Nekludoff, Alexey A.: Mode-Dependent Differentials and Stability of Limits in Partial Differential Equations

This paper proposes a structural reinterpretation of limits, derivatives, and partial differential equations based on the notion of convergence modes. In classical analysis, limits are defined through asymptotic conditions (e.g., ε–δ formulations), which characterize correctness but do not specify the operational structure by which convergence is realized. In practice, however—whether in numerical computation, physical measurement, or multiscale modeling—limits are always approached through conc