141 papers
Motivated by Cid and Mawhin's result linking Brouwer's fixed point theorem to periodic solutions in finite dimensions, this paper establishes that Schauder's fixed point theorem in Banach spaces is equivalent to the existence of periodic solutions for a compact class of Banach-valued differential equations.
This paper presents a computer-assisted proof of a fixed-operation-count solver for the hyperbolic Kepler equation that guarantees a uniform relative error below double-precision machine epsilon using only four Newton corrections, significantly outperforming prior methods requiring 55 iterations.
This paper derives explicit expressions for high-order lump solutions of the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation using the Hirota bilinear method and KP reduction, and analyzes their asymptotic pattern transformations into triangular configurations of fundamental lumps determined by Yablonskii-Vorob'ev polynomials.
This paper introduces the Specific Energy Ratio (SER), a computationally efficient, real-time metric derived from scalar observations via Takens' embedding that estimates local tangential acceleration to identify kinematic transients and high-curvature features within a reconstructed trajectory's cycle, complementing traditional global asymptotic invariants.
This paper introduces the concept of *q-Portion* dominated strategies to establish sharp asymptotic thresholds for the existence of large-scale strategic elimination in random games, while also proposing an efficient, distribution-free algorithm for detecting such strategies.
This study evaluates five readability formulas on Year 1 arithmetic word problems from Chilean textbooks and concludes that existing metrics designed for continuous text are inconsistent and inadequate for this specific context, highlighting the need for specialized readability measures for early-grade math problems.
This paper determines the first-order asymptotic behavior of the proportion of losing positions among integer partitions of N. The proportion tends to zero on the scale 1/(√N log N), but after normalization by its natural scale it does not converge; instead, it exhibits a dyadic sawtooth pattern with a Poisson-parity transition near dyadic boundaries.
This paper analyzes the random geometry and total correlation of the K smallest values in a dependent chi-square sequence, establishing that selected sites become asymptotically uncorrelated for sub-critical selection sizes while exhibiting Poisson-distributed adjacent pairs and positive correlation at the critical square-root threshold.
This paper proposes a numerically stable and efficient partial singular value decomposition method for dual quaternion matrices using the Lanczos algorithm with thick-restart and one-sided reorthogonalization, demonstrating its superior accuracy and computational performance in applications such as color face recognition and video compression.
This paper introduces a novel, higher-precision cubature rule (SM 2 4) derived by optimizing the combination of Anti-Gaussian, Fejer's second, and Lobatto rules, which demonstrates superior accuracy and efficiency over its constituent methods in both theoretical analysis and numerical experiments.