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The total energy of a water molecule inside a carbon nanotube can be determined analytically using point point interactions and the continuous approximation.
These models consist of a system of mass balances for macroscopic species involved in a reaction scheme, which can be determined analytically using a systematic procedure described in Hulhoven, Vande Wouwer, and Bogaerts (2005).
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Temperature profile has previously been determined analytically using the boundary layer and lubrication theory techniques.
The fundamental and the first-order compensatory excitation components are determined analytically using the inverse hFRFs.
A quadratic functional is defined, sensitivity coefficients are determined analytically using a superposition principle, and the Levenberg-Marquardt algorithm is used to solve the inverse problem.
It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques.
The first factor can be determined analytically, as shown in Methods; we refer to it as an analytical prefactor.
Using this model, the transition matrix of the Markov chain associated to the bitstream of the Philips hash can be determined analytically as follows.
Therefore, (h(t)) can be determined analytically.
which implies that f ( t ) can be determined analytically.
Alternatively, it can be determined analytically by applying the following relation.
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