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The spatially periodic orbits on a homoclinic manifold of a torus of spatially independent plane waves were constructed by evaluating the auto-Bäklund transformation.
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Indentations at the corners will allow the expression of the walls as independent planes.
Ilie Nastase took the court against Guillermo Vilas in a 1977 match with a so-called "spaghetti string" racket made of nonintersecting strings on independent planes.
But an MOD spokesperson told The Independent the plane had been on a routine flight and was part of a "longstanding agreement".
The alignment between the two symmetric shapes (face and neurocranium) used their independent midsagittal plane and a reference shape (KNM-ER 406) to highly reduce their degrees of freedom.
These independent slip planes belong to the {111} crystal planes family.
There are eight triangle planes, in which the four upper planes diagonally parallel the four lower, and form four independent slip planes shown in Fig. 2a.
We see that independent in-plane texturing has little effect on the piezoelectric displacement tensor.
For implicitization, we prove that there exist two linearly independent moving planes with total degree one in the parametric variables.
The upper calvariofacial fragment was separated from the lower facial fragment and re-aligned using superposition of their independent midsagittal planes in a range of feasible positions.
To compare the effects of field (or any other particles) the control and the experimental matrices were dumped into two independent colour planes.
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