Correction to “Fundamentals and Applications of Dual‐Frequency Magnetic Particle Spectroscopy: Review for Biomedicine and Materials Characterization”

https://doi.org/10.1002/advs.202416838 In the sentence directly following Equation (12), the effective field, Heff, is defined subsequently in Equation (14), [not (13)]. In the paragraph directly following Equation (16), the Langevin function shall be referenced, cf. Equation (6) [not (5)]. Equation (21) shall be reading the 3rd derivative to ξ, i.e.: d 3 L ( ξ ) d ξ 3 = 6 ξ 4 − 4 coth 2 ξ sinh 2 ξ − 2 sinh 4 ξ → ξ → 0 … $\frac{{{d^3}\mathcal{L}( \xi )}}{{d{\xi ^3}}} = \frac{6}{{{\xi ^4}}} - \frac{{4{{\coth }^2}\xi }}{{{{\sinh }^2}\xi }} - \frac{2}{{{{\sinh }^4}\xi }}\mathop \to \limits^{\xi \to 0} \ldots $ Equation (23) shall be reading the 5th derivative to ξ, i.e.: d 5 L ( ξ ) d ξ 5 = 120 ξ 6 − 16 coth 4 ξ sinh 2 ξ − 88 coth 2 ξ sinh 4 ξ − 16 sinh 6 ξ → ξ → 0 … $\frac{{{d^5}\mathcal{L}( \xi )}}{{d{\xi ^5}}} = \frac{{120}}{{{\xi ^6}}} - \frac{{16{{\coth }^4}\xi }}{{{{\sinh }^2}\xi }} - \frac{{88{{\coth }^2}\xi }}{{\;{{\sinh }^4}\xi }} - \frac{{16}}{{{{\sinh }^6}\xi }}\mathop \to \limits^{\xi \to 0} \ldots $ Equations (31), (32), and (33) shall all be reading only a scalar product after square brackets: m f 1 + 2 f 2 = m p · 2 n ∑ i = 0 n − 1 L [ m p k B T ( B 0 + B 1 sin ( 2 π f 1 t i ) + B 2 sin ( 2 π f 2 t i ) ) ] · sin ( 2 π ( f 1 + 2 f 2 ) t i ) ${m_{{f_1} + 2{f_2}}} = {m_p} \cdot \frac{2}{n}\sum_{i = 0}^{n - 1} \mathcal{L}[ {\frac{{{m_p}}}{{{k_B}T}}( {{B_0} + {B_1}\sin ( {2\pi {f_1}{t_i}} ) + {B_2}\sin ( {2\pi {f_2}{t_i}} )} )} ] \cdot \sin ( {2\pi ( {{f_1} + 2{f_2}} ){t_i}} )$ (31) m f 1 + 3 f 2 = m p · 2 n ∑ i = 0 n − 1 L [ m p k B T ( B 0 + B 1 sin ( 2 π f 1 t i ) + B 2 sin ( 2 π f 2 t i ) ) ] · cos ( 2 π ( f 1 + 3 f 2 ) t i ) ${m_{{f_1} + 3{f_2}}} = {m_p} \cdot \frac{2}{n}\sum_{i = 0}^{n - 1} \mathcal{L}[ {\frac{{{m_p}}}{{{k_B}T}}( {{B_0} + {B_1}\sin ( {2\pi {f_1}{t_i}} ) + {B_2}\sin ( {2\pi {f_2}{t_i}} )} )} ] \cdot \cos ( {2\pi ( {{f_1} + 3{f_2}} ){t_i}} )$ (32) m f 1 + 4 f 2 = m p · 2 n ∑ i = 0 n − 1 L [ m p k B T ( B 0 + B 1 sin ( 2 π f 1 t i ) + B 2 sin ( 2 π f 2 t i ) ) ] · sin ( 2 π ( f 1 + 4 f 2 ) t i ) ${m_{{f_1} + 4{f_2}}} = {m_p} \cdot \frac{2}{n}\sum_{i = 0}^{n - 1} \mathcal{L}[ {\frac{{{m_p}}}{{{k_B}T}}( {{B_0} + {B_1}\sin ( {2\pi {f_1}{t_i}} ) + {B_2}\sin ( {2\pi {f_2}{t_i}} )} )} ] \cdot \sin ( {2\pi ( {{f_1} + 4{f_2}} ){t_i}} )$ (33) In the paragraph following equations (31), (32), and (33), the switching from even to uneven functions can be seen from Equations (24)—(27) [not (28)–(23)].