🔢 Category

math

42 papers

🔢 mathematics

Approaches to Nonlinear Programming Problems: Taylor Series Expansion, RBF Surrogate Modeling, DOE-Based Dimensionality Reduction, and Adaptive Domain Splitting

This paper presents a comprehensive four-component optimization framework that combines DOE-based variable screening, RBF surrogate modeling, adaptive domain splitting, and a hybrid GA–SQP solver to significantly reduce computational effort and convergence time while maintaining accuracy across diverse nonlinear programming problems.

Yara Hossam Eldin Elkassaby, Mohamed H. Gadallah2026-07-23
🔢 mathematics

Exploring Multi-Rhythmicity in the light of Hilbert's 16th Problem : A Liénard--Levenson-Smith Perspective and the Potency of Perturbative Methods

This paper synthesizes mathematical theory and perturbative methods to classify nonlinear oscillators within the generalized Liénard--Levenson--Smith framework, offering insights into Hilbert's 16th problem and the dynamics of multi-rhythmic biological systems while critically addressing the framework's limitations regarding the uniqueness of limit cycles.

Sandip Saha, Gautam Gangopadhyay, Deb Shankar Ray2026-07-23
🔢 mathematics

An Interior-Only Framework for Hessian Recovery: The KR Defect Method, with Uniqueness, Stability, and Boundary-Constrained Applications

This paper introduces the KR defect method, an interior-only framework for Hessian recovery that utilizes strictly internal evaluation points to enable first-order consistent curvature estimation on convex domains, scattered data, and boundary-constrained scenarios where traditional central finite-difference stencils fail, supported by rigorous theoretical proofs and validated through numerical experiments.

RamaKrishna Pasupuleti2026-07-21
🔢 mathematics

Residual-Certified Fractional and Time-Delayed Duffing Dynamics: A Volterra--Memory Framework for Continuous and Discrete Past Dependence

This paper presents a residual-certified computational framework using Volterra formulations and independent error metrics to systematically compare and distinguish the dynamical behaviors of continuous fractional memory, discrete time-delay, and hybrid mechanisms in nonlinear Duffing oscillators, demonstrating that their observed differences are intrinsic rather than numerical artifacts.

Alvaro Salas2026-07-16
🔢 mathematics

Collaboration versus Specialization in Service Systems with Impatient Customers

This paper investigates optimal server assignment policies in tandem queueing systems with impatient customers and collaborative efficiencies, demonstrating that while equal-skilled servers should always collaborate, task-dependent skills lead to a threshold-based policy that balances specialization with dynamic collaboration to maximize long-run throughput.

Bihan Chatterjee, Sigrún Andradóttir, Hayriye Ayhan2026-07-15
🔢 mathematics

A two-stage stochastic optimization model for synchronized two-echelon routing problems

This paper proposes a two-stage stochastic optimization model for synchronized two-echelon city logistics that minimizes lateness, costs, and road mode share, demonstrating a 37% reduction in expected costs compared to deterministic approaches and highlighting the superior reliability and sustainability of flexible sailing services over relocating storage units under uncertainty.

Cigdem Karademir, Jesper J. Zwaginga, Breno A. Beirigo, Bilge Atasoy2026-07-15