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Proposition 4 Cyclic shifting transformation.
Thirdly, by mth shifting transformation of four-dimensional linear systems, multi-wing hyperchaotic attractors are realized.
This shifting transformation is called translation.
In fact, according to shifting transformation of SSR repeat pattern, the "AGC" repeat unit could be theoretically considered as the same pattern of "CAG" for efficient identification.
(i) Shift transformation matrix: (12).
In the "scaling" and "shift" transformation, we multiplied the read counts of selected transcripts by varied quantities (with variations as one fifth of the multiplied values) after applying the "shift" transformation (Additional file 3).
In the "shift" transformation, we added varied quantities (with variations as one fifth of the added values) of read counts into the selected transcripts in either group.
These "shift" transformations permit conservative, skew-symmetric convective operators and symmetric, positive-definite diffusive operators to be obtained for staggered variables using collocated operators.
Shift transformations are not limited to uniform or structured meshes, and this formulation leads to a generalization of the works of Perot (J. Comput. Phys. 159 (2000) 58) and Verstappen and Veldman (J. Comput. Phys. 187 (2003) 343).
In an instrumental prelude at the top of Act II, the electronic sea undergoes a series of dazzling (and dizzying) shape-shifting transformations, at one point appearing to morph into a giant wall of water.
These peripheral, non-scientific concerns are not addressed at length in this manuscript; however they do exist, and their impact to the paradigm shifting healthcare transformation towards individualized medicine will be critical for its success.
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