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The standard deviation coefficient of the normal distribution is 0.02 as for case 1 above.
(beta>0) represents the depletion rate coefficient of the normal population during to the environment pollutant concentration of patch 1.
The gas load and power load are assumed to obey the normal distribution, and two cases are designed to analyze the effect of random factors on the coupled system: case 1, where the standard deviation coefficient of the normal distribution is 0.02, and case 2, where the standard deviation coefficient of the normal distribution is 0.05.
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Analytical expressions for the coefficients of the normal form of the 6th order are derived.
Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format.
The coefficients of the normal distribution are calibrated according the features of the schooling years of a household's head in the empirical data.
The coefficients of the normal distribution are calibrated according the features of amount of land that a household manages in the empirical data.
Whereas Jordan's second quantization procedure applies to the coefficients of the normal modes of the field, Heisenberg & Pauli 1929 started with the fields themselves and subjected them to the canonical procedure.
Comparing the method developed here with other methods of computing the normal forms, it is understood that we may, respectively, obtain the normal forms, the coefficients of the normal forms and the associated near identity non-linear transformations for three resonant cases by using a same main Maple symbolic program.
In fact, for the case of q = 3 K + 1, if equation (22) or (23) or (24) or (32) holds, putting expression into the recursive formulas in Theorem 3.1, respectively, we can always obtain the first pairs of coefficients of the normal form for the saddle point are zero, for example p 1 = q 1 = p 2 = q 2 = ⋯ = p 20 = q 20 = 0, (42).
The estimated coefficients of the normal grey matter component are then used to calculate a reference region TAC as the weighted average of all voxels' contributions [ 25, 26].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com