2388 papers
This paper investigates the bifiltration of bracket ideals and the associated bivariate Hilbert polynomial for complex finite-dimensional filiform Lie algebras, demonstrating that this polynomial serves as a refined invariant capable of distinguishing isomorphism classes that remain indistinguishable by traditional numerical invariants related to centralizers and abelian ideal dimensions.
This paper extends Suzuki's approach to Kannan and Chatterjea type contractions by utilizing the CJM condition to establish the weakest possible conditions that ensure the convergence of all Picard sequences to a fixed point, thereby proving the optimality of these conditions.
This paper proves that the infinite system-size free energy of quantum -spin glasses in a transverse magnetic field converges to that of the quantum random energy model as , achieved by combining non-commutative analytical techniques with the geometry of extreme negative deviations in classical -spin glasses.
This paper characterizes the Cohen-Macaulay property of the square of an edge ideal by constructing the Stanley-Reisner complex of its polarization and applying Reisner's criterion, proving that for several important classes of graphs, is Cohen-Macaulay if and only if is either a pentagon or a single edge.
This paper establishes that the harmonic map heat flow from a compact Riemannian manifold into the moduli space of unit-area flat tori is stable, ergodic, and converges to the normalized hyperbolic measure, with the relative entropy decaying to zero to quantify this information-theoretic equilibrium.
This paper introduces the Poisson tensor completion (PTC) estimator, which leverages inter-sample relationships and models histogram bins as a non-homogeneous Poisson process to achieve a low-rank, non-negative tensor decomposition that significantly outperforms standard histogram-based estimators for sub-Gaussian distributions.
This paper establishes a new characterization of the moderate growth condition in the mixed weight matrix setting by proving its equivalence to a property of the associated weight function, thereby addressing the limitations of previous generalizations.
This paper investigates the Schur product of monomial-Cartesian codes via Minkowski sums of exponent sets to construct improved CSS-T quantum codes and more efficient Private Information Retrieval schemes using -affine variety codes and their subfield-subcodes.
This paper proposes a unified deep meta-learning framework that unrolls an adaptive optimization algorithm to jointly accelerate multi-coil MRI reconstruction and cross-modality synthesis, demonstrating superior generalization and image quality under aggressive undersampling and domain shifts compared to conventional supervised methods.
This paper presents an adaptive proximal safeguarded augmented Lagrangian method for solving nonsmooth difference-of-convex (DC) optimization problems with convex constraints, proving convergence to a generalized KKT point under a modified Slater condition and validating the approach through numerical experiments.
This paper investigates the limit shapes and fluctuations of random Young diagrams arising from symplectic group duality by deriving semiclassical orthogonal polynomials via Christoffel transformation from Krawtchouk polynomials and analyzing their asymptotic behavior through an integral representation, thereby overcoming the lack of a free-fermionic representation available in the general linear case.
This paper introduces a "solver-in-the-loop" framework for 3D Electrical Impedance Tomography that combines a pre-trained 3D generative prior with a rigorous boundary integral equation solver to enforce physical constraints as hard conditions, thereby achieving superior geometric accuracy and data efficiency in reconstructing complex interfaces compared to traditional optimization and deep learning methods.
This paper establishes a cubic braid-type skein theory for the Links-Gould polynomial, proving its universal computability for oriented links and demonstrating its equivalence to the -polynomial, thereby unifying their shared properties such as specialization to the Alexander polynomial and providing a Seifert genus bound.
This paper establishes an explicit formula for the -polynomials of van der Geer--van der Vlugt curves in characteristic 2 by leveraging the structure of Heisenberg groups and Lang torsors, ultimately enabling the construction of examples that attain the Hasse--Weil bound.
This paper constructs examples of noetherian local geometrically normal domains in prime characteristic that are -injective but fail to be -full or -anti-nilpotent, highlighting the critical role of -injectivity's behavior under purely inseparable finite base changes.
This paper proves that for any forest and any hereditary class of theta-free graphs excluding and the line graphs of all subdivisions of some wall, the treewidth is bounded by a polynomial function of the clique number, a result shown to be optimal as both exclusion conditions are necessary.
This paper establishes the non-amenability of mapping class groups for infinite-type surfaces and locally finite infinite graphs of higher ranks, provides an example of a non-amenable point stabilizer in a specific hyperbolic Polish group, and identifies a class of amenable mapping class groups associated with trees and rank-one graphs.
This paper investigates the asymptotic counting of matrices over finite fields that commute with their Frobenius image (and its iterates), providing explicit results for specific cases such as size-2, diagonalizable, and -defined eigenspace matrices while outlining the approach for the general case.
This paper proves that finite groups with semidihedral Sylow 2-subgroups possess a class-preserving Coleman outer automorphism group of odd order, thereby confirming that these groups satisfy the normalizer problem and extending existing results in the field.
This paper proves that every triangle-free graph with sufficiently large chromatic number contains an induced subgraph that is either a -sun for some large or a $4t$-suns in such graphs.