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

%B VIII International Conference on Computational Methods in Marine Engineering %G eng %0 Report %D 2019 %T A continuous dependence result for a dynamic debonding model in dimension one %A Filippo Riva %XIn this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin ﬁlm peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griﬃth’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to diﬀerent natural topologies.

%I SISSA %G en %U http://preprints.sissa.it/xmlui/handle/1963/35329 %1 35640 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2019-03-07T10:11:29Z No. of bitstreams: 1 PREPRINT_A continuous dependence result_Riva.pdf: 414517 bytes, checksum: 2719ac30fe4051bca0f76f6e2f603b4c (MD5) %0 Report %D 2018 %T Canonical Surfaces and Hypersurfaces in Abelian Varieties %A Luca Cesarano %G eng %U https://arxiv.org/abs/1808.05302 %0 Report %D 2018 %T On the Cauchy problem for the wave equation on time-dependent domains %A Gianni Dal Maso %A Rodica Toader %X We introduce a notion of solution to the wave equation on a suitable class of time-dependent domains and compare it with a previous de nition. We prove an existence result for the solution of the Cauchy problem and present some additional conditions which imply uniqueness. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35314 %1 35622 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-04-23T06:03:52Z No. of bitstreams: 1 DM-Toa-18-sissa.pdf: 404543 bytes, checksum: 73bb5b0c57b574d05b3d6f33417016e0 (MD5) %0 Journal Article %J Journal of Scientific Computing %D 2018 %T Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models %A Immanuel Martini %A Bernard Haasdonk %A Gianluigi Rozza %B Journal of Scientific Computing %V 74 %P 197-219 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 %R 10.1007/s10915-017-0430-y %0 Report %D 2018 %T Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations %A Stefano Bianchini %A Laura Spinolo %X We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems. %I SISSA %G en %U http://preprints.sissa.it/handle/1963/35325 %1 35635 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-10-16T11:48:42Z No. of bitstreams: 1 BiaSpiEuler116.pdf: 615669 bytes, checksum: 93b99e76a8c0a0f3e1753969d7170d1e (MD5) %0 Journal Article %J Mathematical Models and Methods in Applied Sciences %D 2018 %T Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue %A Vito Crismale %A Giuliano Lazzaroni %A Gianluca Orlando %XIn this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

%B Mathematical Models and Methods in Applied Sciences %V 28 %P 1371-1412 %G eng %U https://doi.org/10.1142/S0218202518500379 %R 10.1142/S0218202518500379 %0 Book Section %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %D 2018 %T Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods %A Marco Tezzele %A Francesco Ballarin %A Gianluigi Rozza %B Mathematical and Numerical Modeling of the Cardiovascular System and Applications %I Springer %P 185–207 %G eng %0 Journal Article %J J. Elast. %D 2018 %T A Comparison Between Active Strain and Active Stress in Transversely Isotropic Hyperelastic Materials %A Giulia Giantesio %A Alessandro Musesti %A Davide Riccobelli %B J. Elast. %I Springer Nature %G eng %0 Book Section %B Cardiovascular Mechanics %D 2018 %T Computational methods in cardiovascular mechanics %A Auricchio, Ferdinando %A Conti, Michele %A Lefieux, Adrian %A Morganti, Simone %A Alessandro Reali %A Gianluigi Rozza %A Veneziani, Alessandro %E Michel F. Labrosse %XThe introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options. The terminology in silico is, nowadays, commonly accepted for indicating this new source of knowledge added to traditional in vitro and in vivo investigations. The advantages of in silico methodologies are basically the low cost in terms of infrastructures and facilities, the reduced invasiveness and, in general, the intrinsic predictive capabilities based on the use of mathematical models. The disadvantages are generally identified in the distance between the real cases and their virtual counterpart required by the conceptual modeling that can be detrimental for the reliability of numerical simulations.

%B Cardiovascular Mechanics %I CRC Press %P 54 %G eng %U https://www.taylorfrancis.com/books/e/9781315280288/chapters/10.1201%2Fb21917-5 %& Computational methods in cardiovascular mechanics %0 Report %D 2018 %T On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω) %A Emanuele Tasso %X In this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions. %G en %U http://preprints.sissa.it/handle/1963/35324 %1 35634 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-09-24T10:42:46Z No. of bitstreams: 1 On the continuity of the trace operator.pdf: 553250 bytes, checksum: 9693a7e3f871c2668b56f852cf7f6025 (MD5) %0 Book Section %B Spectral and High Order Methods for Partial Differential Equations %D 2017 %T Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation %A Denis Devaud %A Gianluigi Rozza %XIn this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on

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

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

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

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

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

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

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

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

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

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

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

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

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

%B Spectral and High Order Methods for Partial Differential Equations %7 Bittencourt, Dumont, Hesthaven. (Eds). %I Springer %C Heildeberg %V 119 %@ 978-3-319-65869-8 %G eng %0 Journal Article %J SIAM Journal on Numerical Analysis %D 2017 %T On a certified smagorinsky reduced basis turbulence model %A Rebollo, T.C. %A E.D. Ávila %A Marmol, M.G. %A Francesco Ballarin %A Gianluigi Rozza %B SIAM Journal on Numerical Analysis %V 55 %P 3047-3067 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85039928218&doi=10.1137%2f17M1118233&partnerID=40&md5=221d9cd2bcc74121fcef93efd9d3d76c %R 10.1137/17M1118233 %0 Journal Article %J Journal of Differential Equations %D 2017 %T Clifford Tori and the singularly perturbed Cahn–Hilliard equation %A Matteo Rizzi %K Cahn–Hilliard equation %K Clifford Torus %K Lyapunov–Schmidt reduction %K Willmore surface %XIn this paper we construct entire solutions uε to the Cahn–Hilliard equation −ε2Δ(−ε2Δu+W′(u))+W″(u)(−ε2Δu+W′(u))=ε4λε(1−uε), under the volume constraint ∫R3(1−uε)2dx=82π2cε, with cε→1 as ε→0, whose nodal set approaches the Clifford Torus, that is the Torus with radii of ratio 1/2 embedded in R3, as ε→0. It is crucial that the Clifford Torus is a Willmore hypersurface and it is non-degenerate, up to conformal transformations. The proof is based on the Lyapunov–Schmidt reduction and on careful geometric expansions of the Laplacian.

%B Journal of Differential Equations %V 262 %P 5306 - 5362 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039617300530 %R https://doi.org/10.1016/j.jde.2017.01.026 %0 Report %D 2017 %T Complex Friedrichs systems and applications %A Nenad Antonić %A Krešimir Burazin %A Ivana Crnjac %A Marko Erceg %X We provide a suitable extension of the theory of abstract Friedrichs systems from real Hilbert spaces to the complex Hilbert space setting, which allows for applications to partial differential equations with complex coeffcients. We also provide examples where the involved Hilbert space is not the space of square integrable functions, as it was the case in previous works, but rather its closed subspace or the space Hs(Rd;Cr), for real s. This setting appears to be suitable for particular systems of partial differential equations, such as the Dirac system, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the time-harmonic Maxwell system, which are all addressed in the paper. Moreover, for the time-harmonic Maxwell system we also applied a suitable version of the two-field theory with partial coercivity assumption which is developed in the paper. %G en %U http://urania.sissa.it/xmlui/handle/1963/35270 %1 35576 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-01-20T12:35:16Z No. of bitstreams: 1 antonic_burazin_crnjac_erceg2016_preprint.pdf: 308035 bytes, checksum: 7c8e2264f51ab9699c6cbe9585fc047a (MD5) %0 Journal Article %J Journal of Computational Physics %D 2017 %T Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology %A Giuseppe Pitton %A Annalisa Quaini %A Gianluigi Rozza %K Parametrized Navier–Stokes equations %K Reduced basis method %K Stability of flows %K Symmetry breaking bifurcation %XWe focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier–Stokes equations for a Newtonian and viscous fluid in contraction–expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.

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

%B Journal of Computational Physics %V 344 %P 247 - 259 %G eng %U http://www.sciencedirect.com/science/article/pii/S002199911730356X %R https://doi.org/10.1016/j.jcp.2017.04.068 %0 Report %D 2017 %T On contact interactions realised as Friedrichs systems %A Marko Erceg %A Alessandro Michelangeli %X We realise the Hamiltonians of contact interactions in quantum mechanics within the framework of abstract Friedrichs systems. In particular, we show that the construction of the self-adjoint (or even only closed) operators of contact interaction supported at a fixed point can be associated with the construction of the bijective realisations of a suitable pair of abstract Friedrich operators. In this respect, the Hamiltonians of contact interaction provide novel examples of abstract Friedrich systems. %G en %U http://preprints.sissa.it/handle/1963/35298 %1 35604 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2017-10-10T11:23:22Z No. of bitstreams: 1 SISSA_preprint_48-2017-MATE.pdf: 431531 bytes, checksum: 0368c692a322778cda197c49c320b3a6 (MD5) %0 Journal Article %J Nonlinear Analysis %D 2017 %T Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators %A Davide Barilari %A Elisa Paoli %K Curvature %K Hypoelliptic heat equation %K Small time asymptotics %XWe consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We completely describe the small time heat kernel expansions on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the drift field and the curvature-like invariants of the optimal control problem associated with the diffusion operator.

%B Nonlinear Analysis %V 164 %P 118 - 134 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X17302298 %R https://doi.org/10.1016/j.na.2017.09.002 %0 Journal Article %J Engineering with Computers %D 2017 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %B Engineering with Computers %I Springer Nature %V 34 %P 565–576 %8 dec %G eng %U https://doi.org/10.1007/s00366-017-0558-2 %R 10.1007/s00366-017-0558-2 %0 Report %D 2016 %T Coalescence Phenomenon of Quantum Cohomology of Grassmannians and the Distribution of Prime Numbers %A Giordano Cotti %G eng %0 Journal Article %J Journal of High Energy Physics %D 2016 %T Comparing Poisson Sigma Model with A-model %A Bonechi, F. %A Cattaneo, A.S. %A Riccardo Iraso %XWe discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

%B Journal of High Energy Physics %V 2016 %P 133 %8 Oct %G eng %U https://doi.org/10.1007/JHEP10(2016)133 %R 10.1007/JHEP10(2016)133 %0 Journal Article %J Discrete & Continuous Dynamical Systems - S %D 2016 %T On the concentration of entropy for scalar conservation laws %A Stefano Bianchini %A Elio Marconi %K concentration %K Conservation laws %K entropy solutions %K Lagrangian representation %K shocks %XWe prove that the entropy for an $L^∞$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution.

%B Discrete & Continuous Dynamical Systems - S %V 9 %P 73 %G eng %U http://aimsciences.org//article/id/ce4eb91e-9553-4e8d-8c4c-868f07a315ae %R 10.3934/dcdss.2016.9.73 %0 Journal Article %D 2016 %T Confinement of dislocations inside a crystal with a prescribed external strain %A Ilaria Lucardesi %A Marco Morandotti %A Riccardo Scala %A Davide Zucco %X We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach. %G en %U http://urania.sissa.it/xmlui/handle/1963/35247 %1 35558 %2 Mathematics %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-10-20T11:44:46Z No. of bitstreams: 1 LMSZ-preprint.pdf: 547676 bytes, checksum: 5c7add921deefef560aac54da6a584cc (MD5) %0 Journal Article %J Journal of Dynamical and Control Systems %D 2016 %T Conformal Equivalence of 3D Contact Structures on Lie Groups %A Francesco Boarotto %XIn this paper, a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular, we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group $mathbbH^3$ or its conformal classification coincides with the metric one. If a structure is locally conformally flat, then its conformal group is locally isomorphic to $SU(2,1)$.

%B Journal of Dynamical and Control Systems %V 22 %P 251–283 %8 Apr %G eng %U https://doi.org/10.1007/s10883-015-9273-8 %R 10.1007/s10883-015-9273-8 %0 Journal Article %J Annales Henri Poincaré %D 2016 %T Construction of Real-Valued Localized Composite Wannier Functions for Insulators %A Domenico Fiorenza %A Domenico Monaco %A Gianluca Panati %XWe consider a real periodic Schrödinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite Wannier functions. To this aim, we show that in dimension $d\leq 3$, there exists a global frame consisting of smooth quasi-Bloch functions which are both periodic and time-reversal symmetric. Aiming to applications in computational physics, we provide a constructive algorithm to obtain such a Bloch frame. The construction yields the existence of a basis of composite Wannier functions which are real-valued and almost-exponentially localized. The proof of the main result exploits only the fundamental symmetries of the projector on the relevant bands, allowing applications, beyond the model specified above, to a broad range of gapped periodic quantum systems with a time-reversal symmetry of bosonic type.

%B Annales Henri Poincaré %V 17 %P 63–97 %8 Jan %G eng %U https://doi.org/10.1007/s00023-015-0400-6 %R 10.1007/s00023-015-0400-6 %0 Journal Article %J Phys. D %D 2016 %T Correlation functions of the KdV hierarchy and applications to intersection numbers over $\overline\CalM_g,n$ %A Marco Bertola %A Boris Dubrovin %A Di Yang %B Phys. D %V 327 %P 30–57 %G eng %U http://dx.doi.org/10.1016/j.physd.2016.04.008 %R 10.1016/j.physd.2016.04.008 %0 Journal Article %D 2016 %T CORRIGENDUM: The dependence on the monodromy data of the isomonodromic tau function %A Marco Bertola %8 01 %G eng %U http://arxiv.org/abs/1601.04790 %0 Journal Article %J arXiv preprint arXiv:1601.07093 %D 2016 %T Critical points of a perturbed Otha-Kawasaki functional %A Matteo Rizzi %B arXiv preprint arXiv:1601.07093 %G eng %0 Journal Article %J Methods and Applications of Analysis %D 2016 %T Currents and dislocations at the continuum scale %A Riccardo Scala %A Nicolas Van Goethem %XA striking geometric property of elastic bodies with dislocations is that the deformation tensor cannot be written as the gradient of a one-to-one immersion, its curl being nonzero and equal to the density of the dislocations, a measure concentrated in the dislocation lines. In this work, we discuss the mathematical properties of such constrained deformations and study a variational problem in finite-strain elasticity, where Cartesian maps allow us to consider deformations in $L^p$ with $1\leq p<2$, as required for dislocation-induced strain singularities. Firstly, we address the problem of mathematical modeling of dislocations. It is a key purpose of the paper to build a framework where dislocations are described in terms of integral 1-currents and to extract from this theoretical setting a series of notions having a mechanical meaning in the theory of dislocations. In particular, the paper aims at classifying integral 1-currents, with modeling purposes. In the second part of the paper, two variational problems are solved for two classes of dislocations, at the mesoscopic and at the continuum scale. By continuum it is here meant that a countable family of dislocations is considered, allowing for branching and cluster formation, with possible complex geometric patterns. Therefore, modeling assumptions of the defect part of the energy must also be provided, and discussed.

%B Methods and Applications of Analysis %I International Press of Boston %V 23 %P 1–34 %G eng %R 10.4310/MAA.2016.v23.n1.a1 %0 Book %B Springer Briefs in Mathematics %D 2015 %T Certified Reduced Basis Methods for Parametrized Partial Differential Equations %A Jan S Hesthaven %A Gianluigi Rozza %A Benjamin Stamm %K a posteriori error bounds %K empirical interpolation %K parametrized partial differential equations %K reduced basis methods, greedy algorithms %XThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

%B Springer Briefs in Mathematics %7 1 %I Springer %C Switzerland %P 135 %@ 978-3-319-22469-5 %G eng %6 1 %0 Report %D 2015 %T A class of Hamiltonians for a three-particle fermionic system at unitarity %A Michele Correggi %A Gianfausto Dell'Antonio %A Domenico Finco %A Alessandro Michelangeli %A Alessandro Teta %X We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide. %G en %U http://urania.sissa.it/xmlui/handle/1963/34469 %1 34644 %2 Mathematics %4 1 %$ Submitted by Alessandro Michelangeli (alemiche@sissa.it) on 2015-05-21T06:33:20Z No. of bitstreams: 1 SISSA_preprint_22-2015-MATE.pdf: 438261 bytes, checksum: ca05e5e2c5d78d87225a11073cb09d47 (MD5) %0 Journal Article %J Mathematical Methods in the Applied Sciences %D 2015 %T A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity %A Maggiani, Giovanni Battista %A Riccardo Scala %A Nicolas Van Goethem %K 35J58 %K 35Q74 %K compatibility conditions %K elasticity %K Korn inequality %K strain decomposition %K subclass74B05 %XIn this paper, we prove the Saint-Venant compatibility conditions in $L^p$ for $p\in(1,∞)$, in a simply connected domain of any space dimension. As a consequence, alternative, simple, and direct proofs of some classical Korn inequalities in Lp are provided. We also use the Helmholtz decomposition in $L^p$ to show that every symmetric tensor in a smooth domain can be decomposed in a compatible part, which is the symmetric part of a displacement gradient, and in an incompatible part, which is the incompatibility of a certain divergence-free tensor. Moreover, under a suitable Dirichlet boundary condition, this Beltrami-type decomposition is proved to be unique. This decomposition result has several applications, one of which being in dislocation models, where the incompatibility part is related to the dislocation density and where $1 < p < 2$. This justifies the need to generalize and prove these rather classical results in the Hilbertian case ($p = 2$), to the full range $p\in(1,∞)$. Copyright © 2015 John Wiley & Sons, Ltd.

%B Mathematical Methods in the Applied Sciences %V 38 %P 5217-5230 %G eng %U https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3450 %R 10.1002/mma.3450 %0 Journal Article %J SIAM Journal on Control and Optimization %D 2015 %T Complexity of Control-Affine Motion Planning %A Jean, F. %A Dario Prandi %XIn this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time-rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quantitative estimates on the cost of stabilizing the system near a nonequilibrium point of the drift.

%B SIAM Journal on Control and Optimization %V 53 %P 816-844 %G eng %U https://doi.org/10.1137/130950793 %R 10.1137/130950793 %0 Journal Article %J Adv. Calc. Var. %D 2015 %T Constrained BV functions on double coverings for Plateau's type problems %A Stefano Amato %A Giovanni Bellettini %A Maurizio Paolini %XWe link Brakke's "soap films" covering construction with the theory of finite perimeter sets, in order to study Plateau's problem without fixing a priori the topology of the solution. The minimization is set up in the class of $BV$ functions defined on a double covering space of the complement of an $(n − 2)$-dimensional smooth compact manifold $S$ without boundary. The main novelty of our approach stands in the presence of a suitable constraint on the fibers, which couples together the covering sheets. The model allows to avoid all issues concerning the presence of the boundary $S$. The constraint is lifted in a natural way to Sobolev spaces, allowing also an approach based on $Γ$-convergence theory.

%B Adv. Calc. Var. %G en_US %1 7597 %$ Submitted by Stefano Amato (samato@sissa.it) on 2014-12-12T07:20:56Z No. of bitstreams: 1 bvcovering_gen.pdf: 520748 bytes, checksum: 7b3d78994ff2d2ae5cbbe87eaa5f0777 (MD5) %0 Journal Article %J Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %D 2015 %T Convergence rate of the Glimm scheme %A Stefano Modena %A Stefano Bianchini %B Bulletin of the Institute of Mathematics of Academia Sinica (New Series) %G eng %0 Report %D 2015 %T Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets %A Dario Mazzoleni %A Davide Zucco %X We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open set of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it is possible to obtain informations on the geometry of the minimizers of convex combinations: we study, in particular, when these minimizers are no longer convex, and the optimality of balls. As an application of our results we study the boundary of the attainable set for the Dirichlet spectrum. Our techniques involve symmetry results à la Serrin, explicit constants in quantitative inequalities, as well as a purely geometrical problem: the minimization of the Fraenkel 2-asymmetry among convex sets of fixed measure. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35140 %1 35378 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Davide Zucco (dzucco@sissa.it) on 2015-12-03T12:26:59Z No. of bitstreams: 1 Mazzoleni_Zucco_preprint_SISSA.pdf: 437631 bytes, checksum: 990947c0f9a62d173c6e72d105297d19 (MD5) %0 Journal Article %J Comm. Math. Phys. %D 2014 %T Cauchy-Laguerre two-matrix model and the Meijer-G random point field %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B Comm. Math. Phys. %V 326 %P 111–144 %G eng %U http://dx.doi.org/10.1007/s00220-013-1833-8 %R 10.1007/s00220-013-1833-8 %0 Journal Article %J Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 %D 2014 %T Classical W-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We derive explicit formulas for lambda-brackets of the affine classical W-algebras attached to the minimal and short nilpotent elements of any simple Lie algebra g. This is used to compute explicitly the first non-trivial PDE of the corresponding intgerable generalized Drinfeld-Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov's equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h-3 functions, where h is the dual Coxeter number of g. In the case when g is sl_2 both these equations coincide with the KdV equation. In the case when g is not of type C_n, we associate to the minimal nilpotent element of g yet another generalized Drinfeld-Sokolov hierarchy. %B Communications in Mathematical Physics 331, nr. 2 (2014) 623-676 %I SISSA %G en %U http://hdl.handle.net/1963/6979 %1 6967 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:27:20Z No. of bitstreams: 1 1306.1684v1.pdf: 580565 bytes, checksum: de8a5fc99d3eb9f1c4f85b4a2a6592e9 (MD5) %R 10.1007/s00220-014-2049-2 %0 Journal Article %D 2014 %T Comparison between reduced basis and stochastic collocation methods for elliptic problems %A Peng Chen %A Alfio Quarteroni %A Gianluigi Rozza %X The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289-294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229-275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41-44):3187-3206, 2009; Arch Comput Methods Eng 17:435-454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions O (1) to moderate dimensions O (10) and to high dimensions O (100). The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34727 %1 34916 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T11:39:14Z (GMT) No. of bitstreams: 0 %R 10.1007/s10915-013-9764-2 %0 Journal Article %J Annals of Nuclear Energy %D 2014 %T Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics %A Alberto Sartori %A Davide Baroli %A Antonio Cammi %A Davide Chiesa %A Lelio Luzzi %A Roberto R. Ponciroli %A Ezio Previtali %A Marco E. Ricotti %A Gianluigi Rozza %A Monica Sisti %XIn this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor. The results given by the POD-based approach are higher-fidelity with respect to the reference solution than those computed according to the MM-based approach, in particular when the perturbation concerns a reduced region of the core. If the perturbation is homogeneous throughout the core, the two approaches allow obtaining comparable accuracy results on the quantities of interest. As far as the computational burden is concerned, the POD approach ensures a better efficiency rather than direct Modal Method, thanks to the ability of performing a longer computation in the preprocessing that leads to a faster evaluation during the on-line phase.

%B Annals of Nuclear Energy %I Elsevier %V 71 %P 229 %8 09/2014 %G en %U http://urania.sissa.it/xmlui/handle/1963/35039 %1 35270 %2 Physics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-18T12:07:02Z (GMT) No. of bitstreams: 0 %& 217 %R 10.1016/j.anucene.2014.03.043 %0 Journal Article %D 2014 %T Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription %A Rod R. Gover %A Yaiza Canzani %A Dmitry Jakobson %A Raphaël Ponge %A Andrea Malchiodi %X In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures. %I Oxford University Press %G en %U http://urania.sissa.it/xmlui/handle/1963/35128 %1 35366 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:09:57Z No. of bitstreams: 1 preprint2014.pdf: 356671 bytes, checksum: 20e817f9f20d9c72d717e04f94f86bd9 (MD5) %R 10.1093/imrn/rns295 %0 Journal Article %D 2014 %T On conjugate times of LQ optimal control problems %A Andrei A. Agrachev %A Luca Rizzi %A Pavel Silveira %K Optimal control, Lagrange Grassmannian, Conjugate point %X Motivated by the study of linear quadratic optimal control problems, we consider a dynamical system with a constant, quadratic Hamiltonian, and we characterize the number of conjugate times in terms of the spectrum of the Hamiltonian vector field $\vec{H}$. We prove the following dichotomy: the number of conjugate times is identically zero or grows to infinity. The latter case occurs if and only if $\vec{H}$ has at least one Jordan block of odd dimension corresponding to a purely imaginary eigenvalue. As a byproduct, we obtain bounds from below on the number of conjugate times contained in an interval in terms of the spectrum of $\vec{H}$. %I Springer %G en %U http://hdl.handle.net/1963/7227 %1 7261 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-12-03T08:50:15Z No. of bitstreams: 1 1311.2009v1.pdf: 401341 bytes, checksum: 5c32a0e534e70539f1823acdad41ddca (MD5) %R 10.1007/s10883-014-9251-6 %0 Journal Article %D 2014 %T A correction and an extension of Stampacchia's work on the geometric BVP %A Giovanni Vidossich %X G. Stampacchia introduced the geometric boundary value problem for ODEs in his doctoral thesis and published four papers related to it. Here we point out that the proof of his last theorem on the subject is incorrect and we provide a substitute for it as well as a generalizations of some of his earlier results. %I Advanced Nonlinear Studies %G en %U http://urania.sissa.it/xmlui/handle/1963/35023 %1 35263 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-11-17T10:33:42Z (GMT) No. of bitstreams: 0 %0 Journal Article %J International Journal of Non-Linear Mechanics %D 2014 %T Crawling on directional surfaces %A Paolo Gidoni %A Giovanni Noselli %A Antonio DeSimone %K Bio-mimetic micro-robots %K Cell migration %K Crawling motility %K Directional surfaces %K Self-propulsion %XIn this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

%B International Journal of Non-Linear Mechanics %V 61 %P 65 - 73 %G eng %U http://www.sciencedirect.com/science/article/pii/S0020746214000213 %R https://doi.org/10.1016/j.ijnonlinmec.2014.01.012 %0 Journal Article %D 2014 %T Critical points of the Moser-Trudinger functional on a disk %A Andrea Malchiodi %A Luca Martinazzi %X On the 2-dimensional unit disk $B_1$ we study the Moser-Trudinger functional $$E(u)=\int_{B_1}(e^{u^2}-1)dx, u\in H^1_0(B_1)$$ and its restrictions to $M_\Lambda:=\{u \in H^1_0(B_1):\|u\|^2_{H^1_0}=\Lambda\}$ for $\Lambda>0$. We prove that if a sequence $u_k$ of positive critical points of $E|_{M_{\Lambda_k}}$ (for some $\Lambda_k>0$) blows up as $k\to\infty$, then $\Lambda_k\to 4\pi$, and $u_k\to 0$ weakly in $H^1_0(B_1)$ and strongly in $C^1_{\loc}(\bar B_1\setminus\{0\})$. Using this we also prove that when $\Lambda$ is large enough, then $E|_{M_\Lambda}$ has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe. %I European Mathematical Society %G en %U http://hdl.handle.net/1963/6560 %1 6487 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:24:49Z No. of bitstreams: 1 1203.1077v1.pdf: 218315 bytes, checksum: 7e4a2900b082b373371033ed0196f5de (MD5) %R 10.4171/JEMS/450 %0 Thesis %D 2014 %T The curvature of optimal control problems with applications to sub-Riemannian geometry %A Luca Rizzi %K Sub-Riemannian geometry %X Optimal control theory is an extension of the calculus of variations, and deals with the optimal behaviour of a system under a very general class of constraints. This field has been pioneered by the group of mathematicians led by Lev Pontryagin in the second half of the 50s and nowadays has countless applications to the real worlds (robotics, trains, aerospace, models for human behaviour, human vision, image reconstruction, quantum control, motion of self-propulsed micro-organism). In this thesis we introduce a novel definition of curvature for an optimal control problem. In particular it works for any sub-Riemannian and sub-Finsler structure. Related problems, such as comparison theorems for sub-Riemannian manifolds, LQ optimal control problem and Popp's volume and are also investigated. %I SISSA %G en %U http://hdl.handle.net/1963/7321 %1 7367 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Luca Rizzi (lrizzi@sissa.it) on 2014-05-23T12:10:38Z No. of bitstreams: 1 main.pdf: 2357698 bytes, checksum: 7283fc7a064552ee4709b0dfccddf2b8 (MD5) %] Introduction 1) The curvature of optimal control problems 2) Comparison theorems for conjugate points in sub-Riemannian geometry 3) On conjugate times of LQ optimal control problems 4) A formula for Popp's volume in sub-Riemannian geometry %0 Journal Article %J Procedia Engineering %D 2014 %T Curvature-adapted remeshing of CAD surfaces %A Franco Dassi %A Andrea Mola %A Hang Si %XA common representation of surfaces with complicated topology and geometry is through composite parametric surfaces as is the case for most CAD modelers. A challenging problem is how to generate a mesh of such a surface that well approximates the geometry of the surface, preserves its topology and important geometric features, and contains nicely shaped elements. In this work, we present an optimization-based surface remeshing method that is able to satisfy many of these requirements simultaneously. This method is inspired by the recent work of Lévy and Bonneel (Proc. 21th International Meshing Roundtable, October 2012), which embeds a smooth surface into a high-dimensional space and remesh it uniformly in that embedding space. Our method works directly in the 3d spaces and uses an embedding space in R6 to evaluate mesh size and mesh quality. It generates a curvatureadapted anisotropic surface mesh that well represents the geometry of the surface with a low number of elements. We illustrate our approach through various examples.

%B Procedia Engineering %I Elsevier %V 82 %P 253–265 %G en %U https://doi.org/10.1016/j.proeng.2014.10.388 %1 35220 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-11T16:19:16Z No. of bitstreams: 1 art2014.pdf: 3913220 bytes, checksum: ba78b55b28c0eed195d2abc48bd7ca4b (MD5) %R 10.1016/j.proeng.2014.10.388 %0 Journal Article %J Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %D 2013 %T Classical W-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X We provide a description of the Drinfeld-Sokolov Hamiltonian reduction for the construction of classical W-algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations. %B Communications in Mathematical Physics 323, nr. 2 (2013) 663-711 %I Springer %G en %U http://hdl.handle.net/1963/6978 %1 6966 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2013-07-13T15:24:57Z No. of bitstreams: 1 1207.6286v3.pdf: 588052 bytes, checksum: a5630eb1399cba992d56be98f25cdc9c (MD5) %R 10.1007/s00220-013-1785-z %0 Journal Article %J Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 %D 2013 %T A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices %A Denis Devaud %A Andrea Manzoni %A Gianluigi Rozza %K Partial differential equations %XWe consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output. The idea of this method is to compute a first (coarse) RB approximation of the output of interest involving all the parameter components, but with a large tolerance on the a posteriori error estimate; then, we evaluate the ANOVA expansion of the output and freeze the least important parameter components; finally, considering a restricted model involving just the retained parameter components, we compute a second (fine) RB approximation with a smaller tolerance on the a posteriori error estimate. The fine RB approximation entails lower computational costs than the coarse one, because of the reduction of parameter dimensionality. Our result provides a criterion to avoid the computation of those terms in the ANOVA expansion that are related to the interaction between parameters in the bilinear form, thus making the RB-ANOVA-RB procedure computationally more feasible.

%B Comptes Rendus Mathematique. Volume 351, Issue 15-16, August 2013, Pages 593-598 %I Elsevier %G en %U http://hdl.handle.net/1963/7389 %1 7434 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-19T08:56:09Z No. of bitstreams: 1 Devaud_Manzoni_Rozza_2013.pdf: 564002 bytes, checksum: 4c93e74468534915513e6805d440dee9 (MD5) %R 10.1016/j.crma.2013.07.023 %0 Journal Article %J Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %D 2013 %T Common dynamical features of sensory adaptation in photoreceptors and olfactory sensory neurons. %A Giovanna De Palo %A Giuseppe Facchetti %A Monica Mazzolini %A Anna Menini %A Vincent Torre %A Claudio Altafini %XSensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

%B Nature. Scientific Reports 3, Article number: 1251, Published : 13 February 2013 %I SISSA %G en %1 6453 %2 Mathematics %4 1 %$ Submitted by Claudio Altafini (altafini@sissa.it) on 2013-02-27T14:00:21Z\nNo. of bitstreams: 0 %R 10.1038/srep01251 %0 Journal Article %J Journal of Differential Equations %D 2013 %T Concentration of solutions for a singularly perturbed mixed problem in non-smooth domains %A Serena Dipierro %K Finite-dimensional reductions %K Local inversion %K Singularly perturbed elliptic problems %XWe consider a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ whose boundary has an $(n−2)$-dimensional singularity. Assuming $1<p<\frac{n+2}{n−2}$, we prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero.

%B Journal of Differential Equations %V 254 %P 30 - 66 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039612003312 %R https://doi.org/10.1016/j.jde.2012.08.017 %0 Journal Article %J Journal of Geometric Analysis %D 2013 %T The Conformal Willmore Functional: A Perturbative Approach %A Andrea Mondino %XThe conformal Willmore functional (which is conformal invariant in general Riemannian manifolds $(M,g)$ is studied with a perturbative method: the Lyapunov–Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3,g_\epsilon)$ – where $g_\epsilon$ is a metric close and asymptotic to the Euclidean one. With the same technique a non-existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.

%B Journal of Geometric Analysis %V 23 %P 764–811 %8 Apr %G eng %U https://doi.org/10.1007/s12220-011-9263-3 %R 10.1007/s12220-011-9263-3 %0 Journal Article %J Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %D 2013 %T Connected Sum Construction for σk-Yamabe Metrics %A Giovanni Catino %A Lorenzo Mazzieri %X In this paper we produce families of Riemannian metrics with positive constant $\sigma_k$-curvature equal to $2^{-k} {n \choose k}$ by performing the connected sum of two given compact {\em non degenerate} $n$--dimensional solutions $(M_1,g_1)$ and $(M_2,g_2)$ of the (positive) $\sigma_k$-Yamabe problem, provided $2 \leq 2k < n$. The problem is equivalent to solve a second order fully nonlinear elliptic equation. %B Journal of Geometric Analysis 23, nr.2 (2013), pages 812-854 %I Springer %G en %U http://hdl.handle.net/1963/6441 %1 6366 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-29T10:41:53Z No. of bitstreams: 1 0910.5353v2.pdf: 355177 bytes, checksum: 0fa7b4a369607d617c4c167617460165 (MD5) %R 10.1007/s12220-011-9265-1 %0 Journal Article %J International Journal of Non-Linear Mechanics 56, 142-147 (2013) %D 2013 %T Crawlers in viscous environments: linear vs nonlinear rheology %A Antonio DeSimone %A Federica Guarnieri %A Giovanni Noselli %A Amabile Tatone %X We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. %B International Journal of Non-Linear Mechanics 56, 142-147 (2013) %I Elsevier %G en %1 34590 %2 Mathematics %$ Submitted by gnoselli@sissa.it (gnoselli@sissa.it) on 2015-03-07T17:29:52Z No. of bitstreams: 1 viscous_crawlers.pdf: 887755 bytes, checksum: 6022e4160d2eced97b51326bf51e0827 (MD5) %R 10.1016/j.ijnonlinmec.2013.02.007 %0 Report %D 2013 %T On critical behaviour in systems of Hamiltonian partial differential equations %A Boris Dubrovin %A Tamara Grava %A Christian Klein %A Antonio Moro %XWe study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\'e-I (P$_I$) equation or its fourth order analogue P$_I^2$. As concrete examples we discuss nonlinear Schr\"odinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.

%I SISSA %G en %1 7280 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Tamara Grava (grava@sissa.it) on 2014-01-14T18:10:19Z No. of bitstreams: 1 EHfinal_3.pdf: 7760169 bytes, checksum: 1e98e693fbceb1268a5acd269dd9b03e (MD5) %0 Report %D 2013 %T The curvature: a variational approach %A Andrei A. Agrachev %A Davide Barilari %A Luca Rizzi %K Crurvature, subriemannian metric, optimal control problem %X The curvature discussed in this paper is a rather far going generalization of the Riemannian sectional curvature. We define it for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler and sub-Finsler structures; a special attention is paid to the sub-Riemannian (or Carnot-Caratheodory) metric spaces. Our construction of the curvature is direct and naive, and it is similar to the original approach of Riemann. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces. %I SISSA %G en %U http://hdl.handle.net/1963/7226 %1 7260 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-12-03T08:46:32Z No. of bitstreams: 1 1306.5318v3.pdf: 991021 bytes, checksum: f99fb9f1455fa70fbca476e8fd2571af (MD5) %0 Journal Article %J Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %D 2013 %T Curved noncommutative torus and Gauss--Bonnet %A Ludwik Dabrowski %A Andrzej Sitarz %K Geometry %X We study perturbations of the flat geometry of the noncommutative two-dimensional torus T^2_\theta (with irrational \theta). They are described by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra A_\theta of T_\theta. We show, up to the second order in perturbation, that the zeta-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature. %B Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 %I American Institute of Physics %G en %U http://hdl.handle.net/1963/7376 %1 7424 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:10:21Z No. of bitstreams: 1 1204.0420v1.pdf: 126064 bytes, checksum: ffa850e50f99585d61676b1d2398af2f (MD5) %R 10.1063/1.4776202 %0 Journal Article %J Journal of dynamical and control systems %D 2012 %T On a class of vector fields with discontinuity of divide-by-zero type and its applications %A Roberta Ghezzi %A Alexey O. Remizov %XWe study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

%B Journal of dynamical and control systems %I Springer %V 18 %P 135-158 %G en %N 1 %1 7038 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-14T09:32:26Z No. of bitstreams: 1 1007.0912v1.pdf: 311033 bytes, checksum: 66a06c5e2764120aa6d9ac971a82baab (MD5) %R 10.1007/s10883-012-9137-4 %0 Journal Article %J Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %D 2012 %T Classical double, R-operators, and negative flows of integrable hierarchies %A Boris Dubrovin %A Taras V. Skrypnyk %X Using the classical double G of a Lie algebra g equipped with the classical R-operator, we define two sets of functions commuting with respect to the initial Lie–Poisson bracket on g and its extensions. We consider examples of Lie algebras g with the “Adler–Kostant–Symes” R-operators and the two corresponding sets of mutually commuting functions in detail. Using the constructed commutative Hamiltonian flows on different extensions of g, we obtain zero-curvature equations with g-valued U–V pairs. The so-called negative flows of soliton hierarchies are among such equations. We illustrate the proposed approach with examples of two-dimensional Abelian and non-Abelian Toda field equations. %B Theoretical and Mathematical Physics. Volume 172, Issue 1, July 2012, Pages 911-931 %I SISSA %G en %U http://hdl.handle.net/1963/6468 %1 6413 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-02-11T14:56:54Z (GMT) No. of bitstreams: 0 %R 10.1007/s11232-012-0086-6 %0 Journal Article %J Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %D 2012 %T A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group. %A Andrea Malchiodi %A Paul Yang %A Jih-Hsin Cheng %A JennFang Hwang %X In this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 1 %B Journal fur die Reine und Angewandte Mathematik, Issue 671, October 2012, Pages 131-198 %I SISSA %G en %U http://hdl.handle.net/1963/6556 %1 6490 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2013-03-25T14:33:32Z (GMT) No. of bitstreams: 0 %R 10.1515/CRELLE.2011.159 %0 Book Section %B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %D 2012 %T Computing optimal strokes for low reynolds number swimmers %A Antonio DeSimone %A Luca Heltai %A François Alouges %A Lefebvre-Lepot Aline %K Numerical analysis. %XWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

%B Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, %I Springer %@ 9781461439967 %G en %U http://hdl.handle.net/1963/6445 %1 6381 %2 Mathematics %4 1 %# MAT/08 ANALISI NUMERICA %$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:33:50Z\\nNo. of bitstreams: 0 %R 10.1007/978-1-4614-3997-4_13 %0 Journal Article %J Communications in Contemporary Mathematics %D 2012 %T Concentration on circles for nonlinear Schrödinger–Poisson systems with unbounded potentials vanishing at infinity %A Bonheure, Denis %A Di Cosmo, Jonathan %A Mercuri, Carlo %XThe present paper is devoted to weighted nonlinear Schrödinger–Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.

%B Communications in Contemporary Mathematics %I World Scientific %V 14 %P 1250009 %G eng %U https://doi.org/10.1142/S0219199712500095 %R 10.1142/S0219199712500095 %0 Journal Article %J Communications in Partial Differential Equations %D 2012 %T Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids %A Francesco Fanelli %XIn this article we get a result on propagation of geometric properties for solutions of the non-homogeneous incompressible Euler system in any dimension N ≥ 2. In particular, we investigate conservation of striated and conormal regularity, which generalize the 2-D structure of vortex patches. The results we get are only local in time, even for N = 2; however, we provide an explicit lower bound for the lifespan of the solution. In the case of physical dimension N = 2 or 3, we investigate also propagation of Hölder regularity in the interior of a bounded domain.

%B Communications in Partial Differential Equations %I Taylor & Francis %V 37 %P 1553-1595 %G eng %U https://doi.org/10.1080/03605302.2012.698343 %R 10.1080/03605302.2012.698343 %0 Journal Article %D 2012 %T Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density %A Maria Giovanna Mora %A Lucia Scardia %XThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal E^h$, whose energies (per unit thickness) are bounded by $Ch^4$, converge to critical points of the $\Gamma$-limit of $h^{-4}\mathcal E^h$. This is proved under the physical assumption that the energy density $W(F)$ blows up as $\det F\to0$.

%I Elsevier %G en %U http://hdl.handle.net/1963/3466 %1 7112 %2 Mathematics %4 -1 %$ Submitted by Francesca Arici (farici@sissa.it) on 2013-09-18T08:46:46Z No. of bitstreams: 1 0901.4041v1.pdf: 233717 bytes, checksum: 3fc33c8ee52cddb0adf0a197c87d0ce8 (MD5) %R 10.1016/j.jde.2011.09.009 %0 Journal Article %J Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 %D 2012 %T Convex pencils of real quadratic forms %A Antonio Lerario %X We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RP^n (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere S^n; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications of these results, especially in classical convexity theory. We prove the sharp bound b(X)\leq 2n for the total Betti number of X; we show that for odd n this bound is attained only by a singular X. In the nondegenerate case we also prove the bound on each specific Betti number b_k(X)\leq 2(k+2). %B Discrete and Computational Geometry, Volume 48, Issue 4, December 2012, Pages 1025-1047 %I Springer %G en %U http://hdl.handle.net/1963/7099 %1 7097 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-09-17T11:33:51Z No. of bitstreams: 1 1106.4678v3.pdf: 250496 bytes, checksum: 3ad88e26b8325e50857d0d9f9aabd6ad (MD5) %R 10.1007/s00454-012-9460-2 %0 Journal Article %J The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %D 2012 %T Crawling motility through the analysis of model locomotors: two case studies %A Antonio DeSimone %A Amabile Tatone %X We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. %B The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 %I Springer %G en %U http://hdl.handle.net/1963/7017 %1 7014 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-08-12T11:01:46Z No. of bitstreams: 0 %R 10.1140/epje/i2012-12085-x %0 Journal Article %J Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 %D 2012 %T On the critical behavior in nonlinear evolutionary PDEs with small viscocity %A Boris Dubrovin %A Maria Elaeva %X We address the problem of general dissipative regularization of the quasilinear transport equation. We argue that the local behavior of solutions to the regularized equation near the point of gradient catastrophe for the transport equation is described by the logarithmic derivative of the Pearcey function, a statement generalizing the result of A.M.Il\\\'in \\\\cite{ilin}. We provide some analytic arguments supporting such conjecture and test it numerically. %B Russian Journal of Mathematical Physics. Volume 19, Issue 4, December 2012, Pages 449-460 %I SISSA %G en %U http://hdl.handle.net/1963/6465 %1 6409 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:28:04Z\\nNo. of bitstreams: 1\\ndubrovin_elaeva.pdf: 8618184 bytes, checksum: 3c56d1922af7001581ca4ceb4c79cc3b (MD5) %R 10.1134/S106192081204005X %0 Journal Article %J Comptes Rendus Mathematique 349 (2011) 161-166 %D 2011 %T A class of existence results for the singular Liouville equation %A Alessandro Carlotto %A Andrea Malchiodi %X We consider a class of elliptic PDEs on closed surfaces with exponential nonlinearities and Dirac deltas on the right-hand side. The study arises from abelian Chern–Simons theory in self-dual regime, or from the problem of prescribing the Gaussian curvature in presence of conical singularities. A general existence result is proved using global variational methods: the analytic problem is reduced to a topological problem concerning the contractibility of a model space, the so-called space of formal barycenters, characterizing the very low sublevels of a suitable functional. %B Comptes Rendus Mathematique 349 (2011) 161-166 %I Elsevier %G en %U http://hdl.handle.net/1963/5793 %1 5648 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-07T07:37:16Z\\nNo. of bitstreams: 0 %R 10.1016/j.crma.2010.12.016 %0 Journal Article %J Rev. Mat. Iberoamericana %D 2011 %T Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential %A David Ruiz %A Giusi Vaira %B Rev. Mat. Iberoamericana %I Real Sociedad Matemática Española %V 27 %P 253–271 %8 01 %G eng %U https://projecteuclid.org:443/euclid.rmi/1296828834 %0 Report %D 2011 %T Compactness by maximality %A Sandro Zagatti %X We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$. %G en %U http://preprints.sissa.it/handle/1963/35317 %1 35626 %2 Mathematics %4 1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-05-24T07:53:14Z No. of bitstreams: 0 %0 Journal Article %J Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %D 2011 %T Computing global structural balance in large-scale signed social networks. %A Giuseppe Facchetti %A Giovanni Iacono %A Claudio Altafini %K Combinatorial optimization %X Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly \\\"apparent disorder,\\\" rather than true \\\"frustration.\\\" %B Proceedings of the National Academy of Sciences of the United States of America. Volume 108, Issue 52, 27 December 2011, Pages 20953-20958 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/6426 %1 6362 %2 Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-01-25T12:27:12Z\\r\\nNo. of bitstreams: 1\\r\\npnas.1109521108-1.pdf: 1293098 bytes, checksum: 288a1ce2e9407b58249c5ea58a06f31b (MD5) %R 10.1073/pnas.1109521108 %0 Journal Article %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %T Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains %A Serena Dipierro %B Annales de l'I.H.P. Analyse non linéaire %I Elsevier %V 28 %P 107-126 %G eng %U http://www.numdam.org/item/AIHPC_2011__28_1_107_0 %R 10.1016/j.anihpc.2010.11.003 %0 Journal Article %J Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %D 2011 %T Cones of divisors of blow-ups of projective spaces %A Alessio Lo Giudice %A Salvatore Cacciola %A M. Donten-Bury %A O. Dumitrescu %A J. Park %K Mori dream space %X We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points. %B Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187 %I Università degli Studi di Catania. Dipartimento di matematica %G en %U http://hdl.handle.net/1963/6613 %1 6462 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-03-01T08:45:50Z No. of bitstreams: 1 CONES OF DIVISORS OF BLOW-UPS OF PROJECTIVE SPACES: 409758 bytes, checksum: 15d01ca131c41cf5f244bb4621177e36 (MD5) %R 10.4418/2011.66.2.13 %0 Journal Article %J Le Matematiche 66 (2011) 137-151 %D 2011 %T Covered by lines and Conic connected varieties %A Simone Marchesi %A Alex Massarenti %A Saeed Tafazolian %X We study some properties of an embedded variety covered by lines and give a\\r\\nnumerical criterion ensuring the existence of a singular conic through two of\\r\\nits general points. We show that our criterion is sharp. Conic-connected,\\r\\ncovered by lines, QEL, LQEL, prime Fano, defective, and dual defective\\r\\nvarieties are closely related. We study some relations between the above\\r\\nmentioned classes of objects using celebrated results by Ein and Zak. %B Le Matematiche 66 (2011) 137-151 %I Universita\\\' di Catania, Dipartimento di Matematica e Informatica %G en %U http://hdl.handle.net/1963/5788 %1 5641 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-05-03T14:43:36Z\\nNo. of bitstreams: 2\\n1105.5918v2.pdf: 279 bytes, checksum: a3b0f104eb894295409bae95af5b2e16 (MD5)\\n844-3335-1-PB.pdf: 186181 bytes, checksum: b32fc90e8bb7277d82a3c3705174e89a (MD5) %R 10.4418/2011.66.2.12 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %D 2011 %T Crack growth with non-interpenetration : a simplified proof for the pure Neumann problem %A Gianni Dal Maso %A Giuliano Lazzaroni %X We present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1219-1231 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3801 %1 526 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-11-27T10:24:55Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Laz-proc-pre.pdf: 195002 bytes, checksum: 44e408b134f19e4d31e77b3e0762cd73 (MD5) %R 10.3934/dcds.2011.31.1219 %0 Journal Article %J This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4) %D 2011 %T Crepant resolutions of weighted projective spaces and quantum deformations %A Samuel Boissiere %A Etienne Mann %A Fabio Perroni %X We compare the Chen-Ruan cohomology ring of the weighted projective spaces\r\n$\\IP(1,3,4,4)$ and $\\IP(1,...,1,n)$ with the cohomology ring of their crepant\r\nresolutions. In both cases, we prove that the Chen-Ruan cohomology ring is\r\nisomorphic to the quantum corrected cohomology ring of the crepant resolution\r\nafter suitable evaluation of the quantum parameters. For this, we prove a\r\nformula for the Gromov-Witten invariants of the resolution of a transversal\r\n${\\rm A}_3$ singularity. %B This article will be published in 2011 in the \"Nagoya Mathematical Journal\" Volume 201, March 2011, Pages 1-22, under the title \"Computing certain Gromov-Witten invariants of the crepant resolution of P{double-strock}(1, 3, 4, 4) %I SISSA %G en %U http://hdl.handle.net/1963/6514 %1 6463 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-28T17:54:00Z\nNo. of bitstreams: 1\nmath_0610617v2.pdf: 309225 bytes, checksum: 1488b79e5765bdffd4353bd8e04ffa8e (MD5) %0 Report %D 2011 %T Critical points of the Moser-Trudinger functional %A Francesca De Marchis %A Andrea Malchiodi %A Luca Martinazzi %K Moser-Trudinger inequality %I SISSA %G en %U http://hdl.handle.net/1963/4592 %1 4353 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-10-07T11:40:39Z\\nNo. of bitstreams: 1\\n46M_Malchiodi.pdf: 234581 bytes, checksum: 365098bf21692bfa547056b200acb4c6 (MD5) %0 Journal Article %J PNAS 108 (2011) 13978 %D 2011 %T Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions %A Luca Cardamone %A Alessandro Laio %A Rajesh Shahapure %A Antonio DeSimone %B PNAS 108 (2011) 13978 %I National Academy of Sciences %G en %U http://hdl.handle.net/1963/4358 %1 4066 %2 Physics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-28T06:31:24Z\\nNo. of bitstreams: 0 %R 10.1073/pnas.1100549108 %0 Report %D 2010 %T Canonical k-Minkowski Spacetime %A Gherardo Piacitelli %A Ludwik Dabrowski %X A complete classification of the regular representations of the relations [T,X_j] = (i/k)X_j, j=1,...,d, is given. The quantisation of RxR^d canonically (in the sense of Weyl) associated with the universal representation of the above relations is intrinsically \\\"radial\\\", this meaning that it only involves the time variable and the distance from the origin; angle variables remain classical. The time axis through the origin is a spectral singularity of the model: in the large scale limit it is topologically disjoint from the rest. The symbolic calculus is developed; in particular there is a trace functional on symbols. For suitable choices of states localised very close to the origin, the uncertainties of all spacetime coordinates can be made simultaneously small at wish. On the contrary, uncertainty relations become important at \\\"large\\\" distances: Planck scale effects should be visible at LHC energies, if processes are spread in a region of size 1mm (order of peak nominal beam size) around the origin of spacetime. %G en_US %U http://hdl.handle.net/1963/3863 %1 846 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-04-30T11:01:45Z\\r\\nNo. of bitstreams: 1\\r\\n1004.5091v1.pdf: 302332 bytes, checksum: 923a85fa3b4bef96bcf59c115bc3a61e (MD5) %0 Journal Article %J J. Approx. Theory %D 2010 %T Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Approx. Theory %V 162 %P 832–867 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1016/j.jat.2009.09.008 %R 10.1016/j.jat.2009.09.008 %0 Journal Article %J J. Geom. Phys. 60 (2010) 417-429 %D 2010 %T Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality %A Andrea Brini %A Luca Griguolo %A Domenico Seminara %A Alessandro Tanzini %X We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS partition function in a generic flat background for the whole L(p,q) family and provide a solution for its large N dynamics; on the other, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and briefly discuss how it could be restored in a non-perturbative setting. %B J. Geom. Phys. 60 (2010) 417-429 %G en_US %U http://hdl.handle.net/1963/2938 %1 1762 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-12T16:01:18Z\\nNo. of bitstreams: 1\\n0809.1610v1.pdf: 287875 bytes, checksum: feadff501b37135585a6f62946b628de (MD5) %R 10.1016/j.geomphys.2009.11.006 %0 Report %D 2010 %T Cohomology of Skew-holomorphic lie algebroids %A Ugo Bruzzo %A Vladimir Rubtsov %X We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts. %G en_US %U http://hdl.handle.net/1963/3853 %1 856 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-03-08T11:09:57Z\\nNo. of bitstreams: 1\\nHolAlgCohom-2.pdf: 239431 bytes, checksum: 218e3d336432ad269f8f4c67e8d42fa5 (MD5) %0 Journal Article %J Arch. Ration. Mech. Anal. 196 (2010) 907-950 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero. %B Arch. Ration. Mech. Anal. 196 (2010) 907-950 %G en_US %U http://hdl.handle.net/1963/3406 %1 927 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:03:36Z\\nNo. of bitstreams: 1\\nGMMPI.pdf: 466523 bytes, checksum: 004f66da4f9e531a535780337f19e185 (MD5) %R 10.1007/s00205-009-0259-0 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %D 2010 %T Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions %A Jesus Garcia Azorero %A Andrea Malchiodi %A Luigi Montoro %A Ireneo Peral %X In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in. %B Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 %G en_US %U http://hdl.handle.net/1963/3409 %1 926 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-08T11:10:32Z\\nNo. of bitstreams: 1\\nGMMPII.pdf: 324708 bytes, checksum: 4829f5449fac58672d6e7a8e42efb3c4 (MD5) %R 10.1016/j.anihpc.2009.06.005 %0 Journal Article %J Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 %D 2010 %T Continuity of optimal control costs and its application to weak KAM theory %A Andrei A. Agrachev %A Paul Lee %X We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems. %B Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232 %I SISSA %G en %U http://hdl.handle.net/1963/6459 %1 6405 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:56:31Z\\nNo. of bitstreams: 1\\n0909.3826v2.pdf: 264638 bytes, checksum: 5f13730dcb51f57d19a692ea1d6c48c6 (MD5) %R 10.1007/s00526-010-0308-4 %0 Report %D 2010 %T Convergence of equilibria of thin elastic rods under physical growth conditions for the energy density %A Elisa Davoli %A Maria Giovanna Mora %X The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the constrained linear theory, the analogous of von Kármán plate theory for rods, and the linear theory. %G en_US %U http://hdl.handle.net/1963/4086 %1 317 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-10-05T08:49:01Z\\nNo. of bitstreams: 1\\nDavoli-Mora_67M_2010.pdf: 243056 bytes, checksum: 8542ff47b9dc1ae7275fe95bc296a870 (MD5) %0 Journal Article %J Comm. Math. Phys. %D 2009 %T The Cauchy two–matrix model %A Marco Bertola %A M Gekhtman %A J Szmigielski %B Comm. Math. Phys. %V 287 %P 983–1014 %G eng %0 Journal Article %J BMC Research Notes (2009) 2:13 %D 2009 %T Characterization of the time course of changes of the evoked electrical activity in a model of a chemically-induced neuronal plasticity %A Frederic D. Broccard %A Silvia Pegoraro %A Maria Elisabetta Ruaro %A Claudio Altafini %A Vincent Torre %X BACKGROUND: Neuronal plasticity is initiated by transient elevations of neuronal networks activity leading to changes of synaptic properties and providing the basis for memory and learning 1. An increase of electrical activity can be caused by electrical stimulation 2 or by pharmacological manipulations: elevation of extracellular K+ 3, blockage of inhibitory pathways 4 or by an increase of second messengers intracellular concentrations 5. Neuronal plasticity is mediated by several biochemical pathways leading to the modulation of synaptic strength, density of ionic channels and morphological changes of neuronal arborisation 6. On a time scale of a few minutes, neuronal plasticity is mediated by local protein trafficking 7 while, in order to sustain modifications beyond 2-3 h, changes of gene expression are required 8. FINDINGS: In the present manuscript we analysed the time course of changes of the evoked electrical activity during neuronal plasticity and we correlated it with a transcriptional analysis of the underlying changes of gene expression. Our investigation shows that treatment for 30 min. with the GABAA receptor antagonist gabazine (GabT) causes a potentiation of the evoked electrical activity occurring 2-4 hours after GabT and the concomitant up-regulation of 342 genes. Inhibition of the ERK1/2 pathway reduced but did not abolish the potentiation of the evoked response caused by GabT. In fact not all the genes analysed were blocked by ERK1/2 inhibitors. CONCLUSION: These results are in agreement with the notion that neuronal plasticity is mediated by several distinct pathways working in unison. %B BMC Research Notes (2009) 2:13 %I BioMed Central %G en_US %U http://hdl.handle.net/1963/3706 %1 599 %2 Neuroscience %3 Neurobiology %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-08-12T11:40:38Z\\nNo. of bitstreams: 1\\n1756-0500-2-13.pdf: 518127 bytes, checksum: 0cd264c3567a0d1776a5141b6dc5ef4e (MD5) %R 10.1186/1756-0500-2-13 %0 Journal Article %J Adv. Math. %D 2009 %T Commuting difference operators, spinor bundles and the asymptotics of orthogonal polynomials with respect to varying complex weights %A Marco Bertola %A Mo, M. Y. %B Adv. Math. %V 220 %P 154–218 %G eng %0 Journal Article %J Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %D 2009 %T A connection between viscous profiles and singular ODEs %A Stefano Bianchini %A Laura Spinolo %B Rend. Istit. Mat. Univ. Trieste 41 (2009) 35-41 %G en_US %U http://hdl.handle.net/1963/2555 %1 1564 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:38:45Z\\nNo. of bitstreams: 1\\nSissa0508M.pdf: 107079 bytes, checksum: 5af029f1d9bcd4f14be2d8774cfa251e (MD5) %0 Journal Article %J Systems Control Lett. 58 (2009) 213-216 %D 2009 %T Controllability and simultaneous controllability of isospectral bilinear control systems on complex flag manifolds %A Claudio Altafini %X For isospectral bilinear control systems evolving on the so-called complex flag manifolds (i.e., on the orbits of the Hermitian matrices under unitary conjugation action) it is shown that controllability is almost always verified. Easy and generic sufficient conditions are provided. The result applies to the problem of density operator controllability of finite dimensional quantum mechanical systems. In addition, we show that systems having different drifts (corresponding for example to different Larmor frequencies) are simultaneously controllable by the same control field. %B Systems Control Lett. 58 (2009) 213-216 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3523 %1 741 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-19T09:39:57Z\\nNo. of bitstreams: 1\\nquens-controll.pdf: 158724 bytes, checksum: 19e7a4ce17acbe97895e145a95916c7a (MD5) %R 10.1016/j.sysconle.2008.10.008 %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %D 2009 %T Controllability of the discrete-spectrum Schrodinger equation driven by an external field %A Thomas Chambrion %A Paolo Mason %A Mario Sigalotti %A Ugo Boscain %X We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete nonresonant\\nspectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the\\nGalerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential controlled by suitable potentials. %B Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009) 329-349 %G en_US %U http://hdl.handle.net/1963/2547 %1 1572 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-10T13:32:19Z\\nNo. of bitstreams: 1\\n2008-ttinger.pdf: 270196 bytes, checksum: e706dbae08d996576cefe55f53d7284e (MD5) %R 10.1016/j.anihpc.2008.05.001 %0 Journal Article %J Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %D 2009 %T Controllability on the group of diffeomorphisms %A Andrei A. Agrachev %A Marco Caponigro %X Given a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M. %B Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009) 2503-2509 %G en_US %U http://hdl.handle.net/1963/3396 %1 936 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-11T12:06:43Z\\nNo. of bitstreams: 1\\nAgrachev_Caponigro.pdf: 145136 bytes, checksum: 90eebd9912f15c33d1d93f5108ab93aa (MD5) %R 10.1016/j.anihpc.2009.07.003 %0 Journal Article %J Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %D 2009 %T On the convergence of viscous approximations after shock interactions %A Alberto Bressan %A Carlotta Donadello %X We consider a piecewise smooth solution to a scalar conservation law, with possibly interacting shocks. We show that, after the interactions have taken place, vanishing viscosity approximations can still be represented by a regular expansion on smooth regions and by a singular perturbation expansion near the shocks, in terms of powers of the viscosity coefficient. %B Discrete Contin. Dyn. Syst. 23 (2009) 29-48 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3412 %1 923 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-09T12:23:11Z\\nNo. of bitstreams: 1\\n019.pdf: 273198 bytes, checksum: 4513df79a27da75ea57c4374c83b0cf6 (MD5) %R 10.3934/dcds.2009.23.29 %0 Journal Article %J J. Phys. A %D 2009 %T Cubic string boundary value problems and Cauchy biorthogonal polynomials %A Marco Bertola %A Gekhtman, M. %A Szmigielski, J. %B J. Phys. A %V 42 %P 454006, 13 %G eng %U http://0-dx.doi.org.mercury.concordia.ca/10.1088/1751-8113/42/45/454006 %R 10.1088/1751-8113/42/45/454006 %0 Journal Article %J Frontiers of Mathematics in China %D 2008 %T Cantor families of periodic solutions for completely resonant wave equations %A Massimiliano Berti %A Philippe Bolle %X We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods. © 2008 Higher Education Press. %B Frontiers of Mathematics in China %V 3 %P 151-165 %G eng %R 10.1007/s11464-008-0011-3 %0 Journal Article %J Advances in Mathematics %D 2008 %T Cantor families of periodic solutions for wave equations via a variational principle %A Massimiliano Berti %A Philippe Bolle %X We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation-variational in nature-defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to "small divisors" phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical "Arnold non-degeneracy condition" of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. © 2007 Elsevier Inc. All rights reserved. %B Advances in Mathematics %V 217 %P 1671-1727 %G eng %R 10.1016/j.aim.2007.11.004 %0 Journal Article %J Nonlinear Differential Equations and Applications %D 2008 %T Cantor families of periodic solutions of wave equations with C k nonlinearities %A Massimiliano Berti %A Philippe Bolle %X We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C k . It requires a modified Nash-Moser iteration scheme with interpolation estimates for the inverse of the linearized operators and for the composition operators. © 2008 Birkhaueser. %B Nonlinear Differential Equations and Applications %V 15 %P 247-276 %G eng %R 10.1007/s00030-007-7025-5 %0 Journal Article %J Front. Math. China 3 (2008) 239-252 %D 2008 %T Concentrating solutions of some singularly perturbed elliptic equations %A Andrea Malchiodi %X We study singularly perturbed elliptic equations arising from models in physics or biology, and investigate the asymptotic behavior of some special solutions. We also discuss some connections with problems arising in differential geometry. %B Front. Math. China 3 (2008) 239-252 %G en_US %U http://hdl.handle.net/1963/2657 %1 1466 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-05-12T13:25:45Z\\nNo. of bitstreams: 1\\nprocmalchiodi.pdf: 183157 bytes, checksum: 5d6ee64d87eb139b09968558c74ab0f5 (MD5) %R 10.1007/s11464-008-0015-z %0 Journal Article %J Advanced nonlinear studies %D 2008 %T On concentration of positive bound states for the Schrödinger-Poisson problem with potentials %A Ianni, Isabella %A Giusi Vaira %XWe study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

%B Advanced nonlinear studies %I Advanced Nonlinear Studies, Inc. %V 8 %P 573–595 %G eng %R 10.1515/ans-2008-0305. %0 Journal Article %J Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 %D 2008 %T Convergence of equilibria of three-dimensional thin elastic beams %A Maria Giovanna Mora %A Stefan Müller %X A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter $h$ of the cross-section tends to zero. More precisely, we show that stationary points of the nonlinear elastic functional $E^h$, whose energies (per unit cross-section) are bounded by $Ch^2$, converge to stationary points of the $\\\\varGamma$-limit of $E^h/h^2$. This corresponds to a nonlinear one-dimensional model for inextensible rods, describing bending and torsion effects. The proof is based on the rigidity estimate for low-energy deformations by Friesecke, James and Müller and on a compensated compactness argument in a singular geometry. In addition, possible concentration effects of the strain are controlled by a careful truncation argument. %B Proc. Roy. Soc. Edinburgh Sect. A 138 (2008) 873-896 %G en_US %U http://hdl.handle.net/1963/1896 %1 2339 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-24T10:09:06Z\\nNo. of bitstreams: 1\\n69M-2006.pdf: 3633291 bytes, checksum: b5dba64c671bbcd8b87e52ce24963341 (MD5) %R 10.1017/S0308210506001120 %0 Journal Article %J Comm. Math. Phys. 271 (2007) 289-373 %D 2007 %T Canonical structure and symmetries of the Schlesinger equations %A Boris Dubrovin %A Marta Mazzocco %X The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m×m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation ofthe general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates. %B Comm. Math. Phys. 271 (2007) 289-373 %G en_US %U http://hdl.handle.net/1963/1997 %1 2199 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-08-30T08:59:18Z\\nNo. of bitstreams: 1\\nmathDG0311261v4.pdf: 748258 bytes, checksum: c550bb118062fa82741da16a2735b68f (MD5) %R 10.1007/s00220-006-0165-3 %0 Journal Article %J International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059 %D 2007 %T Chen-Ruan cohomology of ADE singularities %A Fabio Perroni %K Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence %X We study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism. %B International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059 %I SISSA %G en %U http://hdl.handle.net/1963/6502 %1 6447 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-27T13:02:56Z\nNo. of bitstreams: 1\nmath_0605207v2.pdf: 502025 bytes, checksum: c85d5727542636dfdf53276f3ceaf9cd (MD5) %R 10.1142/S0129167X07004436 %0 Journal Article %D 2007 %T The cohomological crepant resolution conjecture for P(1,3,4,4) %A Samuel Boissiere %A Fabio Perroni %A Etienne Mann %X We prove the cohomological crepant resolution conjecture of Ruan for the\r\nweighted projective space P(1,3,4,4). To compute the quantum corrected\r\ncohomology ring we combine the results of Coates-Corti-Iritani-Tseng on\r\nP(1,1,1,3) and our previous results. %I SISSA %G en %U http://hdl.handle.net/1963/6513 %1 6464 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Fabio Perroni (perroni@sissa.it) on 2013-02-28T17:55:28Z\nNo. of bitstreams: 1\n0712.3248v1.pdf: 182952 bytes, checksum: a5a581e6ba586472b9418608365283cf (MD5) %0 Journal Article %J Bioinformatics 23 (2007) 1640-1647 %D 2007 %T Comparing association network algorithms for reverse engineering of large scale gene regulatory networks: synthetic vs real data %A Nicola Soranzo %A Ginestra Bianconi %A Claudio Altafini %X Motivation: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of nonlinear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). Results: In our simulations we see that all network inference algorithms obtain better performances from data produced with \\\"structural\\\" perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from E. coli gene profiling data: the edges of the \\\"physical\\\" network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. Availability: Software and supplementary material are freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/ %B Bioinformatics 23 (2007) 1640-1647 %G en_US %U http://hdl.handle.net/1963/2028 %1 2168 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-03T12:44:53Z\\nNo. of bitstreams: 1\\nSoBiAl07.pdf: 261510 bytes, checksum: dde8f62bdbd57a761204f8533569885a (MD5) %R 10.1093/bioinformatics/btm163 %0 Report %D 2007 %T The complete one-loop spin chain for N=2 Super-Yang-Mills %A Paolo Di Vecchia %A Alessandro Tanzini %X We show that the complete planar one-loop mixing matrix of the N=2 Super Yang--Mills theory can be obtained from a reduction of that of the N=4 theory. For composite operators of scalar fields, this yields an anisotropic XXZ spin chain, whose spectrum of excitations displays a mass gap. %G en_US %U http://hdl.handle.net/1963/2309 %1 1707 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:28:13Z\\nNo. of bitstreams: 1\\n0412283v1.pdf: 110673 bytes, checksum: 9f881078e3eb69765e2c6e294569fd70 (MD5) %0 Report %D 2007 %T Computing Amplitudes in topological M-theory %A Giulio Bonelli %A Alessandro Tanzini %A Maxim Zabzine %X We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants. %B JHEP 03 (2007) 023 %G en_US %U http://hdl.handle.net/1963/1901 %1 2335 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-12-07T16:26:28Z\\nNo. of bitstreams: 1\\nhep-th0611327.pdf: 307312 bytes, checksum: 9a3a9891aca40624a44c7a531765695b (MD5) %R 10.1088/1126-6708/2007/03/023 %0 Journal Article %J Adv. Math. 209 (2007) 460-525 %D 2007 %T Concentration on minimal submanifolds for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u= u^p$ in $\\\\Omega \\\\subseteq \\\\R^N$, where $\\\\Omega$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\partial \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, ..., N-2\\\\}$. We impose Neumann boundary conditions, assuming $15. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. %B C. R. Math. Acad. Sci. Paris 342 (2006) 589-594 %G en_US %U http://hdl.handle.net/1963/1712 %1 2439 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-18T10:08:04Z\\nNo. of bitstreams: 1\\nmath.DG0504319.pdf: 158321 bytes, checksum: 4a76e9fa42a9ea4440d0fcd628df9c34 (MD5) %R 10.1016/j.crma.2006.02.010 %0 Journal Article %J Duke Math. J. 134 (2006) 359-419 %D 2006 %T Cantor families of periodic solutions for completely resonant nonlinear wave equations %A Massimiliano Berti %A Philippe Bolle %X We prove the existence of small amplitude, $2\\\\pi \\\\slash \\\\om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \\\\om $ belonging to a Cantor-like set of positive measure and for a new set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem. In spite of the complete resonance of the equation we show that we can still reduce the problem to a {\\\\it finite} dimensional bifurcation equation. Moreover, a new simple approach for the inversion of the linearized operators required by the Nash-Moser scheme is developed. It allows to deal also with nonlinearities which are not odd and with finite spatial regularity. %B Duke Math. J. 134 (2006) 359-419 %G en_US %U http://hdl.handle.net/1963/2161 %1 2083 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T09:53:35Z\\nNo. of bitstreams: 1\\n0410618v1.pdf: 427752 bytes, checksum: 08750b5fadd830fbe76aa48d54824f17 (MD5) %R 10.1215/S0012-7094-06-13424-5 %0 Journal Article %J J. Math. Sci. 135 (2006) 3109-3124 %D 2006 %T Classification of stable time-optimal controls on 2-manifolds %A Ugo Boscain %A Igor Nikolaev %A Benedetto Piccoli %B J. Math. Sci. 135 (2006) 3109-3124 %G en_US %U http://hdl.handle.net/1963/2196 %1 2048 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-11T07:48:50Z\\nNo. of bitstreams: 1\\nboscain-paper.pdf: 322031 bytes, checksum: 560c6fdce3f93d196d1cc9d9c4115edb (MD5) %R 10.1007/s10958-006-0148-0 %0 Journal Article %J SIAM J. Control Optim. 45 (2006) 226-245 %D 2006 %T Common Polynomial Lyapunov Functions for Linear Switched Systems %A Paolo Mason %A Ugo Boscain %A Yacine Chitour %X In this paper, we consider linear switched systems $\\\\dot x(t)=A_{u(t)} x(t)$, $x\\\\in\\\\R^n$, $u\\\\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\\\\bf UAS} for short). We first prove that, given a {\\\\bf UAS} system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov function is not uniformly bounded over all the {\\\\bf UAS} systems. This result answers a question raised by Dayawansa and Martin. A generalization to a class of piecewise-polynomial Lyapunov functions is given. %B SIAM J. Control Optim. 45 (2006) 226-245 %G en_US %U http://hdl.handle.net/1963/2181 %1 2063 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-04T14:36:21Z\\nNo. of bitstreams: 1\\n0403209v2.pdf: 244831 bytes, checksum: 1762d79876f9eb915a68dbc25d9a3a21 (MD5) %R 10.1137/040613147 %0 Journal Article %J J. Reine Angew. Math. 594 (2006) 137-174 %D 2006 %T Compactness of solutions to some geometric fourth-order equations %A Andrea Malchiodi %X We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics. %B J. Reine Angew. Math. 594 (2006) 137-174 %G en_US %U http://hdl.handle.net/1963/2126 %1 2117 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T08:13:05Z\\nNo. of bitstreams: 1\\n0410140v2.pdf: 335757 bytes, checksum: 30341fcdac6b4d8f187b4bab1191c993 (MD5) %R 10.1515/CRELLE.2006.038 %0 Journal Article %J Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %D 2006 %T Concentration at manifolds of arbitrary dimension for a singularly perturbed Neumann problem %A Fethi Mahmoudi %A Andrea Malchiodi %X We consider the equation $- \\\\e^2 \\\\D u + u = u^p$ in $\\\\O \\\\subseteq \\\\R^N$, where $\\\\O$ is open, smooth and bounded, and we prove concentration of solutions along $k$-dimensional minimal submanifolds of $\\\\pa \\\\O$, for $N \\\\geq 3$ and for $k \\\\in \\\\{1, \\\\dots, N-2\\\\}$. We impose Neumann boundary conditions, assuming $1<\\\\frac{N-k+2}{N-k-2}$ and $\\\\e \\\\to 0^+$. This result settles in full generality a phenomenon previously considered only in the particular case $N = 3$ and $k = 1$. %B Atti Accad. Naz Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 17 (2006) 279-290 %G en_US %U http://hdl.handle.net/1963/2170 %1 2074 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-03T12:23:19Z\\nNo. of bitstreams: 1\\nMahmoudiMalchiodi06.pdf: 624613 bytes, checksum: 030160de63323a3b0c3864b8f5102b0b (MD5) %0 Journal Article %J Comm. Math. Phys. 266 (2006) 471-497 %D 2006 %T Conservative Solutions to a Nonlinear Variational Wave Equation %A Alberto Bressan %A Zheng Yuxi %X We establish the existence of a conservative weak solution to the Cauchy problem for the nonlinear variational wave equation $u_{tt} - c(u)(c(u)u_x)_x=0$, for initial data of finite energy. Here $c(\\\\cdot)$ is any smooth function with uniformly positive bounded values. %B Comm. Math. Phys. 266 (2006) 471-497 %G en_US %U http://hdl.handle.net/1963/2184 %1 2060 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T08:06:00Z\\nNo. of bitstreams: 1\\n0502058v1.pdf: 265359 bytes, checksum: 77983b4834210b17aa4c758dbf189d4a (MD5) %R 10.1007/s00220-006-0047-8 %0 Journal Article %J Int. J. Mod. Phys. A 21 (2006) 3133-3150 %D 2006 %T A cyclic integral on k-Minkowski noncommutative space-time %A Alessandra Agostini %A Giovanni Amelino-Camelia %A Michele Arzano %A Francesco D'Andrea %X We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this ``cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a ``canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators. %B Int. J. Mod. Phys. A 21 (2006) 3133-3150 %G en_US %U http://hdl.handle.net/1963/2158 %1 2086 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T08:56:14Z\\nNo. of bitstreams: 1\\n0407227v1.pdf: 219700 bytes, checksum: 4a7f6665bddfb66793e39aa4a8e3ce25 (MD5) %R 10.1142/S0217751X06031077 %0 Journal Article %J Phys. Rev. A 72 (2005) 012112 %D 2005 %T Commuting multiparty quantum observables and local compatibility %A Claudio Altafini %X A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not happen in a concise manner. In particular, it is shown that two ``fully nontrivial\\\'\\\' $n$-qubit observables are compatible locally and globally if and only if they are equal up to sign. In addition, the formula gives insight into the construction of new paradoxes of the type of the Kochen-Specker Theorem, which can then be easily rephrased into proposals for new no hidden variable experiments of the type of the ``Bell Theorem without inequalities\\\'\\\'. %B Phys. Rev. A 72 (2005) 012112 %G en_US %U http://hdl.handle.net/1963/2228 %1 2016 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T14:36:34Z\\nNo. of bitstreams: 1\\nqu-ent-comm.pdf: 168766 bytes, checksum: 05858df702df633ee1fa71d76f76d1b4 (MD5) %R 10.1103/PhysRevA.72.012112 %0 Book Section %B Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 %D 2005 %T Complete systems of invariants for rank 1 curves in Lagrange Grassmannians %A Igor Zelenko %X Curves in Lagrange Grassmannians naturally appear when one studies intrinsically \\\"the Jacobi equations for extremals\\\", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of finding of invariants of curves in Lagrange Grassmannians w.r.t. the action of the linear Symplectic group. In the present paper we develop a new approach to differential geometry of so-called rank 1 curves in Lagrange Grassmannian, i.e., the curves with velocities being rank one linear mappings (under the standard identification of the tangent space to a point of the Lagrange Grassmannian with an appropriate space of linear mappings). The curves of this class are associated with \\\"the Jacobi equations for extremals\\\", corresponding to control systems with scalar control and to rank 2 vector distributions. In particular, we construct the tuple of m principal invariants, where m is equal to half of dimension of the ambient linear symplectic space, such that for a given tuple of arbitrary m smooth functions there exists the unique, up to a symplectic transformation, rank 1 curve having this tuple, as the tuple of the principal invariants. This approach extends and essentially simplifies some results of our previous paper (J. Dynamical and Control Systems, 8, 2002, No. 1, 93-140), where only the uniqueness part was proved and in rather cumbersome way. It is based on the construction of the new canonical moving frame with the most simple structural equation. %B Differential geometry and its applications, 367-382, Matfyzpress, Prague, 2005 %G en_US %U http://hdl.handle.net/1963/2310 %1 1706 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:39:11Z\\nNo. of bitstreams: 1\\n0411190v1.pdf: 227302 bytes, checksum: f4c17631a146df10f7ea9facaa0949b2 (MD5) %0 Journal Article %J Geometric and Functional Analysis 15 (6) 1162-1222 (2005) %D 2005 %T Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains %A Andrea Malchiodi %X We prove new concentration phenomena for the equation −ɛ2 Δu + u = up in a smooth bounded domain R3 and with Neumann boundary conditions. Here p > 1 and ɛ > 0 is small. We show that concentration of solutions occurs at some geodesics of ∂Ω when ɛ → 0. %B Geometric and Functional Analysis 15 (6) 1162-1222 (2005) %I Springer %G en %U http://hdl.handle.net/1963/4866 %1 4645 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T13:51:52Z\\nNo. of bitstreams: 1\\nMalchiodi03.pdf: 521628 bytes, checksum: 3aa8a237bad84b04bdd17669f210e057 (MD5) %R 10.1007/s00039-005-0542-7 %0 Journal Article %J SIAM J. Math. Anal. 36 (2005) 1293-1309 %D 2005 %T Conservation laws with time dependent discontinuous coefficients %A Giuseppe Maria Coclite %A Nils Henrik Risebro %X We consider scalar conservation laws where the flux function depends discontinuously on both the spatial and temporal location. Our main results are the existence and well-posedness of an entropy solution to the Cauchy problem. The existence is established by showing that a sequence of front tracking approximations is compact in L1, and that the limits are entropy solutions. Then, using the definition of an entropy solution taken form [11], we show that the solution operator is L1 contractive. These results generalize the corresponding results from [16] and [11]. %B SIAM J. Math. Anal. 36 (2005) 1293-1309 %I SISSA Library %G en %U http://hdl.handle.net/1963/1666 %1 2452 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:06:09Z (GMT). No. of bitstreams: 1\\n96_02.pdf: 3363466 bytes, checksum: 5ed39a522bb68737585e74668afafc5a (MD5)\\n Previous issue date: 2002 %R 10.1137/S0036141002420005 %0 Journal Article %J J. Dyn. Control Syst. 11 (2005) 297-327 %D 2005 %T On curvatures and focal points of distributions of dynamical Lagrangian distributions and their reductions by first integrals %A Andrei A. Agrachev %A Natalia N. Chtcherbakova %A Igor Zelenko %X Pairs (Hamiltonian system, Lagrangian distribution), called dynamical Lagrangian distributions, appear naturally in Differential Geometry, Calculus of Variations and Rational Mechanics. The basic differential invariants of a dynamical Lagrangian distribution w.r.t. the action of the group of symplectomorphisms of the ambient symplectic manifold are the curvature operator and the curvature form. These invariants can be seen as generalizations of the classical curvature tensor in Riemannian Geometry. In particular, in terms of these invariants one can localize the focal points along extremals of the corresponding variational problems. In the present paper we study the behavior of the curvature operator, the curvature form and the focal points of a dynamical Lagrangian distribution after its reduction by arbitrary first integrals in involution. The interesting phenomenon is that the curvature form of so-called monotone increasing Lagrangian dynamical distributions, which appear naturally in mechanical systems, does not decrease after reduction. It also turns out that the set of focal points to the given point w.r.t. the monotone increasing dynamical Lagrangian distribution and the corresponding set of focal points w.r.t. its reduction by one integral are alternating sets on the corresponding integral curve of the Hamiltonian system of the considered dynamical distributions. Moreover, the first focal point corresponding to the reduced Lagrangian distribution comes before any focal point related to the original dynamical distribution. We illustrate our results on the classical $N$-body problem. %B J. Dyn. Control Syst. 11 (2005) 297-327 %G en_US %U http://hdl.handle.net/1963/2254 %1 1993 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-18T08:53:27Z\\nNo. of bitstreams: 1\\n0409152v1.pdf: 335893 bytes, checksum: bf4dfeb39ad05ff60c2c2cc745fa0fc1 (MD5) %R 10.1007/s10883-005-6581-4 %0 Journal Article %J Int. J. Numer. Meth. Fluids %D 2004 %T Calculation of impulsively started incompressible viscous flows %A Marra, Andrea %A Andrea Mola %A Quartapelle, Luigi %A Riviello, Luca %B Int. J. Numer. Meth. Fluids %V 46 %P 877–902 %G eng %0 Journal Article %J Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %D 2004 %T Coarse-grained models of materials with non-convex free-energy: two case studies %A Antonio DeSimone %X Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. %B Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 %I Elsevier %G en %U http://hdl.handle.net/1963/4884 %1 4664 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-24T06:59:37Z\\nNo. of bitstreams: 0 %R 10.1016/j.cma.2003.12.064 %0 Journal Article %J Phys. Rev. A 70 (2004) 062321 %D 2004 %T Coherent control of open quantum dynamical systems %A Claudio Altafini %X A systematic analysis of the behavior of the quantum Markovian master equation driven by coherent control fields is proposed. Its irreversible character is formalized using control-theoretic notions and the sets of states that can be reached via cohere nt controls are described. The analysis suggests to which extent (and how) it is possible to counteract the effect of dissipation. %B Phys. Rev. A 70 (2004) 062321 %G en_US %U http://hdl.handle.net/1963/2227 %1 2017 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-15T14:29:53Z\\nNo. of bitstreams: 1\\nqopen-coher2.pdf: 226720 bytes, checksum: c93d394691258c3d18b40d7992b70274 (MD5) %R 10.1103/PhysRevA.70.062321 %0 Journal Article %J Comm. Pure Appl. Math. 57 (2004) 1075-1109 %D 2004 %T On the convergence rate of vanishing viscosity approximations %A Alberto Bressan %A Tong Yang %X Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound $\\\\big\\\\|u(t,\\\\cdot)-u^\\\\ve(t,\\\\cdot)\\\\big\\\\|_{\\\\L^1}= \\\\O(1)(1+t)\\\\cdot \\\\sqrt\\\\ve|\\\\ln\\\\ve|$ on the distance between an exact BV solution $u$ and a viscous approximation $u^\\\\ve$, letting the viscosity coefficient $\\\\ve\\\\to 0$. In the proof, starting from $u$ we construct an approximation of the viscous solution $u^\\\\ve$ by taking a mollification $u*\\\\phi_{\\\\strut \\\\sqrt\\\\ve}$ and inserting viscous shock profiles at the locations of finitely many large shocks, for each fixed $\\\\ve$. Error estimates are then obtained by introducing new Lyapunov functionals which control shock interactions, interactions between waves of different families and by using sharp decay estimates for positive nonlinear waves. %B Comm. Pure Appl. Math. 57 (2004) 1075-1109 %I Wiley %G en_US %U http://hdl.handle.net/1963/2915 %1 1785 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:30:25Z\\nNo. of bitstreams: 1\\nmath.AP0307141.pdf: 265243 bytes, checksum: 795adebd067228364ac1240add5f7b02 (MD5) %R 10.1002/cpa.20030 %0 Journal Article %J Calc. Var. Partial Differential Equations 16 (2003) 299-333 %D 2003 %T The calibration method for the Mumford-Shah functional and free-discontinuity problems %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X We present a minimality criterion for the Mumford-Shah functional, and more generally for non convex variational integrals on SBV which couple a surface and a bulk term. This method provides short and easy proofs for several minimality results. %B Calc. Var. Partial Differential Equations 16 (2003) 299-333 %I Springer %G en_US %U http://hdl.handle.net/1963/3051 %1 1282 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T15:00:19Z\\nNo. of bitstreams: 1\\n0105013v1.pdf: 428802 bytes, checksum: de75d15134f2a74b36b0d71355e04835 (MD5) %R 10.1007/s005260100152 %0 Thesis %D 2003 %T Control Problems for Systems of Conservation Laws %A Giuseppe Maria Coclite %K Asymptotic Stabilization %I SISSA %G en %U http://hdl.handle.net/1963/5325 %1 5154 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Gerardina Cargnelutti (gerry@sissa.it) on 2012-02-01T11:55:57Z\\nNo. of bitstreams: 1\\nPhD_Coclite_Giuseppe_Maria.pdf: 6164510 bytes, checksum: 461d3d4a88e73be06d19b21a85ab149a (MD5) %0 Journal Article %J J. Math. Phys. 44 (2003) 2357-2372 %D 2003 %T Controllability properties for finite dimensional quantum Markovian master equations %A Claudio Altafini %X Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail. %B J. Math. Phys. 44 (2003) 2357-2372 %I American Institute of Physics %G en_US %U http://hdl.handle.net/1963/2909 %1 1791 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T12:05:33Z\\nNo. of bitstreams: 1\\nquant-ph0211194.pdf: 250415 bytes, checksum: e28216a9c4ccbc9174b725f864ec205a (MD5) %R 10.1063/1.1571221 %0 Journal Article %J J. Convex Anal. 9 (2002) 1-29 %D 2002 %T The Calibration Method for Free-Discontinuity Problems on Vector-Valued Maps %A Maria Giovanna Mora %X The calibration method is a classical minimality criterion, which has been recently adapted to functionals with free discontinuities by Alberti, Bouchitté, Dal Maso. In this paper we present a further generalization of this theory to functionals defined on vector-valued maps. %B J. Convex Anal. 9 (2002) 1-29 %I Heldermann Verlag %G en_US %U http://hdl.handle.net/1963/3049 %1 1284 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-09T14:39:36Z\\nNo. of bitstreams: 1\\nvcal_method.pdf: 345795 bytes, checksum: 8f1703daddffd1c18d837fccf4dfc9bf (MD5) %0 Journal Article %J Commun. Pure Appl. Anal. 1 (2002) 161-190 %D 2002 %T A center manifold technique for tracing viscous waves %A Stefano Bianchini %A Alberto Bressan %X In this paper we introduce a new technique for tracing viscous travelling profiles. To illustrate the method, we consider a special 2 x 2 hyperbolic system of conservation laws with viscosity, and show that any solution can be locally decomposed as the sum of 2 viscous travelling profiles. This yields the global existence, stability and uniform BV bounds for every solution with suitably small BV data. %B Commun. Pure Appl. Anal. 1 (2002) 161-190 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3075 %1 1258 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-10T10:55:34Z\\nNo. of bitstreams: 1\\npreprint2001_53.pdf: 444727 bytes, checksum: 26cee63284464e4850e1e6426216fe70 (MD5) %0 Journal Article %J Nonlinear Anal. 48 (2002) 481-504 %D 2002 %T Chaotic dynamics for perturbations of infinite-dimensional Hamiltonian systems %A Massimiliano Berti %A Carlo Carminati %B Nonlinear Anal. 48 (2002) 481-504 %I Elsevier %G en %U http://hdl.handle.net/1963/1279 %1 3176 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:42Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0362-546X(00)00200-5 %0 Journal Article %J J. Math. Phys. %D 2002 %T Coherent state realizations of $\rm su(n+1)$ on the $n$-torus %A de Guise, Hubert %A Marco Bertola %B J. Math. Phys. %V 43 %P 3425–3444 %G eng %0 Journal Article %J J.Math.Phys. 43(2002), no.5, 2051 %D 2002 %T Controllability of quantum mechanical systems by root space decomposition of su(N) %A Claudio Altafini %B J.Math.Phys. 43(2002), no.5, 2051 %I SISSA Library %G en %U http://hdl.handle.net/1963/1613 %1 2505 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:18Z (GMT). No. of bitstreams: 1\\nquant-ph0110147.pdf: 211574 bytes, checksum: a43e52a6eec3e4a8127b810133d57645 (MD5)\\n Previous issue date: 2002 %R 10.1063/1.1467611 %0 Journal Article %J Interfaces Free Bound. 7 (2002) 345-370 %D 2002 %T Curvature theory of boundary phases: the two-dimensional case %A Andrea Braides %A Andrea Malchiodi %X We describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted. %B Interfaces Free Bound. 7 (2002) 345-370 %I European Mathematical Society %G en_US %U http://hdl.handle.net/1963/3537 %1 1164 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T15:34:33Z\\nNo. of bitstreams: 1\\n2001BM.pdf: 361945 bytes, checksum: eb748fdc7f69d6fef497ebaf68f155a6 (MD5) %0 Journal Article %J Discrete Cont. Dyn. Syst. 7 (2001) 449-476 %D 2001 %T A case study in vanishing viscosity %A Stefano Bianchini %A Alberto Bressan %B Discrete Cont. Dyn. Syst. 7 (2001) 449-476 %I American Institute of Mathematical Sciences %G en_US %U http://hdl.handle.net/1963/3091 %1 1242 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-14T08:16:28Z\\nNo. of bitstreams: 1\\ncasestudy.pdf: 289769 bytes, checksum: d1ec5d9048e85bd7ebbd1e3de3259336 (MD5) %0 Journal Article %J Differential Geom. Appl. 14 (2001) 151-156 %D 2001 %T Complex Lagrangian embeddings of moduli spaces of vector bundles %A Ugo Bruzzo %A Fabio Pioli %X By means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds. %B Differential Geom. Appl. 14 (2001) 151-156 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2885 %1 1815 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T10:08:27Z\\nNo. of bitstreams: 1\\n0010249v1.pdf: 141027 bytes, checksum: 1c49d04b301d728d577cf724722b5af7 (MD5) %R 10.1016/S0926-2245(00)00040-1 %0 Journal Article %J Math. Control Signals Systems 14 (2001) 173-193 %D 2001 %T Controllability for discrete systems with a finite control set %A Yacine Chitour %A Benedetto Piccoli %B Math. Control Signals Systems 14 (2001) 173-193 %I Springer %G en_US %U http://hdl.handle.net/1963/3114 %1 1219 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-15T10:33:44Z\\nNo. of bitstreams: 1\\ncontrollability.pdf: 247896 bytes, checksum: 6f94f9b27348f59bb506c1e79beba6e1 (MD5) %R 10.1007/PL00009881 %0 Journal Article %J Mathematical Physics, Analysis and Geometry 4: 293–377, 2001 %D 2001 %T On the Critical Behavior, the Connection Problem and the Elliptic Representation of a Painlevé VI Equation %A Davide Guzzetti %K Painleve Equations, Isomonodromy deformations %X In this paper we find a class of solutions of the sixth Painlevé equation appearing in\r\nthe theory of WDVV equations. This class covers almost all the monodromy data associated to\r\nthe equation, except one point in the space of the data. We describe the critical behavior close to\r\nthe critical points in terms of two parameters and we find the relation among the parameters at\r\nthe different critical points (connection problem). We also study the critical behavior of Painlevé\r\ntranscendents in the elliptic representation. %B Mathematical Physics, Analysis and Geometry 4: 293–377, 2001 %I Kluwer Academic Publishers %G en %1 6477 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T09:51:54Z\nNo. of bitstreams: 1\n05-ElliptMu01.pdf: 612332 bytes, checksum: a0c74f3a94a9fc629c50e8bc47cb1939 (MD5) %R 10.1023/A:1014265919008 %0 Journal Article %J European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %D 2000 %T The Calibration Method for Free Discontinuity Problems %A Gianni Dal Maso %X The calibration method is used to identify some minimizers of the Mumford-Shah functional. The method is then extended to more general free discontinuity problems. %B European Congress of Mathematics. Volume I : Barcelona, July 10-14, 2000 / Carles Casacuberta ... [et al.], editors. , Boston : Birkhauser, 2001, p. 317-326. %I SISSA Library %G en %U http://hdl.handle.net/1963/1496 %1 2667 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:13Z (GMT). No. of bitstreams: 1\\r\\nmath.OC0006016.pdf: 150581 bytes, checksum: dde42438e52ad82f5980d68f697f90c8 (MD5)\\r\\n Previous issue date: 2000 %0 Journal Article %J Chinese Ann. Math. B, 2000, 21, 269 %D 2000 %T On the convergence of Godunov scheme for nonlinear hyperbolic systems %A Alberto Bressan %A Helge Kristian Jenssen %B Chinese Ann. Math. B, 2000, 21, 269 %I SISSA Library %G en %U http://hdl.handle.net/1963/1473 %1 2690 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:02:54Z (GMT). No. of bitstreams: 0\\n Previous issue date: 2000 %0 Journal Article %J C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %D 1999 %T The calibration method for the Mumford-Shah functional %A Giovanni Alberti %A Guy Bouchitte %A Gianni Dal Maso %X In this Note we adapt the calibration method to functionals of Mumford-Shah type, and provide a criterion (Theorem 1) to verify that a given function is energy minimizing. Among other applications, we use this criterion to show that certain triple-junction configurations are minimizing (Example 3). %B C. R. Acad. Sci. Paris Ser. I Math. 329 (1999), no. 3, 249-254 %I Elsevier %G en %U http://hdl.handle.net/1963/1235 %1 2708 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:55:07Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1999 %R 10.1016/S0764-4442(00)88602-4 %0 Journal Article %J Comm. Math. Phys. 206 (1999) 265-272 %D 1999 %T Categorial mirror symmetry for K3 surfaces %A Claudio Bartocci %A Ugo Bruzzo %A Guido Sanguinetti %X We study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$. %B Comm. Math. Phys. 206 (1999) 265-272 %I Springer %G en_US %U http://hdl.handle.net/1963/2887 %1 1813 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T10:27:18Z\\nNo. of bitstreams: 1\\n9811004v2.pdf: 164135 bytes, checksum: 85c711ba84f77d68351d95af3caad50c (MD5) %R 10.1007/s002200050705 %0 Journal Article %J Phys. Lett. B %D 1999 %T Correspondence between Minkowski and de Sitter quantum field theory %A Marco Bertola %A Gorini, Vittorio %A Moschella, Ugo %A Schaeffer, Richard %B Phys. Lett. B %V 462 %P 249–253 %G eng %0 Thesis %D 1998 %T On the Cauchy Problem for the Whitham Equations %A Tamara Grava %K Korteweg de Vries equation %I SISSA %G en %U http://hdl.handle.net/1963/5555 %1 5382 %2 Mathematics %3 Mathematical Physics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-02-24T08:14:13Z\\nNo. of bitstreams: 1\\nPhD_Grava_Tamara.pdf: 3951334 bytes, checksum: 2a0b9e024dd0a2bc9c856a24c123e9c3 (MD5) %0 Journal Article %J Potential Anal. 7 (1997), no. 4, 765-803 %D 1997 %T Capacity theory for monotone operators %A Gianni Dal Maso %A Igor V. Skrypnik %X If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$. %B Potential Anal. 7 (1997), no. 4, 765-803 %I Springer %G en %U http://hdl.handle.net/1963/911 %1 2880 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:26Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %R 10.1023/A:1017987405983 %0 Journal Article %J Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %D 1997 %T Comportamento asintotico delle soluzioni di problemi di Dirichlet %A Gianni Dal Maso %B Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277 %G it %U http://hdl.handle.net/1963/6438 %1 6378 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:47:36Z\\nNo. of bitstreams: 1\\nDM-97-UMI.pdf: 232404 bytes, checksum: 9b45a539545e2635c8ffedf2ec7a0648 (MD5) %0 Journal Article %J Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %D 1996 %T A capacity method for the study of Dirichlet problems for elliptic systems in varying domains %A Gianni Dal Maso %A Rodica Toader %B Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277 %I SISSA Library %G en %U http://hdl.handle.net/1963/989 %1 2867 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:41:21Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %D 1995 %T Capacity and Dirichlet problems in varying domains %A Gianni Dal Maso %I SISSA Library %G en %U http://hdl.handle.net/1963/950 %1 3504 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:40:53Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997 %D 1995 %T Classical solutions for a perturbed N-body system %A Gianfausto Dell'Antonio %B Topological nonlinear analysis, II (Frascati, 1995), 1--86, Progr. Nonlinear Differential Equations Appl., 27, Birkhauser Boston, Boston, MA, 1997 %I SISSA Library %G en %U http://hdl.handle.net/1963/126 %1 16 %2 LISNU %3 Interdisciplinary Laboratory for Advanced Studies %$ Made available in DSpace on 2004-09-01T12:22:18Z (GMT). No. of bitstreams: 1\\nILAS_1_96.pdf: 4461254 bytes, checksum: eae522e49d94ff9b35a3067aa9f62b0a (MD5)\\n Previous issue date: 1996 %0 Journal Article %J Proc.Amer.Math.Soc. 112 (1991), no.2, 413 %D 1991 %T A class of absolute retracts of dwarf spheroidal galaxies %A Alberto Bressan %A Arrigo Cellina %A Andrzej Fryszkowski %B Proc.Amer.Math.Soc. 112 (1991), no.2, 413 %I SISSA Library %G en %U http://hdl.handle.net/1963/837 %1 2954 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:33Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1989 %0 Journal Article %J J.Math.Phys.31:45,1990 %D 1990 %T Chern-Simons forms on principal superfiber bundles %A Giovanni Landi %A Claudio Bartocci %A Ugo Bruzzo %X A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a ``superextension\\\'\\\' of the Dirac monopole is discussed. %B J.Math.Phys.31:45,1990 %I SISSA Library %G en %U http://hdl.handle.net/1963/590 %1 3314 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:34:46Z (GMT). No. of bitstreams: 1\\n109_87.pdf: 683027 bytes, checksum: c0d44fdabb8144815d764846f5241132 (MD5)\\n Previous issue date: 1987 %R 10.1063/1.528826 %0 Journal Article %J Differential Integral Equations 3 (1990), no.6, p.1151-1166. %D 1990 %T Correctors for the homogeneization of monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B Differential Integral Equations 3 (1990), no.6, p.1151-1166. %I SISSA Library %G en %U http://hdl.handle.net/1963/812 %1 2979 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:16Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989 %0 Journal Article %J J. Differential Equations 82 (1989), no. 1, 1-14 %D 1989 %T On the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version) %A Giovanni Vidossich %B J. Differential Equations 82 (1989), no. 1, 1-14 %I SISSA Library %G en %U http://hdl.handle.net/1963/666 %1 3260 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:04Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J J. Differential Equations 82 (1989), no. 1, 1--14 %D 1989 %T On the continuous dependence of solutions of boundary value problems for ordinary differential equations %A Giovanni Vidossich %B J. Differential Equations 82 (1989), no. 1, 1--14 %I SISSA Library %G en %U http://hdl.handle.net/1963/633 %1 3820 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:35:41Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %R 10.1016/0022-0396(89)90164-2 %0 Journal Article %J J. Analyse Math. 53 (1989), 269--289 %D 1989 %T Convergence of unilateral problems for monotone operators %A Gianni Dal Maso %A Anneliese Defranceschi %B J. Analyse Math. 53 (1989), 269--289 %I SISSA Library %G en %U http://hdl.handle.net/1963/722 %1 3069 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:36:45Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1988 %0 Journal Article %J Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %D 1986 %T Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) %A Gianni Dal Maso %B Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190 %I SISSA Library %G en %U http://hdl.handle.net/1963/353 %1 3614 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:28:39Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1984 %0 Journal Article %D 1982 %T A criterion for he existence of maximal solutions of strongly nonlinear elliptic problems %A Giovanni Vidossich %I SISSA Library %G en %U http://hdl.handle.net/1963/161 %1 3806 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:26:06Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1982