arXiv subjects

Chamila Gamage

Publications and source records attributed to Chamila Gamage.

3 recordsLinked to original sources

arXiv2026

Capacity-Constrained Wasserstein Barycenters: Existence, Duality, and Entropic Regularization

We introduce a capacity-constrained Wasserstein barycenter problem in which each transport plan from an input measure to the barycenter is bounded by a prescribed capacity measure. On compact domains, we prove existence of capacity-constrained barycenters and establish a strong duality formula. We then study an entropy-regularized version under bounded capacity-density assumptions. The regularized problem has a unique optimal tuple of transport plans and a unique barycenter, while its dual involves an explicit capped-exponential penalty. Whenever dual maximizers exist, the optimal densities satisfy a capacity-clipped Gibbs formula. Finally, we prove an $O(ε)$ estimate for the optimal values and show that the regularized plans converge to the minimum-entropy optimal solution of the unregularized problem.

math.OC↗

arXiv2026

Scaffold Write Debug: A Three-Stage Approach to Proof Writing in Introductory Real Analysis

This article describes Scaffold Write Debug, a three-stage instructional approach used in an introductory real analysis course to support students learning mathematical proof. The approach combines guided proof completion, independent proof writing, and the analysis and correction of faulty proofs. The goal is to help students understand proof structure, develop confidence in writing proofs, and become more careful readers of mathematical arguments. The paper presents classroom examples, instructor observations, and student responses, and discusses how the approach can be incorporated into a proof-based course.

math.HO↗

arXiv2026

Learning and Teaching Calculus Through Its History

This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like infinity, area, motion, and continuous change slowly evolved through solving problems and cultural exchange. I argue that bringing this history into the classroom helps students see calculus as more than a set of procedures: it becomes a story of human creativity and persistence. By revisiting the questions early mathematicians struggled with, students can better appreciate and better understand the core ideas behind the formulas they use today.

math.HO↗