David Gómez-Ullate
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  • Academic Research
    • Applied Machine Learning
    • Financial Mathematics
    • Infotaxis
    • Integrable and Chaotic Dynamical Systems
    • Lie Groups in Mathematical Physics
    • Orthogonal Polynomials
    • Quantum Many-Body Problems
  • Industrial Projects
    • ATENEA for Aerospace Manufacturing
    • Climate Risk and the Future of Insurance
    • COVID-19 Impact of NPIs
    • Fraud Detection in Electronic Payments
    • Green Navigation
    • NeoCam
    • Non-Intrusive Load Monitoring
    • Predicting Drifting Buoys
    • Smart Advertising Decisions
    • Smart Retrieval and Structuring of Legal Documents
    • SNOMED-CT Coding for Pathology Reports
    • Tun-AI
  • Publications
    • New Analysis in the Preliminary Design for LNG and LPG Ships
    • HADAD: Hexagonal A-Star with Differential Algorithm Designed for Weather Routing
    • HADAD: Hexagonal A-Star with Differential Algorithm Designed for Weather Routing
    • Hybrid Search Method for Zermelo's Navigation Problem
    • Classification of Exceptional Jacobi Polynomials
    • Thresholding Methods in Non-Intrusive Load Monitoring
    • NeoCam: An Edge-Cloud Platform for Non-Invasive Real-Time Monitoring in Neonatal Intensive Care Units
    • Effectiveness of Non-Pharmaceutical Interventions in Nine Fields of Activity to Decrease SARS-CoV-2 Transmission (Spain, September 2020--May 2021)
    • Green Navigation: Optimización de Rutas Marítimas
    • Tun-AI: Using Echosounder Buoy Technology to Study Tuna Behaviour at Sea
    • Exceptional Gegenbauer Polynomials via Isospectral Deformation
    • TUN-AI: Tuna Biomass Estimation with Machine Learning Models Trained on Oceanography and Echosounder FAD Data
    • Toward Automated Feature Extraction for Deep Learning Classification of Electrocardiogram Signals
    • Complete Classification of Rational Solutions of A2-Painlevé Systems
    • Non-Intrusive Load Monitoring Using Multi-Output CNNs
    • Exceptional Legendre Polynomials and Confluent Darboux Transformations
    • Fall Detection from Electrocardiogram (ECG) Signals and Classification by Deep Transfer Learning
    • Ladder Operators and Rational Extensions
    • Spectral Theory of Exceptional Hermite Polynomials
    • Corrigendum on the Proof of Completeness for Exceptional Hermite Polynomials
    • Cyclic Maya Diagrams and Rational Solutions of Higher Order Painlevé Systems
    • Rational Solutions of Painlevé Systems.
    • Assessing the Effect of Advertising Expenditures upon Sales: A Bayesian Structural Time Series Model
    • A Bochner Type Characterization Theorem for Exceptional Orthogonal Polynomials
    • Big data: conceptos, tecnologías y aplicaciones
    • Opponent Aware Reinforcement Learning
    • Validating Ocean General Circulation Models via Lagrangian Particle Simulation and Data from Drifting Buoys
    • Durfee Rectangles and Pseudo-Wronskian Equivalences for Hermite Polynomials
    • Shape Invariance and Equivalence Relations for Pseudo-Wronskians of Laguerre and Jacobi Polynomials
    • Bayesian Factorization Machines for Risk Management and Robust Decision Making
    • On the Performance of Blind-Infotaxis under Inaccurate Modeling of the Environment
    • Recurrence Relations for Exceptional Hermite Polynomials
    • Oscillation Theorems for the Wronskian of an Arbitrary Sequence of Eigenfunctions of Schrödinger's Equation
    • Extended Krein-Adler Theorem for the Translationally Shape Invariant Potentials
    • Geometry-Induced Fluctuations of Olfactory Searches in Bounded Domains
    • Multifractality and Long Memory of a Financial Index
    • Rational Extensions of the Quantum Harmonic Oscillator and Exceptional Hermite Polynomials
    • A Conjecture on Exceptional Orthogonal Polynomials
    • Asymptotic and Interlacing Properties of Zeros of Exceptional Jacobi and Laguerre Polynomials
    • Scaling, Stability and Distribution of the High-Frequency Returns of the Ibex35 Index
    • Understanding Complex Dynamics by Means of an Associated Riemann Surface
    • Two-Step Darboux Transformations and Exceptional Laguerre Polynomials
    • On Orthogonal Polynomials Spanning a Non-Standard Flag
    • Exceptional Orthogonal Polynomials and the Darboux Transformation
    • Integrability and Nonlinear Phenomena
    • An Extension of Bochner's Problem: Exceptional Invariant Subspaces
    • An Extended Class of Orthogonal Polynomials Defined by a Sturm--Liouville Problem
    • Towards a Theory of Chaos Explained as Travel on Riemann Surfaces
    • Asymptotically Isochronous Systems:
    • Nonlinear Evolution Equations and Dynamical Systems 2007: 17th NEEDS Workshop, L'Ametlla de Mar, Spain
    • Quasi-Exact Solvability in a General Polynomial Setting
    • A New Class of Solvable Many-Body Problems with Constraints, Associated with an Exceptional Polynomial Subspace of Codimension 2
    • Two Novel Classes of Solvable Many-Body Problems of Goldfish Type with Constraints
    • Dynamical Systems on Infinitely Sheeted Riemann Surfaces
    • Quasi-Exact Solvability beyond the Sl(2) Algebraization
    • Structure Theorems for Linear and Non-Linear Differential Operators Admitting Invariant Polynomial Subspaces
    • Group Theory and Numerical Analysis
    • The Transition from Regular to Irregular Motions, Explained as Travel on Riemann Surfaces
    • Quasi-Exact Solvability and the Direct Approach to Invariant Subspaces
    • Periods of the Goldfish Many-Body Problem:
    • A Survey of Quasi-Exactly Solvable Systems and Spin Calogero-Sutherland Models
    • Supersymmetry and Algebraic Darboux Transformations
    • Reply to Comment on The Darboux Transformation and Algebraic Deformations of Shape-Invariant Potentials
    • New Many-Body Problems in the Plane with Periodic Solutions
    • The Darboux Transformation and Algebraic Deformations of Shape-Invariant Potentials
    • Dunkl Operators and Calogero-Sutherland Models
    • On the Sutherland Spin Model of B N Type and Its Associated Spin Chain
    • Quasi-Exact Solvability And Calogero-Sutherland Models
    • New Spin Calogero--Sutherland Models Related to BN-type Dunkl Operators
    • A N -Type Dunkl Operators and New Spin Calogero-Sutherland Models
    • Exact Solutions of a New Elliptic Calogero--Sutherland Model
    • Quasi-Exactly Solvable Generalizations of Calogero--Sutherland Models
    • Técnicas Algebraicas En Sistemas Cuánticos de Muchas Partículas
    • New Algebraic Quantum Many-Body Problems
    • Symmetry Classification of Systems of Differential-Difference Equations
    • Symmetries of Discrete Dynamical Systems Involving Two Species
  • Recent & Upcoming Outreach
    • ICMS Mini-Symposium 2024
    • Research Features Coverage on Tun-AI
    • Mathematical Optimization for Safer and Decarbonized Maritime Transport
    • Mathematical Optimization of Maritime Shipping Routes
    • CITIC-UDC Coverage on NPI Effectiveness Results
    • Simons Center Workshop 2023
    • Smart Shipping, Weather Routing and WASP Simulation
    • OpenCV Blog Episode 32 Interview on NeoCam
    • Diario de Cadiz Coverage of NeoCam International Award
    • IEEE PowerTech 2021 Presentation on NILM
    • Interview for RSME on the COVID-19 Response
    • Radio 3 Interview on Big Data and Coronavirus Privacy
    • Interview in eldiario.es on Data Transparency and COVID-19
    • Fundacion BBVA Feature on COVID-19 Prediction Models
    • Fundacion Descubre Note on ICU Occupancy Predictive Model
    • Las Matematicas frente a la COVID-19
    • BIDAS 4 Presentation on NILM
    • JURIX 2019 IberLegal Industry Session Talk
    • EL PAIS Coverage on Anti-Fraud Mathematics
    • ICMAT Coverage of BBVA-Funded Banking Fraud Detection Project
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Exceptional Orthogonal Polynomials and the Darboux Transformation

Oct 1, 2010·
David Gómez-Ullate
David Gómez-Ullate
,
N Kamran
,
R Milson
Cite DOI
Type
Journal article
Publication
Journal of Physics A: Mathematical and Theoretical
Last updated on Oct 1, 2010
David Gómez-Ullate
Authors
David Gómez-Ullate
Professor of Applied Mathematics — Head of Mathematics, School of Science & Technology, IE University
← On Orthogonal Polynomials Spanning a Non-Standard Flag Jan 1, 2012
Integrability and Nonlinear Phenomena Oct 1, 2010 →

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