🔢 mathematics

Geometry-Preserving Optimal Control of Implicitly Singularly Perturbed Systems with Sliding and Exit Constraints

This paper introduces a reciprocal Cauchy regularization method that ensures geometry-preserving optimal control for implicitly singularly perturbed systems by establishing exact equivalence between full and reduced dynamics on the singular hyperplane, providing rigorous convergence bounds for off-hyperplane trajectories, and decoupling exit constraints into a real-time safety layer to guarantee invariant safe regions.

Volodymyr Gotsulenko2026-09-18
🔢 mathematics

Multi-Period Sustainable Healthcare Supply Chain Network Design: A Mixed-Integer Linear Programming Approach

This study presents a multi-period mixed-integer linear programming model that optimizes sustainable healthcare supply chain network design by simultaneously balancing cost efficiency, environmental carbon limits, and service-level requirements across a four-echelon network, demonstrating robust performance and full demand satisfaction under baseline conditions.

Abdulhadi A. Altherwi2026-09-17
🔢 mathematics

Certified Monotone-Face Krylov Acceleration for Box-Constrained Time-Fractional Boundary Control

This paper introduces SARC, a certified monotone-face Krylov acceleration method that significantly outperforms standard projected-gradient iterations in solving box-constrained time-fractional boundary control problems by combining spectrally bounded safeguards with active-set identification to achieve rapid convergence to the optimal solution.

Thiziri sifaoui, KARIM Benalia, Sara bendjeddou2026-09-17
🔢 mathematics

A Hybrid Fractional-Order Dynamical Model for ECG Morphology: Caputo Memory, Identifiability, and Reproducible PQRST Reconstruction

This paper presents a hybrid fractional-order dynamical model that combines a periodic phase oscillator with a Caputo fractional relaxation equation to reconstruct ECG morphology, demonstrating through rigorous mathematical analysis and reproducible synthetic testing that this approach offers superior accuracy and parameter identifiability compared to traditional integer-order models.

Taylan Demi̇r, Atakan Koçyiğit2026-09-17
🔢 mathematics

Analytical Soliton Dynamics and Spatiotemporal Warping of the (2+1)-Dimensional Potential CDGKS Equation via Local Composite Derivatives

This paper extends the (2+1)-dimensional potential CDGKS equation to a local composite derivative framework, deriving closed-form soliton and lump solutions via a composite Cole-Hopf transformation to demonstrate that while wave amplitudes remain invariant, their spatiotemporal trajectories undergo continuous warping governed by deformation kernel factors.

Juan Eduardo Nápoles Valdés, Darwin Peña-González, Roberto Torres-Peña2026-09-16
🔢 mathematics

Residual-adaptive truncation in an arbitrary-order tangent iteration for π\pi: quadratic growth of the accuracy exponent

This paper introduces a residual-adaptive truncation rule for an arbitrary-order tangent iteration to compute π\pi, which leverages the alternating arctangent series to achieve quadratic growth in the decimal accuracy exponent, thereby enabling the rapid convergence from a single Chudnovsky approximation to over one million correct decimal places.

Shih-Han Wang2026-09-16
🔢 mathematics

On the convergence of the new SOR-like method for solving absolute value equations

This paper refutes the original convergence proof of the new SOR-like method for absolute value equations by providing a counterexample, and establishes a rigorous convergence criterion based on a control matrix that identifies a more reliable optimal parameter pair (1, 1) which, despite potentially requiring more iterations, yields lower total computing time.

Liqian Lin, Dongmei Yu, Cairong Chen, Deren Han2026-09-16