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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

Well-Possedness and Iterative Approximation for Elliptic Problems with Nonlinear Logarithmic Robin Boundary Conditions

This paper establishes the well-posedness and convergence of an iterative linearization scheme for an elliptic boundary value problem featuring nonlinear logarithmic Robin boundary conditions, supported by qualitative analysis and finite element numerical validation.

Chokri Elhechmi, Gmar Benhenda2026-07-21

🔢 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

An analysis of mixed-integer linear programming formulations for the Maximally Diverse Grouping Problem

This paper analyzes and proposes new mixed-integer linear programming formulations for the Maximally Diverse Grouping Problem, demonstrating through computational study that models based on item-item assignments outperform those using item-group assignments by providing stronger LP relaxations and superior branching performance.

Arne Schulz2026-07-15

🔢 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

🔢 mathematics

Elimination strata for torus-dynamical Fuchsian systems and the fixed-component Heun problem

This paper resolves the fixed-component Heun problem for torus-dynamical Fuchsian systems by characterizing the specific algebraic conditions under which eliminating one component yields a genuine four-singularity Heun equation, thereby defining complex and real elimination strata without relying on restrictive assumptions on the residue at zero.

Yutong Zhang, Yaoran Yang2026-07-14

🔢 mathematics

Grid-Induced and Refinement-Stable Switches in Cost-Sensitive Selection: A Technical Note

This technical note introduces a diagnostic refinement test to distinguish between grid-induced transient switches and stable, scale-separated transitions in cost-sensitive selection problems by analyzing how finite-grid breakpoints behave under mesh refinement.

Luc de Veigy2026-07-14

🔢 mathematics

Complete Low-Degree Magnitude-Homology Signatures in Fixed Windows for Finite Graphs

This paper presents an efficient computational method combining boundary matrices, normal forms, and closed-form formulas to calculate low-degree integral magnitude homology for finite graphs, demonstrating its superior ability to distinguish nonisomorphic graph pairs compared to ordinary invariants through extensive analysis of standard families and small connected graphs.

朱瑶君2026-07-14

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