7425 papers
This paper develops a non-abelian, gauge-theoretic framework for the Schwarzian derivative and second-order differential equations on Riemann surfaces, applying it to generalize Dedekind's approach to higher-genus curves via matrix-valued equations on the Hodge bundle, analyze periods of cubic threefolds, and model mechanical mass-spring systems.
This paper establishes sharp estimates for functions harmonic with respect to -dependent rectilinear stable processes in balls under radial exterior data, utilizing the construction of global barrier functions for the associated -dependent rectilinear fractional Laplacian.
This thesis extends the relative -contractibility of Koras-Russell threefolds and their higher-dimensional prototypes to arbitrary Noetherian base schemes, thereby establishing the existence of the first known family of smooth "exotic" motivic spheres in dimensions that are -homotopic to, but not isomorphic to, the punctured affine space .
The paper introduces the Pivotal Information Criterion (PIC), a continuous optimization method that dynamically selects its penalty parameter at the detection boundary to overcome the high false discovery rates and computational infeasibility of traditional criteria like BIC and AIC in high-dimensional settings.
This paper improves the known lower bound on the size of transitive subgraphs in -majority tournaments from to , demonstrating an exponential improvement in the dependence of the exponent on .
This paper introduces a flux-limited viscosity solution framework for evolutive Hamilton-Jacobi equations with time-measurable Hamiltonians and discontinuous flux limiters on a 1-dimensional junction, proving a comparison principle and establishing existence results for convex cases via optimal control.
This paper introduces a general category-theoretic framework for epistemic uncertainty that unifies various imprecise probability theories, models their interrelationships, and demonstrates how both Bayesian updating and possibilistic conditioning emerge as specific instances of a generalized belief updating process based on change of enrichment.
This paper establishes a converse Lyapunov theorem for the boundedness of reachability sets in infinite-dimensional systems with Lipschitz continuous flows, demonstrating its applicability to semi-linear evolution equations and deriving a result for forward completeness in ordinary differential equations without restricting input magnitudes.
This paper demonstrates that co-Hopfianity is not a profinite property by constructing two finitely generated residually finite groups with isomorphic profinite completions, where one is co-Hopfian and the other is not, utilizing Wise's Rips construction and a specific preimage subgroup technique.
This paper demonstrates that, contrary to the classical Grunwald–Wang theorem's special case where the obstruction is a group of order 2, the obstruction in the generalized setting for valued fields is not always finite nor bounded independently of the number of places, even for rational function fields.
This paper demonstrates the existence of planar rational curves over the finite field with arbitrarily large degrees that possess a unique singularity of multiplicity 2, a phenomenon that is restricted to degrees of at most 6 in characteristic 0.
This paper presents a statistically robust framework for reconstructing metal–semiconductor contact regions by combining topological gradients with shape optimization, establishing a central limit theorem for convergence and utilizing a key parameter to refine interface sensitivity and distinguish true structural features from noise.
This paper initiates a systematic study of arrow pattern avoidance in permutations by establishing structural results such as arrow-Wilf equivalence and enumerating various avoidance classes, including those involving pairs of patterns that prohibit fixed points.
This paper demonstrates that while pure optimal strategies exist in infinite-horizon Markov decision processes with finite state and action spaces under diffuse charges satisfying the time value of money principle, optimal strategies (neither pure nor randomized) may fail to exist entirely if the aggregation charge is constructed without such assumptions.
This paper investigates paths in the p-Bratteli diagram for odd primes to prove the vanishing of sign balance from inversions and to define new families of -Fibonacci numbers based on descents, which generalize the OEIS sequence A391520.
This paper presents a comparative numerical study of six graph-based splitting algorithms specialized for linear subspaces, identifying optimal relaxation parameters and analyzing iteration counts to reveal performance patterns that may inform future theoretical analysis.
This paper establishes that geodesic disks are the unique domains maximizing the first non-trivial Neumann eigenvalue among all simply connected regions of the sphere with a fixed area.
This paper presents a randomized polynomial-time algorithm for learning read-once determinants by establishing its equivalence to a black-box version of the Principal Minor Assignment Problem and resolving the latter through the introduction of the rank-one extension property.
This paper introduces the extrinsic bi-conformal heat flow for biharmonic maps on 4-manifolds and proves that this flow exists globally and remains smooth without developing finite-time singularities.
This paper characterizes the extreme and exposed points of the unit ball in the -norm for shift-invariant spaces generated by the Gaussian function and quasi shift-invariant spaces generated by the hyperbolic secant.