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Strongly Interacting Spinless Fermions in D=1 and 2 Dimensions: A Perturbative-Variational ApproachMar 15 1995We propose a perturbative-variational approach to interacting fermion systems on 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. ... More

The Role of Boundary Conditions in the Real-Space Renormalization GroupSep 11 1995We show that the failure of the real-space RG method in the 1D tight-binding model is not intrinsic to the method as considered so far but depends on the choice of boundary conditions. For fixed BC's the failure does happen. For free BC's we present a ... More

Dualities in Spin LaddersJun 11 1997We introduce a set of discrete modular transformations $T_\ell,U_\ell$ and $S_\ell$ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder ... More

The Short Range RVB State of Even Spin Ladders: A Recurrent Variational ApproachApr 25 1997Using a recursive method we construct dimer and nondimer variational ansatzs of the ground state for the two-legged ladder, and compute the number of dimer coverings, the energy density and the spin correlation functions. The number of dimer coverings ... More

Distribution free goodness-of-fit tests for linear processesMar 02 2006This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale ... More

A Rotating-Valence-Bond scenario for the 2D Antiferromagnetic Heisenberg ModelJan 25 1996We propose that the valence bonds forming the ground state of the 2D-AF Heisenberg model on a square lattice may rotate under the effect of the antiferromagnetic background. To test this idea we apply a real space renormalization group approach to construct ... More

Topological Heat Transport and Symmetry-Protected Boson CurrentsJun 24 2016Jul 25 2017The study of non-equilibrium properties in topological systems is of practical and fundamental importance. Here, we analyze the stationary properties of a two-dimensional bosonic Hofstadter lattice coupled to two thermal baths in the quantum open-system ... More

Real Space Renormalization Group Methods and Quantum GroupsJul 26 1995Jul 27 1995We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is preserved under the ... More

The Renormalization Group Method and Quantum Groups: the postman always rings twiceNov 27 1995We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant Hamiltonians, that of ... More

Analytic Formulations of the Density Matrix Renormalization GroupNov 16 1995We present two new analytic formulations of the Density Matrix Renormalization Group Method. In these formulations we combine the block renormalization group (BRG) procedure with Variational and Fokker-Planck methods. The BRG method is used to reduce ... More

Dynamics of Thermal Effects in the Spin-Wave Theory of Quantum AntiferromagnetsDec 14 2011Jan 17 2013We derive a master equation that allows us to study non-equilibrium dynamics of a quantum antiferromagnet. By resorting to spin-wave theory, we obtain a closed analytic form for the magnon decay rates. These turn out to be closely related to form factors, ... More

The Correlated Block Renormalization GroupDec 18 1995We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of its neighbours. ... More

Multivariate Orthogonal Polynomials and Modified Moment FunctionalsJan 26 2016Sep 10 2016Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained by adding to ... More

Chaos in the Classical Analogue of the Hofstadter ProblemAug 11 1998The behaviour of an electron in a potential that resembles that of a bidimensional solid with a perpendicular magnetic field applied is studied from a classical point of view. This problem presents the standard features of chaos and some interesting new ... More

Sobolev orthogonal polynomials on the unit ball via outward normal derivativesDec 03 2015We analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which involves the outward normal derivatives on the sphere. Using their representation in terms of spherical harmonics, algebraic and analytic properties ... More

The effects of thermal and correlated noise on magnons in a quantum ferromagnetFeb 28 2018Nov 05 2018The dynamics and thermal equilibrium of spin waves (magnons) in a quantum ferromagnet as well as the macroscopic magnetisation are investigated. Thermal noise due to an interaction with lattice phonons and the effects of spatial correlations in the noise ... More

Distribution Regression in Duration Analysis: an Application to Unemployment SpellsApr 12 2019This article proposes estimation and inference procedures for distribution regression models with randomly right-censored data. The proposal generalizes classical duration models to a situation where slope coefficients can vary with the elapsed duration, ... More

Some remarks on the coincidence set for the Signorini problemDec 10 2018We study some properties of the coincidence set for the boundary Signorini problem, improving some results from previous works by the second author and collaborators. Among other new results, we show here that the convexity assumption on the domain made ... More

Bayesian model selection for linear regressionDec 15 2015In this note we introduce linear regression with basis functions in order to apply Bayesian model selection. The goal is to incorporate Occam's razor as provided by Bayes analysis in order to automatically pick the model optimally able to explain the ... More

Experimental Quantum Computations on a Topologically Encoded QubitMar 21 2014The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant quantum computing ... More

Chiral Topological Superconductors Enhanced by Long-Range InteractionsJul 07 2017Jan 11 2018We study the phase diagram and edge states of a two-dimensional p-wave superconductor with long-range hopping and pairing amplitudes. New topological phases and quasiparticles different from the usual short-range model are obtained. When both hopping ... More

Quantum Error Correction with the Semion CodeOct 18 2018We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string operators that implement ... More

Topological Phases in Nodeless Tetragonal SuperconductorsMar 30 2018Jan 23 2019We compute the topological phase diagram of 2D tetragonal superconductors for the only possible nodeless pairing channels compatible with that crystal symmetry. Subject to a Zeeman field and spin-orbit coupling, we demonstrate that these superconductors ... More

Finsler metrics and relativistic spacetimesNov 19 2013Sep 15 2014Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other parts of Physics. ... More

A numerical algorithm for singular optimal LQ control systemsMar 09 2012A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear-quadratic optimal control problems is presented. The algorithm is based on the presymplectic constraint algorithm (PCA) by Gotay-Nester \cite{Go78,Vo99} ... More

Small-spatial scale variations of nebular properties and the abundance discrepancy in three Galactic HII regionsMar 12 2010We present results of long-slit spectroscopy in several slit positions that cover different morphological structures of the central parts of three bright Galactic HII regions: M8, M17 and NGC7635. We study the spatial distributions of a large number of ... More

Luminous red stars in Local Group dwarf elliptical galaxies: an intermediate-age population?Apr 02 1997Apr 02 1997In this paper, we show that the optically bright stars above the tip of the first red giant branch (TRGB) in the color magnitude (CM) diagrams of nearby dwarf elliptical (dE) galaxies, commonly interpreted as indication of the existence of an intermediate-age ... More

A Hamiltonian Algorithm for Singular Optimal LQ Control SystemsApr 11 2012A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the well-known Rabier-Rheinhboldt ... More

Wide Field Observations of the Ursa Minor dSph galaxyApr 28 1999Ursa Minor (UMi) is one of the closest satellites of the Milky Way (d=69 kpc). It is possibly a disrupted dSph interacting with the external Galactic halo. This makes its study quite necessary in the forementioned context. In this paper we present preliminary ... More

Light Stops in a minimal U(1)x extension of the MSSMSep 08 2015Dec 16 2015In order to reproduce the measured mass of the Higgs boson mh = 125GeV in the minimal supersymmetric standard model, one usually has to rely on heavy stops, increasing the fine tuning of the electroweak scale. By introducing a new gauge sector, the Higgs ... More

Effects of orbital angular momentum on few-cycle pulse shape: Coupling between the temporal and angular momentum degrees of freedomFeb 26 2019Feb 27 2019We describe the coupling between orbital angular momentum (OAM) and temporal degrees of freedom in pulsed Laguerre-Gauss beams. The effects of this coupling are to increase significantly the duration of few-cycle pulses when the OAM carried by the pulse ... More

Self-trapped pulsed beams with finite power in pure cubic Kerr media excited by time-diffracting, space-time beamsMay 21 2018Nov 02 2018We study the nonlinear propagation of diffraction-free, space-time wave packets, also called time-diffracting beams because their spatiotemporal structure reproduces diffraction in time. We report on the spontaneous formation of propagation-invariant, ... More

Parametrization of the Tkatchenko-Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid waterApr 03 2017Apr 24 2017We present a list of optimized damping range parameters $s_R$ to be used with the Tkatchenko-Scheffler van der Waals dispersion-correction scheme [Phys. Rev. Lett. 102, 073005 (2009)]. The optimal $s_R$ are obtained for seven popular generalized-gradient ... More

Time-diffracting beams: On their nature, diffraction-free propagation as needles of light, and nonlinear generationFeb 28 2018We investigate on the properties of the recently introduced time-diffracting (TD) beams in free space. They are shown to be paraxial and quasi-monochromatic realizations of localized waves, spatiotemporal localized waves travelling undistorted at arbitrary ... More

On the Bahadur slope of the Lilliefors and the Cramér--von Mises tests of normalityDec 22 2006We find the Bahadur slope of the Lilliefors and Cram\'{e}r--von Mises tests of normality.

Velocity measurements in General Relativity revisitedJul 14 2011In this work we generalize an earlier treatment of the measurements of velocities at the event horizon of a black hole. This is intended as a pedagogical exercise as well as one more contribution to the resolution of some unphysical interpretations related ... More

Focusing mKdV Breather Solutions with Nonvanishing Boundary Conditions by the Inverse Scattering MethodOct 18 2011Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain the square k^2 of a focusing modified Korteweg-de Vries (mKdV) breather solution with non zero vacuum parameter b^2 . We are able to factorize and simplify it in order ... More

Isotropic subspaces of Orlik-Solomon algebrasJul 15 2010We give a combinatorial characterization of isotropic subspaces in the Orlik- Solomon algebra of a hyperplane arrangement in terms of decorations of its intersection lattice. We then use this characterization to prove a result that relates these isotropic ... More

Gaussian beams diffracting in timeSep 23 2017Dec 13 2017We show how to transform the mathematical expression of any monochromatic paraxial light beam into the expression of a pulsed beam whose diffraction is switched from the axial direction to its temporal structure. We exemplify this transformation with ... More

Spontaneous localization in self-focusing of ultrashort light pulsesDec 28 2018This is a summary directed to PhD students of the research work conducted on the problem of the production of "light bullets", or multidimensional wave packets that propagate without distortion in unbounded, homogeneous, nonlinear media, and on the actual ... More

A model for the wind-driven current in the wavy oceanic surface layer: apparent friction velocity reduction and roughness length enhancementMay 07 2018A simple analytical model is developed for the current induced by the wind and modified by surface wind-waves in the oceanic surface layer, based on a first-order turbulence closure and including the effect of a vortex force representing the Stokes drift ... More

A polynomial generalization of the Euler characteristic for algebraic setsNov 15 2011We present a method to compute the Euler characteristic of an algebraic subset of $\bc^n$. This method relies on clasical tools such as Gr\"obner basis and primary decomposition. The existence of this method allows us to define a new invariant for such ... More

Nonlinear stability of Gardner breathersMay 10 2017Sep 22 2017We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are $H^2(\mathbb{R})$ stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional ... More

Combinatorial differential operators in: Faà di Bruno formula, enumeration of ballot paths, enriched rooted trees and increasing rooted treesOct 12 2016We obtain a differential equation for the enumeration of the path length of general increasing trees. By using differential operators and their combinatorial interpretation we give a bijective proof of a version of Fa\`a di Bruno formula, and model the ... More

Modified Theories of Gravity: Traversable WormholesJul 13 2011This MSc thesis is divided in to two parts. The first, covers the foundations of theories of gravitation, and, the second incorporates original work on the subject of the existence of traversable wormholes in $f(R)$ modified theories of gravity. A short ... More

Are the calorimetric and elastic Debye temperatures of glasses really different?May 04 2004Below 1 K, the specific heat Cp of glasses depends approximately linearly on temperature T, in contrast with the cubic dependence observed in crystals, and which is well understood in terms of the Debye theory. That linear contribution has been ascribed ... More

An upper limit to the orbital angular momentum of a vortex-carrying ultrashort pulseDec 28 2018The magnitude of the topological charge of the vortex of a ring-shaped pulse is found to be limited by the squared mean frequency of the pulse spectrum at the ring relative to its variance. This limitation implies a upper bound to the orbital angular ... More

Nonlinear lossy light bullets in self-focusing media with nonlinear absorptionDec 23 2017We review the properties of nonlinear, multidimensional localized waves whose stationary propagation is sustained by a dynamic equilibrium between self-focusing and nonlinear losses. Their finite-energy versions preserve light bullet behavior well-beyond ... More

Colloquium: Criticality and dynamical scaling in living systemsDec 12 2017May 15 2018A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e. in the ... More

Well-posedness and stability results for the Gardner equationOct 19 2011In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy ... More

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological InsulatorsMay 04 2011We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine ... More

Collider production of Electroweak resonances from photon-photon statesOct 20 2017Oct 22 2018We estimate production cross sections for 2-body resonances of the Electroweak Symmetry Breaking sector (in $W_LW_L$ and $Z_LZ_L$ rescattering) from $\gamma\gamma$ scattering. We employ unitarized Higgs Effective Field Theory amplitudes previously computed ... More

On the importance of the few most massive stars: the ionizing cluster of NGC 588Jul 28 2004We present the results of a double analysis of the ionizing cluster in NGC 588, a giant HII region (GHR) in the outskirts of the nearby galaxy M33. For this purpose, we obtained ground based long-slit spectroscopy and combined it with archival ground ... More

Reducing Spacetime to Binary InformationOct 18 2012We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the ... More

Quantum speedup for active learning agentsJan 20 2014Jul 14 2014Can quantum mechanics help us in building intelligent robots and agents? One of the defining characteristics of intelligent behavior is the capacity to learn from experience. However, a major bottleneck for agents to learn in any real-life situation is ... More

Overcoming efficiency constraints on blind quantum computationNov 18 2014Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, ... More

Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net CondensatesJul 27 2006Jul 29 2006We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles ... More

Topological Quantum Error Correction with Optimal Encoding RateFeb 06 2006May 22 2006We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We ... More

An Interferometry-Free Protocol for Demonstrating Topological OrderMay 01 2007Nov 06 2008We propose a protocol to demonstrate the topological order of a spin-1/2 lattice model with four-body interactions. Unlike other proposals, it does not rely on the controlled movement of quasiparticles, thus eliminating the addressing, decoherence and ... More

Topological Quantum DistillationMay 16 2006Mar 29 2007We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows ... More

A bilayer Double Semion Model with Symmetry-Enriched Topological OrderApr 29 2016Sep 14 2016We construct a new model of two-dimensional quantum spin systems that combines intrinsic topo- logical orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched ... More

numericalsgps, a GAP package for numerical semigroupsJun 06 2015The package numericalsgps performs computations with and for numerical semigroups. Recently also affine semigroups are admitted as objects for calculations. This manuscript is a survey of what the package does, and at the same time of the trending topics ... More

Optimal domain of $q$-concave operators and vector measure representation of $q$-concave Banach latticesNov 07 2015Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous ... More

Local Unitary Quantum Cellular AutomataAug 31 2007In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act ... More

Optimal extensions for $p$-th power factorable operatorsNov 07 2015Let $X(\mu)$ be a function space related to a measure space $(\Omega,\Sigma,\mu)$ with $\chi_\Omega\in X(\mu)$ and let $T\colon X(\mu)\to E$ be a Banach space valued operator. It is known that if $T$ is $p$-th power factorable then the largest function ... More

Single-Step Distillation Protocol with Generalized Beam SplittersMay 23 2003We develop a distillation protocol for multilevel qubits (qudits) using generalized beam splitters like in the proposal of Pan et al. for ordinary qubits. We find an acceleration with respect to the scheme of Bennet et al. when extended to qudits. It ... More

Strong extensions for $q$-summing operators acting in $p$-convex Banach function spaces for $1 \le p \le q$Jun 30 2015Let $1\le p\le q<\infty$ and let $X$ be a $p$-convex Banach function space over a $\sigma$-finite measure $\mu$. We combine the structure of the spaces $L^p(\mu)$ and $L^q(\xi)$ for constructing the new space $S_{X_p}^{\,q}(\xi)$, where $\xi$ is a probability ... More

Generating sequences and Poincaré series for a finite set of plane divisorial valuationsJun 17 2008Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, $\gr_V R$. We prove ... More

Perfect domination in rectangular grid graphsNov 27 2007A dominating set $S$ in a graph $G$ is said to be perfect if every vertex of $G$ not in $S$ is adjacent to just one vertex of $S$. Given a vertex subset $S'$ of a side $P_m$ of an $m\times n$ grid graph $G$, the perfect dominating sets $S$ in $G$ with ... More

Optical spectral pulse shaping by combining two oppositely chirped fiber Bragg gratingAug 23 2006Feb 28 2007In this letter we present a new technique for pulse shaping. The desired pulse is shaped by two apodized chirped fiber Bragg gratings which dispersions are adjusted to be cancelled. This technique exploits the well-known property of linearly-chirped gratings, ... More

Three-dimensional Accelerating Electromagnetic WavesMar 25 2013We present a general theory of three-dimensional nonparaxial spatially-accelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories. We provide classification ... More

Nonlinear unbalanced Bessel beams in the collapse of Gaussian beams arrested by nonlinear lossesMay 20 2008Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over ... More

Quantitative Spectroscopy of the Young Stellar Population in Star Forming GalaxiesOct 02 2018The determination of chemical composition is crucial for investigating the formation and evolution of star forming galaxies and provides a powerful tool to constrain the effects of galactic winds and accretion from the cosmic web. In this regard stellar ... More

Heat current through an artificial Kondo impurity beyond linear responseOct 03 2017We investigate the heat current of a strongly interacting quantum dot in the presence of a voltage bias in the Kondo regime. Using the slave- boson mean-field theory, we discuss the behavior of the energy flow and the Joule heating. We find that both ... More

Normal mode coupling and Bloch states in elliptically birefringent 1D photonic crystalsJul 12 2007Aug 06 2007An analysis is presented of frequency versus wave-vector dispersion in elliptically birefringent one-dimensional layered periodic structures. The presence of local normal mode polarization state variations from one layer to the next is found to lead to ... More

First stability eigenvalue characterization of CMC Hopf tori into Riemannian Killing submersionsOct 15 2013We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also ... More

The asymptotic expansion for the factorial and Lagrange inversion formulaFeb 20 2010We obtain an explicit simple formula for the coefficients of the asymptotic expansion for the factorial of a natural number,in terms of derivatives of powers of an elementary function. The unique explicit expression for the coefficients that appears to ... More

Quantum superintegrability and exact solvability in N dimensionsOct 16 2001A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian alone. The ... More

Optimality conditions in convex multiobjective SIPAug 10 2016The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. ... More

Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear ElectrodynamicsJul 09 2017Aug 28 2017We study decay of small solutions of the Born-Infeld equation in 1+1 dimensions, a quasilinear scalar field equation modeling nonlinear electromagnetism, as well as branes in String theory and minimal surfaces in Minkowski space-times. From the work of ... More

Slopes of trigonal fibred surfaces and of higher dimensional fibrationsNov 20 2008We give lower bounds for the slope of higher dimensional fibrations over curves under conditions of GIT-semistability of the fibres, using a generalization of a method of Cornalba and Harris. With the same method we establish a sharp lower bound for the ... More

Lie discrete symmetries of lattice equationsJul 07 2003We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries ... More

Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approachFeb 26 2007An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin ... More

Asymptotic behaviour of the Christoffel functions on the Unit Ball in the presence of a Mass on the SphereMay 25 2017We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal polynomials and the classical ... More

On the Slope of Fibred SurfacesJan 27 1999Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global properties of S influence ... More

A Note on a Conjecture of XiaoJan 27 1999Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of $f$ is ample when the slope of the fibration is less than 4, ... More

Nonlinear stability of higher order mKdV breathersApr 05 2018Oct 05 2018We are interested in stability results for breather solutions of the 5th, 7th and 9th order mKdV equations. We show that these higher order mKdV breathers are stable in $H^2(\R)$, in the same way as \emph{classical} mKdV breathers. We also show that breather ... More

A Time-Segmented Consortium Blockchain for Robotic Event RegistrationApr 08 2019A blockchain, during its lifetime, records large amounts of data, that in a common usage its kept on its entirety. In a robotics environment, the old information is useful for human evaluation, or oracles interfacing with the blockchain but it is not ... More

Lie Symmetries and Exact Solutions of First Order Difference SchemesFeb 25 2004May 28 2004We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries ... More

Local Normal Mode Coupling and Energy Band Splitting in Elliptically Birefringent 1D Magnetophotonic CrystalsOct 16 2007An analysis is presented of wave-vector dispersion in elliptically birefringent stratified magneto-optic media having one-dimensional periodicity. It is found that local normal-mode polarization-state differences between adjacent layers lead to mode coupling ... More

Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential EquationsNov 22 2015Feb 23 2016The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate ... More

Spin-Orbit Coupling in Diamond and Zincblende HeterostructuresJul 12 2004Spin splittings in III-V materials and heterostructures are of interest because of potential applications, mainly in spintronic devices. A necessary condition for the existence of these spin splittings is the absence of inversion symmetry. In bulk zincblende ... More

On the construction of partial difference schemes II: discrete variables and Schwarzian latticesJul 03 2014Apr 26 2016In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing an arbitrary partial differential equation on an arbitrary lattice. An open problem is the meaning ... More

Global solutions and stability properties of the 5th order Gardner equationJan 10 2019Jan 14 2019In this work, we deal with the initial value problem of the 5th-order Gardner equation in $\mathbb{R}$, presenting the local well-posedness result in $H^2(\mathbb{R})$. As a consequence of the local result, in addition to $H^2$-energy conservation law, ... More

Absence of Perfect Conductance Quantization of Helical-edge Transport in Graphene under a Strong, Tilted Magnetic FieldAug 02 2015Oct 27 2015In a recent experiment, Young et al. [Nature {\bf 505}, 528 (2014)] observed a metal to insulator transition as well as transport through helical edge states in monolayer graphene under a strong, tilted magnetic field. Under such conditions, the bulk ... More

Canonical formulation of Poincare BFCG theory and its quantizationSep 12 2014Mar 29 2015We find the canonical formulation of the Poincare BFCG theory in terms of the spatial 2-connection and its canonically conjugate momenta. We show that the Poincare BFCG action is dynamically equivalent to the BF action for the Poincare group and we find ... More

Stability conditions and positivity of invariants of fibrationsDec 19 2012Jul 25 2013We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection ... More

On the stability of an adaptive learning dynamics in traffic gamesJul 03 2018This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes ... More

Poincaré sphere representation for spatially varying birefringenceDec 09 2017Dec 14 2017The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional "Poincar\'e hypersphere". ... More

Dynamics of breathers in the Gardner hierarchy: universality of the variational characterizationJan 29 2019We present a new variational characterization of breather solutions of any equation of the \emph{focusing} Gardner hierarchy. This hierarchy is characterized by a nonnegative index $n$, and $2n+1$ represents the order of the corresponding PDE member. ... More