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In the field of crop research, the study of roots involves many challenges, particularly the lack of effective methods for identifying crop roots. To deal with this problem, this study proposes a solution strategy: in applying strontium to crop leaves, the roots of different crops are distinguished. In this study, we applied strontium ions to the leaves of hydroponically grown wheat, and these strontium ions were partially absorbed by the leaves and transported to the roots. Therefore, the strontium concentration of roots was significantly increased through the foliar application of strontium. After mixing the treated wheat with the untreated wheat root, the greater the biomass of the wheat root applied with strontium ions, the higher the strontium concentration in the mixed root. Based on this phenomenon, we can establish the relationship between wheat root biomass and strontium concentration in mixed roots through linear fitting. Furthermore, we can also use the relationship between root biomass and root length to establish the correlation between strontium concentration in mixed roots and the root length of wheat with strontium ions. After measuring the strontium concentration of the mixed roots to be distinguished, the root biomass and root length of wheat applied with strontium ions can be calculated according to the equation obtained through linear fitting. The accuracy of this method was verified through a comparison with the actual value and the existing root staining method. The results show that the coefficient of determination (R2) of the root biomass estimation equation obtained through linear fitting reached 0.83, which is statistically significant (p < 0.01). The Pearson correlation coefficient with the measured value was more than 0.9, showing a very high correlation and significance. The root length estimation equation derived from the relationship between the root biomass, strontium concentration and root length was compared with the real root length value and the root length value obtained using the staining method. The Pearson correlation coefficient also exceeded 0.8 and reached a statistically significant level (p < 0.01). This study confirms that strontium ions can be absorbed and transported to roots through wheat leaves and successfully developed a new method for predicting the length of wheat roots, providing an effective new tool for wheat root research. [ABSTRACT FROM AUTHOR]

In this paper, an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms is investigated in detail. The equation for the one-dimensional magnetic systems is integrable and admits exact solutions. It is more accurate than the nonlinear Schrödinger equation in describing wave propagation in the ocean and optical fibers. First, the modulation instability of solutions is analyzed in the presence of small perturbation. Second, breather and rogue wave solutions of this equation are constructed via the modified Darboux transformation method. The effects of the higher-order terms are investigated graphically. Specially, the interactions between two breathers are studied by adjusting the spectral parameters and the collisions between breather and rogue waves are also discussed. [ABSTRACT FROM AUTHOR]