Analytical Characterization of Single Wall Carbon Nanotubes

Captain Robert F. Scott

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[math] \begin{equation} x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } } +1sin (x) + \lim_{x \to \infty} \exp(-x) = 0 \frac{n!}{k!(n-k)!} = \binom{n}{k} \end{equation} [/math]

[math] \begin{equation} \left(\! \begin{array}{c} n \\ r \end{array} \!\right) = \frac{n!}{r!(n-r)!} k_{n+1} = n^2 + k_n^{(n-2\gamma)\sum_{i=1}^{10} t_i\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x - k_{n-1}} \end{equation} [/math]

[math] \begin{equation} A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} \end{equation} [/math]

[math]E = \frac{k_\text{ET}}{k_f+k_\text{ET}+\sum{k_i}},[/math]

[math]E=\frac{1}{1+(r/R_0)^6}[/math]

with [math]R_0[/math] being the Förster distance of this pair of donor and acceptor, i.e. the distance at which the energy transfer efficiency is 50%.