A numerically certified face-by-face solver fills the low-ratio gap in Mangasarian’s Newton method on synthetic tests, matches production-solver timing on the largest cases, and narrows the gap on the Netlib benchmark through a three-method frontier, though it still trails HiGHS.
We construct an infinite tower of skew Hadamard matrices of orders 4(76t+3 + 1), t ≥ 0, beginning with order 1,376, using one fixed order-18 finite-field construction.
A systematic attack on Turyn’s 1972 converse conjecture closes every remaining non-prime-power case through q = 2000 and proves a semiprime nonexistence theorem, while the full conjecture remains open.
The paper extends earlier work on harmonic divisor matrices to a much sparser version of the Redheffer matrix, bounding its smallest singular value and determining its largest.
An iterated convex relaxation always converges to a fixed point, can stop finitely near regular CAZAC sequences, and has an exact regularity count at Zadoff–Chu points.
The paper settles two conjectures about harmonic divisor matrices and describes the extreme eigenvalues and singular values of a family linking them to the classical Redheffer matrix.
A direct formula for a real Hadamard matrix of order 2q(q + 1) for every prime power q ≡ 1 (mod 4), with proof and exact checks.
A recursive construction for partitioned difference families with geometric block sizes, with a proof and exact verification code.
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