yusuke1997/dblp-id-title huggingface dataset:
Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations
The Stability of Mixed hp -Finite Element Methods for Stokes Flow on High Aspect Ratio Elements
Tikhonov Regularization within Ensemble Kalman Inversion
Higher-Order Fourier Approximation in Scattering by Two-Dimensional, Inhomogeneous Media
A Linear Algebraic Analysis of Diffusion Synthetic Acceleration for the Boltzmann Transport Equation II: The Simple Corner Balance Method
Stable and Accurate Least Squares Radial Basis Function Approximations on Bounded Domains
A Meshfree Method for a PDE-Constrained Optimization Problem
On Taylor Model Based Integration of ODEs
Renormalized Meshfree Schemes I: Consistency, Stability, and Hybrid Methods for Conservation Laws
Space-Time FEM-BEM Couplings for Parabolic Transmission Problems
Jacobi Correction Equation, Line Search, and Conjugate Gradients in Hermitian Eigenvalue Computation I: Computing an Extreme Eigenvalue
The Variable-Order Discontinuous Galerkin Time Stepping Scheme for Parabolic Evolution Problems is Uniformly L ∞ -Stable
A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion-Reaction Problems
Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients
Properly Posed Sets of Nodes for Multivariate Lagrange Interpolation in C s
Error Bounds for Approximate Eigenvalues of Periodic-Coefficient Linear Delay Differential Equations
Alternating Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a Positive-Type Memory Term
Unconditional Stability for Multistep ImEx Schemes: Theory
Matrix-free Interpolation on the Sphere
Spherical Designs for Approximations on Spherical Caps
A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
Error Analysis of a Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data
A Least-Squares Finite Element Method for the Magnetostatic Problem in A Multiply Connected Lipschitz Domain
An Euler-Bernoulli Beam with Dynamic Contact: Discretization, Convergence, and Numerical Results
Rank-Adaptive Time Integration of Tree Tensor Networks
Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge-Ampère Equation in Dimensions Two and Higher
Calculus on Surfaces with General Closest Point Functions
Dynamic Ritz Projection of Mean Curvature Flow and Optimal \(\boldsymbol{L^2}\) Convergence of Parametric FEM
On the Construction and Analysis of High Order Locally Conservative Finite Volume-Type Methods for One-Dimensional Elliptic Problems
Robust DPG Test Spaces and Fortin Operators - The \(\boldsymbol{H^1}\) and \({\boldsymbol{H}}\boldsymbol{(\mathrm{div})}\) Cases
Overlapping Schwarz Methods for Isogeometric Analysis
Design of Absorbing Boundary Conditions for Schrödinger Equations in R d
Kernel Interpolation of High Dimensional Scattered Data
Specialized Partitioned Additive Runge-Kutta Methods for Systems of Overdetermined DAEs with Holonomic Constraints
Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages
Numerical Schemes for Signature Kernels
Optimal Error Estimates of Linearized Crank-Nicolson Galerkin FEMs for the Time-Dependent Ginzburg-Landau Equations in Superconductivity
The Residual-Free-Bubble Finite Element Method on Anisotropic Partitions
Function, Gradient, and Hessian Recovery Using Quadratic Edge-Bump Functions
Superconvergence of Discontinuous Galerkin Methods for Two-Dimensional Hyperbolic Equations
A Priori and A Posteriori W 1, INFINITY Error Analysis of a QC Method for Complex Lattices
Convergence of Linearized and Adjoint Approximations for Discontinuous Solutions of Conservation Laws. Part 2: Adjoint Approximations and Extensions
Numerical Analysis of a Hyperbolic Hemivariational Inequality Arising in Dynamic Contact
Weak Consistency of a Staggered Finite Volume Scheme for Lagrangian Hydrodynamics
A Modified Tikhonov Regularization for Stable Analytic Continuation
Local Energy Estimates for the Fractional Laplacian
Invariant Cubature Formulae for Spheres and Balls by Combinatorial Methods
hp-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems
A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems
Handling Convexity-Like Constraints in Variational Problems
Numerical Solution of Projected Algebraic Riccati Equations
Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions
Computing A Alpha, log(A), and Related Matrix Functions by Contour Integrals
A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence
High-Order Compact Schemes for Parabolic Problems with Mixed Derivatives in Multiple Space Dimensions
The L 2 -Projection and Quasi-Optimality of Galerkin Methods for Parabolic Equations
An analogue to the A(θ)-stability concept for implicit-explicit BDF methods
Stability Analysis of Discontinuous Galerkin Discrete Shock Profiles for Steady Scalar Conservation Laws
A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation
Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations
Approximating Stochastic Evolution Equations with Additive White and Rough Noises
Root Following in Evans Function Computation
Uniform Stability of a Finite Difference Scheme for Transport Equations in Diffusive Regimes
A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems
Constructive Approximation of High-Dimensional Functions with Small Efficient Dimension with Applications in Uncertainty Quantification
Localized Implicit Time Stepping for the Wave Equation
Analysis of Radial Complex Scaling Methods: Scalar Resonance Problems
Optimal Convergence for the Implicit Space-Time Discretization of Parabolic Systems with p-Structure
New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation
Generalized Spectrum of Second Order Differential Operators
Modified Combined Field Integral Equations for Electromagnetic Scattering
Adaptive First-Order System Least-Squares Finite Element Methods for Second-Order Elliptic Equations in Nondivergence Form
A Posteriori Error Control for Fourth-Order Semilinear Problems with Quadratic Nonlinearity
A Mass Conserving Mixed $hp$-FEM Scheme for Stokes Flow. Part III: Implementation and Preconditioning
Stabilized Finite Elements for a Reaction-Dispersion Saddle-Point Problem with NonConstant Coefficients
On Preconditioned Iterative Methods for Certain Time-Dependent Partial Differential Equations
First-Order System \CL\CL * (FOSLL*): Scalar Elliptic Partial Differential Equations
Centered-Potential Regularization for the Advection Upstream Splitting Method
Condition Number Estimates for the Nonoverlapping Optimized Schwarz Method and the 2-Lagrange Multiplier Method for General Domains and Cross Points
Finite Element Method for Stokes Equations under Leak Boundary Condition of Friction Type
A Posteriori Error Estimates for Convex Boundary Control Problems
hp-Finite Elements for Fractional Diffusion
On the Error Analysis of Stabilized Finite Element Methods for the Stokes Problem
Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups
Quadrilateral H(div) Finite Elements
Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems
Numerical Analysis of a Nonlinear Evolutionary System with Applications in Viscoplasticity
Approximation Theory for the p-Version of the Finite Element Method in Three Dimensions. Part 1: Approximabilities of Singular Functions in the Framework of the Jacobi-Weighted Besov and Sobolev Spaces
Modified Energy for Split-Step Methods Applied to the Linear Schrödinger Equation
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
Convergence of Numerical Approximations of the Incompressible Navier-Stokes Equations with Variable Density and Viscosity
A Two-Dimensional Version of the Godunov Scheme for Scalar Balance Laws
A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations
Error Expansion for an Upwind Scheme Applied to a Two-Dimensional Convection-Diffusion Problem
A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case
Discrete Reliability for Crouzeix-Raviart FEMs
On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
The Gradient Discretization Method for Slow and Fast Diffusion Porous Media Equations
Nonlinear Stability Analysis for the Method of Transport for the Elastic-Plastic Wave Equation
Approximate Calculation of Sums I: Bounds for the Zeros of Gram Polynomials
An Adaptive Surface Finite Element Method Based on Volume Meshes
Rigorous Numerics for Nonlinear Differential Equations Using Chebyshev Series
High-Order Schemes, Entropy Inequalities, and Nonclassical Shocks
Eigenfunction Expansion Method for Multiple Solutions of Semilinear Elliptic Equations with Polynomial Nonlinearity
Subgrid Stabilized Defect Correction Methods for the Navier-Stokes Equations
Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem
Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Harmonic Scattering Problems in Two-Layered Media
Globally Structured Three-Dimensional Analysis-Suitable T-Splines: Definition, Linear Independence and m-graded local refinement
Convergence of the Supercell Method for Defect Modes Calculations in Photonic Crystals
Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection
A High Order Finite Difference Method for the Elastic Wave Equation in Bounded Domains with Nonconforming Interfaces
Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations
Simple and Efficient ALE Methods with Provable Temporal Accuracy up to Fifth Order for the Stokes Equations on Time Varying Domains
Truncation Errors in Exponential Fitting for Oscillatory Problems
Analysis of the Brezzi-Pitkäranta Stabilized Galerkin Scheme for Creeping Flows of Bingham Fluids
A Convergent Numerical Scheme for Scattering of Aperiodic Waves from Periodic Surfaces Based on the Floquet-Bloch Transform
Analysis and Approximation of the Velocity Tracking Problem for Navier-Stokes Flows with Distributed Control
Superconvergence of Finite Element Approximations for the Stokes Problem by Projection Methods
On the Approximation of the Fokker-Planck Equation of the Finitely Extensible Nonlinear Elastic Dumbbell Model I: A New Weighted Formulation and an Optimal Spectral-Galerkin Algorithm in Two Dimensions
Analysis of a Fluid-Structure Interaction Problem Recast in an Optimal Control Setting
A Robust A Posteriori Error Estimator for Divergence-Conforming Discontinuous Galerkin Methods for the Oseen Equation
Approximate Euler Method for Parabolic Stochastic Partial Differential Equations Driven by Space-Time Lévy Noise
Harmonic Functions on Finitely Connected Tori
A Local Discontinuous Galerkin Approximation for the \(\boldsymbol{{p}}\) -Navier-Stokes System, Part II: Convergence Rates for the Velocity
Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity
Finite Element Approximations to the Discrete Spectrum of the Schrödinger Operator with the Coulomb Potential
High Order Splitting Methods for SDEs Satisfying a Commutativity Condition
Symmetric Coupling for Eddy Current Problems
Analysis of a Hybridized/Interface Stabilized Finite Element Method for the Stokes Equations
On the Edge Recovery Property of Noncovex Nonsmooth Regularization in Image Restoration
Linear Rational Finite Differences from Derivatives of Barycentric Rational Interpolants
Locally Conservative Fluxes for the Continuous Galerkin Method
Low Discrepancy Constructions in the Triangle
A Mixed Spectral-Difference Method for the Steady State Boltzmann-Poisson System
Entropic Discretization of a Quantum Drift-Diffusion Model
Kernel-Based Discretization for Solving Matrix-Valued PDEs
Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations
Regularization Based on All-At-Once Formulations for Inverse Problems
A Convergent Structure-Preserving Finite-Volume Scheme for the Shigesada-Kawasaki-Teramoto Population System
A Local Discontinuous Galerkin Approximation for the p -Navier-Stokes System, Part I: Convergence Analysis
A Nonconforming Generalized Finite Element Method for Transmission Problems
Approximation of Bayesian Inverse Problems for PDEs
The Derivation of Hybridizable Discontinuous Galerkin Methods for Stokes Flow
Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
An Optimal Adaptive Finite Element Method
Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid
Partitioned Time Stepping Method for Fully Evolutionary Stokes-Darcy Flow with Beavers-Joseph Interface Conditions
Inf-Sup Stable Finite Elements on Barycentric Refinements Producing Divergence-Free Approximations in Arbitrary Dimensions
Stair Matrices and Their Generalizations with Applications to Iterative Methods I: A Generalization of the Successive Overrelaxation Method
A Preconditioner for the FETI-DP Formulation with Mortar Methods in Two Dimensions
Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems
An Optimal Shape Design Problem for Plates
Second-Order Convergence of Monotone Schemes for Conservation Laws
An Extension of the Euler-Maclaurin Summation Formula to Functions with Near Singularity
A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons
Local A Posteriori Estimates on a Nonconvex Polygonal Domain
Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
A Pressure-Robust Discretization of Oseen's Equation Using Stabilization in the Vorticity Equation
A Spacetime DPG Method for the Schrödinger Equation
A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
Arnoldi Algorithms with Structured Orthogonalization
A Posteriori Error Estimates for Schrödinger Operators Discretized with Linear Combinations of Atomic Orbitals
Sobolev Gradient Flow for the Gross-Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
A Priori and A Posteriori Analysis of Mixed Finite Element Methods for Nonlinear Elliptic Equations
Branching Random Walk Solutions to the Wigner Equation
Accuracy of Spectral Element Method for Wave, Parabolic, and Schrödinger Equations
A Prolongation/Restriction Operator for Whitney Elements on Simplicial Meshes
Convergence Analysis of Markov Chain Monte Carlo Linear Solvers Using Ulam-von Neumann Algorithm
Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
Robust Preconditioning Estimates for Convection-Dominated Elliptic Problems via a Streamline Poincaré-Friedrichs Inequality
Spectral Approximation on the Unit Ball
A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity
A Convergent Finite Difference Scheme for the Camassa-Holm Equation with General H 1 Initial Data
Computation of Sum of Squares Polynomials from Data Points
A Posteriori Error Analysis of Two-Stage Computation Methods with Application to Efficient Discretization and the Parareal Algorithm
Stability of the Nyström Method for the Sherman-Lauricella Equation
Sharp Bounds on the Smallest Eigenvalue of Finite Element Equations with Arbitrary Meshes without Regularity Assumptions
Estimating Multidimensional Density Functions Using the Malliavin-Thalmaier Formula
Analysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth Data
Partitioned Time Stepping for a Parabolic Two Domain Problem
Multistep methods for SDEs and their application to problems with small noise
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
Polynomial Extension Operators. Part II
The l 1 -Error Estimates for a Hamiltonian-Preserving Scheme for the Liouville Equation with Piecewise Constant Potentials
High Order Conformal Symplectic and Ergodic Schemes for the Stochastic Langevin Equation via Generating Functions
A Sequential Least Squares Method for Poisson Equation Using a Patch Reconstructed Space
First-Order System Least-Squares for Darcy-Stokes Flow
An Efficient and Convergent Finite Element Scheme for Cahn-Hilliard Equations with Dynamic Boundary Conditions
An Optimal Control-Based Numerical Method for Scalar Transmission Problems with Sign-Changing Coefficients
On the Regularity of Approximate Solutions to Conservation Laws with Piecewise Smooth Solutions
Energy-Corrected Finite Element Methods for Corner Singularities
Asymptotic High-Order Schemes for 2˟2 Dissipative Hyperbolic Systems
Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method
Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity
Optimized Additive Schwarz with Harmonic Extension as a Discretization of the Continuous Parallel Schwarz Method
Conditioning Analysis of Nonlocal Integral Operators in Fractional Sobolev Spaces
Semi-iterative Regularization in Hilbert Scales
Error Analysis of a First-Order IMEX Scheme for the Logarithmic Schrödinger Equation
Numerical Schemes for the Optimal Input Flow of a Supply Chain
A Posteriori Error Estimation for Control-Constrained, Linear-Quadratic Optimal Control Problems
Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions
Numerical Methods for the Generalized Hopf Bifurcation
Time-Average on the Numerical Integration of Nonautonomous Differential Equations
A Stabilized Nonconforming Finite Element Method for the Surface Biharmonic Problem
Sharp CFL, Discrete Kinetic Formulation, and Entropic Schemes for Scalar Conservation Laws
A Posteriori Error Estimation for the Discrete Duality Finite Volume Discretization of the Laplace Equation
Semi-discretization for Stochastic Scalar Conservation Laws with Multiple Rough Fluxes
Total Variation Minimization with Finite Elements: Convergence and Iterative Solution
\(p\) -Robust Equilibrated Flux Reconstruction in \(\boldsymbol{H}(\textrm{curl})\) Based on Local Minimizations: Application to a Posteriori Analysis of the Curl-Curl Problem
Numerical Analysis for Convergence of a Sample-Wise Backpropagation Method for Training Stochastic Neural Networks
A Method of Projection of Delta Waves in a Godunov Scheme and Application to Pressureless Fluid Dynamics
Maximum Norm A Posteriori Error Estimates for a One-Dimensional Convection-Diffusion Problem
Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems
A Unifying Framework for Interpolatory \({\boldsymbol{\mathcal{L}_2}}\)-Optimal Reduced-Order Modeling
Variational Extrapolation of Implicit Schemes for General Gradient Flows
Robust Eigenvalue Computation for Smoothing Operators
Iterative Substructuring Methods for Spectral Element Discretizations of Elliptic Systems. II: Mixed Methods for Linear Elasticity and Stokes Flow
Inexact Newton Dogleg Methods
Error Analysis of Supremizer Pressure Recovery for POD based Reduced-Order Models of the Time-Dependent Navier-Stokes Equations
L2-Projected Least-Squares Finite Element Methods for the Stokes Equations
Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods
Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
A Stable Numerical Scheme for Stochastic Differential Equations with Multiplicative Noise
Inverse Wave-Number-Dependent Source Problems for the Helmholtz Equation
A Hellan-Herrmann-Johnson-like Method for the Stream Function Formulation of the Stokes Equations in Two and Three Space Dimensions
Energy- and Quadratic Invariants-Preserving Integrators Based upon Gauss Collocation Formulae
Strong Stability Preserving Explicit Linear Multistep Methods with Variable Step Size
Analysis of a Space-Time Hybridizable Discontinuous Galerkin Method for the Advection-Diffusion Problem on Time-Dependent Domains
Moment Preserving Fourier-Galerkin Spectral Methods and Application to the Boltzmann Equation
Large Time Behavior of Nonlinear Finite Volume Schemes for Convection-Diffusion Equations
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Long Time Stability of High Order MultiStep Numerical Schemes for Two-Dimensional Incompressible Navier-Stokes Equations
A Priori Error Analysis of Local Incremental Minimization Schemes for Rate-Independent Evolutions
A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries
On Nonconservative Algorithms for Grid Interfaces
Stability and Convergence Analysis of Time-Domain Perfectly Matched Layers for the Wave Equation in Waveguides
Solving Parabolic Moving Interface Problems with Dynamical Immersed Spaces on Unfitted Meshes: Fully Discrete Analysis
On the Full and Global Accuracy of a Compact Third Order WENO Scheme
On Gauss-Lobatto Integration on the Triangle
Stable Discretizations of Elastic Flow in Riemannian Manifolds
A Polynomial Formulation of Adaptive Strong Stability Preserving Multistep Methods
The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem
Function Approximation on Arbitrary Domains Using Fourier Extension Frames
Renormalized Meshfree Schemes II: Convergence for Scalar Conservation Laws
A Two-Level Preconditioned Helmholtz Subspace Iterative Method for Maxwell Eigenvalue Problems
A Posteriori Error Estimates for Higher Order Space-Time Galerkin Discretizations of Nonlinear Parabolic Problems
Convergence of a Higher Order Scheme for the Korteweg-De Vries Equation
Fast Multipole Method for Multivariable Integrals
Numerical Approximation of the Lifshitz-Slyozov-Wagner Equation
On the Convergence of Mortar Edge Element Methods in R 3
Future Polynomial Regularization of Ill-Posed Volterra Equations
High Order Discontinuous Galerkin Methods for Elliptic Problems on Surfaces
The Finite Mass Method
A Piecewise Constant Algorithm for Weighted L 1 Approximation over Bounded or Unbounded Regions in R s
High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs
Probability and Pathwise Order of Convergence of a Semidiscrete Scheme for the Stochastic Manakov Equation
An Exponential Spectral Method Using VP Means for Semilinear Subdiffusion Equations with Rough Data
Stability Theory for Difference Approximations of Euler-Korteweg Equations and Application to Thin Film Flows
A Discontinuous Petrov-Galerkin Method for Time-Fractional Diffusion Equations
Variance Reduction Methods for Simulation of Densities on Wiener Space
Explicit Runge-Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems
Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations
On the Approximation of the Vlasov-Poisson System by Particle Methods
Error Estimation of the Relaxation Finite Difference Scheme for the Nonlinear Schrödinger Equation
A Posteriori Error Estimations of Some Cell Centered Finite Volume Methods for Diffusion-Convection-Reaction Problems
The L 2 -norm Stability Analysis of Runge-Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations
A Strongly Convergent Numerical Scheme from Ensemble Kalman Inversion
Global Superconvergence of the Lowest-Order Mixed Finite Element on Mildly Structured Meshes
Postprocessing Fourier Galerkin Method for the Navier-Stokes Equations
Analysis of Highly Accurate Finite Element Based Algorithms for Computing Distances to Level Sets