Firstly by applying the Maximum Principle developed in this paper, the necessary and sufficient solvability condition of the finite horizon mean-field optimal control problem is presented in an explicit expression form (in analytical form) for the first time, which is completely different from the operator-type conditions obtained in previous works.
Her deliberation and analytical approach in the first-movement development section and in the second movement appeared to be focused less on Beethoven than on the isolated beauty of a particularly lovely turn of phrase or an exquisite pianissimo.
If the termination criteria are met, the solution suggested by the hybrid approach is accepted; otherwise, the results are used to revise the problem to be resolved by the analytical model in the third iteration, and so on.
The first and possibly most essential step towards validating differentiating metabolites is therefore reanalysis of a subset of the samples by using a different method targeted specifically towards the differentiating metabolites, to confirm the initial findings and reduce the possibility of analytical bias of the first method in the discovery phase.
These results are used to validate the computational model and to confirm predicted trends from an analytical model presented in the first of this two-paper series.
This velocity v max agrees quite well with the analytical result obtained in the first order of the 1 / Z expansion, see the previous section.
The analytical framework developed in the first step will be used to analyse the data, and will be further specified in an iterative manner, in order to integrate new explanatory elements categories.
The analytical framework applied in the first strand of SVQ (and developed further in a related study of nuclear risks commissioned by the Health and Safety Executive [ 28]) suggests that there might be a case for higher values to be assigned to QALYs delivered to those categories of patient.
Jones, insisting that law was a science, treated his subject matter in an analytical (emphasizing the first principles of natural reason), historical (comparative law) and synthetic fashion.
The determination of the parameters required to set up the analytical model is discussed in the first part of the paper.
Policy workshops provide students with an opportunity to use the analytical skills they have acquired in the first year in the program to analyze complex and challenging policy issues, usually for real clients.
