If S + and S −, however, denote upper and lower half spheres of the norm sphere S, and (K^={yin mathbb {R}^{n}: ||y||^leq 1}), then O_{S} A)=intlimits_{G Acap S^h_{K^(N x dx+ intlimits_{G Acap S^h_{K^(N x dx,; Ain mathfrak{B}_{S} where Gleft Acap S^right)=left{varthetain mathbb{R}^{n-1}:, exists,eta=eta vartheta), s.t., left vartheta^{T},etaright)^{T}in Acap S^right}.
The upper left figure shows the spheres of the binned geometrical distances of 1.0, 2.0, and 3.0 Å for the centered carbon atom.
Although the agents in the upper sphere can use their power, the street-level workers who are at the bottom of the decision-making process also have discretionary power that they can exercise and thereby change the implementation process [ 43].
The change of the electrical resistance was measured by applying constant current and displacement amplitudes to the upper sphere contact specimen, fixing the flat specimen.
where (G(A)={ vartheta in {mathbb {R}}^{n-1}:exists eta =eta (vartheta) text {with } (vartheta ^{T},eta)^T in A }) and ((mathfrak {B}^n cap mathbb {S})^+) denotes the Borel σ-field on the upper half-sphere of (mathbb {S}).
For many within the Lebanese and Muslim communities who pursue a politics of recognition, it is one thing entirely to be subjected to a racist encounter on the train, but to have such racist views spouted from the upper echelon of the political sphere elicits a different level of vulnerability.
The version transmitted by Ibn al-Biṭrîq diverges and considers the Milky Way to be a phenomenon exclusively of the heavenly spheres, not of the upper part of the atmosphere.
Demand Media, meanwhile, is clearly operating in a lower sphere, which is the area between the upper half of the UGC space up to the lower half of the premium space.
This should be of little surprise to anyone, given that gender inequality continues to permeate every sphere of life, the upper echelons of the corporate world included.
