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Discriminant-Guided Preprocessing for Local Solution Algorithms of Second-Order Euler Operators

This paper introduces a discriminant-guided preprocessing method implemented in Macaulay2 that accelerates the computation of local solutions for second-order Euler-type differential operators near x = 0 by detecting complex conjugate indicial roots to construct an oscillatory basis, thereby reducing symbolic branch-management overhead and execution time without impacting non-oscillatory cases.

Enangnon Fiacre LOKOSSOU2026-07-07

🔢 mathematics

Delayed Repression and Emergent Instability in Adaptive Multi-Agent Systems

This paper demonstrates that processing delays in institutional regulation alone can destabilize otherwise stable multi-agent systems through a supercritical Hopf bifurcation, causing large-amplitude oscillations in reactive agents while fixed-policy agents remain immune and Q-learning agents exhibit partial resilience due to memory-based damping.

Igor Itkin2026-07-06

🔢 mathematics

The Generalized Fermat-Torricelli-Weber Problem

This paper introduces a new generalized Fermat–Torricelli–Weber problem and a corresponding subgradient algorithm within a unified Hilbert space framework that connects it to mixed split feasibility problems, establishing convergence results and demonstrating practical applications in image deblurring.

SUBRATA RANA, Binayak S. Choudhury2026-07-06

🔢 mathematics

Threshold Dynamics of a Spatially Heterogeneous SVEIAR-B Reaction-Diffusion Model under Media Intervention *

This paper establishes the global well-posedness and threshold dynamics of a spatially heterogeneous SVEIAR-B reaction-diffusion epidemic model incorporating media intervention, demonstrating that disease extinction or persistence is determined by the basic reproduction number $R_0$ while highlighting the critical roles of media intensity, vaccination, and spatial heterogeneity in shaping epidemic outcomes.

Lixia Shi, Weimin Hu, Youhui Su, Qian Wen2026-07-06

🔢 mathematics

$\Delta$ as a Dynamical Order Parameter for Non-Abelian Synchronization:\ the Case of $SU(2)$

This paper introduces and validates a scalar order parameter $\Delta$ that quantifies the splitting between Lyapunov branches in non-Abelian oscillator networks, demonstrating its utility as a robust measure of non-Abelian synchronization effects in $SU(2)$ systems even under non-Hermitian perturbations.

Mostafa Sayyah2026-07-06✓ Author reviewed ⓘ

🔢 mathematics

Regularized Multiwavelet Collocation Methods for Ill-Posed Fredholm Integral Equations of the First Kind

This paper proposes a unified regularized multiwavelet collocation framework for solving ill-posed Fredholm integral equations of the first kind, demonstrating that basis selection is a critical component of the regularization strategy that directly influences stability, noise sensitivity, and reconstruction accuracy across different smoothness regimes.

Ahmed Kaffel2026-07-03

🔢 mathematics

A Variable-Step IMEX-BDF2 Finite Element Method for the Navier–Stokes Equations: Optimal $L^2$ Error Estimates for Velocity and Pressure

This paper establishes fully optimal $L^2$ error estimates for both velocity and pressure in a variable-step IMEX-BDF2 finite element method for the Navier–Stokes equations by leveraging discrete orthogonal convolution kernels and negative-norm arguments to address time-step variations.

Hongfei Fu, Baolin Kuang, Rihui Lan, Shusen Xie2026-07-03

🔢 mathematics

A Facultative Mutualism Model with Internal Competition for Interactions between University and Technical-Vocational Qualification Frameworks in Tanzania

This study employs a facultative mutualism model based on nonlinear differential equations to demonstrate that balancing articulation mechanisms with institutional competition is essential for achieving a stable, sustainable, and mutually beneficial interaction between Tanzania's University and Technical-Vocational Qualification Frameworks.

Justine KIra2026-07-02

🔢 mathematics

A Block Hybrid Method for Third- and Fourth-Order Nonlinear Boundary Value Problems

This study proposes a stable and accurate unified block hybrid method for solving third- and fourth-order nonlinear boundary value problems that overcomes the ill-conditioning limitations of spectral collocation methods by partitioning the domain into blocks and recovering lower-order derivatives through successive integration, thereby achieving high convergence orders with significantly lower condition numbers.

Mpho Mendy Nefale, Olumuyiwa Otegbeye, Shina Daniel Oloniiju2026-07-02

🔢 mathematics

A Randomized Bracketing Method for Derivative-Free Root Finding with Uniform Spacing Contraction

This paper introduces and analyzes a randomized, derivative-free root-finding method that preserves bracketing by sampling multiple interior points to contract the search interval, proving its convergence properties and demonstrating its effectiveness as a robust, tunable alternative for expensive or parallelizable black-box function evaluations.

Dinesh Kumar, Sudesh K. Srivastav2026-07-01

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math

Discriminant-Guided Preprocessing for Local Solution Algorithms of Second-Order Euler Operators

Delayed Repression and Emergent Instability in Adaptive Multi-Agent Systems

The Generalized Fermat-Torricelli-Weber Problem

Threshold Dynamics of a Spatially Heterogeneous SVEIAR-B Reaction-Diffusion Model under Media Intervention *

Δ\DeltaΔ as a Dynamical Order Parameter for Non-Abelian Synchronization:\ the Case of SU(2)SU(2)SU(2)

Regularized Multiwavelet Collocation Methods for Ill-Posed Fredholm Integral Equations of the First Kind

A Variable-Step IMEX-BDF2 Finite Element Method for the Navier–Stokes Equations: Optimal L2L^2L2 Error Estimates for Velocity and Pressure

A Facultative Mutualism Model with Internal Competition for Interactions between University and Technical-Vocational Qualification Frameworks in Tanzania

A Block Hybrid Method for Third- and Fourth-Order Nonlinear Boundary Value Problems

A Randomized Bracketing Method for Derivative-Free Root Finding with Uniform Spacing Contraction

$\Delta$ as a Dynamical Order Parameter for Non-Abelian Synchronization:\ the Case of $SU(2)$

A Variable-Step IMEX-BDF2 Finite Element Method for the Navier–Stokes Equations: Optimal $L^2$ Error Estimates for Velocity and Pressure