4965 papers
This paper investigates a geometric algorithm for constructing biharmonic and conformal-biharmonic maps into spheres, demonstrating that while the approach faces strong restrictions for biharmonic maps on closed domains due to the maximum principle, it offers greater flexibility on non-compact domains and successfully generates explicit critical points for conformal-biharmonic maps between spheres.
This paper establishes a bridge between homotopy type theory and information theory by defining probability types, demonstrating that homotopy cardinality respects dependent sums but not products, and deriving Shannon entropy and its chain rule as the homotopy cardinality of specific types constructed via deloopings of finite cyclic groups.
This paper proves a theorem by C. Miranda regarding the Hölder regularity of generalized layer potential convolution operators acting on the boundary of a open set when the densities are of class .
This paper classifies intermediate t-structures on the local derived category of a 3-fold flopping contraction and minimal resolutions of Kleinian singularities, thereby describing the complete lattice of torsion classes for associated modification and preprojective algebras and providing foundational steps for understanding spherical objects in derived categories of surfaces and 3-folds.
This paper resolves Joel Hamkins' question by proving that no extensional Rosser formula of any complexity exists, while demonstrating that a positive answer holds under the weaker condition of "Conditional Extensionality," which allows for a -formula that is both extensional and -flexible.
This paper establishes that for discretely observed oscillating Brownian motion, the maximum likelihood estimator of the self-organized criticality level achieves -consistency and converges stably to a bivariate Poisson-type distribution, despite the non-standard challenge posed by the discontinuity of the transition density at the true parameter.
This paper provides the first complete characterization of optimal dynamic portfolio choice for monotone mean-variance utility in asset models with independent returns under minimal assumptions, establishing a link between maximal utility and the monotone Sharpe ratio while deriving conditions under which classical mean-variance efficient portfolios remain optimal.
This paper establishes the existence of equilibria for a class of Mean Field Games involving reflected stochastic differential equations by utilizing the framework of relaxed controls and martingale problems.
This paper introduces the -transformation, a new integral operator constructed via kernel fusion of the fractional Fourier transform, and establishes its fundamental properties alongside a comprehensive survey of its associated uncertainty principles, including Heisenberg's, Hardy's, Pitt's, and Beurling-Hörmander's theorems.
This paper establishes the existence and uniqueness of solutions to reflected generalized backward stochastic differential equations (GRBSDEs) with RCLL random obstacles under a general filtration supporting Brownian motion and an independent integer-valued random measure, while also linking these solutions to optimal control problems over stopping times.
This paper establishes a symmetric multivariate Elekes-Rónyai theorem providing a lower bound on the size of the image of a polynomial over finite sets unless the polynomial exhibits specific additive or multiplicative degeneracies, while also proving a generalized Erdős-Szemerédi theorem for two polynomials in higher dimensions.
This paper establishes that the tropical rank of a semimodule of tropical rational functions equals its topological dimension, while demonstrating that verifying tropical independence is equivalent to solving a turn-based stochastic mean-payoff game and that computing the tropical rank is NP-hard.
This paper proposes and analyzes two scalable augmented Lagrangian preconditioners for solving block-structured linear systems arising from fictitious domain discretizations of Poisson and Stokes problems, demonstrating their robustness and effectiveness through spectral analysis and extensive numerical tests in two and three dimensions.
This paper investigates the geometry of compact Kähler manifolds with partially semi-positive curvature by proving that such manifolds are rationally connected under specific positivity conditions and establishing structure theorems that classify them as either having high rational dimension or admitting a locally constant fibration with rationally connected fibers and a Ricci-flat base.
This paper introduces new techniques to provide a unified framework for computing the metric entropy of ellipsoids in Banach spaces, delivering precise asymptotic expansions with explicit constants, improved second-order terms, and the first exact characterization for infinite-dimensional bodies, with significant applications to function classes in Sobolev and Besov spaces and machine learning.
This paper establishes the global well-posedness of the elastic-viscous-plastic (EVP) sea-ice model under inviscid Voigt-regularization, thereby resolving the long-standing issue of handling viscosity coefficients without cutoff that has hindered the analysis of related sea-ice models.
This paper establishes the existence, energy decay, and blow-up behavior of solutions for a three-dimensional piezoelectric beam model with nonlinear dampings and supercritical sources by utilizing nonlinear semigroups, the potential well method, and differential inequality techniques, while removing restrictive conditions on model coefficients.
This paper advances the theory of holonomic D-modules by establishing the invariance of Euler characteristics under localization and regular singular twists, proving local generic vanishing theorems via twisting with differential forms, and providing a direct construction of the Laplace transform for Stokes-filtered sheaves that completes the correspondence with holonomic D-modules.
This paper introduces and analyzes a divide-and-conquer algorithm for quantizing one-dimensional probability distributions, establishing a universal Wasserstein-1 error bound and demonstrating through numerical experiments that the method achieves optimal convergence rates while offering superior stability under arithmetic operations compared to existing schemes.
This paper investigates the geometric properties of tetrahedra with a fixed base by characterizing the closure and boundary of the set formed by the cosines of the face angles at the apex.