7084 papers
This paper proves Kanade's previously open conjecture regarding dilogarithm identities and Nahm sums by leveraging Kirillov's identities and a dilogarithm ladder, while also proposing two new conjectures involving rank-2 matrices inspired by these results.
This paper applies the Chemical Reaction Network theory (CRNT) and the symbolic package EpidCRN to analyze multi-strain rumor spreading models on online social networks, revealing that stability transitions occur via "relay" mechanisms governed by siphon-induced transcritical bifurcations and invasion inequalities.
This paper establishes the existence of global-in-time, -corotational wave map solutions that asymptotically decompose into an arbitrary number of alternating-sign concentric bubbles with vanishing radiation, utilizing a backward construction method and a novel Morawetz-type functional to prove the soliton resolution conjecture for .
This paper unconditionally proves the quantum unique ergodicity conjecture for Pitale lifts on hyperbolic 4-manifolds by employing a novel amplification method with favorable geometric properties to overcome the challenges posed by non-temperedness.
This paper investigates the relationship between perfect divisibility and perfect weighted divisibility in graphs, demonstrating that -free or claw-free minimally nonperfectly divisible graphs contain no clique cutset, thereby providing a conditional answer to a question posed by Hoàng.
This paper extends the weighted -Hardy inequalities and identities to the full range , while also establishing a new sharp remainder formula for general weighted -Rellich inequalities involving quasilinear second-order degenerate elliptic operators.
This survey article reviews the theory of twisted dynamical zeta functions of Ruelle and Selberg and explores Fried's conjecture, drawing from a mini-course delivered at the Institut Henri Poincaré.
This paper constructs the Extended Real Line with Reentry (ERI), a compact, path-connected, T₁ space that is US but not KC, thereby providing an explicit counterexample that separates these properties in the Wilansky hierarchy while demonstrating that its only continuous real-valued functions are constants.
This paper introduces the concept of the asymptotic mean of digits in the generalized -representation of real numbers and investigates the topological, metric, and fractal properties of sets defined by the existence or specific values of these means, while also exploring their connections to digit frequencies and fractal geometry.
This paper investigates the topological, metric, and fractal properties of subsets of the interval defined by specific asymptotic means of digits in their ternary representations, while exploring their relationship to numbers characterized by fixed digit frequencies.
This paper investigates the topological, metric, and fractal properties of the set of real numbers whose 4-adic digits possess existing frequencies and a specific asymptotic mean, providing an algorithm for constructing such points and establishing conditions for their Lebesgue measure and Hausdorff dimension.
This paper establishes the well-posedness of deterministic particle dynamics with time-evolving weights and their associated Kolmogorov and mean-field equations under mild regularity assumptions, utilizing entropy estimates and the relative entropy method to rigorously derive the mean-field limit.
This paper introduces a geometric analysis of a recently proposed family of geometric analog error correction codes to characterize their m-height profiles, thereby expanding the limited range of available code families for handling multiple outliers in crossbar-based in-memory computing.
This paper establishes a characterization of the small finitistic dimension of a commutative ring in terms of the vanishing of Ext groups for finitely generated ideals, proving that fPD if and only if the vanishing of for implies its vanishing for all , and applies this result to derive the inequality fPD and analyze various classes of rings such as -rings and DW-rings.
This study introduces Equilibrium-Informed Neural Networks (EINNs), a novel deep learning approach that reverses the traditional parameter-search process by inferring system parameters from candidate equilibrium states to efficiently detect critical bifurcation thresholds and tipping points in complex nonlinear dynamical systems.
This paper introduces Dictionary Based Pattern Entropy (DPE), a novel framework that combines Algorithmic and Shannon Information Theories to infer causal directions and identify driving subpatterns in symbolic sequences by quantifying how compact, rule-based patterns in a cause systematically reduce uncertainty in an effect, demonstrating robust performance across diverse synthetic and real-world datasets.
This paper applies a probabilistic machine learning framework to analyze Collatz stopping times up to , demonstrating that a Bayesian hierarchical Negative Binomial regression outperforms a mechanistic odd-block generator in predictive likelihood while revealing that low-order modular structure significantly drives the observed heterogeneity.
Building on the work of Katzarkov, Kontsevich, Pantev, and Yu regarding the irrationality of very general cubic fourfolds, this paper establishes that the primitive cohomology of any rational smooth complex cubic fourfold is isomorphic as a Hodge structure to the twisted middle cohomology of a projective K3 surface.
This paper introduces a canonical Polish groupoid constructed from the unitary group and dual space of a separable unital C*-algebra, demonstrating that for Type I algebras, the associated reduced groupoid C*-algebra is Morita equivalent to the original algebra tensored with compact operators and admits a canonical diagonal embedding that characterizes commutativity.
This paper presents a multi-agent system that autonomously discovers mathematical concepts, such as homology, by dynamically interweaving conjecture generation, proof attempts, and counterexample analysis, demonstrating that optimizing these local processes effectively aligns with human notions of mathematical interestingness.