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In the non-isotropic case, the U and V matrices are determined from the SVD as follows: (16) and in the isotropic case, from (17) For the non-isotropic case (18) and for the isotropic case (19) The mean structure is estimated as the arithmetic average of the optimally translated and rotated structures (20) (21) Both of these solutions are independent of the covariance matrix.
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Based on PVGIS program, the results of calculation of the yearly average values of the optimal panel inclination, solar irradiation on the horizontal, vertical and optimally inclined plane, ratio of diffuse to global solar irradiation, linke turbidity, average daytime temperature and 24 h average of temperature for 13 cities in the Republic of Srpska are given.
In order to assess the suboptimality caused by codebook transformation, one would like to compare the system performance in terms of the average distortion of quantizers using transformed codebooks with that of the optimally designed codebooks.
The response of the optimally controlled quasi-Hamiltonian system is predicted by solving the averaged Fokker Planck Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimate errors of system states.
Finally, the stationary probability density of the amplitude and mean amplitude of the optimally controlled systems are obtained from solving the reduced Fokker Planck Kolmogorov equation associated with fully completed averaged Itô equations.
Third, the asymptotic Lyapunov stability with probability one of the optimally controlled system with worst disturbances is analyzed by evaluating the maximal Lyapunov exponent of the fully averaged Itô equations.
Thus, the four fibre orientations and laminae thicknesses are to be determined optimally by defining a design index comprising a weighted average of the objective functions and determining the minimum.
Then the average behaviour of an optimally controlled system is calculated and compared to that of an optimal passive system.
This can help 'save' the batch (give a product having the desired values of the average molecular weights) optimally, in as short a reaction time as possible.
From these paired trajectories we estimated the rotation, translation and time shift that optimally align the average trajectory of the protein of interest to the average trajectory of Abp1.
We consider the flow rate assignment problem on a wireless link with randomly varying channel gain, to optimally trade off average transmit power and the average utility of the smoothed flow data rate.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com