math papers | Gist.Science

An alternative proof of Miyashita's theorem in a skew polynomial ring II

This paper provides proofs for Miyashita's characterizations of separable and Hirata separable polynomials in the general skew polynomial ring $B[X;\rho,D]$ , extending the author's previous elementary proofs from the specific automorphism and derivation cases.

Satoshi Yamanaka2026-03-10🔢 math

A Distributed Method for Cooperative Transaction Cost Mitigation

This paper proposes a distributed convex optimization protocol that enables portfolio managers to iteratively adjust their independent trades based on shared cost estimates, thereby significantly reducing market impact and transaction costs without requiring the disclosure of private trading strategies or direct communication between managers.

Nikhil Devanathan, Logan Bell, Dylan Rueter, Stephen Boyd2026-03-10🔢 math

LegONet: Plug-and-Play Structure-Preserving Neural Operator Blocks for Compositional PDE Learning

LegONet introduces a compositional, plug-and-play framework for learning PDE solvers by utilizing structure-preserving operator blocks on shared spectral representations to separate boundary handling and mechanism learning, thereby enabling stable, reusable, and reconfigurable neural operators across diverse equations and conditions.

Jiahao Zhang, Yueqi Wang, Guang Lin2026-03-10🔢 math

Closed Reeb orbits on contact type hypersurfaces in $T^*S^n$

This paper establishes that dynamically convex, closed contact type hypersurfaces in $T^*S^n$ enclosing the zero section possess at least $[\frac{n+1}{2}]$ closed Reeb orbits, and further guarantees the existence of at least two irrationally elliptic orbits under non-degeneracy and finiteness conditions.

Huagui Duan, Zihao Qi2026-03-10🔢 math

A Structure-Preserving LOBPCG Algorithm for the Bethe-Salpeter Eigenvalue Problem

This paper proposes a structure-preserving LOBPCG algorithm, enhanced with an improved Hetmaniuk-Lehoucq trick and an adaptive multi-level orthogonalization strategy, to efficiently and accurately solve the Bethe-Salpeter eigenvalue problem while naturally extending to symplectic eigensolvers.

Xinyu Shan, Meiyue Shao2026-03-10🔢 math

Curve Lengthening Bifurcations in Modally Filtered Nonlinear Schrödinger Systems

This paper develops extensions of parametric nonlinear Schrödinger equations for phase-sensitive optical resonance that preserve the curve lengthening bifurcation by constructing specific down-phase self-interaction operators, thereby maintaining linear stability while enabling a sign flip in the normal velocity's linear term.

Keith Promislow, Abba Ramadan2026-03-10🔢 math

Hard/Soft NLoS Detection via Combinatorial Data Augmentation for 6G Positioning

This paper proposes the combinatorial data augmentation-guided NLoS detection (CDA-ND) algorithm, which generates NLoS evidence vectors from multilateration-based location clusters to enable both hard and soft NLoS detection modes, significantly improving 6G positioning accuracy in indoor factory environments by reducing mean absolute error by up to 66%.

Sang-Hyeok Kim (Inha University, South Korea), Seung Min Yu (Korea Railroad Research Institute, South Korea), Jihong Park (Singapore University of Technology and Design, Singapore), Seung-Woo Ko (Inha University, South Korea)2026-03-10🔢 math

A note on small cap square function and decoupling estimates for the parabola

This paper establishes sharp, up to polylogarithmic factors, small cap square function and decoupling estimates for the parabola using axis-parallel rectangles of dimensions $\delta \times \delta^\beta$ for $0 \leq \beta \leq 1 $, thereby complementing existing results for the range$ 1 \leq \beta \leq 2$.

Jongchon Kim, Liang Wang, Chun Keung Yeung2026-03-10🔢 math

Probing Lorentz symmetry violation via the Casimir effect in rectangular cavities

This paper investigates the Casimir effect in rectangular cavities as a probe for Lorentz symmetry violation, demonstrating how a fixed background four-vector induces anisotropic, direction-dependent corrections to the vacuum energy while preserving the separability of field modes.

M. B. Cruz, E. R. Bezerra de Mello, A. Martín-Ruiz2026-03-10🔢 math

Contravariantly infinite resolving subcategories

This paper defines contravariantly infinite subcategories of finitely generated modules over a commutative Noetherian ring and establishes several criteria for such infiniteness specifically in the case where the ring is a local complete intersection.

Gen Tanigawa2026-03-10🔢 math

Estimation of differential entropy for normal populations under prior information

This paper addresses the point-wise and interval estimation of differential entropy for two normal populations under order-restricted prior information by deriving improved estimators that dominate the best affine equivariant estimator and comparing various confidence interval methods through numerical studies and a real-world application.

Somnath Mandal, Lakshmi Kanta Patra2026-03-10🔢 math

Vector-Valued Invariants Associated with All Irreducible Representations for a Finite Group

This paper investigates the complex reflection group associated with the octahedral group by determining its irreducible representations and character table, computing the modules of vector-valued invariants for each representation, and deriving explicit dimension formulas for the corresponding rings of invariants.

A. K. M. Selim Reza, Manabu Oura, Masashi Kosuda2026-03-10🔢 math

The Exact Erd\H{o}s-Ko-Rado Theorem for 3-wise $t$ -intersecting uniform families

This paper establishes that for sufficiently large $n$ and $k$ , the maximum size of a 3-wise $t$ -intersecting family of $k$ -element subsets is $\binom{n-t}{k-t}$ , with the bound being asymptotically tight under the condition $n \geq \frac{\sqrt{4t+9}-1}{2}k$ for $t \geq 46$ .

Peter Frankl, Jian Wang2026-03-10🔢 math

Parameter Estimation for Complex {\alpha}-Fractional Brownian Bridge

This paper establishes the well-posedness of a complex $\alpha$ -fractional Brownian bridge and proves the strong consistency and asymptotic distribution of its least squares parameter estimator for $H \in (1/2, 1)$ , revealing a unique two-dimensional limiting distribution with non-Cauchy marginals derived via complex Malliavin calculus.

Yong Chen, Lin Fang, Ying Li, Hongjuan Zhou2026-03-10🔢 math

Entropies, cross-entropies and Rényi divergence: sharp three-term inequalities for probability density functions

This paper establishes a new sharp three-term inequality linking differential Rényi entropy, Rényi divergence, and Rényi cross-entropy for probability density functions, demonstrating that equality holds when one density is an escort of the other and using this result to derive further sharp bounds involving various informational functionals like absolute moments and Fisher information.

Razvan Gabriel Iagar, David Puertas-Centeno2026-03-10🔢 math

Aero-Promptness: Drag-Aware Aerodynamic Manipulability for Propeller-driven Vehicles

This paper introduces Drag-Aware Aerodynamic Manipulability (DAAM), a geometric framework for control allocation in redundant multirotors that utilizes a Riemannian metric to explicitly account for motor torque limits and aerodynamic drag, thereby generating a state-dependent manipulability volume that serves as a natural barrier function to optimize redundancy resolution while characterizing the resulting smooth manifolds and global jump discontinuities.

Antonio Franchi2026-03-10🔢 math

Post-Hoc Large-Sample Statistical Inference

This paper develops a theory of asymptotic post-hoc inference that utilizes e-values to create sharper confidence sets and p-values with weaker assumptions than existing nonasymptotic methods, thereby allowing valid statistical conclusions even when significance levels are chosen after observing the data.

Ben Chugg, Etienne Gauthier, Michael I. Jordan, Aaditya Ramdas, Ian Waudby-Smith2026-03-10🔢 math

Primitive recursive categoricity spectra

This paper investigates the primitive recursive analogue of computable categoricity spectra, demonstrating that these notions coincide for several natural classes of structures, including relatively $\Delta_{2}^{0}$ -categorical equivalence structures and linear orders, relatively $\Delta_{3}^{0}$ -categorical Boolean algebras, and computably categorical trees as partial orders.

Nikolay Bazhenov, Heer Tern Koh, Keng Meng Ng2026-03-10🔢 math

Primitive recursive categoricity spectra of functional structures

This paper investigates the relationship between degrees of categoricity and their punctual (primitive recursive) analogues for functional structures, demonstrating that these notions coincide for non- $\Delta_{1}^{0}$ -categorical injection structures but diverge for certain $\Delta_{1}^{0}$ -categorical ones, while also establishing the existence of specific PR-degrees with distinct properties in every non-zero c.e. Turing degree.