Publications (95)
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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 $…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.
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…
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…
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…
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…
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…
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…
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…
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…
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…
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]$…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
Steady solutions for the Schrödinger map equation
Claudia GarcÃa, 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…
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,…
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…
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…
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.
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…
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…
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…
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…
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…
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.…
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…
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…
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 - Îu + V(x) u=0, \hbox{} (t, x) \in {\mathbf R} \times {\mathbf R}^n, \end{equation} $$u(0)…
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…
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…
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…
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…
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…
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…
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|^…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…