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Constructing Mathematical Meaning through Authentic Nutrition Problems in Higher Education

This study demonstrates that undergraduate nutrition students construct meaningful mathematical understanding in STEM contexts not merely by achieving procedural accuracy, but by coordinating quantities, representations, and disciplinary assumptions through authentic problem-solving, a process best captured by analyzing collaborative reasoning and individual artifacts rather than aggregate grades alone.

Luisa Morales-Maure, Marisa Montesano de Talavera, Orlando García Marimón, David Guete Garcia2026-09-01

🔢 mathematics

A scale-covariant pre-solve screening algorithm for scalar finite-difference discretizations on positive nonuniform meshes

This paper presents a scale-covariant, pre-solve screening algorithm for scalar finite-difference discretizations on positive nonuniform meshes that combines a deterministic, certified acceptance test with a risk-calibrated empirical rejection rule to validate stability and provide error certificates without requiring a reference solution.

Andrey Krylov2026-09-01

🔢 mathematics

Emergent Fibonacci Structure from Local Growth Rules

This paper introduces a local growth model based on three physical principles that naturally generates a parametric family of spiral tilings, demonstrating that the Fibonacci structure emerges exactly at a critical point as an energetically privileged and robust configuration within this broader morphological landscape.

Richard Taylor2026-09-01

🔢 mathematics

An equivalence between Schauder's fixed point theorem and periodic solutions in Banach spaces

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.

Jorge Novoa2026-08-31

🔢 mathematics

A fixed-operation-count solver for the hyperbolic Kepler equation with a proven uniform error bound

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.

Hitaishi Chillara2026-08-31

🔢 mathematics

Pattern Transformation in Higher-Order Lump Solutions of the Generalized Calogero-Bogoyavlenskii-Schiff Equation

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.

XiaoJing Chen, ZhenYun Qin, Gui Mu, TingYou Wang, FuZhuang Zheng2026-08-31

🔢 mathematics

SER: A Metric Expressing the Local Intention of a Trajectory

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.

Vishnu Vijayakumar2026-08-31

🔢 mathematics

Asymptotic Analysis for Pure Dominated Strategy in Random Games

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.

Xihao Song2026-08-31

🔢 mathematics

A comparison of readability formulas applied to arithmetical word problems for Year 1 of primary school

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.

Pamela Reyes Santander, Mario Díaz Díaz2026-08-28

🔢 mathematics

The Nim-Sum of a Random Integer Partition

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.

Daewon Kim2026-08-28✓ Author reviewed ⓘ

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