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In many practical problems such as engineering design problems, criteria functions cannot be given explicitly in terms of design variables.
Under this circumstance, values of criteria functions for given values of design variables are usually obtained by some analyses such as structural analysis, thermodynamical analysis or fluid mechanical analysis.
The analysis is focused on the formulation and application of the so-called Caratheodory−Boltyanskii criteria (functions B x, t, u) and An xn, tn, un, θn)), transformed by the authors to the canonical equations and other forms of the necessary and locally sufficient optimality conditions.
Comparison of S with general classes of resolution-based quality criteria functions (Rs, Rp, and Rmin) shows superior features such as correct assessment of favorable separation conditions, preservation of peak pair contributions, elimination of arbitrary cut-off values, and a unique capability to interpret absolute significance of function values through a simple inequality.
In addition, taking predictive variables in snow deposition/erosion model as evaluation criteria, functions of initial snow cover positions versus fence parameters are established.
When there are exactly three decision makers arranged in hierarchical order trying to optimize their own criteria functions, the resulting problem is called a tri-level programming problem.
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By designing the objective function and determining the constraints, the optimization problem of minimizing the evaluation criteria function is solved.
HPLC optimization strategy consists of four elements; experimental design, retention modeling, quality criteria function, and optimum search method.
Data for the model were selected according to a criteria function defined as the ideal process condition.
These parameters can be expressed exactly by using of multi criteria function, while N x) is variable in the height of each segment.
The PHB far exceeded the Resource Conservation and Recovery Act criteria, functioned in Hanford's semiarid climate, limited drainage to well below the 0.5 mm yr−1 performance criterion, limited runoff, and minimized erosion and bio-intrusion.
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