Infinite families of non-fibered twisted torus knots
This paper presents explicit infinite families of non-fibered twisted torus knots by demonstrating that the leading coefficients of their Alexander polynomials can assume arbitrary integer values.
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math
5420 papers
Subcritical bifurcations of shear flows
This paper provides numerical evidence demonstrating that the Hopf bifurcation occurring at the upper marginal stability curve for various shear flows in the incompressible Navier-Stokes equations is subcritical.
A table of knotoids in up to seven crossings
This paper presents a complete classification of spherical knotoids with up to six crossings and a conjectured complete classification up to seven crossings, utilizing a suite of invariants to distinguish equivalence classes while exploring their symmetries and applications to protein entanglement.
On Local Regularity of Distributional Solutions to the Navier--Stokes Equations
This paper establishes a sharp regularity result in spatial variables for distributional solutions to the Navier-Stokes equations that satisfy the Prodi-Serrin condition, without requiring the solutions to belong to the local Leray-Hopf class.
Dimension of the singular set in the parabolic obstacle problem
This paper establishes that the singular set in the parabolic obstacle problem for general obstacles has a parabolic Hausdorff dimension of at most , extending a previous result limited to constant Laplacian obstacles by combining a truncated parabolic frequency formula with monotonicity estimates and an iterative argument.
The five-sequence of adjoints for combinatorial simplicial complexes
This paper investigates a five-sequence of adjoint functors induced by functions between vertex sets of simplicial complexes, utilizing this structure to establish three categorical frameworks where the Stanley-Reisner correspondence yields dualities with commutative monomial rings.
One-sided large deviations for the ground-state energy of spin glasses
This paper establishes a large-deviation principle for the maximal energy of a spin glass with spins by deriving a Parisi-type formula for fractional moments and leveraging convex duality to show that the rate function is asymptotically quadratic near its minimum if and only if an external magnetic field is present.
Decay of correlations on Abelian covers of isometric extensions of volume-preserving Anosov flows
This paper establishes an asymptotic expansion in inverse powers of time for the correlation functions of isometric extensions of volume-preserving Anosov flows defined on Abelian covers of closed manifolds.
Normalized solutions to mass supercritical Schrödinger equations with radial potentials
This paper establishes the existence of two normalized solutions with a prescribed -norm for the stationary nonlinear Schrödinger equation with a radial potential in the mass-supercritical regime, utilizing Morse theory, spectral arguments, and radial blow-up analysis under minimal assumptions on the potential's sign, behavior at infinity, and regularity.
Computing Stationary Distribution via Dirichlet-Energy Minimization by Coordinate Descent
This paper presents an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains via Dirichlet-energy minimization and coordinate descent, thereby clarifying its behavior, establishing exponential convergence for specific chain classes, and suggesting practical scheduling strategies to accelerate convergence.
Spinor moving frame, type II superparticle quantization, hidden symmetry of linearized 10D supergravity, and superamplitudes
This paper utilizes a covariant spinor moving frame quantization of type IIA and IIB superparticles to reveal a hidden symmetry in linearized supergravity, demonstrating that both theories can be described by identical analytic on-shell superfields and superamplitudes while highlighting specific challenges in extending this formalism to include D0-branes.
Exponential stability of the linearized viscous Saint-Venant equations using a quadratic Lyapunov function
This paper establishes the exponential stability of the linearized viscous Saint-Venant equations in the norm by constructing an explicit diagonal quadratic Lyapunov function and deriving sufficient conditions on boundary parameters for small viscosities.
Long-time behaviour of a nonlocal stochastic fractional reaction--diffusion equation arising in tumour dynamics
This paper introduces a stochastic nonlocal fractional reaction-diffusion model for tumour dynamics driven by multiplicative fractional Brownian motion, establishing well-posedness, deriving explicit blow-up time bounds and probabilities via a Doss-Sussmann transformation, and illustrating how anomalous diffusion and correlated noise jointly influence long-term tumour progression or extinction.
Matchings in hypergraphs via Ore-degree conditions
This paper establishes new Ore-degree conditions that guarantee the existence of matchings in -uniform hypergraphs by proving upper bounds on the Ore-degree for intersecting hypergraphs and demonstrating that exceeding a specific threshold ensures the presence of pairwise disjoint edges.
On semilinear Grushin--Schrödinger equation in
This paper establishes the existence of nontrivial nonnegative weak solutions to a semilinear Grushin-Schrödinger equation in with controlled potentials by proving the embedding of the associated energy space into a weighted Lebesgue space and deriving subsequent regularity results.
On the Rigid-Ruling Folding of Curved Creases: Conjugate-Net Preserving Isometric Deformations of Semi-Discrete Globally Developable Conjugate-Nets
This paper investigates rigid-ruling folding motions of curved creases by deriving conditions for the foldability of developable semi-discrete conjugate nets and applying these findings to enable the sequential construction of foldable patterns and characterize the compatibility of planar and constant fold-angle creases.
Higher-Order Normality and No-Gap Conditions in Impulsive Control with -Control Topology
This paper establishes that a notion of higher-order normality, derived from iterated Lie brackets, is sufficient to prevent infimum gaps in impulsive extensions of control-affine systems under an -control topology, thereby extending existing no-gap results beyond the more common -trajectory framework.
Countable models of weakly quasi-o-minimal theories II
This paper confirms Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.
On the monogenicity and Galois groups of
This paper characterizes the monogenicity of irreducible trinomials of the form (where is prime) by classifying them according to their Galois groups, thereby extending the authors' previous research.
Minimizers for boundary reactions: renormalized energy, location of singularities, and applications
This paper demonstrates that, unlike the Casten-Holland and Matano theorem for interior reactions, nonconstant stable solutions for boundary reactions can exist in convex domains such as squares and regular polygons (but not circles), with their existence and the location of boundary singularities determined by a new renormalized energy function derived from the domain's conformal structure.