clopen.solutions

Open problems

980 registered problems.

OP-00767 Solution claimed
Characterizing realizable geodesic scattering data
DG · AIM Open Applied Problems · geometric inverse problems · scattering relation · simple surfaces
OP-00768 Solution claimed
Automorphism-invariant one-dependent colorings of regular trees
PR · AIM Open Applied Problems · finitely dependent processes · proper colorings · regular trees
OP-00769 Solution claimed
The sharp local maneuvering time for a shallow-water tank
OC · AIM Open Applied Problems · local controllability · Saint-Venant equations · water tank
OP-00770 Solution claimed
Sharp characterization of exactly trackable boundary heat fluxes
AP · AIM Open Applied Problems · boundary control · heat equation · tracking controllability
OP-00771 Solution claimed
Sharp local approximation widths for rough elliptic equations
NA · AIM Open Applied Problems · elliptic equations with rough coefficients · Kolmogorov n-widths · multiscale finite element methods
OP-00772 Solution claimed
Boundary observation of a Schrödinger field with slower surface dispersion
OC · AIM Open Applied Problems · dynamic boundary conditions · observability · Schrödinger equation
OP-00773 Solution claimed
Does integration of uniformly derivative-bounded analytic functions suffer the dimensional curse?
NA · AIM Open Applied Problems · curse of dimensionality · information-based complexity · numerical integration
OP-00774 Solution claimed
Sharp asymptotic constant for rational approximation of fractional inverse powers
NA · AIM Open Applied Problems · fractional powers · rational approximation · Stieltjes functions
OP-00775 Solution claimed
Draws in the undirected trapping game on percolation clusters
PR · AIM Open Applied Problems · combinatorial games · site percolation
OP-00776 Solution claimed
Uniqueness of nonnegative heat controls at the minimum time
AP · AIM Open Applied Problems · constrained control · heat equation · minimal control time
OP-00777 Solution claimed
Deciding nonnegativity of unnormalized univariate trace polynomials
AG · AIM Open Applied Problems · decidability · power sums · trace polynomials
OP-00778 Solution claimed
Strong convergence rate of the fractional WIS Euler integrator
NA · AIM Open Applied Problems · fractional Brownian motion · strong convergence · Wick–Itô–Skorohod integral
OP-00779 Solution claimed
Maximal motion-planning complexity of aspherical connected sums
AT · AIM Open Applied Problems · aspherical manifolds · connected sums · topological complexity
OP-00780 Solution claimed
The centre-rank formula for aspherical motion planning
AT · AIM Open Applied Problems · aspherical manifolds · centre of the fundamental group · topological complexity
OP-00781 Solution claimed
Small mod-two area cycles in drawings with bounded pairwise intersections
CO · AIM Open Applied Problems · Heilbronn problems · mod-two cycles · topological graphs
OP-00782 Solution claimed
Positive equilibrium attraction for an irreversible catalytic reaction
AP · AIM Open Applied Problems · chemical reaction networks · convergence to equilibrium · reaction-diffusion systems
OP-00783 Solution claimed
Calderón–Zygmund estimates for general concave nonlocal equations
AP · AIM Open Applied Problems · Bellman equations · fully nonlinear integro-differential equations · Sobolev estimates
OP-00784 Solution claimed
Polynomial decay for KdV with three critical linear modes
AP · AIM Open Applied Problems · critical lengths · decay rates · Korteweg–de Vries equation
OP-00785 Solution claimed
Continuation of the cutoff Boltzmann flow from macroscopic bounds
AP · AIM Open Applied Problems · Boltzmann equation · conditional regularity
OP-00786 Solution claimed
Unconditional uniqueness for entropy-dissipating reaction–diffusion
AP · AIM Open Applied Problems · reaction–diffusion systems · renormalized solutions · uniqueness
OP-00787 Solution claimed
Characterizing discrete sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · Pisot numbers
OP-00788 Solution claimed
Relative density of sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · relatively dense sets
OP-00789 Solution claimed
An extreme solitary wave for the bidirectional Whitham system
AP · AIM Open Applied Problems · highest waves · solitary waves · Whitham–Boussinesq system
OP-00790 Solution claimed
A bounded number of flat transversals for fat convex sets
MG · AIM Open Applied Problems · fat convex sets · geometric transversals · Helly-type theorems
OP-00791 Solution claimed
The zero center-of-mass diffusion limit for kinetic FENE fluids
AP · AIM Open Applied Problems · dilute polymeric fluids · FENE dumbbell model
OP-00792 Solution claimed
A finite three-ample complex with nontrivial fundamental group
AT · AIM Open Applied Problems · ample simplicial complexes · fundamental group
OP-00793 Solution claimed
Continuity of finite-cluster mass at the onset of Flory gelation
AP · AIM Open Applied Problems · coagulation equations · gelation
OP-00794 Solution claimed
Finite propagation in fourth-order aggregation–diffusion
AP · aggregation-diffusion equations · AIM Open Applied Problems · finite speed of propagation · thin-film equations
OP-00795 Solution claimed
Continuity for degenerate fractional-pressure porous-medium flow
AP · AIM Open Applied Problems · continuity of weak solutions · fractional pressure · porous medium equations
OP-00796 Solution claimed
Optimal obstacle regularity for stable jump kernels with only angular integrability
AP · AIM Open Applied Problems · nonlocal obstacle problems · stable operators
OP-00797 Solution claimed
Counting half-integral polygons with collinear interior lattice points
CO · AIM Open Applied Problems · lattice polygons · rational polygons
OP-00798 Solution claimed
Counting Ehrhart quasipolynomials of half-integral polygons
CO · AIM Open Applied Problems · Ehrhart quasipolynomials · rational polygons
OP-00799 Solution claimed
Ergodicity of higher-dimensional Ising clumps
PR · AIM Open Applied Problems · cubical sets · Markov chains · topology-preserving dynamics
OP-00800 Solution claimed
Comparison for viscosity solutions of infinity-fractional diffusion
AP · AIM Open Applied Problems · comparison principles · infinity fractional Laplacian · viscosity solutions
OP-00801 Solution claimed
Integral optimal flat-norm decompositions in codimension one
DG · AIM Open Applied Problems · flat norm · integral currents
OP-00802 Solution claimed
Intercritical norm inflation for the dispersion-managed Schrödinger equation
AP · AIM Open Applied Problems · dispersion management · nonlinear Schrödinger equations · norm inflation
OP-00803 Solution claimed
Global smooth propagation for a laser envelope coupled to ionization
AP · AIM Open Applied Problems · laser filamentation · nonlinear Schrödinger equations
OP-00804 Solution claimed
Exponential excursion tails for topology-preserving Ising disks
PR · AIM Open Applied Problems · rare events · self-avoiding polygons · topology-preserving dynamics
OP-00805 Solution claimed
An algebraic vanishing-noise rate for kinetic mean-field games
AP · AIM Open Applied Problems · kinetic mean-field games · vanishing viscosity · variational methods
OP-00806 Solution claimed
Uniform convergence of value functions in local mean-field games
AP · AIM Open Applied Problems · Hamilton–Jacobi equations · mean-field games · vanishing viscosity
OP-00807 Solution claimed
Zero in the upper-Laplacian spectrum of low-degree simplicial complexes
SP · AIM Open Applied Problems · branching random walks · simplicial complexes · upper Laplacian
OP-00808 Solution claimed
Asymmetry at the Macbeath point of a convex body
MG · AIM Open Applied Problems · centers of convex bodies · convex bodies
OP-00809 Solution claimed
Mass conservation for fractional porous-medium flow on noncompact manifolds
AP · AIM Open Applied Problems · fractional porous medium equations · mass conservation · Riemannian manifolds
OP-00810 Solution claimed
Point-source solutions of fractional porous-medium diffusion on manifolds
AP · AIM Open Applied Problems · fractional porous medium equations · fundamental solutions · Riemannian manifolds
OP-00811 Solution claimed
Topological complexity in the homogeneous medial regime for all sample sizes
AT · AIM Open Applied Problems · random simplicial complexes · topological complexity
OP-00812 Solution claimed
Minimal persistence grids versus homological Morse lower bounds
AT · AIM Open Applied Problems · multigraded Betti numbers · multiparameter persistent homology
OP-00813 Solution claimed
A finite-integrability ABP estimate for general nonlocal Pucci operators
AP · AIM Open Applied Problems · Aleksandrov–Bakelman–Pucci estimates · integro-differential equations · Pucci extremal operators
OP-00814 Solution claimed
Odd Euler characteristic for flag-no-square four-manifolds
GT · AIM Open Applied Problems · Euler characteristic · flag-no-square triangulations · four-manifolds
OP-00815 Solution claimed
Can one-dimensional entropy-dissipating systems have two bounded solutions?
AP · AIM Open Applied Problems · entropy solutions · hyperbolic conservation laws
OP-00816 Solution claimed
Coarse Hilbert embeddings of persistence diagrams
MG · AIM Open Applied Problems · coarse embeddings · persistence diagrams · Wasserstein distance