A valuation is a function | · | from a field K into [0, ∞) such that 0 is the unique element having the 0 valuation, |rs| = |r| · |s| and the triangle inequality holds, i.e., r + s ≤ r + s, ∀ r, s ∈ K. A field K is called a valued field if K carries a valuation.
A valuation is a function | ⋅ | from a field K into [ 0, ∞ ) such that 0 is the unique element having the 0 valuation, | r s | = | r | | s | and the triangle inequality is replaced by | r + s | ≤ max { | r |, | s | }. The field K is called a valued field if K carries a valuation. The usual absolute values of R and C are the examples of valuations.
The Steiner point map s : K n → R n is the unique vector valued rigid motion equivariant and continuous valuation.
307] The Steiner point map s : K n → R n is the unique vector valued rigid motion equivariant and continuous valuation.
Thus, optimal decision making is likely to rest on a number of valuation processes and it is critical that we develop a framework of possible valuation processes so that we can begin to identify the unique functional roles different areas contribute to decision making.
Viacom's recent acquisitions of iFilm (December 2005, 3.3 million U.S. uniques) and Atom/Shockwave (August 2006, 1.3 million U.S. uniques) for $50 million and $200 million, respectively suggest a per-unique-visitor valuation of $15-$15-$20
Grouper's per-unique-visitor valuation, by comparision, is roughly $70 $12020, depending on whether you look at June or July 2006 data.
It was shown there that such central notions like projection, centroid and difference body operators can be characterized as unique Minkowski valuations compatible with affine transformations of R n (see [23,24,37,60,64] for related results).
"The market brings the valuation.
