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There is no "head" position on a sphere.
In effect the loudspeaker could be placed at virtually every spatial position on a sphere of 90 cm diameter from the centre of the owl's head.
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In the first instance, the branching problem of the manipulator was considered and its solution was used to locate positions on a sphere that can be attained by the end effector.
Nodes in Geodemlia are positioned on a sphere inspired by the shape of the earth.
In the absence of measurement errors, i.e., d ̂ i = d ( x, a i ), it is clear that the geometric locus of the target node position lies on a sphere with the radius d x,a i ) and center a i.
However, we do not state it over a uniform distribution (which would make it a null model description), as the knowledge of correspondence of T ¯ j k + 1 with S i k + 1 gives clues about its position on the sphere (provided the assigned correspondence is a 'good' one).
By simple geometric calculations, we can compute the 3D position on the sphere via the reversed projection by the following method.
The angles θ and φ are introduced in the standard form: e x = sinθcosφ, e y = sinθsinφ, and e z = cosθ, where e a is an a-component of the unit vector Because the envelope functions and Coulomb matrix elements are directly proportional to e a and n a, respectively, the angle dependence of should be sensitive to the donor position on the sphere.
In the current prototype there are 80 such elements positioned around a sphere.
On the other hand, the Moon is relatively near, and so its projected position on the celestial sphere is different for various places of observation on Earth.
Right ascension is measured along the celestial equator from the vernal equinox (i.e., the position on the celestial sphere where the Sun crosses the celestial equator from south to north on the first day of spring).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com