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Definition 2.2 Given a gauge function φ, the mapping J φ : X → 2 X ∗ defined by J φ ( x ) = { u ∗ ∈ X ∗ : 〈 x, u ∗ 〉 = ∥ x ∥ ∥ u ∗ ∥ ; ∥ u ∗ ∥ = φ ( ∥ x ∥ ) }. is called the duality mapping with gauge function φ, where X is any normed space.
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There is a trend emerging in corporate boardrooms to request fairness opinions – typically used in merger deals to give a gauge of a company's worth – in non-merger situations.
Their apparent sizes on the sky give a measure of whether the radiation from them traveled to Earth on straight or curved lines, giving a gauge of cosmic geometry, as if an optician was trying to estimate the power of a lens by measuring the size of newsprint seen through it.
Irradiation with 0.25 GeV Au ions provide a useful tool to check the texture of the sample, in particular to give a gauge length reference to separate "weak" links and high-Jc links.
After a wash of data on labor, housing and manufacturing output on Thursday, investors were given a chance gauge the economic standing of consumers which showed weak inflation and stumbling sentiment.
Given a function (called a gauge of ), one says that a tagged partition is -fine if for every.
Weyl exploited these features of the conformal structure, and suggested that given a conformal structure, a gauge could be chosen at each point in a smooth but otherwise arbitrary manner, such that the metric (8) at any point of the manifold is conventional or undetermined to the extent that the metric is equally valid.
The n-fold DT is given by a gauge transformation, then a generalized DT is proposed through the Taylor expansion and a limit procedure.
As a follow-up to the housing charrette, participants were given a short survey to gauge their preferences for lot and block layout.
They provide concrete feedback (many for free), give us instant information about food facts or calorie counts, and give us a gauge of how we are doing.
Dividing one by the other gives an alternative gauge of prices, which increased by almost 18% nationally in the year to April and by over 95% in Beijing (see chart 1).In this section Home truths Sino cure Unholy mess The banks battle back Who's the patsy?
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