2572 papers
This paper presents a minicourse from the 2024 Bialystok School on Geometry and Physics that explores the algebraic foundations of barycentric algebras, followed by an examination of their diverse examples, applications, and structural relevance.
This paper investigates -Poncelet pairs formed by a circle and parabolas from a confocal family, proving that such pairs exist for all parabolas in the family only when the circle contains the focus () or is centered at the focus (), a property termed -isoperiodicity which is then used to construct explicit algebraic solutions to Painlevé VI equations.
This paper presents a formalization of Borel determinacy in the Lean 4 theorem prover, including definitions of Gale-Stewart games and a proof of Martin's theorem that closely follows his original "purely inductive" argument.
This paper introduces an efficient algorithm that rapidly computes a complete curve of post hoc false discovery proportion bounds along a path of increasing selection sets by leveraging the forest structure of the reference family and the incremental nature of adding single hypotheses.
This paper investigates the geometry of strong -structures with torsion by establishing curvature characterizations, linking Ricci-flat solutions to the heterotic system via reduction, constructing new examples with non-Ricci-flat connections, and classifying associated -flows using representation theoretic methods.
This paper employs purely planimetric methods, including Joachimsthal notation, to independently prove Poncelet's Theorem for triangles and quadrilaterals inscribed in a circle and circumscribed about a parabola, establishing specific geometric conditions for their existence and characterizing the resulting quadrilaterals as antiparallelograms.
This paper presents explicit formulas for the Alexander polynomial of pretzel knots, characterizes those with trivial polynomials, and utilizes these results to construct a new family of knots that are topologically slice but not smoothly slice.
This paper introduces a new scoring variant of the combinatorial game Nim that generalizes both normal and misère play rules, and analyzes its theoretical properties, including optimal strategies and payoff functions.
This paper establishes the global-in-time existence of strong solutions for a class of fractional parabolic reaction-diffusion systems governed by spectral fractional Laplacians with polynomial growth nonlinearities, while also presenting numerical simulations to address an open theoretical question.
This paper demonstrates that even in a non-additive setting, the existence of a codereliction within a monoidal coalgebra modality inherently induces an additive enrichment via bialgebra convolution, thereby uniquely characterizing differential linear categories and establishing the uniqueness of coderelictions.
Motivated by prior work on post-critically finite cubic polynomials, this paper proposes a Markov model based on critical orbits to describe the factorization of iterated PCF cubic polynomials over and constructs groups that are conjectured to contain the Galois groups of these iterations.
This paper establishes the stability and uniqueness of a stochastic branching algorithm for solving semilinear heat equations by deriving sufficient criteria for the integrability of random functionals to prevent solution explosion.
This paper develops Generalized Method of Moments (GMM) and M estimators for network-dependent data by establishing a novel uniform law of large numbers that ensures their consistency and asymptotic normality, while also providing complete procedures for practical estimation and inference.
This paper introduces a Fourier-type formalism on non-commutative spaces to establish two versions of the Hörmander-Mikhlin -multiplier theorem for locally compact Kac groups and semi-finite von Neumann algebras, which generalize classical results and are applied to evolution equations in non-commutative settings.
This paper analyzes the theoretical foundations, error bounds, and numerical approximations of the State-Dependent Riccati Equation (SDRE) approach for nonlinear optimal control, introducing a residual-minimizing decomposition strategy and demonstrating through numerical experiments that the Newton-Kleinman iterative method offers superior stability and cost-effectiveness compared to the offline-online approach.
This paper introduces a general scenario reduction method for distributionally robust optimization that projects the original ambiguity set onto a reduced set of scenarios, providing theoretical quality bounds and demonstrating significant computational efficiency with minimal loss in solution accuracy across discrete and continuous distributions.
This paper introduces the operator on higher-dimensional almost Kähler manifolds to investigate the -problem and establish uniqueness and local existence results for a generalized Monge-Ampère equation, ultimately providing an elliptic system for the operator and reorganizing the work of Tosatti-Weinkove-Yau.
This paper demonstrates that bounded divergence-free drifts in the advection-diffusion equation on reduce solution concentration—manifested as increased variance, entropy, and decreased norms compared to the heat equation—though this effect does not hold on the torus .
This paper establishes that for hypergraphs derived from cross-free connected subgraphs of a bounded-genus host graph, there exists a support graph that also maintains bounded genus, thereby generalizing prior planar results and providing a unified framework for solving packing, covering, and coloring problems on surfaces.
This paper proposes and analyzes a stochastic algorithm that provably converges almost surely to the operator norm of the difference between two linear maps—one accessible only via forward evaluation and the other only via adjoint evaluation—by performing a random search on a generalized Rayleigh quotient with optimal step sizes.