Zhang Extrapolation (ZE) Relationship, Formulas and Simple Derivation as well as Predictive Application Based on VAH (Victory After Hardship) Years 1918 and 1945

As a hot topic of future measure and control (FMAC) and also an attempt, this paper focuses on the predictive application of the Zhang extrapolation (ZE) formulas, based on two significant VAH (victory after hardship, where victory may also mean great important peace) years: 1918 and 1945. It begins with a brief introduction to the concept of VAH years and the extrapolative relationships between them. Subsequently, the simple derivation of the ZE formulas and their theoretical validation using Taylor expansion are presented. Then, forward and backward Zhang extrapolations are performed on the basis of the critical VAH years 1918 and 1945, illustrating the reliability and accuracy of the ZE formulas in analyzing historic VAH events. Finally, the ZE formulas are used to predict four potential future VAH years: 2026, 2053, 2080, and 2107, offering theoretical support for analyzing future development trends.