276 papers
This paper claims to utilize the 52 known even perfect numbers to establish a structural regularity governed by a characteristic quadratic mapping and a predictive formulation based on the baseline 12k + 7, aiming to model the macroscopic spacing of perfect numbers and estimate higher-order candidates while transcending traditional computational limits.
This paper presents a compartmental mathematical model for cyber-attack propagation on computer networks, proving its stability and conducting sensitivity and bifurcation analyses to demonstrate that transmission rates are the dominant factor in malware spread while robust recovery and control mechanisms can effectively mitigate infections.
This paper proposes and analyzes a residual-certified implicit product-integration method for nonlinear Caputo–Volterra equations that ensures discrete existence and uniqueness under a computable diagonal condition, provides a posteriori error bounds separating iteration and discretization errors, and achieves second-order convergence on graded meshes for solutions with initial singularities.
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.
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.
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.
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.
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.
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.
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.