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In this work a new projection basis for the substructure method is presented.
The initial full eigenvalue problem is so replaced by a reduced one considering an efficient projection basis.
POD is then implemented to extract, from the sequence of subspaces, a projection basis that describes the state dependent variance of the Krylov subspaces.
Traces of slip planes and cracks formed at hardness impressions in (210) and (001) cleavage surfaces were analyzed on a stereographic projection basis.
To achieve this goal, we present an approach for determining a projection basis that uses a goal-oriented, model-constrained optimization framework.
The modal truncation augmentation method (MTAM) is also presented to handle the modal truncation problem by making the equilibrium equations into a subspace equation spanned in terms of the columns of a projection basis given in the GMAM.
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For the high and low energy X-ray spectra S H (E) and S L (E), the measured projections g H and g L are [ 4] (2) g H ln I H I 0 = ln ∫ 0 E m H S H E exp − B 1 μ 1 E − B 2 μ 2 E d E, g L ln I L I 0 = ln ∫ 0 E m L S L E exp − B 1 μ 1 E − B 2 μ 2 E d E, where B i is the projection of basis material coefficient b i and is represented by (3) B i = ∫ l b i x, y d l, i = 1,2.
Most musical QBE searches do an encoding of the song signal using some compression algorithm, such as Mel Frequency Cepstral Coefficients (MFCCs) or projections onto basis functions, which is the MPEG-7 standard.
When the basis projection images have been acquired, the CBCT unit reconstructs the primary projection frames to provide standard viewing displays of coronal, sagittal and axial images similar to the MSCT data display (Fig. 2) [22].
In the same manner as Fourier transform can be defined as being a projection on the basis of complex exponentials, the wavelet transform is introduced as projection of the signal on the basis of scaled and time-shifted versions of the original wavelet (so-called mother wavelet) in order to study its local characteristics [25].
At certain degree intervals, single projection images or "basis" images, are acquired.
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