papers

Publications (95)

math.AP2025

Turbulent solutions of the binormal flow and the 1D cubic Schrödinger equation

Valeria Banica, Luis Vega

In the last three decades there has been an intense activity on the exploration of turbulent phenomena of dispersive equations, as for instance the growth of Sobolev norms since th…

math.AP2023

Reconnection of infinitely thin antiparallel vortices and coherent structures

Sergei Iakunin, Luis Vega

One of the characteristic features of turbulent flows is the emergence of many vortices which interact, deform, and intersect, generating a chaotic movement. The evolution of a pai…

cs.CG2016

Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces

Cameron Chalk, Erik D. Demaine, Martin L. Demaine +4

We show how to design a universal shape replicator in a self-assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of con…

math.AP2008

On the equipartition of energy for critical NLW

Luis Vega, Nicola Visciglia

We study some qualitative properties of global solutions to the following focusing and defocusing critical : \begin{equation*} \Box u+ λu|u|^{2^*-2}=0, \hbox{} λ\in {\mathbf…

math.AP2008

On the stability of a singular vortex dynamics

Valeria Banica, Luis Vega

In this paper we address the question of the singular vortex dynamics exhibited in [15], which generates a corner in finite time. The purpose is to prove that under some appropriat…

cs.LG2026

Nemotron 3 Nano Omni: Efficient and Open Multimodal Intelligence

NVIDIA, :, Amala Sanjay Deshmukh +204

We introduce Nemotron 3 Nano Omni, the latest model in the Nemotron multimodal series and the first to natively support audio inputs alongside text, images, and video. Nemotron 3 N…

math.HO2025

How to Fight Fraudulent Publishing in the Mathematical Sciences: Joint Recommendations of the IMU and the ICIAM

Ilka Agricola, Lynn Heller, Wil Schilders +3

These recommendations were formulated by the authors in close collaboration with the IMU Committee on Publishing (chaired by Ilka Agricola) and have been endorsed by the Executive…

math.AP2008

Scaling-sharp dispersive estimates for the Korteweg-de Vries group

Raphaël Côte, Luis Vega

We prove weighted estimates on the linear KdV group, which are scaling sharp. This kind of estimates are in the spirit of that used to prove small data scattering for the generaliz…

cs.CL2025

Nemotron-H: A Family of Accurate and Efficient Hybrid Mamba-Transformer Models

NVIDIA, :, Aaron Blakeman +198

As inference-time scaling becomes critical for enhanced reasoning capabilities, it is increasingly becoming important to build models that are efficient to infer. We introduce Nemo…

math.AP2012

Self-adjoint extensions of Dirac operators with Coulomb type singularity

Naiara Arrizabalaga, Javier Duoandikoetxea, Luis Vega

In this work we construct self-adjoint extensions of the Dirac operator associated to Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The resul…

math.AP2026

Evolution of viscous vortex filaments and soliton-type propagation

Marco A. Fontelos, Mikel Ispizua, Luis Vega

We study the evolution of a viscous incompressible fluid whose initial vorticity is supported on a smooth open curve. We show that, for and sufficiently small Reynolds n…

math.AP2023

Blow-up for the 1D cubic NLS

Valeria Banica, Renato LucÃ, Nikolay Tzvetkov +1

We consider the 1D cubic NLS on and prove a blow-up result for functions that are of borderline regularity, i.e. for any for the Sobolev scale and $…

math.AP2013

Shell interactions for Dirac operators

Naiara Arrizabalaga, Albert Mas, Luis Vega

The self-adjointness of is studied, where is the free Dirac operator in and is a measure-valued potential. The potentials under consid…

cs.CL2025

NVIDIA Nemotron 3: Efficient and Open Intelligence

NVIDIA, :, Aaron Blakeman +356

We introduce the Nemotron 3 family of models - Nano, Super, and Ultra. These models deliver strong agentic, reasoning, and conversational capabilities. The Nemotron 3 family uses a…

math.AP2020

On the unique continuation of solutions to non-local non-linear dispersive equations

Carlos E. Kenig, Didier Pilod, Gustavo Ponce +1

We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if are two suitable solutio…

cs.CL2026

Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning

NVIDIA, :, Aaron Blakeman +571

We introduce Nemotron 3 Ultra, a 550 billion total and 55 billion active parameter Mixture-of-Experts Hybrid Mamba-Attention language model. We pre-trained Nemotron 3 Ultra on 20 t…

astro-ph.GA2018

Asymmetric emission of the [OIII]5007 profile in narrow-line Seyfert 1 galaxies

Eduardo O. Schmidt, Gabriel A. Oio, Diego Ferreiro +2

Many active galactic nuclei (AGN) and particularly narrow-line Seyfert 1 (NLS1) galaxies, usually exhibit blueshifts and blue wings in several emission lines, which are mainly asso…

math.AP2017

Singularity formation for the 1-D cubic NLS and the Schrödinger map on

Valeria Banica, Luis Vega

In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac- function and some other related equations. We first recall that…

cs.CG2016

Optimal Staged Self-Assembly of General Shapes

Cameron Chalk, Eric Martinez, Robert Schweller +3

We analyze the number of tile types , bins , and stages necessary to assemble squares and scaled shapes in the staged tile assembly model. For squar…

math.AP2009

Stability in of circular vortex patches

Thomas C. Sideris, Luis Vega

The motion of incompressible and ideal fluids is studied in the plane. The stability in of circular vortex patches is established among the class of all bounded vortex patche…

cs.LG2025

NVIDIA Nemotron Nano V2 VL

NVIDIA, :, Amala Sanjay Deshmukh +121

We introduce Nemotron Nano V2 VL, the latest model of the Nemotron vision-language series designed for strong real-world document understanding, long video comprehension, and reaso…

math.AP2025

Asymptotic fractional uncertainty principle for the Helmholtz equation with periodic scattering data

Javier Canto, Nico Michele Schiavone, Luis Vega

We investigate the fractional dispersion of solutions to the Helmholtz equation with periodic scattering data. We show that, under appropriate rescaling, the interaction between th…

math.AP2008

Magnetic virial identities, weak dispersion and Strichartz inequalities

Luca Fanelli, Luis Vega

We show a family of virial-type identities for the Schrödinger and wave equations with electromagnetic potentials. As a consequence, some weak dispersive inequalities in space dim…

math.AP2026

Bifurcation and global continuation of travelling-rotating Schrödinger maps on the sphere

Juan Carlos Sampedro, Luis Vega

We study travelling-rotating solutions of the Schrödinger map equation into the sphere, viewed as tangent profiles of rigid vortex filaments. Two first integrals reduce the profil…

math.AP2024

Multifractality and polygonal vortex filaments

Valeria Banica, Daniel Eceizabarrena, Andrea. R. Nahmod +1

In this proceedings article we survey the results in [5] and their motivation, as presented at the 50th Journées EDP 2024. With the aim of quantifying turbulent behaviors of vorte…

math.AP2021

Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow

Valeria Banica, Luis Vega

We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicit…

math.HO2025

Fraudulent Publishing in the Mathematical Sciences

Ilka Agricola, Lynn Heller, Wil Schilders +3

This report is the first of two publications of a joint Working Group of the International Mathematical Union (IMU) and the International Council of Industrial and Applied Mathemat…

math.AP2010

On the existence of maximizers for a family of Restriction Theorems

Luca Fanelli, Luis Vega, Nicola Visciglia

We prove the existence of maximizers for a general family of restrictions operators, up to the end-point. We also provide some counterxamples in the end-point case.

math.AP2022

Static and Dynamical, Fractional Uncertainty Principles

Sandeep Kumar, Felipe Ponce-Vanegas, Luis Vega

We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty princip…

math.AP2006

Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials

Michael Goldberg, Luis Vega, Nicola Visciglia

In each dimension n >= 2, we construct a class of nonnegative potentials that are homogeneous of order -sigma, chosen from the range 0 < sigma < 2, and for which the perturbed Schr…

math.AP2011

Selfsimilar solutions of the binormal flow and their stability

Valeria Banica, Luis Vega

We review some recent results concerning the evolution of a vortex filament and its relation to the cubic non-linear Schrödinger equation. Selfsimilar solutions and questions rela…

math.NA2017

On the Relationship between the One-Corner Problem and the -Corner Problem for the Vortex Filament Equation

Francisco de la Hoz, Luis Vega

In this paper, we give evidence that the evolution of the Vortex Filament Equation for a regular -corner polygon as initial datum can be explained at infinitesimal times as the…

cs.CL2025

NVIDIA Nemotron Nano 2: An Accurate and Efficient Hybrid Mamba-Transformer Reasoning Model

NVIDIA, :, Aarti Basant +214

We introduce Nemotron-Nano-9B-v2, a hybrid Mamba-Transformer language model designed to increase throughput for reasoning workloads while achieving state-of-the-art accuracy compar…

math.AP2011

Uniqueness Properties of Solutions to Schrödinger Equations

Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce +1

In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schrödinger equations. In this equations we include linear ones w…

math.AP2015

Vortex Filament Equation for a Regular Polygon

Francisco de la Hoz, Luis Vega

In this paper, we study the evolution of the vortex filament equation (VFE), with being a regular planar poly…

cs.LG2026

Nemotron 3 Super: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning

NVIDIA, :, Aakshita Chandiramani +544

We describe the pre-training, post-training, and quantization of Nemotron 3 Super, a 120 billion (active 12 billion) parameter hybrid Mamba-Attention Mixture-of-Experts model. Nemo…

math.CA2025

A theorem concerning Fourier transforms: A survey

Aingeru Fernández-Bertolin, Luis Vega

In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic ana…

astro-ph.GA2016

Spectral nuclear properties of NLS1 galaxies

Eduardo O. Schmidt, Diego Ferreiro, Luis Vega +1

It is not yet well known whether narrow line Seyfert 1 (NLS1) galaxies follow the relation found for normal galaxies. Emission lines, such as [SII] or [OIII]$…

math.AP2006

On the Local Smoothing for the Schroedinger Equation

Luis Vega, Nicola Visciglia

We prove a family of identities that involve the solutions to the free Schreodinger equation. As a consequence of these identities we shall deduce a lower bound for the local smoot…

math.AP2012

Scattering for solutions of NLS in the exterior of a 2d star--shaped obstacle

Fabrice Planchon, Luis Vega

We prove that solutions to non-linear Schrödinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non…

math.AP2018

Uniqueness Properties for Discrete equations and Carleman estimates

Aingeru Fernández-Bertolin, Luis Vega

Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness resul…

math.AP2020

On the energy of critical solutions of the binormal flow

Valeria Banica, Luis Vega

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model i…

math.AP2014

Shell interactions for Dirac operators: on the point spectrum and the confinement

Naiara Arrizabalaga, Albert Mas, Luis Vega

Spectral properties and the confinement phenomenon for the coupling are studied, where is the free Dirac operator in and is a mea…

math.AP2007

On the Dirac delta as initial condition for nonlinear Schrödinger equations

Valeria Banica, Luis Vega

In this article we will study the initial value problem for some Schrödinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results…

math.AP2011

Carleman estimates and necessary conditions for the existence of waveguides

Luis Escauriaza, Luca Fanelli, Luis Vega

We study via Carleman estimates the sharpest possible exponential decay for {\it waveguide} solutions to the Laplace equation $$(\partial^2_t+\triangle)u=Vu+W\cdot(\partial_t,\nabl…

math.AP2019

Self-similar dynamics for the modified Korteweg-de Vries equation

Simão Correia, Raphaël Côte, Luis Vega

We prove a local well posedness result for the modified Korteweg-de Vries equation in a critical space designed so that is contains self-similar solutions. As a consequence, we can…

math.AP2016

On the regularity of solutions to the -generalized Korteweg-de Vries equation

Carlos E. Kenig, Felipe Linares, Gustavo Ponce +1

This work is concerned with special regularity properties of solutions to the -generalized Korteweg-de Vries equation. In \cite{IsazaLinaresPonce} it was established that if the…

math.AP2014

The initial value problem for the binormal flow with rough data

Valeria Banica, Luis Vega

In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove…

math.AP2022

Carleman type inequalities for fractional relativistic operators

Luz Roncal, Diana Stan, Luis Vega

In this paper we derive Carleman estimates for the fractional relativistic operator. We consider changing-sign solutions to the heat equation for such operators. We prove monotonic…

math.AP2004

Self-binormal solutions of the Localized Induction Approximation: Singularity formation

Susana Gutierrez, Luis Vega

We investigate the formation of singularities in a self-similar form of regular solutions of the Localized Induction Approximation (also referred as to the binormal flow). This equ…

math.AP2012

The forward problem for the electromagnetic Helmholtz equation with critical singularities

Juan Antonio Barceló, Luis Vega, Miren Zubeldia

We study the forward problem of the magnetic Schrödinger operator with potentials that have a strong singularity at the origin. We obtain new resolvent estimates and give some app…

math.AP2023

New Conservation Laws and Energy Cascade for 1d Cubic NLS and the Schrödinger map

Valeria Banica, Luis Vega

We review some recent results concerning the Initial Value Problem of 1d-cubic non-linear Schrödinger equation (NLS) and other related systems as the Schrödinger Map. For the lat…

math.AP2023

Steady solutions for the Schrödinger map equation

Claudia García, Luis Vega

In this paper we use bifurcation methods to construct a new family of solutions of the binormal flow, also known as the vortex filament equation, which do not change their form. Ou…

math.AP2023

Evolution of viscous vortex filaments and desingularization of the Biot-Savart integral

Marco A. Fontelos, Luis Vega

We consider a viscous fluid with kinematic viscosity and initial data consisting of a smooth closed vortex filament with circulation . We show that, for short enough time,…

math-ph2016

A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions

Thomas Ourmières-Bonafos, Luis Vega

We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a -compact surface without boundary. To do so we are…

math.NT2015

The vortex filament equation as a pseudorandom generator

Francisco de la Hoz, Luis Vega

In this paper, we consider the evolution of the so-called vortex filament equation (VFE), \begin{equation*} \mathbf X_t = \mathbf X_s\wedge\mathbf X_{ss}, \end{equation*} taking a…

math.AP2000

On the support of solutions to the g-KdV equation

Carlos E. Kenig, Gustavo Ponce, Luis Vega

We discuss the question whether solutions of the initial value problem for the generalized KdV equation can have compact support at two different times.

math.AP2019

Some lower bounds for solutions of Schrodinger evolutions

Mikel Agirre, Luis Vega

We present some lower bounds for regular solutions of Schrödinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass a…

math.AP2006

Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity

Benoit Perthame, Luis Vega

We consider the Helmholtz equation with a variable index of refraction , which is not necessarily constant at infinity but can have an angular dependency like $n(x)\to n\_\in…

math.NA2008

A numerical study of the self-similar solutions of the Schroedinger Map

Francisco de la Hoz, Carlos Garcia-Cervera, Luis Vega

We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-param…

math.AP2012

A Theorem of Paley-Wiener Type for Schrödinger Evolutions

Carlos E. Kenig, Gustavo Ponce, Luis Vega

We prove unique continuation principles for solutions of evolution Schrödinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener…

math.AP2020

Riemann's non-differentiable function and the binormal curvature flow

Valeria Banica, Luis Vega

We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature fl…

math.AP2007

Schrödinger Maps and their associated Frame Systems

Andrea Nahmod, Jalal Shatah, Luis Vega +1

In this paper we establish the equivalence of solutions between Schrödinger map into or and their associated gauge invariant Schrödinger equations.…

math.SP2018

On the improvement of the Hardy inequality due to singular magnetic fields

Luca Fanelli, David Krejcirik, Ari Laptev +1

We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimen…

math.CA2019

Bilinear identities involving the -plane transform and Fourier extension operators

David Beltran, Luis Vega

We prove certain bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the -plane transform. As the e…

math.AP2007

Asymptotic Lower Bounds for a class of Schroedinger Equations

Luis Vega, Nicola Visciglia

We shall study the following initial value problem: \begin{equation}{\bf i}\partial_t u - Δu + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)…

math.AP2020

Evolution of polygonal lines by the binormal flow

Valeria Banica, Luis Vega

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr{ö}dinger equation on R in link with initial data a sum of Dirac masses. Secondly we show…

cs.LG2019

Relay: A High-Level Compiler for Deep Learning

Jared Roesch, Steven Lyubomirsky, Marisa Kirisame +7

Frameworks for writing, compiling, and optimizing deep learning (DL) models have recently enabled progress in areas like computer vision and natural language processing. Extending…

math.AP2006

On uniqueness properties of solutions of the k-generalized KdV equations

Luis Escauriaza, Carlos E. Kenig, Gustavo Ponce +1

In this paper we study uniqueness properties of solutions of the k-generalized Korteweg-de Vries equation. Our goal is to obtain sufficient conditions on the behavior of the differ…

math.CA1998

A bilinear approach to the restriction and Kakeya conjectures

Terence Tao, Ana Vargas, Luis Vega

Bilinear restriction estimates have been appeared in work of Bourgain, Klainerman, and Machedon. In this paper we develop the theory of these estimates (together with the analogues…

math.SP2017

Absence of eigenvalues of two-dimensional magnetic Schroedinger operators

Luca Fanelli, David Krejcirik, Luis Vega

By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr…

math.AP2025

On low regularity well-posedness of the binormal flow

Valeria Banica, Renato LucÃ, Nikolay Tzvetkov +1

We focus on a class of solutions of the binormal flow, model of the evolution of vortex filaments, that generate several corner singularities in finite time. This phenomenon has be…

math.AP2011

On the stability of self-similar solutions of 1D cubic Schrodinger equations

Susana Gutierrez, Luis Vega

In this paper we will study the stability properties of self-similar solutions of 1-d cubic NLS equations with time-dependent coefficients of the form iu_t+u_{xx}+\frac{u}{2} (|u|^…

math.NA2021

Vortex Filament Equation for a regular polygon in the hyperbolic plane

Francisco de la Hoz, Sandeep Kumar, Luis Vega

The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean…

math-ph2013

Relativistic Hardy inequalities in magnetic fields

Luca Fanelli, Luis Vega, Nicola Visciglia

We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal mag…

math.AP2008

Bilinear virial identities and applications

Fabrice Planchon, Luis Vega

We prove bilinear virial identities for the nonlinear Schrodinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear impr…

cs.LG2019

A Hardware-Software Blueprint for Flexible Deep Learning Specialization

Thierry Moreau, Tianqi Chen, Luis Vega +8

Specialized Deep Learning (DL) acceleration stacks, designed for a specific set of frameworks, model architectures, operators, and data types, offer the allure of high performance…

math.AP2009

Endpoint Strichartz estimates for the magnetic Schrodinger equation

Piero D'Ancona, Luca Fanelli, Luis Vega +1

We prove Strichartz estimates for the Schroedinger equation with an electromagnetic potential, in dimension . The decay and regularity assumptions on the potentials are alm…

math.AP2022

Eigenvalue curves for generalized MIT bag models

Naiara Arrizabalaga, Albert Mas, Tomás Sanz-Perela +1

We study spectral properties of Dirac operators on bounded domains with boundary conditions of electrostatic and Lorentz scalar type and which depend on a…

math.AP2018

Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

Simão Correia, Raphaël Côte, Luis Vega

We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted W^{1,\infty} aroun…

math.SP2016

Spectral stability of Schroedinger operators with subordinated complex potentials

Luca Fanelli, David Krejcirik, Luis Vega

We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subo…

math.NA2011

Discrete conservation laws and the convergence of long time simulations of the mKdV equation

Carlos Gorria, Miguel A. Alejo, Luis Vega

Pseudospectral collocation methods and finite difference methods have been used for approximating an important family of soliton like solutions of the mKdV equation. These solution…

math.AP2009

Scattering for 1D cubic NLS and singular vortex dynamics

Valeria Banica, Luis Vega

In this paper we study the stability of the self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These par…

math.AP2011

Existence of maximizers for Sobolev-Strichartz inequalities

Luca Fanelli, Luis Vega, Nicola Visciglia

We prove the existence of maximizers of Sobolev-Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperb…

math.NA2019

On the Evolution of the Vortex Filament Equation for regular -polygons with nonzero torsion

Francisco de la Hoz, Sandeep Kumar, Luis Vega

In this paper, we consider the evolution of the Vortex Filament equation (VFE): \begin{equation*} \mathbf X_t = \mathbf Xs \wedge \mathbf Xss, \end{equation*} taking -sided regu…

cs.CL2025

Nemotron 3 Nano: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning

NVIDIA, :, Aaron Blakeman +311

We present Nemotron 3 Nano 30B-A3B, a Mixture-of-Experts hybrid Mamba-Transformer language model. Nemotron 3 Nano was pretrained on 25 trillion text tokens, including more than 3 t…

math.AP2025

Multifractality and intermittency in the limit evolution of polygonal vortex filaments

Valeria Banica, Daniel Eceizabarrena, Andrea R. Nahmod +1

With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functi…

math.AP2007

Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces

Axel Gruenrock, Luis Vega

We study the Cauchy problem for the modified KdV equation for data u_0 in the space ^H^r_s defined by the norm ||u_0||_{^H^r_s}:=||<ξ>^s u^_0||_{L^r'_ξ}. Local well-posedness of…

math-ph2015

An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators

Naiara Arrizabalaga, Albert Mas, Luis Vega

In this article we investigate spectral properties of the coupling , where is the free Dirac operator in , and is an elec…

math.AP2013

Stability of the selfsimilar dynamics of a vortex filament

Valeria Banica, Luis Vega

In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (L…

math.AP2011

The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation

Miguel A. Alejo, Claudio Muñoz, Luis Vega

Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingl…

math.AP2021

On the one dimensional cubic NLS in a critical space

Marco Bravin, Luis Vega

In this note we study the initial value problem in a critical space for the one dimensional Schrödinger equation with a cubic non-linearity and under some smallness conditions. In…

cs.CR2016

Power Side Channels in Security ICs: Hardware Countermeasures

Lu Zhang, Luis Vega, Michael Taylor

Power side-channel attacks are a very effective cryptanalysis technique that can infer secret keys of security ICs by monitoring the power consumption. Since the emergence of pract…

math.AP2019

Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models

Carlos E. Kenig, Gustavo Ponce, Luis Vega

We prove that if are solutions of the Benjamin-Ono equation defined in which agree in an open set , then $u_1\equi…

math.AP2018

A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator

Biagio Cassano, Fabio Pizzichillo, Luis Vega

We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued…