Diamond now operates as a homogeneous component of PwC's Advisory Services.
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Assume the symmetric polynomial to be homogeneous of degree; different homogeneous components can be decomposed separately.
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When using affine transformations, the homogeneous component of a coordinate vector ( normally called " w " ) will never be altered.
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After carrying out the matrix multiplication, the homogeneous component " w c " will, in general, not be equal to 1.
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A compound system consisting of two interacting closed homogeneous component subsystems has a potential energy of interaction E ^ { \ mathrm { pot } } _ { 12 } between the subsystems.
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Any nonzero polynomial may be decomposed, in a unique way, as a sum of homogeneous polynomials of different degrees, which are called the "'homogeneous components "'of the polynomial.
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That construction only uses the surjective morphisms & rho; " n " without mentioning the injective morphisms & phi; " n " : it constructs the homogeneous components of & Lambda; " R " separately, and equips their direct sum with a ring structure using the & rho; " n ".
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An ideal I \ subset A is "'homogeneous "'if, for every element a \ in I, its homogeneous components belong also to I . ( Equivalently, they are graded submodules of " A "; see # Graded module . ) The intersections of a homogeneous ideal I with the A _ i are called the "'homogeneous parts "'of I.
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