5835 papers
This paper establishes a necessary and sufficient condition for decomposing the complete graph on vertices into isomorphic copies of a Cayley graph on a CI-group , while also providing a constructive method for such factorizations.
This paper resolves two longstanding problems from 1990 regarding indefinite integral ternary quadratic forms, highlighted by Margulis and initiated by Serre, by developing new tools to handle high ramification in sums weighted by diophantine invariants.
This paper investigates the long-time asymptotic behavior of multivariate Hawkes processes with power-law decaying interactions, employing a combination of short-range interaction techniques, -stable law properties, and Tauberian theorems to model realistic systems like neural networks with long-range connections.
This paper constructs a presheaf of Koszul complexes on weighted finite subsets of Euclidean space, utilizing linearized coefficients and change-of-coordinates maps to form a Čech-Koszul bicomplex whose degree-0 cocycles capture homotopical relationships between locally defined least squares solutions on data overlaps.
This paper proves that augmented admissible sets in Iwahori-Weyl groups are dual EL-shellable, thereby resolving a conjecture of Görtz and establishing the Cohen-Macaulayness of special fibers for local models with parahoric level structure—including previously open cases in residue characteristic 2 and non-reduced root systems—through a characteristic-free, intrinsic construction that yields an explicit shelling and inductive building procedure.
This paper demonstrates that while the "spectral density" derived from Gurau's resolvent trace yields valid probability measures on average for certain random tensor ensembles, it fails to correspond to a probability measure for individual deterministic tensors, thereby proving it is not a pointwise-defined probability distribution.
This paper introduces a Bayesian framework for linear programming under learned uncertainty that integrates data-driven posterior updates with robust optimization and scenario-based strategies to provide rigorous, finite-sample feasibility guarantees and improved decision safety compared to naive approaches.
This paper establishes a minimax theory for nonparametric regression under covariate shift by introducing a transfer function to characterize convergence rates that range from classical benchmarks to accelerated regimes involving multiplicative sample size interactions, all achievable by a design-adaptive estimator even with unbounded covariate support.
This paper establishes the existence and nonexistence of ground states for mass-critical N-coupled attractive Fermi nonlinear Schrödinger systems in ring-shaped potentials based on the strength of interactions relative to a critical constant derived from a finite-rank Lieb-Thirring inequality, while also characterizing the mass concentration behavior of these states as the interaction strength approaches this critical threshold.
This paper proposes a joint optimization algorithm for transmit precoding and discrete phase-shift reflection in an extremely large-scale RIS-aided near-field secure communication system with artificial jamming, effectively maximizing secrecy rates even when eavesdroppers are located close to the RIS and in the same direction as legitimate users.
This paper establishes the Morita invariance of several classes of ring extensions and provides a counterexample of a class that is not Morita invariant, building upon previous results by Miyashita and Ikehata.
This paper characterizes weakly separable polynomials in skew polynomial rings and explores the relationship between separability and weak separability in rings of derivation type, building upon the generalization of separable extensions introduced by Hamaguchi and Nakajima.
The paper proposes PriorIDENT, a prior-informed weak-form sparse-regression framework that integrates compact physics priors into dictionary construction to robustly identify governing partial differential equations from noisy spatiotemporal data while outperforming existing baselines in accuracy and stability.
This paper generalizes and improves upon Hamaguchi and Nakajima's work by characterizing weakly separable polynomials over commutative rings using derivatives and discriminants, while also establishing necessary and sufficient conditions for such polynomials in noncommutative skew polynomial rings.
This paper revisits the Friedrichs model to derive precise asymptotic results, including the Breit-Wigner formula and spectral concentration, for resonances near embedded eigenvalues, while also establishing exact properties for sojourn time, scattering amplitude, and time delay in the context of rank-one perturbations of the Laplacian.
This paper investigates the Martin boundary of space-time Markov chains associated with finitely supported random walks to establish structural connections between various compactifications and harmonic function boundaries, ultimately demonstrating that the noncommutative Shilov boundary of the associated tensor algebra coincides with its Toeplitz -algebra.
Motivated by non-abelian Hodge theory, this paper formulates a Hodge-theoretic version of Grothendieck's anabelian conjecture by replacing Galois actions with natural -actions, proving an analog of Mochizuki's theorem for smooth projective hyperbolic curves over and extending the result to higher-dimensional ball quotient manifolds.
This paper investigates the structural implications of vanishing -degree Turán densities in hypergraphs, proving that for -uniform hypergraphs with vanishing 2-degree Turán density, a specific global vertex ordering (2-vanishing order) must exist, thereby generalizing classical results on zero Turán density and demonstrating that unlike the classical case, 2-degree Turán densities accumulate at zero.
This paper establishes that Sobolev maps on the product of two Euclidean domains with invertible differentials preserving or swapping the factor spaces are necessarily split when the dimension , a result that fails for and for lower regularity spaces with .
This paper revises Gauss's Lemma by introducing the concept of "metrical distortion" as a non-identity isometry between double tangential and tangential spaces, and concretely defines the exterior differential via covariant gradient transport to incorporate a "differential slip" representing scalar gauge theory, ultimately distinguishing between geodesically radial volume preservation (metrical distortion) and length preservation (exponential mapping) through the example of the 2-sphere.