$$\begin{eqnarray*} \alpha & = & v_{s}\epsilon \\ K & = & K_{c}+K_{s}\\ r & = & ... ...eft(n\pi \alpha \right)^{2}}\left(\frac{v_{s}}{v_{c}}\right)^{2} \end{eqnarray*}$$

stationary string

$$\begin{eqnarray*} M_{xx}(\omega ) & = & AD_{\xi }\epsilon ^{2}\left[\frac{1}{\le... ...\left(\epsilon \left(\omega +i\delta \right)\right)^{K-2}\right] \end{eqnarray*}$$

$$\begin{eqnarray*} A & = & \frac{1}{L_{y}}\left(\frac{2ev_{F}}{\pi ^{2}\alpha }\right)^{2}\left(\frac{v_{s}}{v_{c}}\right)^{K_{c}} \end{eqnarray*}$$

rigid string

for $\omega \ll \omega _{0}$

$$\begin{eqnarray*} M_{xx}(\omega ) & = & AD_{\xi }\epsilon ^{2}\left[\frac{1}{\le... ... +i\delta \right)\right)^{2}}{\left(1+K\right)K}\right]\right\} \end{eqnarray*}$$

for $\omega \gg \omega _{0}$

$$\begin{eqnarray*} M_{xx}(\omega ) & = & \frac{AD_{\xi }\epsilon ^{2}}{\sqrt{\eps... ...(K+\frac{5}{2}\right)\left(K+\frac{3}{2}\right)}\right]\right\} \end{eqnarray*}$$

$$\begin{eqnarray*} A & = & \frac{1}{L_{y}}\left(\frac{2ev_{F}}{\pi ^{2}\alpha }\r... ...ht)^{K_{c}}\left(\frac{m\omega _{0}}{2\pi }\right)^{\frac{3}{2}} \end{eqnarray*}$$

gaussian string

$$\begin{eqnarray*} M_{xx}(\omega ) & = & \epsilon ^{2}\int \frac{dk}{2\pi }D_{\xi... ...}+1\right)\left(K+\frac{k^{2}\lambda ^{2}}{2\pi }\right)}\right] \end{eqnarray*}$$

$$\begin{eqnarray*} A & = & \frac{1}{L_{y}}\left(\frac{2ev_{F}}{\pi ^{2}\alpha }\r... ...ight)^{K_{c}}\left(1-\frac{\lambda ^{2}}{\pi \alpha ^{2}}\right) \end{eqnarray*}$$

if we insert $D(k)=D_{0}exp(2l-K_{c}l-\lambda ^{2}k^{2}l/2\pi )$ we have

$$\begin{eqnarray*} M_{xx}(\omega ) & = & E+\epsilon ^{2}D_{\xi 0}e^{\left(2-K_{c}... ...ga +i\delta \right)\right)^{2}}{K\left(K+1\right)}\right)\right] \end{eqnarray*}$$

floppy string $n=2$

$$\begin{eqnarray*} M_{xx}(\omega ) & = & D_{\xi }\epsilon ^{2}\left[\frac{A_{2}}{... ...ft(K+\frac{3}{4}\right)\left(K+\frac{7}{4}\right)}\right)\right] \end{eqnarray*}$$

$$\begin{eqnarray*} A_{2} & = & \frac{1}{\lambda L_{y}}\left(\frac{2ev_{F}}{\pi ^{... ...c{1}{2\sqrt{\pi s}}\frac{\lambda }{\alpha }\right)^{\frac{3}{2}} \end{eqnarray*}$$

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The translation was initiated by Uri London on 2005-03-06