7036 papers
This paper presents a novel, fully closed, and hyperbolic two-fluid model for compressible two-phase flows derived via a new Stationary Action Principle, which introduces the interfacial work to ensure physical soundness across all flow topologies and provides a robust foundation for numerical simulations.
This paper introduces Calabi--Yau quadruples to demonstrate that their associated Higgs categories are -Calabi--Yau Frobenius extriangulated categories with canonical -cluster-tilting subcategories, thereby proving that both relative Amiot--Guo--Keller and Higgs constructions transform silting reduction into Calabi--Yau reduction.
This paper establishes that the number of rational points on an elliptic curve whose -coordinates lie in a -dimensional generalized arithmetic progression is bounded by a constant raised to the power of the curve's Mordell-Weil rank, a result derived by combining gap principles for large canonical heights with spherical code bounds and which implies restrictions on sets of points with small sumsets.
This paper constructs relatively bounded toroidal and toric models for fibrations over curves.
This paper proves Clark Kimberling's conjectures regarding his 2017 binary sequence by utilizing the Walnut theorem-prover to establish its connection to the infinite Tribonacci word and to determine its subword complexity and critical exponent.
This paper establishes weak and strong elliptic Harnack inequalities for mixed local and nonlocal -energy forms on metric measure spaces by employing the De Giorgi--Nash--Moser method under axiomatic assumptions including the Poincaré and cutoff Sobolev inequalities.
This paper introduces a principled framework for testing excessive influence in linear least-squares models by deriving exact influence formulas and their corresponding extreme value distributions, thereby enabling rigorous hypothesis tests to distinguish between natural sampling variation and problematic data subsets across various scientific domains.
This paper proposes an auto-adaptive sampling method for Physics Informed Neural Networks (PINNs) that utilizes arbitrary problem-specific heuristics to accurately resolve interfacial regions in Allen-Cahn equations without post-hoc resampling, demonstrating superior performance over residual-adaptive frameworks.
This paper establishes the relationship between pairings of May operads and compatible pairs of indexing systems, demonstrating that operad pairings induce system pairings and that, in many cases, compatible indexing systems can be realized by pairings of -operads.
This paper establishes the non-uniqueness of positive solutions for Cauchy problems of supercritical semilinear heat equations by proving that the existence of a positive radial singular stationary solution guarantees at least two distinct solutions starting from that singular initial data.
The paper introduces FMint-SDE, a multimodal foundation model based on decoder-only transformers that leverages in-context learning and error correction to provide a general-purpose, efficient, and accurate solution for simulating stochastic differential equations across diverse scientific domains.
This paper presents numerically stable, closed-form algorithms for computing the eigenvalues of real, diagonalizable matrices using four specific invariants, demonstrating that these methods are both more accurate for repeated eigenvalues and approximately ten times faster than the LAPACK library while maintaining comparable precision.
This paper develops pivotal and spherical versions of graded extension theory for tensor categories, defining corresponding Brauer-Picard 2-categorical groups, classifying extensions via monoidal 2-functors, and establishing an obstruction theory for extending these structures.
This paper establishes that for certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, the potential -convergence of the corresponding collapsing Ricci-flat Kähler metrics can be improved to metric convergence on a generic region.
This paper proposes a novel communication-efficient decentralized symmetric ADMM algorithm that utilizes multiple communication rounds per iteration to achieve linear convergence and reduce total communication costs compared to existing methods.
This paper provides a complete characterization of all model category structures on finite lattices by utilizing transfer systems, thereby establishing new connections between abstract homotopy theory and equivariant methods.
This paper proves that the Halton sequence is not quasi-uniform in any dimension with pairwise relatively prime bases, and extends this result to disprove the quasi-uniformity of certain Halton-type sequences, including the Faure sequence.
This paper constructs probabilistically strong, strictly dissipative solutions to the three-dimensional Euler equations with additive noise that satisfy the local energy inequality, and uses these results to establish non-unique ergodicity for the forced system.
This paper establishes a machine-checked impossibility result proving that direct compositional measures cannot terminate step-duplicating recursors, while demonstrating that projection-based methods successfully escape this barrier and providing a complete certified termination chain for a minimal witness calculus.
The paper proposes Deep FlexQP, a deep unfolding-based solver that accelerates nonlinear programming by learning dimension-agnostic parameters for a robust, always-feasible convex QP relaxation, thereby significantly improving the speed and success rates of SQP and safety filter applications while providing rigorous performance guarantees.