Newman (1928) pointed out that there is always a structure of arbitrarily "constructed" relations with any given structure if only the number of basic entities, in this case sense data, is large enough.
Because no elaborate excitation equipment is used, the dynamics of the machine tool structure with arbitrarily feed rate or working position can be easily identified using the proposed active excitation modal analysis method.
The fit between the other three experimental diffraction patterns and the proposed structures is summarized in Figure 2. In cases where a particular experimental pattern could not be matched by a candidate structure, an arbitrarily large error has been included.
The catalytic structure was arbitrarily defined as the one having two hairpin-loops connected by one multi-loop, where the size of loops is allowed to vary (in Shapiro's notation [ 14], it is written as ((((H S)((H S M S), where H is hairpin-loop, and S is stem, and M is multi-loop).
Multiple biclustering structures have been proposed [ 1], with some approaches constraining them to exhaustive, exclusive, non-overlapping structures, and others allowing more flexible structures with arbitrarily positioned overlapping biclusters [ 7].
Presented here are three kinematic representations of large rotations for accurate modeling of highly flexible beam-like structures undergoing arbitrarily large three-dimensional elastic deformation and/or rigid-body motion.
Moreover, crystallography can solve structures of arbitrarily large molecules, whereas solution-state NMR is restricted to relatively small ones (less than 70 kDa).
Our approach reduced the chance of overlooking structures outside arbitrarily predefined ROIs [ 7] and identified the critical areas with 1 mm resolution.
In addition, we present an approach to compare models against multiple reference structures simultaneously without arbitrarily selecting one reference structure for the target, or removing parts that show variability.
While this approach is appropriate for assessment of the average seismic risk to a large population of structures, seismic upgrading of arbitrarily selected structures for risk reduction should not be based on the average structure risk because the physical configuration details differ among individual structures having the same classification.
