With layer-by-layer removing the specimen surface, the C and O quantities decrease and reach zero level at the depth ≈ 6 nm (Fig. 4).
B x0; R) is the ball centered at x0 ∈ ℝ N with the radius R > 0, ( D 0 1, p - 1 denotes the dual space of D 0 1, p , the norm in L p is denoted by |·| p, the quantity O(ε t ) denotes |O(ε t )/ε t | ≤ C, o(ε t ) means |o(ε t )/ε t | → 0 as ε → 0 and o(1) is a generic infinitesimal value.
In particular, the quantity O 1 ( ε t ) means that there exist the constants C 1, C 2 > 0 such that C 1 ε t ≤ O 1 ( ε t ) ≤ C 2 ε t as ε is small.
(O (varepsilon )) denotes a quantity satisfying (|O varepsilon)| /varepsilonleq C), (o varepsilon)) means (|o varepsilon)|/varepsilonrightarrow0) as (varepsilonrightarrow0) and (o (1 )) is a generic infinitesimal value.
The objective function in (29) involves the quantity Pr ( O, Q, E, F | λ ̄ ) which could be expressed analytically as: Pr ( O, Q, E, F | λ ̄ c ) = π q 0 ( c ) ∏ t = 1 T − 1 a q t q t + 1 ( c ) ∏ t = 1 T u q t e t ( c ) w q t e t f t ( c ) b q t e t f t ( c ) ( o t ) (70).
The objective function in (81) involves the quantity Pr ( O, Q, F, E | λ ̄ ) which could be expressed analytically as Pr ( O, Q, F, E | λ ̄ c ) = π q 0 ( c ) ∏ t = 1 T − 1 a q t q t + 1 ( c ) ∏ t = 1 T w q t f t ( c ) u q t f t e t ( c ) b q t f t e t ( c ) ( o t ) (83).
Risk analysis performed by experts, providing predictions and assessing uncertainties related to the following quantities: o Proportion of successful treatments for patients at the hospital H o Successful treatment of patient L. The risk analyses are carried out according to the approach outlined in the previous section.
The quantity d o, being bounded by the interval (0, 1], can be considered an inefficiency measure. In this model, DMU0 is considered efficient if and only if d o = −0 or (sumnolimits_{r = 1}^{s} {u_{r} y_{r0} } = 1).
Now, returning to the relation (62), we deduce that the determining of the sign σ2/(4πGρ i ) is identified if the sign of the quantity Q o x = I 0 x K 0 x - 1 2 (65). is identified.
The solvent contribution must be included in the model to avoid systematic errors in Y c which will lead to a systematic error in the other parameters because the function minimised during refinement (Equation 1 [25]) contains the observed quantity Y o which has contributions from all atoms, including solvent, however disordered it may be.
