Computationally speaking, this diminishing may be realized by removing two rings of vertices from the 600-cell, each ring having 10 vertices, and each lying in mutually orthogonal planes, and taking the convex hull of the remaining vertices.
32.
In fact,, ? 1 and ? 8 are three mutually orthogonal linear combinations of the quark pairs, and; they are at the centre of the pseudo-scalar nonet of mesons with all the main quantum numbers equal to zero.
33.
The latin squares produced in this way from an orthogonal array will be orthogonal latin squares, so the " k " " 2 columns other than the indexing columns will produce a set of " k " " 2 mutually orthogonal latin squares.
34.
:: Under the circumstances, " A " can be always taken to be a symmetric matrix, in which case the spectral theorem can be applied : any such matrix is diagonalizable, with real eigenvalues, and mutually orthogonal eigenvectors . talk ) 19 : 47, 23 November 2008 ( UTC)
35.
He is notable for his breakthrough work along with R . C . Bose and S . S . Shrikhande in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4 " n " + 2 for every " n ".
36.
In both cases, the transverse directions are unaffected and the three planes meeting at each corner of the cuboids are " mutually orthogonal " ( in the sense of "'E "'1, 2 at right, and in the sense of "'E "'3 at left ).
37.
Due to the mutually orthogonal property, there is exactly one instance somewhere in the table for any pair of elements, such as ( white foreground, monospace ), or ( " fjords ", navy background ) etc ., and also all possible such pairs of values of distinct " dimensions " are represented exactly once each.
38.
We all know that given x, y, z etc that the square root of the sum of the squares ( x ^ 2 + y ^ 2 + z ^ 2 ) ^ 1 / 2 is a metric that equates to the distance between points 0, 0, 0 and x, y, z in a mutually orthogonal geometry.
39.
To illustrate, suppose we have a system of N bosons that occupy mutually orthogonal single-particle states | \ phi _ 1 \ rang, | \ phi _ 2 \ rang, | \ phi _ 3 \ rang, etc . Using the usual representation, we demonstrate the system by assigning a state to each particle and then imposing exchange symmetry.
40.
Here we utilized the cross-normalization condition l ^ an _ a = n ^ al _ a =-1 as well as the requirement that g _ { ab } + l _ an _ b + n _ al _ b should span the induced metric h _ { AB } for cross-sections of { v = constant, r = constant }, where dv and dr are not mutually orthogonal.
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