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Accelerated observers and the notion of singular spacetimeOct 24 2017Jan 18 2018Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers ... More

Einstein-Cartan-Dirac gravity with $U(1)$ symmetry breakingFeb 06 2019Einstein-Cartan theory is an extension of the standard formulation of General Relativity where torsion (the antisymmetric part of the affine connection) is non-vanishing. Just as the space-time metric is sourced by the stress-energy tensor of the matter ... More

Cosmological future singularities in interacting dark energy modelsJul 21 2016Dec 05 2016The existence of interactions between dark matter and dark energy has been widely studied, since they can fit well the observational data and may provide new physics through such an interaction. In this work we analyze these models and investigate their ... More

Geometric inequivalence of metric and Palatini formulations of General RelativityJul 09 2019Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual ... More

New scalar compact objects in Ricci-based gravity theoriesJun 11 2019Taking advantage of a previously developed method, which allows to map solutions of General Relativity into a broad family of theories of gravity based on the Ricci tensor (Ricci-based gravities), we find new exact analytical scalar field solutions by ... More

Mapping nonlinear gravity into General Relativity with nonlinear electrodynamicsJul 17 2018Oct 26 2018We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into General Relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows ... More

Born-Infeld inspired modifications of gravityApr 11 2017May 17 2017General Relativity has shown an outstanding observational success in the scales where it has been directly tested. However, modifications have been intensively explored in the regimes where it seems either incomplete or signals its own limit of validity. ... More

Charged black holes in Palatini $f(R)$ theoriesJan 10 2013In $f(R)$ extensions of General Relativity the Palatini approach provides ghost-free theories with second-order field equations and allows to obtain charged black hole solutions which depart from the standard Reissner-Nordstr\"om solution.

Deforming solitons in generalized Abelian Higgs modelsNov 09 2011Apr 09 2012This work deals with several aspects of the extension to Abelian Higgs models of the deformation method originally developed for scalar field models. We present several examples allowing to transform self-dual solutions of different generalized Abelian ... More

BPS solitons in a Dirac-Born-Infeld actionJan 31 2014We present several classes of solitons in ($1+1$)-dimensional models where the standard canonical kinetic term is replaced by a Dirac-Born-Infeld (DBI) one. These are static solutions with finite energy and different properties, namely, they can have ... More

Generalized sine-Gordon solitonsJun 20 2011Jul 26 2011In this paper we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection ... More

Unveiling the Dynamics of the UniverseJul 11 2016Jul 27 2016We explore the dynamics and evolution of the Universe at early and late times, focusing on both dark energy and extended gravity models and their astrophysical and cosmological consequences. Modified theories of gravity not only provide an alternative ... More

Nonsingular charged black holes à la PalatiniJul 18 2012We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of General Relativity ... More

Non-topological solitons in field theories with kinetic self-couplingMay 01 2007Aug 07 2007We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space dimensions which ... More

Generalized gauge field theories with non-topological soliton solutionsAug 04 2007We perform a systematic analysis of the conditions under which \textit{generalized} gauge field theories of compact semisimple Lie groups exhibit electrostatic spherically symmetric non-topological soliton solutions in three space dimensions. By the term ... More

Geons as wormholes of modified gravityJan 02 2016Wormholes may arise as solutions of extensions of General Relativity without violation of the energy conditions. Working in a Palatini approach we consider classical geometries supporting such wormholes. It is shown that the resulting space-times represent ... More

Soliton solutions in relativistic field theories and gravitationDec 11 2007Mar 26 2011We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components scalar fields and ... More

Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actionsSep 20 2016May 13 2019A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of Riemannian metrics ... More

Wormholes as a cure for black hole singularitiesJan 02 2016Using exactly solvable models, it is shown that black hole singularities in different electrically charged configurations can be cured. Our solutions describe black hole space-times with a wormhole giving structure to the otherwise point-like singularity. ... More

Minimum main sequence mass in quadratic Palatini $f(\mathcal{R})$ gravityJun 11 2019General Relativity yields an analytical prediction of a minimum required mass of roughly $\sim 0.08-0.09 M_{\odot}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those ... More

What is a singular black hole beyond General Relativity?Feb 04 2017Exploring the characterization of singular black hole spacetimes, we study the relation between energy density, curvature invariants, and geodesic completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic fluid. Working in a metric-affine ... More

Minimum main sequence mass in quadratic Palatini $f(\mathcal{R})$ gravityJun 11 2019Aug 01 2019General Relativity yields an analytical prediction of a minimum required mass of roughly $\sim 0.08-0.09 M_{\odot}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those ... More

Exact Baker-Campbell-Hausdorff formula for the contact Heisenberg algebraSep 06 2016Sep 15 2016In this work we introduce the contact Heisenberg algebra which is the restriction of the Jacobi algebra on contact manifolds to the linear and constant functions. We give the exact expression of its corresponding Baker-Campbell-Hausdorff formula. We argue ... More

Q-singularitiesJul 21 2016The existence of interactions among dark matter and dark energy have been widely studied in the literature, since such models fit well the observational data and may provide new physics through such an interaction. Here we analyze this kind of models, ... More

Gauss-Bonnet black holes supported by a nonlinear electromagnetic fieldMar 14 2015We study $D$-dimensional charged static spherically symmetric black hole solutions in Gauss-Bonnet theory coupled to nonlinear electrodynamics defined as arbitrary functions of the field invariant and constrained by several physical conditions. These ... More

Lyapunov decay in quantum irreversibilityDec 14 2015The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. ... More

Photon-mediated qubit interactions in 1D discrete and continous modelsFeb 19 2015In this work we study numerically and analytically the interaction of two qubits in a one-dimensional waveguide, as mediated by the photons that propagate through the guide. We develop strategies to assert the Markovianity of the problem, the effective ... More

On gravitational waves in Born-Infeld inspired non-singular cosmologiesJul 27 2017Jul 03 2018We study the evolution of gravitational waves for non-singular cosmological solutions within the framework of Born-Infeld inspired gravity theories, with special emphasis on the Eddington-inspired Born-Infeld theory. We review the existence of two types ... More

Novel couplings between nonmetricity and matterJan 03 2019We present a novel theory of gravity, namely, an extension of symmetric teleparallel gravity. This is done by introducing a new class of theories where the nonmetricity $Q$ is coupled nonminimally to the matter Lagrangian. This nonminimal coupling entails ... More

On the binary origin of FS CMa stars: young massive clusters as test bedsOct 17 2016Oct 21 2016FS CMa stars are low-luminosity objects showing the B[e] phenomenon whose evolutionary origin is yet to be unraveled. Various binary-related hypotheses have been recently proposed, two of them involving the spiral-in evolution of the binary orbit. The ... More

Compact Groups analysis using weak gravitational lensingFeb 01 2017We present a weak lensing analysis of a sample of SDSS Compact Groups (CGs). Using the measured radial density contrast profile, we derive the average masses under the assumption of spherical symmetry, obtaining a velocity dispersion for the Singular ... More

Structure and dynamics in low density regions: galaxy-galaxy correlations inside cosmic voidsDec 13 2018We compute the galaxy-galaxy correlation function of low-luminosity SDSS-DR7 galaxies $(-20 < M_{\rm r} - 5\log_{10}(h) < -18)$ inside cosmic voids identified in a volume limited sample of galaxies at $z=0.085$. To identify voids, we use bright galaxies ... More

Early-time cosmic dynamics in $f(R)$ and $f(|\hatΩ|)$ extensions of Born-Infeld gravityNov 23 2014We consider two types of modifications of Born-Infeld gravity in the Palatini formulation and explore their dynamics in the early universe. One of these families considers $f(R)$ corrections to the Born-Infeld Lagrangian, which can be seen as modifications ... More

Palatini wormholes and energy conditions from the prism of General RelativityJul 05 2016Nov 09 2017Wormholes are hypothetical shortcuts in spacetime that in General Relativity unavoidably violate all of the pointwise energy conditions. In this paper, we consider several wormhole spacetimes that, as opposed to the standard \emph{designer} procedure ... More

A correspondence between modified gravity and General Relativity with scalar fieldsOct 09 2018Jan 22 2019We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a different scalar ... More

Coupling matter in modified $Q$-gravityJun 27 2018We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is nonminimally coupled ... More

Distance weighted city growthSep 17 2012Feb 07 2013Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e.\ a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of city-like structures which ... More

Metallicity and colours in galaxy pairs in chemical hydrodynamical simulationsNov 18 2005Using chemical hydrodynamical simulations consistent with a Lambda-CDM model, we study the role played by mergers and interactions in the regulation of the star formation activity, colours and the chemical properties of galaxies in pairs. A statistical ... More

Measuring and using non-markovianityMay 13 2015We construct measures for the non-Markovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative measures, based ... More

Uncertainties in Atmospheric Muon-Neutrino Fluxes Arising from Cosmic-Ray PrimariesDec 09 2016We present an updated calculation of the uncertainties on the atmospheric muon-neutrino flux arising from cosmic-ray primaries. For the first time, we include recent measurements of the cosmic-ray primaries collected since 2005. We apply a statistical ... More

Seesaw Majoron Model of Neutrino Mass and Novel Signals in Higgs Boson Production at LEPMar 16 1998We perform a careful study of the neutral scalar sector of a model which includes a singlet, a doublet, and a triplet scalar field under $SU(2)$. This model is motivated by neutrino physics, since it is simply the most general version of the seesaw model ... More

Palatini $f(R)$ Black Holes in Nonlinear ElectrodynamicsOct 04 2011The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their ... More

Nonsingular Black Holes in $f(R)$ TheoriesSep 08 2015We study the structure of a family of static, spherically symmetric space-times generated by an anisotropic fluid and governed by a particular type of $f(R)$ theory. We find that for a range of parameters with physical interest, such solutions represent ... More

Brane-world and loop cosmology from a gravity-matter coupling perspectiveMay 28 2014We show that the effective brane-world and the loop quantum cosmology background expansion histories can be reproduced from a modified gravity perspective in terms of an $f(R)$ gravity action plus a $g(R)$ term non-minimally coupled with the matter Lagrangian. ... More

Semiclassical geons at particle acceleratorsJun 27 2013Jan 31 2014We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic ... More

Nonsingular black holes in quadratic Palatini gravityDec 02 2011Jul 25 2012We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{core}\approx N_q^{1/2}l_P/3$, where ... More

The quantum, the geon, and the crystalJul 28 2015Effective geometries arising from a hypothetical discrete structure of space-time can play an important role in the understanding of the gravitational physics beyond General Relativity. To discuss this question, we make use of lessons from crystalline ... More

Non-Riemannian geometry: towards new avenues for the physics of modified gravityJun 06 2015Less explored than their metric (Riemannian) counterparts, metric-affine (or Palatini) theories bring an unexpected phenomenology for gravitational physics beyond General Relativity. Lessons of crystalline structures, where the presence of defects in ... More

The sparkling Universe: Clustering of voids and void clumpsMar 30 2017We analyse the clustering of cosmic voids using a numerical simulation and the main galaxy sample from the Sloan Digital Sky Survey. We take into account the classification of voids into two types that resemble different evolutionary modes: those with ... More

Void DynamicsOct 29 2014Cosmic voids are becoming key players in testing the physics of our Universe. Here we concentrate on the abundances and the dynamics of voids as these are among the best candidates to provide information on cosmological parameters. Cai, Padilla \& Li ... More

Reissner-Nordström black holes in extended Palatini theoriesJul 25 2012We study static, spherically symmetric solutions with an electric field in an extension of general relativity (GR) containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area ... More

Nonsingular Black Holes in Palatini Extensions of General RelativityJan 11 2013We discuss static, spherically symmetric solutions with an electric field in a quadratic extension of general relativity formulated in the Palatini approach (assuming that metric and connection are independent fields). Unlike the usual metric formulation ... More

Importance of torsion and invariant volumes in Palatini theories of gravityJun 18 2013Oct 26 2013We study the field equations of extensions of General Relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set ... More

Black hole solutions in functional extensions of Born-Infeld gravityAug 17 2016Sep 08 2016We consider electrovacuum black hole spacetimes in classical extensions of Eddington-inspired Born-Infeld gravity. By rewriting Born-Infeld action as the square root of the determinant of a matrix $\hat{\Omega}$, we consider the family of models $f (|\hat{\Omega}|)$, ... More

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamicsApr 11 2012Sep 28 2013We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of ... More

The sparkling Universe: a scenario for cosmic void motionsNov 20 2015Jun 22 2016We perform a statistical study of the global motion of cosmic voids using both a numerical simulation and observational data. We analyse their relation to large-scale mass flows and the physical effects that drive those motions. We analyse the bulk motions ... More

Tracking Dengue Epidemics using Twitter Content Classification and Topic ModellingMay 03 2016Detecting and preventing outbreaks of mosquito-borne diseases such as Dengue and Zika in Brasil and other tropical regions has long been a priority for governments in affected areas. Streaming social media content, such as Twitter, is increasingly being ... More

Triplets of Quasars at high redshift I: Photometric dataJan 26 2008We have conducted an optical and infrared imaging in the neighbourhoods of 4 triplets of quasars. R, z', J and Ks images were obtained with MOSAIC II and ISPI at Cerro Tololo Interamerican Observatory. Accurate relative photometry and astrometry were ... More

Voids and Superstructures: correlations and induced large-scale velocity flowsMay 18 2017The expanding complex pattern of filaments, walls and voids build the evolving cosmic web with material flowing from underdense onto high density regions. Here we explore the dynamical behaviour of voids and galaxies in void shells relative to neighboring ... More

Classical resolution of black hole singularities via wormholesApr 27 2015Mar 05 2016In certain extensions of General Relativity, wormholes generated by spherically symmetric electric fields can resolve black hole singularities without necessarily removing curvature divergences. This is shown by studying geodesic completeness, the behavior ... More

Quadratic Palatini gravity and stable black hole remnantsNov 25 2013We present a four-dimensional Planck-scale corrected quadratic extension of General Relativity (GR) where no a priori relation between metric and connection is imposed (Palatini formalism). Static spherically symmetric electrovacuum solutions are obtained ... More

Black holes in extended gravity theories in Palatini formalismJan 14 2013We consider several physical scenarios where black holes within classical gravity theories including $R^2$ and Ricci-squared corrections and formulated \`a la Palatini can be analytically studied.

Melvin Universe in Born-Infeld gravityApr 08 2015We consider a magnetic flux pointing in the $z$ direction of an axially symmetric space-time (Melvin Universe) in a Born-Infeld-type extension of General Relativity (GR) formulated in the Palatini approach. Large magnetic fields could have been produced ... More

Geonic black holes and remnants in Eddington-inspired Born-Infeld gravityNov 04 2013Apr 28 2014We show that electrically charged solutions within the Eddington-inspired Born-Infeld theory of gravity replace the central singularity by a wormhole supported by the electric field. As a result, the total energy associated with the electric field is ... More

Crystal clear lessons on the microstructure of space-time and modified gravityDec 15 2014Jun 12 2015We argue that a microscopic structure for space-time such as that expected in a quantum foam scenario, in which microscopic wormholes and other topological structures should play a relevant role, might lead to an effective metric-affine geometry at larger ... More

Born-Infeld gravity and its functional extensionsJun 04 2014Aug 04 2014We investigate the dynamics of a family of functional extensions of the (Eddington-inspired) Born-Infeld gravity theory, constructed with the inverse of the metric and the Ricci tensor. We provide a generic formal solution for the connection and an Einstein-like ... More

Compact vortex in a generalized Born-Infeld modelMar 25 2011Nov 17 2011We study vortexlike solutions in a generalized Born-Infeld model. The model is driven by two distinct parameters, one which deals with the Born-Infeld term, and the other, which controls the presence of high-order power term in the covariant derivative ... More

Black hole formation from a null fluid in extended Palatini gravitySep 15 2012We study the formation and perturbation of black holes by null fluxes of neutral matter in a quadratic extension of General Relativity formulated a la Palatini. Working in a spherically symmetric space-time, we obtain an exact analytical solution for ... More

Microscopic wormholes and the geometry of entanglementFeb 20 2014Jun 02 2014It has recently been suggested that Einstein-Rosen (ER) bridges can be interpreted as maximally entangled states of two black holes that form a complex Einstein-Podolsky-Rosen (EPR) pair. This relationship has been dubbed as the ER = EPR correlation. ... More

Impact of curvature divergences on physical observers in a wormhole space-time with horizonsFeb 04 2016The impact of curvature divergences on physical observers in a black hole space-time which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of General Relativity coupled to Maxwell's electrodynamics ... More

Geometric aspects of charged black holes in Palatini theoriesJun 06 2015Charged black holes in gravity theories in the Palatini formalism present a number of unique properties. Their innermost structure is topologically nontrivial, representing a wormhole supported by a sourceless electric flux. For certain values of their ... More

Nonsingular BTZ-type solutions of $2+1$ Born-Infeld gravitySep 19 2016We study Born-Infeld gravity coupled to a static, nonrotating electric field in $2+1$ dimensions and find exact analytical solutions. Two families of such solutions represent geodesically complete, and hence nonsingular, spacetimes. Another family represents ... More

Mapping Ricci-based theories of gravity into general relativityJan 31 2018We show that the space of solutions of a wide family of Ricci-based metric-affine theories of gravity can be put into correspondence with the space of solutions of general relativity (GR). This allows us to use well-established methods and results from ... More

Semiclassical geons as solitonic black hole remnantsJun 11 2013We find that the end state of black hole evaporation could be represented by non-singular and without event horizon stable solitonic remnants with masses of the order the Planck scale and up to 16 units of charge. Though these objects are locally indistinguishable ... More

Geodesic completeness in a wormhole spacetime with horizonsAug 13 2015The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of General Relativity formulated within the Palatini approach and coupled ... More

Black holes in five-dimensional Palatini $f(R)$ gravity and implications for the AdS/CFT correspondenceMay 01 2014We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric ... More

A Dark Hydrogen Cloud in the Virgo ClusterFeb 16 2005VIRGOHI21 is an HI source detected in the Virgo Cluster survey of Davies et al. (2004) which has a neutral hydrogen mass of 10^8 M_solar and a velocity width of Delta V_20 = 220 km/s. From the Tully-Fisher relation, a galaxy with this velocity width would ... More

21-cm synthesis observations of VIRGOHI 21 - a possible dark galaxy in the Virgo ClusterJun 11 2007Many observations indicate that dark matter dominates the extra-galactic Universe, yet no totally dark structure of galactic proportions has ever been convincingly identified. Previously we have suggested that VIRGOHI 21, a 21-cm source we found in the ... More

A Low-Frequency Tone Sweep Method for in-Service Fault Location in Sub-Carrier Multiplexed Optical Fiber NetworksSep 06 2016We demonstrate an optical fiber fault location method based on the frequency response of the modulated fiber optical backscattered signal in a steady state low-frequency step regime. Careful calibration and measurement allows for the reconstruction of ... More

Nonlinear Schrödinger equation on graphs: recent results and open problemsApr 03 2013Apr 08 2013In the present paper an introduction to the new subject of nonlinear dispersive hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of nonlinear Schr\"odinger equation. Special consideration ... More

Average-Case Perturbations and Smooth Condition NumbersDec 11 2008Dec 17 2008We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with the classical condition number, and study some interesting examples.

Asymptotic analysis of the Askey-scheme I: from Krawtchouk to CharlierJan 05 2005We analyze the Charlier polynomials C(n,x)and their zeros asymptotically for large n. We obtain asymptotic approximations, using the limit relation between the Krawtchouk and Charlier polynomials, involving some special functions. We give numerical examples ... More

Asymptotic analysis of the derivatives of the inverse error functionJul 09 2006Jun 05 2007The inverse of the error function, $\operatorname{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as $n\to \infty$ ... More

Some observations on a Kapteyn seriesOct 03 2005We study the Kapteyn series $% %TCIMACRO{\dsum \limits_{n=1}^{\infty}}% %BeginExpansion {\displaystyle\sum\limits_{n=1}^{\infty}} %EndExpansion t^{n}\mathrm{J}_{n}(nz) $. We find a series representation in powers of $z$ and analyze its radius of convergence. ... More

Lagrangian pairs of pantsFeb 08 2018We construct a Lagrangian submanifold, inside the cotangent bundle of a real torus, which we call a Lagrangian pair of pants. It is given as the graph of the differential of a smooth function defined on the real blow up of a Lagrangian coamoeba. Lagrangian ... More

Lagrangian submanifolds from tropical hypersurfacesApr 04 2018We prove that a smooth tropical hypersurface in $\mathbb{R}^3$ can be lifted to a smooth embedded Lagrangian submanifold in $(\mathbb{C}^*)^3$. This completes the proof of the result announced in the article "Lagrangian pairs pants" arXiv:1802.02993. ... More

A molecular method applied to a non-local PDE in stratified Lie groupsJul 03 2013In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.

Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groupsJul 23 2010We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev ... More

Non-local diffusion equations with Lévy-type operators and divergence free driftMay 13 2012Dec 13 2012We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a method that ... More

On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$Aug 11 2006Let $G_1 \times G_2$ be a subgroup of $\mathrm{SO}_3(\mathbb{R})$ such that the two factors $G_1$ and $G_2$ are non-trivial groups. We show that if $G_1 \times G_2$ is not abelian, then one factor is the (abelian) group of order 2, and the other factor ... More

An incoherent simple groupJul 18 2005We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

AFT Gravitational Model - Unity of All Elementary Particles in Sp(12,C)Feb 09 2010Oct 09 2012A new unifying theory was recently proposed by the author in the publication "Arrangement field theory - beyond strings and loop gravity -". Such theory describes all fields (gravitational, gauge and matter fields) as entries in a matricial superfield ... More

Embedding into manifolds with torsionDec 22 2008Mar 26 2009We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be ... More

Variétés abéliennes sur les corps de fonctions de courbes sur des corps locaux supérieursSep 25 2015Let $k$ be a higher-dimensional local field and $X$ be a smooth projective geometrically integral curve over $k$. Let $K$ be the function field of $X$. We define Tate-Shafarevich groups of an abelian variety via cohomology classes locally trivial at each ... More

Asymptotic analysis of the Bell polynomials by the ray methodSep 03 2007We analyze the Bell polynomials $B_{n}(x)$ asymptotically as $n\to\infty$. We obtain asymptotic approximations from the differential-difference equation which they satisfy, using a discrete version of the ray method. We give some examples showing the ... More

On the Parameters of r-dimensional Toric CodesDec 13 2005From a rational convex polytope of dimension $r\ge 2$ J.P. Hansen constructed an error correcting code of length $n=(q-1)^r$ over the finite field $\fq$. A rational convex polytope is the same datum as a normal toric variety and a Cartier divisor. The ... More

Invariant forms, associated bundles and Calabi-Yau metricsApr 26 2007Oct 25 2007We develop a method, initially due to Salamon, to compute the space of ``invariant'' forms on an associated bundle X=P\times_G V, with a suitable notion of invariance. We determine sufficient conditions for this space to be d-closed. We apply our method ... More

Error estimates for the Gregory-Leibniz series and the alternating harmonic series using Dalzell integralsAug 30 2018The computation of Dalzell integrals $\int_0^1 \frac{x^m (1-x)^n}{1+x^2} \, dx > 0$ gives new error estimates for the partial sums of the Gregory-Leibniz series $1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} \pm \ldots$ and for the alternating harmonic ... More

Regularity of the derivatives of $p$-orthotropic functions in the plane for $1<p<2$Feb 12 2018We present a proof of the $C^1$ regularity of $p$-orthotropic functions in the plane for $1<p<2$, based on the monotonicity of the derivatives. Moreover we achieve an explicit logarithmic modulus of continuity.

A convex relaxation to compute the nearest structured rank deficient matrixApr 21 2019Given an affine space of matrices $L$ and a matrix $\theta \in L$, consider the problem of finding the closest rank deficient matrix to $\theta$ on $L$ with respect to the Frobenius norm. This is a nonconvex problem with several applications in estimation ... More