7189 papers
This paper investigates the singularities and striction curves of two-ruled hypersurfaces in Euclidean four-space by introducing the concept of pseudo-non-degeneracy and analyzing the geometric relationship between these hypersurfaces and their generating curves via Frenet-type frames and height functions.
This expanded lecture notes from the 2025 Lie-Stormer Summer School explore classical invariants by highlighting analogies between binary quartics and ternary cubics, presenting triangle groups in elliptic and hyperbolic settings, and discussing Hilbert's work on polynomials that are powers, supplemented by exercises and a section on Pfaffians.
This paper demonstrates that for asymptotic bases of order 2 with weaker representation function growth rates, the properties of having a divergent representation function, being decomposable into two bases, and containing a minimal basis are independent, thereby refining earlier results by Erdős and Nathanson through an inductive construction on exponentially growing intervals.
This paper investigates the enumeration of permutations avoiding two flat partially ordered patterns by establishing connections to -Fibonacci numbers and restricted permutations to derive generating functions, while also extending existing results on separable permutations with respect to multiple statistics.
This paper establishes the existence of radial solutions with a prescribed -norm for a -Laplacian equation involving a general radial potential by employing a variational min-max argument supported by a new global boundedness result for subsolutions and a corresponding Pohozaev identity.
This paper introduces a highly scalable, structure-aware parallel presolve framework for arrowhead linear programs integrated into the PIPS-IPM++ solver, which significantly outperforms state-of-the-art tools like PaPILO and Gurobi in runtime while effectively reducing problem size in distributed high-performance computing environments.
This paper investigates nonconvex real-valued functions whose truncations become quasiconvex or convex beyond a certain level, with a specific focus on -smooth functions whose level sets lie within the positive definite region of their Hessian matrices, demonstrating the injectivity of their restricted gradients in that region.
This paper introduces a geometric rank on imaginaries for the theory of beautiful pairs of algebraically closed fields that refines SU-rank, characterizes forking, and provides an explicit criterion for independence in .
This paper establishes the non-radial linear stability of liquid Lane-Emden stars against irrotational perturbations by proving that the associated linear operator is strictly positive whenever the radial mode is stable, despite the inability to control the gradient norm of the perturbations.
This paper demonstrates that while order-preserving Lipschitz maps from subsets of one-dimensional partially ordered Hilbert spaces into Hadamard posets can always be extended without increasing the Lipschitz constant, such extensions are generally impossible in higher dimensions unless the order on the domain is trivial, thereby proving that no order-theoretic generalization of Kirszbraun's theorem exists.
This paper addresses the ill-posed nature of kinematic differential equations in two-phase flows with discontinuous velocity fields by employing differential inclusions to rigorously define co-moving sets and prove an extended Reynolds transport theorem that accounts for phase change and interfacial slip.
This paper establishes dimension expansion results for -point configuration sets generated by real analytic functions, proving that such sets attain positive Lebesgue measure or strictly larger Hausdorff dimensions under specific conditions by leveraging optimal -based Sobolev estimates for Fourier integral operators and extending the Mattila-Sjölin and Falconer-type frameworks.
This paper introduces the numerical invariants of birational and strong complete regularity for Fano type pairs using qdlt models and dual complexes, establishes their fundamental properties and connections to K-stability, and proves that maximal birational strong complete regularity implies 1-complementarity while the associated jumping thresholds satisfy the ascending chain condition.
This paper characterizes centered weighted composition operators on -spaces without assuming a product structure, introduces the concept of spectrally half-centered operators to analyze unbounded cases, and provides criteria for centered weighted shifts on directed trees of types I–IV.
This paper employs first-order logic tools to unify and extend existing algebraic and spectral characterizations regarding the isomorphism of controllable graphs and the cospectrality of distance-regularized graphs.
This paper demonstrates that while the No Free Lunch theorem holds under uniform sampling, algebraic reformulations of permutation-based optimization benchmarks create structured local violations that alter algorithm rankings and performance patterns, necessitating problem-aware algorithm selection.
This technical note extends the results of Kosygina, Mountford, and Peterson on generalized Pólya's urns from a specific weight function to a broader family of functions relevant to Tóth's study of polynomially self-repelling walks, thereby facilitating future research on the scaling limits of these processes.
This paper proposes a two-step stochastic optimization framework that combines gradient and negative curvature steps with adaptive step sizes and early stopping to achieve high-probability convergence to second-order stationary points, offering complexity guarantees that match deterministic rates up to noise-dependent terms.
This paper proposes a two-time-scale design for local safety filters in networked systems that eliminates the need for global coordination by using derivative estimation, while providing explicit bounds on safety degradation relative to the time-scale parameter and estimation errors.
This paper introduces cycle matrices as a basis for describing non-equilibrium properties in Markov chains, proving that the kernel of the interaction graph's incidence matrix is isomorphic to the space of anti-symmetric matrices with zero row sums.