mirror of
https://github.com/vale981/master-thesis
synced 2025-03-04 17:41:43 -05:00
168 lines
11 KiB
TeX
168 lines
11 KiB
TeX
\documentclass{article}
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\usepackage{amsmath}
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\begin{document}
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\[\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left({\left(B_{n} C_{n}
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G_{l} + B_{n} G_{l} \overline{W_{l}}\right)} e^{\left(W_{l} r + C_{n} t
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+ r \overline{W_{l}}\right)} - {\left(B_{n} C_{n} \overline{G_{l}} -
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B_{n} W_{l} \overline{G_{l}} + {\left(B_{n} C_{n} G_{l} - B_{n} C_{n}
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\overline{G_{l}} + B_{n} W_{l} \overline{G_{l}} + B_{n} G_{l}
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\overline{W_{l}}\right)} e^{\left(C_{n} r + r
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\overline{W_{l}}\right)}\right)} e^{\left(W_{l} t\right)}\right)}
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e^{\left(-C_{n} t - W_{l} t - r \overline{W_{l}}\right)}}{C_{n}^{2} -
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C_{n} W_{l} + {\left(C_{n} - W_{l}\right)} \overline{W_{l}}}\]
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\[\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{B_{m} B_{n} C_{m}^{2}
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C_{n}^{2} G_{l} L_{k}^{2} P_{k} e^{\left(-C_{m} t - C_{n} t\right)} +
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B_{m} B_{n} C_{m} C_{n}^{3} G_{l} L_{k}^{2} P_{k} e^{\left(-C_{m} t -
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C_{n} t\right)} + B_{m} B_{n} C_{m}^{2} C_{n} G_{l} L_{k}^{3} P_{k}
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e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n} C_{m} C_{n}^{2} G_{l}
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L_{k}^{3} P_{k} e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} L_{k}^{2} P_{k} W_{l} e^{\left(-C_{m} t - C_{n}
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t\right)} + B_{m} B_{n} C_{n}^{3} G_{l} L_{k}^{2} P_{k} W_{l}
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e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n} C_{m}^{2} G_{l}
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L_{k}^{3} P_{k} W_{l} e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n}
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C_{n}^{2} G_{l} L_{k}^{3} P_{k} W_{l} e^{\left(-C_{m} t - C_{n}
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t\right)} - B_{m} B_{n} C_{m}^{2} C_{n}^{2} G_{l} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n} C_{m} C_{n}^{3} G_{l}
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P_{k} W_{l}^{2} e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} L_{k} P_{k} W_{l}^{2} e^{\left(-C_{m} t - C_{n}
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t\right)} - B_{m} B_{n} C_{m} C_{n}^{2} G_{l} L_{k} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n} C_{m} C_{n} G_{l}
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L_{k}^{2} P_{k} W_{l}^{2} e^{\left(-C_{m} t - C_{n} t\right)} - B_{m}
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B_{n} C_{n}^{2} G_{l} L_{k}^{2} P_{k} W_{l}^{2} e^{\left(-C_{m} t -
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C_{n} t\right)} - B_{m} B_{n} C_{m} G_{l} L_{k}^{3} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n} C_{n} G_{l} L_{k}^{3}
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P_{k} W_{l}^{2} e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} P_{k} W_{l}^{3} e^{\left(-C_{m} t - C_{n}
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t\right)} - B_{m} B_{n} C_{n}^{3} G_{l} P_{k} W_{l}^{3} e^{\left(-C_{m}
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t - C_{n} t\right)} - B_{m} B_{n} C_{m}^{2} G_{l} L_{k} P_{k} W_{l}^{3}
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e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n} C_{n}^{2} G_{l} L_{k}
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P_{k} W_{l}^{3} e^{\left(-C_{m} t - C_{n} t\right)} - 2 \, B_{m} B_{n}
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C_{n} G_{l} L_{k}^{2} P_{k} W_{l}^{3} e^{\left(-C_{m} t - C_{n}
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t\right)} - 2 \, B_{m} B_{n} G_{l} L_{k}^{3} P_{k} W_{l}^{3}
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e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n} C_{m} C_{n} G_{l}
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P_{k} W_{l}^{4} e^{\left(-C_{m} t - C_{n} t\right)} + B_{m} B_{n}
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C_{n}^{2} G_{l} P_{k} W_{l}^{4} e^{\left(-C_{m} t - C_{n} t\right)} +
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B_{m} B_{n} C_{m} G_{l} L_{k} P_{k} W_{l}^{4} e^{\left(-C_{m} t - C_{n}
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t\right)} + B_{m} B_{n} C_{n} G_{l} L_{k} P_{k} W_{l}^{4}
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e^{\left(-C_{m} t - C_{n} t\right)} + 2 \, B_{m} B_{n} C_{n} G_{l} P_{k}
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W_{l}^{5} e^{\left(-C_{m} t - C_{n} t\right)} + 2 \, B_{m} B_{n} G_{l}
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L_{k} P_{k} W_{l}^{5} e^{\left(-C_{m} t - C_{n} t\right)} - B_{m} B_{n}
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C_{m}^{2} C_{n}^{2} G_{l} L_{k}^{2} P_{k} e^{\left(-C_{m} t - W_{l}
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t\right)} - B_{m} B_{n} C_{m} C_{n}^{3} G_{l} L_{k}^{2} P_{k}
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e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{m}^{2} C_{n} G_{l}
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L_{k}^{3} P_{k} e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{m}
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C_{n}^{2} G_{l} L_{k}^{3} P_{k} e^{\left(-C_{m} t - W_{l} t\right)} -
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B_{m} B_{n} C_{m}^{2} C_{n} G_{l} L_{k}^{2} P_{k} W_{l} e^{\left(-C_{m}
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t - W_{l} t\right)} + B_{m} B_{n} C_{n}^{3} G_{l} L_{k}^{2} P_{k} W_{l}
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e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{m}^{2} G_{l}
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L_{k}^{3} P_{k} W_{l} e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n}
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C_{n}^{2} G_{l} L_{k}^{3} P_{k} W_{l} e^{\left(-C_{m} t - W_{l}
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t\right)} + B_{m} B_{n} C_{m}^{2} C_{n}^{2} G_{l} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n} C_{m} C_{n}^{3} G_{l}
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P_{k} W_{l}^{2} e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} L_{k} P_{k} W_{l}^{2} e^{\left(-C_{m} t - W_{l}
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t\right)} + B_{m} B_{n} C_{m} C_{n}^{2} G_{l} L_{k} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n} C_{m} C_{n} G_{l}
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L_{k}^{2} P_{k} W_{l}^{2} e^{\left(-C_{m} t - W_{l} t\right)} + B_{m}
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B_{n} C_{n}^{2} G_{l} L_{k}^{2} P_{k} W_{l}^{2} e^{\left(-C_{m} t -
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W_{l} t\right)} + B_{m} B_{n} C_{m} G_{l} L_{k}^{3} P_{k} W_{l}^{2}
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e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n} C_{n} G_{l} L_{k}^{3}
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P_{k} W_{l}^{2} e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} P_{k} W_{l}^{3} e^{\left(-C_{m} t - W_{l}
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t\right)} - B_{m} B_{n} C_{n}^{3} G_{l} P_{k} W_{l}^{3} e^{\left(-C_{m}
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t - W_{l} t\right)} + B_{m} B_{n} C_{m}^{2} G_{l} L_{k} P_{k} W_{l}^{3}
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e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{n}^{2} G_{l} L_{k}
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P_{k} W_{l}^{3} e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{m}
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C_{n} G_{l} P_{k} W_{l}^{4} e^{\left(-C_{m} t - W_{l} t\right)} - B_{m}
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B_{n} C_{n}^{2} G_{l} P_{k} W_{l}^{4} e^{\left(-C_{m} t - W_{l}
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t\right)} - B_{m} B_{n} C_{m} G_{l} L_{k} P_{k} W_{l}^{4}
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e^{\left(-C_{m} t - W_{l} t\right)} - B_{m} B_{n} C_{n} G_{l} L_{k}
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P_{k} W_{l}^{4} e^{\left(-C_{m} t - W_{l} t\right)} + B_{m} B_{n}
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C_{m}^{3} C_{n}^{2} G_{l} L_{k} P_{k} e^{\left(-C_{n} t - W_{l}
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t\right)} + B_{m} B_{n} C_{m}^{2} C_{n}^{3} G_{l} L_{k} P_{k}
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e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{m}^{3} C_{n} G_{l}
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L_{k}^{2} P_{k} e^{\left(-C_{n} t - W_{l} t\right)} - B_{m} B_{n} C_{m}
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C_{n}^{3} G_{l} L_{k}^{2} P_{k} e^{\left(-C_{n} t - W_{l} t\right)} -
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B_{m} B_{n} C_{m}^{2} C_{n} G_{l} L_{k}^{3} P_{k} e^{\left(-C_{n} t -
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W_{l} t\right)} - B_{m} B_{n} C_{m} C_{n}^{2} G_{l} L_{k}^{3} P_{k}
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e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{m}^{3} C_{n}^{2}
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G_{l} P_{k} W_{l} e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n}
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C_{m}^{2} C_{n}^{3} G_{l} P_{k} W_{l} e^{\left(-C_{n} t - W_{l}
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t\right)} - B_{m} B_{n} C_{m}^{3} G_{l} L_{k}^{2} P_{k} W_{l}
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e^{\left(-C_{n} t - W_{l} t\right)} - B_{m} B_{n} C_{n}^{3} G_{l}
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L_{k}^{2} P_{k} W_{l} e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n}
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C_{m}^{2} G_{l} L_{k}^{3} P_{k} W_{l} e^{\left(-C_{n} t - W_{l}
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t\right)} - B_{m} B_{n} C_{n}^{2} G_{l} L_{k}^{3} P_{k} W_{l}
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e^{\left(-C_{n} t - W_{l} t\right)} - B_{m} B_{n} C_{m}^{3} C_{n} G_{l}
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P_{k} W_{l}^{2} e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{m}
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C_{n}^{3} G_{l} P_{k} W_{l}^{2} e^{\left(-C_{n} t - W_{l} t\right)} -
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B_{m} B_{n} C_{m}^{3} G_{l} L_{k} P_{k} W_{l}^{2} e^{\left(-C_{n} t -
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W_{l} t\right)} - B_{m} B_{n} C_{n}^{3} G_{l} L_{k} P_{k} W_{l}^{2}
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e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{m} G_{l} L_{k}^{3}
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P_{k} W_{l}^{2} e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{n}
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G_{l} L_{k}^{3} P_{k} W_{l}^{2} e^{\left(-C_{n} t - W_{l} t\right)} -
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B_{m} B_{n} C_{m}^{2} C_{n} G_{l} P_{k} W_{l}^{3} e^{\left(-C_{n} t -
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W_{l} t\right)} - B_{m} B_{n} C_{m} C_{n}^{2} G_{l} P_{k} W_{l}^{3}
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e^{\left(-C_{n} t - W_{l} t\right)} - B_{m} B_{n} C_{m}^{2} G_{l} L_{k}
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P_{k} W_{l}^{3} e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n}
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C_{n}^{2} G_{l} L_{k} P_{k} W_{l}^{3} e^{\left(-C_{n} t - W_{l}
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t\right)} + B_{m} B_{n} C_{m} G_{l} L_{k}^{2} P_{k} W_{l}^{3}
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e^{\left(-C_{n} t - W_{l} t\right)} + B_{m} B_{n} C_{n} G_{l} L_{k}^{2}
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P_{k} W_{l}^{3} e^{\left(-C_{n} t - W_{l} t\right)} - B_{m} B_{n}
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C_{m}^{3} C_{n}^{2} G_{l} L_{k} P_{k} - B_{m} B_{n} C_{m}^{2} C_{n}^{3}
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G_{l} L_{k} P_{k} - B_{m} B_{n} C_{m}^{3} C_{n} G_{l} L_{k}^{2} P_{k} +
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B_{m} B_{n} C_{m} C_{n}^{3} G_{l} L_{k}^{2} P_{k} + B_{m} B_{n}
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C_{m}^{2} C_{n} G_{l} L_{k}^{3} P_{k} + B_{m} B_{n} C_{m} C_{n}^{2}
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G_{l} L_{k}^{3} P_{k} + B_{m} B_{n} C_{m}^{3} C_{n}^{2} G_{l} P_{k}
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W_{l} + B_{m} B_{n} C_{m}^{2} C_{n}^{3} G_{l} P_{k} W_{l} + B_{m} B_{n}
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C_{m}^{3} G_{l} L_{k}^{2} P_{k} W_{l} - B_{m} B_{n} C_{n}^{3} G_{l}
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L_{k}^{2} P_{k} W_{l} - B_{m} B_{n} C_{m}^{2} G_{l} L_{k}^{3} P_{k}
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W_{l} - B_{m} B_{n} C_{n}^{2} G_{l} L_{k}^{3} P_{k} W_{l} + B_{m} B_{n}
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C_{m}^{3} C_{n} G_{l} P_{k} W_{l}^{2} - B_{m} B_{n} C_{m} C_{n}^{3}
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G_{l} P_{k} W_{l}^{2} + B_{m} B_{n} C_{m}^{3} G_{l} L_{k} P_{k}
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W_{l}^{2} + B_{m} B_{n} C_{n}^{3} G_{l} L_{k} P_{k} W_{l}^{2} - B_{m}
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B_{n} C_{m} G_{l} L_{k}^{3} P_{k} W_{l}^{2} - B_{m} B_{n} C_{n} G_{l}
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L_{k}^{3} P_{k} W_{l}^{2} - 2 \, B_{m} B_{n} C_{m}^{3} G_{l} P_{k}
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W_{l}^{3} - B_{m} B_{n} C_{m}^{2} C_{n} G_{l} P_{k} W_{l}^{3} - B_{m}
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B_{n} C_{m} C_{n}^{2} G_{l} P_{k} W_{l}^{3} + B_{m} B_{n} C_{m}^{2}
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G_{l} L_{k} P_{k} W_{l}^{3} + B_{m} B_{n} C_{n}^{2} G_{l} L_{k} P_{k}
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W_{l}^{3} - B_{m} B_{n} C_{m} G_{l} L_{k}^{2} P_{k} W_{l}^{3} + B_{m}
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B_{n} C_{n} G_{l} L_{k}^{2} P_{k} W_{l}^{3} + 2 \, B_{m} B_{n} G_{l}
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L_{k}^{3} P_{k} W_{l}^{3} + 2 \, B_{m} B_{n} C_{m} G_{l} P_{k}
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W_{l}^{5} - 2 \, B_{m} B_{n} G_{l} L_{k} P_{k} W_{l}^{5}}{C_{m}^{4}
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C_{n}^{3} L_{k}^{2} + C_{m}^{3} C_{n}^{4} L_{k}^{2} + C_{m}^{4}
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C_{n}^{2} L_{k}^{3} - C_{m}^{2} C_{n}^{4} L_{k}^{3} - C_{m}^{3}
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C_{n}^{2} L_{k}^{4} - C_{m}^{2} C_{n}^{3} L_{k}^{4} - C_{m}^{4}
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C_{n}^{3} W_{l}^{2} - C_{m}^{3} C_{n}^{4} W_{l}^{2} - C_{m}^{4}
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C_{n}^{2} L_{k} W_{l}^{2} + C_{m}^{2} C_{n}^{4} L_{k} W_{l}^{2} -
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C_{m}^{4} C_{n} L_{k}^{2} W_{l}^{2} - C_{m} C_{n}^{4} L_{k}^{2}
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W_{l}^{2} - C_{m}^{4} L_{k}^{3} W_{l}^{2} + C_{n}^{4} L_{k}^{3}
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W_{l}^{2} + C_{m}^{3} L_{k}^{4} W_{l}^{2} + C_{m}^{2} C_{n} L_{k}^{4}
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W_{l}^{2} + C_{m} C_{n}^{2} L_{k}^{4} W_{l}^{2} + C_{n}^{3} L_{k}^{4}
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W_{l}^{2} + C_{m}^{4} C_{n} W_{l}^{4} + C_{m}^{3} C_{n}^{2} W_{l}^{4} +
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C_{m}^{2} C_{n}^{3} W_{l}^{4} + C_{m} C_{n}^{4} W_{l}^{4} + C_{m}^{4}
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L_{k} W_{l}^{4} - C_{n}^{4} L_{k} W_{l}^{4} - C_{m}^{3} L_{k}^{2}
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W_{l}^{4} - C_{n}^{3} L_{k}^{2} W_{l}^{4} + C_{m}^{2} L_{k}^{3}
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W_{l}^{4} - C_{n}^{2} L_{k}^{3} W_{l}^{4} - C_{m} L_{k}^{4} W_{l}^{4} -
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C_{n} L_{k}^{4} W_{l}^{4} - C_{m}^{2} C_{n} W_{l}^{6} - C_{m} C_{n}^{2}
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W_{l}^{6} - C_{m}^{2} L_{k} W_{l}^{6} + C_{n}^{2} L_{k} W_{l}^{6} +
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C_{m} L_{k}^{2} W_{l}^{6} + C_{n} L_{k}^{2} W_{l}^{6}} + \frac{B_{m}
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B_{n} C_{n} G_{l} L_{k} P_{k} e^{\left(-C_{n} t - L_{k} t\right)} +
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B_{m} B_{n} G_{l} L_{k}^{2} P_{k} e^{\left(-C_{n} t - L_{k} t\right)} +
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B_{m} B_{n} C_{n} G_{l} P_{k} W_{l} e^{\left(-C_{n} t - L_{k}
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t\right)} - B_{m} B_{n} G_{l} L_{k} P_{k} W_{l} e^{\left(-C_{n} t -
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L_{k} t\right)} - 2 \, B_{m} B_{n} G_{l} P_{k} W_{l}^{2} e^{\left(-C_{n}
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t - L_{k} t\right)} - B_{m} B_{n} C_{n} G_{l} L_{k} P_{k}
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e^{\left(-L_{k} t - W_{l} t\right)} - B_{m} B_{n} G_{l} L_{k}^{2} P_{k}
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e^{\left(-L_{k} t - W_{l} t\right)} + B_{m} B_{n} C_{n} G_{l} P_{k}
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W_{l} e^{\left(-L_{k} t - W_{l} t\right)} + B_{m} B_{n} G_{l} L_{k}
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P_{k} W_{l} e^{\left(-L_{k} t - W_{l} t\right)}}{C_{m} C_{n}^{2}
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L_{k}^{2} + C_{m} C_{n} L_{k}^{3} - C_{n}^{2} L_{k}^{3} - C_{n}
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L_{k}^{4} - C_{m} C_{n} L_{k}^{2} W_{l} - C_{m} L_{k}^{3} W_{l} + C_{n}
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L_{k}^{3} W_{l} + L_{k}^{4} W_{l} - C_{m} C_{n}^{2} W_{l}^{2} - C_{m}
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C_{n} L_{k} W_{l}^{2} + C_{n}^{2} L_{k} W_{l}^{2} + C_{n} L_{k}^{2}
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W_{l}^{2} + C_{m} C_{n} W_{l}^{3} + C_{m} L_{k} W_{l}^{3} - C_{n} L_{k}
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W_{l}^{3} - L_{k}^{2} W_{l}^{3}}\]
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\end{document}
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