Starting with the general theory established in Kanatani (1984) of describing the directional distributions of orientations, mathematical formulations have been extended to address the directional distributions of vector-valued directional data, which is the most common data type being dealt with in micromechanical investigations.
Problem solving consisted of the five general stages: problem orientation, problem definition and formulation, generation of alternatives, decision making, and verification.
This primal linear programming model represents an output-oriented approach, while its dual formulation indicates an input orientation (for a given level of outputs, inputs are minimized).
We propose a new cut-based formulation based on orientation properties which is stronger than the undirected cut-based model.
Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult.
Thus, the CNS does not treat gravitational force simply as an external load, but rather as an orientation reference that biases the formulation of motor commands [6].
It may have a structural basis, whereby the gravitational field acts as an orientation reference that biases the formulation of motor commands.
We focus on the variable returns to scale production possibility set; our results do not depend on any particular DEA LP formulation, primal/dual form or orientation.
However, current algorithms adopt an over-simplified formulation which ignores the orientation of the bus pin, the chip performance may be deteriorated.
Then, the recently developed hyperspherical harmonic formulation for the description of orientation distributions is extended to represent grain boundary statistics.
The formulation accounts for variant morphologies, orientation relationships, and retained austenite that are uniquely inherent to lath martensitic microstructures.
