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This inequality is optimal in the case of the spheres.
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In the case of the sphere, he discovered that if you repeated a geometric unit made up of specially proportioned struts and hubs the overall shape of the spherical structure would remain the same as it contracted and expanded.
In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic.
In the case of the sphere, (3.130) is satisfied.
In the case of the sphere, the calculations of (3.130) in detail are shown as follows: (C.1) (C.1).
In the case of the sphere in Fig. 8 that corresponds to letting the angular momentum ( ell rightarrow +infty ).
Approximate values and their graph by this finite element method are shown in the case of the sphere.
In the case of the sphere, all the (m_{gamma})s will be equal to 1 and we will describe the (mathcal{H}_{gamma}) in Sect.
(a) The concrete forms of Δ k x k, j, Δ k y k, j and Δ k z k, j in the case of the sphere. .
The concrete forms of Δ j x j, k, Δ j y j, k and Δ j z j, k in the case of the sphere.
(c) The concrete forms of Δ k x j, k, Δ k y j, k and Δ k z j, k in the case of the sphere. .
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