2545 papers
This paper investigates how various finitary conditions, such as weakly left noetherian and weakly left coherent properties, interact with graph products of monoids, establishing that these properties are preserved under retracts and proving that while the converse holds for most conditions, the weakly left noetherian property requires a precise characterization of the constituent monoids and their graph structure.
This paper proposes a multiphase cubic MARS method that achieves high-order accuracy in both time and space for tracking interfaces of multiple materials with arbitrary topology and geometry by utilizing graph-based representations, adaptive marker distribution, and robust junction handling.
This paper proves a conjecture by Trinh and Xue regarding intersections of blocks in cyclotomic Hecke algebras for all exceptional finite reductive groups except , while also proposing and partially confirming generalizations to Suzuki, Ree, non-rational Coxeter, and spetsial complex reflection groups.
This paper introduces the concept of strongly -inverse monoids, provides a presentation for the universal -generated strongly -inverse monoid with a given maximum group image, and applies this framework to fully characterize one-relator special inverse monoids with cyclically reduced relators that possess this property.
This paper establishes the global-in-time well-posedness of stochastic third-grade fluid equations on a two-dimensional torus with additive noise and proves the existence, uniqueness, and first-order optimality conditions for a velocity tracking control problem by transforming the system into an equivalent pathwise deterministic one.
This paper constructs and classifies all differential symmetry breaking operators between principal series representations of the de Sitter and Lorentz groups , proving that all such operators are necessarily differential and constitute "sporadic" cases that cannot be derived from meromorphic families via residue formulas.
This paper investigates equivalent characterizations of totally acyclicity for acyclic complexes of projective, injective, and flat modules over arbitrary rings, linking these conditions to homological invariants like silp(R), spli(R), and sfli(R) while refining existing results on the equality of these invariants and extending characterizations of Iwanaga-Gorenstein rings and the Nakayama conjecture to the non-commutative setting.
This paper establishes a connection between the fixed points of the Josephus function and the Chinese Remainder Theorem, then utilizes a non-standard fractional base $3/2$ expansion to identify digit patterns that enable a recursive procedure for determining these fixed points.
This paper classifies projective Legendrian subvarieties that are homogeneous under their stabilizers within the projectivized nilpotent orbits of complex semi-simple Lie algebras, specifically providing a classification of equivariant Legendrian embeddings of rational homogeneous spaces into adjoint varieties.
This paper proposes an efficient iterative stochastic precoding algorithm for MIMO networks over generalized fading channels that maximizes long-term average weighted sum rates by utilizing a novel matrix fractional programming-based lower bound on expected data rates, requiring only the first and second moments of channel statistics rather than specific distribution models.
This paper establishes that a commutator is a -element for all if and only if is central modulo , a result that generalizes the Baer--Suzuki and Glauberman -theorems and is applied to prove that a conjugacy class satisfying generates a solvable subgroup.
This paper introduces a unified Davis-Wielandt shell framework for the graphical stability analysis of MIMO LTI systems, proposing a novel rotated scaled relative graph (-SRG) concept that yields the least conservative closed-loop stability criterion among existing two-dimensional graphical conditions.
This paper presents a novel entropy-stable nodal discontinuous Galerkin scheme for the Euler equations with gravity that achieves well-balancing for general hydrostatic and moving equilibrium states through a linear entropy correction to the source term, while maintaining compatibility with positivity-preserving limiters and demonstrating robustness in numerical experiments.
This paper defines a speed measure for locally bounded variation curves in metric spaces, characterizes their continuity and absolute continuity through this measure, identifies its Radon-Nikodým derivative as the metric speed, and establishes an extension of the Banach-Zaretsky theorem.
This paper establishes the local well-posedness of the generalized parabolic Anderson model and the -equation on the two-dimensional torus with random, noise-correlated coefficients by proving that naive renormalisation fails due to variance blow-up and instead demonstrating convergence through the use of random renormalisation functions supported by novel stochastic estimates.
This paper establishes sharp estimates for specific Littlewood-Paley square functions on , which are then used to prove the boundedness of maximal Fourier multiplier operators of Bochner-Riesz type, thereby generalizing a 1983 result by A. Carbery.
This paper establishes necessary and sufficient conditions for the compactness of the embedding on the half-space with general singular weights, proving that compactness holds if and only if the measure has finite mass and satisfies a global tightness condition characterized by coercive tail inequalities and, in singular cases, weighted Hardy inequalities.
This paper investigates the Bott-Chern and Aeppli cohomologies of twistor spaces associated with compact self-dual 4-manifolds to characterize the validity of the -lemma, while explicitly computing the Dolbeault cohomology for the twistor space of the flat 4-torus as a specific example where the lemma fails.
This paper derives exact formulas for the proportions of derangements and derangements of -power order in various affine classical groups, utilizing a new generating function for specific integer partitions in the unitary case and verifying -polynomial identities in the symplectic and orthogonal cases.
This paper advances the dimension theory of sets and measures by weakening Hochman's exponential separation condition, demonstrating the equivalence of modified and original definitions for homogeneous self-similar IFS on , and proving the density of specific subsets defined by Assouad, Hausdorff, and dimensions within their respective spaces.