601393 2008 en_Ud 00aA Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds0 aGaussBonnetlike formula on twodimensional almostRiemannian manif3 aWe consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent, then they define a classical Riemannian metric on $M$ (the metric for which they are orthonormal) and they give to $M$ the structure of metric space. If $X$ and $Y$ become linearly dependent somewhere on $M$, then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way are called almost-Riemannian structures. They are special cases of rank-varying sub-Riemannian structures, which are naturally defined in terms of submodules of the space of smooth vector fields on $M$. Almost-Riemannian structures show interesting phenomena, in particular for what concerns the relation between curvature, presence of conjugate points, and topology of the manifold. The main result of the paper is a generalization to almost-Riemannian structures of the Gauss-Bonnet formula.1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aSigalotti, Mario uhttp://hdl.handle.net/1963/186901036nas a2200133 4500008004300000245007100043210006900114520059000183100002100773700002200794700002500816700002500841856003600866 2008 en_Ud 00aGlobally stable quasistatic evolution in plasticity with softening0 aGlobally stable quasistatic evolution in plasticity with softeni3 aWe study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/196500681nas a2200109 4500008004300000245012000043210006900163520026100232100002100493700002100514856003600535 2008 en_Ud 00aGradient bounds for minimizers of free discontinuity problems related to cohesive zone models in fracture mechanics0 aGradient bounds for minimizers of free discontinuity problems re3 aIn this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.1 aDal Maso, Gianni1 aGarroni, Adriana uhttp://hdl.handle.net/1963/172300617nas a2200109 4500008004300000245007000043210006900113520025100182100001700433700002100450856003600471 2007 en_Ud 00aGaussian estimates for hypoelliptic operators via optimal control0 aGaussian estimates for hypoelliptic operators via optimal contro3 aWe obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitable optimal control problem.1 aBoscain, Ugo1 aPolidoro, Sergio uhttp://hdl.handle.net/1963/199401442nas a2200097 4500008004300000245010600043210006900149520107200218100001801290856003601308 2006 en_Ud 00aOn geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 10 ageodesic equivalence of Riemannian metrics and subRiemannian met3 aThe present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem.1 aZelenko, Igor uhttp://hdl.handle.net/1963/220500286nas a2200085 4500008004300000245004900043210004900092100002300141856003600164 2006 en_Ud 00aGlimm interaction functional for BGK schemes0 aGlimm interaction functional for BGK schemes1 aBianchini, Stefano uhttp://hdl.handle.net/1963/177000711nas a2200109 4500008004300000245009600043210006900139520031700208100002100525700001900546856003600565 2005 en_Ud 00aGel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited0 aGelfandZakharevich Systems and Algebraic Integrability the Volte3 aIn this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/168900651nas a2200109 4500008004300000245005100043210005000094520031700144100002100461700002300482856003600505 2005 en_Ud 00aGlobal solutions of the Hunter-Saxton equation0 aGlobal solutions of the HunterSaxton equation3 aWe construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp estimates on the continuity of solutions with respect to the initial data.1 aBressan, Alberto1 aConstantin, Adrian uhttp://hdl.handle.net/1963/225600958nas a2200121 4500008004300000245009200043210006900135520053000204100002400734700002000758700002200778856003600800 2005 en_Ud 00aGround states of nonlinear Schroedinger equations with potentials vanishing at infinity0 aGround states of nonlinear Schroedinger equations with potential3 aWe deal with a class on nonlinear Schr\\\\\\\"odinger equations \\\\eqref{eq:1} with potentials $V(x)\\\\sim |x|^{-\\\\a}$, $0<\\\\a<2$, and $K(x)\\\\sim |x|^{-\\\\b}$, $\\\\b>0$. Working in weighted Sobolev spaces, the existence of ground states $v_{\\\\e}$ belonging to $W^{1,2}(\\\\Rn)$ is proved under the assumption that $p$ satisfies \\\\eqref{eq:p}. Furthermore, it is shown that $v_{\\\\e}$ are {\\\\em spikes} concentrating at a minimum of ${\\\\cal A}=V^{\\\\theta}K^{-2/(p-1)}$, where $\\\\theta= (p+1)/(p-1)-1/2$.1 aAmbrosetti, Antonio1 aFelli, Veronica1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/235200797nas a2200121 4500008004300000245007900043210006900122520038600191100002200577700002100599700001900620856003600639 2004 en_Ud 00aA geometric approach to the separability of the Neumann-Rosochatius system0 ageometric approach to the separability of the NeumannRosochatius3 aWe study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.1 aBartocci, Claudio1 aFalqui, Gregorio1 aPedroni, Marco uhttp://hdl.handle.net/1963/254101156nas a2200121 4500008004300000245006500043210006400108260001900172520076900191100002100960700001700981856003600998 2003 en_Ud 00aGaudin models and bending flows: a geometrical point of view0 aGaudin models and bending flows a geometrical point of view bIOP Publishing3 aIn this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.1 aFalqui, Gregorio1 aMusso, Fabio uhttp://hdl.handle.net/1963/288401411nas a2200109 4500008004300000245012000043210006900163260001000232520100100242100002201243856003601265 2003 en_Ud 00aGeometric motion control for a kinematically redundant robotic chain: application to a holonomic mobile manipulator0 aGeometric motion control for a kinematically redundant robotic c bWiley3 aFor kinematically redundant robotic manipulators, the extra degrees of freedom available allows freedom in the generation of the trajectories of the end-effector. In this paper, for this scope, we use techniques for motion control of rigid bodies on Riemannian manifolds (and Lie groups in particular) to design workspace control algorithms for the end-effector of the robotic chain and then to pull them back to joint space, all respecting the different geometric structures of the two underlying model spaces. The trajectory planner makes use of geometric splines. Examples of the different kinds of curves that are obtained via the De Casteljau algorithm in correspondence of different metric structures in SE(3) are reported. The feedback module, instead, consists of a Lyapunov based PD controller defined from a suitable notion of error distance on the Lie group. The motivating application of our work is a holonomic mobile manipulator for which simulation results are described in detail.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/301900403nas a2200097 4500008004100000245011900041210006900160260001800229100002200247856003600269 2002 en d00aOn the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields0 ageneration of sequential unitary gates from continuous time Schr bSISSA Library1 aAltafini, Claudio uhttp://hdl.handle.net/1963/161401353nas a2200121 4500008004300000245003200043210003200075260001300107520103200120100002501152700001801177856003601195 2002 en_Ud 00aGeometry of Jacobi Curves I0 aGeometry of Jacobi Curves I bSpringer3 aJacobi curves are deep generalizations of the spaces of \\\"Jacobi fields\\\" along Riemannian geodesics. Actually, Jacobi curves are curves in the Lagrange Grassmannians. In our paper we develop differential geometry of these curves which provides basic feedback or gauge invariants for a wide class of smooth control systems and geometric structures. Two principal invariants are the generalized Ricci curvature, which is an invariant of the parametrized curve in the Lagrange Grassmannian endowing the curve with a natural projective structure, and a fundamental form, which is a fourth-order differential on the curve. The so-called rank 1 curves are studied in more detail. Jacobi curves of this class are associated with systems with scalar controls and with rank 2 vector distributions.\\nIn the forthcoming second part of the paper we will present the comparison theorems (i.e., the estimates for the conjugate points in terms of our invariants( for rank 1 curves an introduce an important class of \\\"flat curves\\\".1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/311000314nas a2200109 4500008004100000245003300041210003300074260001800107100002500125700001800150856003600168 2002 en d00aGeometry of Jacobi curves II0 aGeometry of Jacobi curves II bSISSA Library1 aAgrachev, Andrei, A.1 aZelenko, Igor uhttp://hdl.handle.net/1963/158901286nas a2200109 4500008004300000245007200043210006900115260003700184520089400221100002501115856003601140 2002 en_Ud 00aGlobal calibrations for the non-homogeneous Mumford-Shah functional0 aGlobal calibrations for the nonhomogeneous MumfordShah functiona bScuola Normale Superiore di Pisa3 aUsing a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/308900435nas a2200121 4500008004100000245003800041210003700079260001800116520010100134100002100235700002100256856003600277 2001 en d00aGamma-limit of periodic obstacles0 aGammalimit of periodic obstacles bSISSA Library3 aWe compute the Gamma-limit of a sequence obstacle functionals in the case of periodic obstacles.1 aDal Maso, Gianni1 aTrebeschi, Paola uhttp://hdl.handle.net/1963/149500342nas a2200097 4500008004100000245006700041210006400108260001300172100002300185856003600208 2001 en d00aA Glimm type functional for a special Jin-Xin relaxation model0 aGlimm type functional for a special JinXin relaxation model bElsevier1 aBianchini, Stefano uhttp://hdl.handle.net/1963/135500375nas a2200109 4500008004100000245006200041210006200103260001800165100002300183700002300206856003600229 2001 en d00aGlobal continuous Riemann solver for nonlinear elasticity0 aGlobal continuous Riemann solver for nonlinear elasticity bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149300612nas a2200157 4500008004100000022001400041245010500055210006900160300001400229490000800243100001900251700001800270700001900288700002300307856012400330 2000 eng d a0550-321300aA general construction of conformal field theories from scalar anti-de Sitter quantum field theories0 ageneral construction of conformal field theories from scalar ant a619–6440 v5871 aBertola, Marco1 aBros, Jacques1 aMoschella, Ugo1 aSchaeffer, Richard uhttps://www.math.sissa.it/publication/general-construction-conformal-field-theories-scalar-anti-de-sitter-quantum-field00524nas a2200157 4500008004100000022001400041245005900055210005900114300001400173490000600187100002300193700001900216700001900235700002100254856009100275 1998 eng d a0202-289300aGeneration of primordial fluctuations in curved spaces0 aGeneration of primordial fluctuations in curved spaces a121–1270 v41 aSchaeffer, Richard1 aMoschella, Ugo1 aBertola, Marco1 aGorini, Vittorio uhttps://www.math.sissa.it/publication/generation-primordial-fluctuations-curved-spaces01087nas a2200121 4500008004100000245007400041210006900115260001800184520068400202100002100886700002300907856003500930 1998 en d00aA generic classification of time-optimal planar stabilizing feedbacks0 ageneric classification of timeoptimal planar stabilizing feedbac bSISSA Library3 aConsider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.1 aBressan, Alberto1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/99800347nas a2200109 4500008004100000245005100041210005100092260001800143100001700161700002300178856003600201 1998 en d00aGeometric control approach to synthesis theory0 aGeometric control approach to synthesis theory bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/127700741nas a2200097 4500008004100000245005600041210005600097520043400153100002000587856003600607 1998 en d00aGeometry and analytic theory of Frobenius manifolds0 aGeometry and analytic theory of Frobenius manifolds3 aMain mathematical applications of Frobenius manifolds are\\r\\nin the theory of Gromov - Witten invariants, in singularity theory, in\\r\\ndifferential geometry of the orbit spaces of reflection groups and of their\\r\\nextensions, in the hamiltonian theory of integrable hierarchies. The theory\\r\\nof Frobenius manifolds establishes remarkable relationships between\\r\\nthese, sometimes rather distant, mathematical theories.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/648800493nas a2200121 4500008004100000020001800041245004600059210004600105260001000151520015400161100002000315856003600335 1995 en d a3-540-60542-800aGeometry of 2D topological field theories0 aGeometry of 2D topological field theories bSISSA3 aThese notes are devoted to the theory of “equations of associativity”\\r\\ndescribing geometry of moduli spaces of 2D topological field theories.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/648301159nas a2200109 4500008004100000245006900041210006800110260001000178520080500188100002000993856003601013 1993 en d00aGeometry and integrability of topological-antitopological fusion0 aGeometry and integrability of topologicalantitopological fusion bSISSA3 aIntegrability of equations of topological-antitopological fusion (being proposed\\r\\nby Cecotti and Vafa) describing the ground state metric on a given 2D topological\\r\\nfield theory (TFT) model, is proved. For massive TFT models these equations\\r\\nare reduced to a universal form (being independent on the given TFT model) by\\r\\ngauge transformations. For massive perturbations of topological conformal field theory\\r\\nmodels the separatrix solutions of the equations bounded at infinity are found\\r\\nby the isomonodromy deformations method. Also it is shown that the ground state\\r\\nmetric together with some part of the underlined TFT structure can be parametrized\\r\\nby pluriharmonic maps of the coupling space to the symmetric space of real positive\\r\\ndefinite quadratic forms.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/648100370nas a2200121 4500008004100000245004000041210003900081260001800120100002600138700002100164700002800185856003500213 1990 en d00aG-convergence of monotone operators0 aGconvergence of monotone operators bSISSA Library1 aChiadò Piat, Valeria1 aDal Maso, Gianni1 aDefranceschi, Anneliese uhttp://hdl.handle.net/1963/68000355nas a2200109 4500008004100000245005600041210005400097260001800151100002000169700002100189856003500210 1990 en d00aA general chain rule for distributional derivatives0 ageneral chain rule for distributional derivatives bSISSA Library1 aAmbrosio, Luigi1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/65000381nas a2200097 4500008004100000245009600041210006900137260001800206100002400224856003500248 1990 en d00aA general existence theorem for boundary value problems for ordinary differential equations0 ageneral existence theorem for boundary value problems for ordina bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/63200393nas a2200109 4500008004100000245007700041210006900118260001800187100002100205700002200226856003500248 1988 en d00aGeneralized Baire category and differential inclusions in Banach spaces.0 aGeneralized Baire category and differential inclusions in Banach bSISSA Library1 aBressan, Alberto1 aColombo, Giovanni uhttp://hdl.handle.net/1963/53800303nas a2200109 4500008004100000245003000041210002900071260001800100100002000118700002000138856003500158 1987 en d00aGraded Chern-Simons terms0 aGraded ChernSimons terms bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/508