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Multi-Objective Mixed-Integer Linear Programming for Optimal Security Resource Allocation: Evidence from Nigeria's Multidimensional Security Crisis

This study addresses Nigeria's escalating security crisis by formulating a Multi-Objective Mixed-Integer Linear Programming model to optimize resource allocation across six geopolitical zones, demonstrating through theoretical proofs and Monte Carlo validation that a balanced strategic approach can reduce conflict intensity by 95.9% compared to the business-as-usual baseline while maximizing recovery.

Sani Rabiu2026-10-14

🔢 mathematics

Residual-Corrected Adaptive Chebyshev Operational-Matrix Method Nonlinear Differential Equations, via numerical inverse Laplace transformation

This paper presents an adaptive, residual-corrected Chebyshev operational-matrix method that leverages numerical inverse Laplace transformation to solve nonlinear ordinary differential equations with spectral accuracy and automatic stopping criteria based on residual tolerance.

Jumah Aswad Zarnan, Wafaa Mustafa Hameed2026-10-14

🔢 mathematics

Adaptive Dealiasing and Corrected Contour Integration for Exponential Time-Differencing Spectral Methods

This paper identifies and corrects a coefficient bias in the common half-contour shortcut for ETDRK4 methods that degrades temporal accuracy, while also demonstrating that although adaptive exponential filtering improves upon hard spectral truncation, classical exact dealiasing strategies remain superior for known polynomial degrees.

Adnan Daraghmeh, Arvind Kumar Prajapati, Alvaro H. Salas2026-10-13

🔢 mathematics

Exact pulse modulation and perturbation response in time-dependent two-mode KdV equations

This paper establishes the necessary and sufficient conditions for localized pulses in time-dependent two-mode Korteweg–de Vries equations to exhibit variable amplitude or speed while maintaining a constant spatial scale, providing a classification of such solutions, their transformational equivalence to autonomous systems, and exact benchmarks for their perturbation responses.

Imad Jaradat2026-10-13

🔢 mathematics

Open-Loop Nash Limits for Caputo Differential Games: Preceding-Node L1 Discretization

This paper establishes that open-loop Nash equilibria for finite-horizon Caputo fractional differential games can be rigorously recovered as the weak-* and uniform limits of discrete Nash profiles generated by preceding-node L1 time stepping, thereby validating the convergence of numerical approximations to the continuous hereditary game.

George Lymperis, Lambros B. Drossos2026-10-13

🔢 mathematics

Robust Generalized Nash Equilibria under Uncertain Shared Constraints: A Variational Approach to Decentralized Resource Allocation

This paper proposes a robust variational framework for decentralized resource allocation under uncertain shared constraints, utilizing a budgeted polyhedral uncertainty set and linear-programming duality to derive a unique, convex equilibrium that guarantees feasibility against disturbances while quantifying the trade-off between resource utilization and protection conservatism.

SOUMAYA ET-TRYKY, Khalid El Hajioui2026-10-13✓ Author reviewed ⓘ

🔢 mathematics

A compensated coupling bound for the average sensitivity of polynomial threshold functions

This paper establishes a new, uniform upper bound on the average sensitivity of polynomial threshold functions of degree $d$ on the $n$ -dimensional Boolean cube by refining the weighted Fourier-grading argument to eliminate a degree-squared loss, yielding a bound of approximately $3.19 d \sqrt{n}$ that is asymptotically sharp for the underlying coupling relaxation.

Prathmesh Lagdive, Vaibhav Aglave, Suraj Damre2026-10-13

🔢 mathematics

Dynamic behavior of a two-dimensional discrete-time HIV infection model: stability and bifurcation analysis

This study analyzes the dynamical behavior of a two-dimensional discrete-time HIV infection model derived via forward Euler discretization, establishing stability conditions for its fixed points and demonstrating through analytical and numerical methods that varying infection rates can trigger flip and Neimark-Sacker bifurcations leading to complex periodic, quasiperiodic, and chaotic oscillations.

Sarah Ramadan, Sanaa Salman, Ahmed EL-Sayed2026-10-12

🔢 mathematics

A Structure-Preserving LOBPCG Method for Computing Several of the Largest Generalized Singular Triplets

This paper proposes a structure-preserving LOBPCG method that leverages the Hermitian-definite Jordan--Wielandt pencil and an adapted IHL trick to efficiently compute the largest generalized singular triplets without explicitly forming normal-equation matrices, thereby offering significant computational advantages over unstructured and Gram-matrix-based approaches.

Xinyu Shan2026-10-12

🔢 mathematics

Effect of edge-stretching on Steklov eigenvalues and sharp Steklov eigenvalue bounds on leaf--boundary trees

This paper investigates the effect of edge-stretching on Steklov eigenvalues of leaf-boundary trees, proving that these eigenvalues decrease monotonically under the operation to establish an optimal upper bound of $\lambda_2 \le D/\ell$ (improving upon previous results), while also providing explicit spectral formulas for level-regular trees and a general bound for higher eigenvalues.

Jiangdong Ai, Yizhe Ji, Xiaopan Lian, Kun Yang2026-10-12

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