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To ensure the smooth transition from historical data

LaTeX Math Inline
body[(t_1,q_1)... (t_N, q_N)]
 to the production forecasts in future time moments
LaTeX Math Inline
body--uriencoded--[(t_%7BN+1%7D,q_%7BN+1%7D), ...]
one may wish to math production at the last historical moment
LaTeX Math Inline
body(t_N, q_N)
 which leads to the following form of Arp's model:

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