Pure and applied mathematics including algebra, analysis, geometry, and combinatorics.
Gram-matrix positivity converts the boundary identity into finite-dimensional linear algebra, yielding an exact two-parameter admissibility region and a complete dimension classification.
Arithmetic level-d estimates, sieve-based exponential sums, and random sparsification yield a stretched-exponential upper bound for every exponent below 1/2.
A symmetric meromorphic construction places the preimages of 0, 1, and infinity on the real axis while making every other point divisor non-Blaschke in both half-planes.
A new Bochner identity turns a Calabi-operator positivity condition into a rigidity result for Kähler–Einstein manifolds.
A covariate-balanced empirical measure lets randomized-experiment analyses improve efficiency while retaining valid distribution and survival-curve shape.
Permuting nonconstant edge coefficients gives an arbitrary-field bound of $2\lceil\mathrm{ed}(H)\rceil+1$, connecting polynomial structure to hypergraph density.
Under proper edge colouring, an existence proof partitions every sufficiently large complete graph into two vertex-disjoint rainbow cycles.
A large-step inexact Halpern wrapper accelerates tensor-based monotone variational-inequality solvers from polynomial rates up to a claimed near-$T^{-p}$ convergence rate.
Unfolding and refolding witness graphs lets the authors characterize critical activation density for every fixed graph H, including witnesses larger than the host graph.
Expected self-intersection time is O(√n log n) on bounded-degree graphs and O(√n) for regular graphs with a uniform spectral gap.
