# [Article] The Early Cham Language, And Its Relationship to by G. E. Marrison

By G. E. Marrison

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M P (x). (ε + m)! ε 50 M. ) for the Laplace spherical harmonic functions Yεm (θ, φ). A square integrable periodic function f on R (= a function on the torus T := R/Z) 2βinx (L 2 with the period 1 can be expressed as a Fourier series f (x) = ∞ n=0 an e convergence). Representation theoretically, this amounts to saying that L 2 (T ) is decomposed as the direct sum of the irreducible (1-dimensional) unitary representations R → x ∈∞ e2βinx ∈ U (1) (n ∈ Z) of R which is trivial on Z. In the same way, since these representations Uε exhaust all (equivalence classes) of irreducible unitary representations of S O(3) one obtains L 2 (S 2 ) = ∞ ε=0 ⊕ H˜ε (a direct sum).

Basis images are created from volume data and radians data in preprocess functions that measure the differences between edited images and rendered images. The minimization problem is solved by using the basis images and the resulting image is displayed in real-time. Once a satisfactory visual appearance has been obtained, the user can verify the appearances by viewing from different viewpoints.

4). In one dimension, the “volume” of the interval between one and two standard deviations is equal to the radius of the unit interval. In two dimensions the area of the annulus between one and two standard deviations is relatively larger than the area of the unit disc. In higher dimensions the trend continues, with the available volume overwhelmingly concentrated near the outside. Discussion∈ of the multivariate Gaussian is simplified by a “whitening” transformation ci ≈ ci / ξi from the original hyperellipsoidal density to an isotropic density.