Purification purification that eliminates eighty per cent (80%) of existing impurities or the reduction or elimination produced by a chemical substance with a minimum degree of purity, so that the product may be appropriate for uses such as:
Purification. The Parties agree to a process of purification of the armed forces, within the framework of the peace process and with a view to the supreme objective of national reconciliation, based on evaluation of all members of the armed forces by an ad hoc Commission.
Purification. 2.3.1 Issuance of the agreement giving legal form to and formalizing the ad hoc Commission: A+5.
Purification. With isolated crude Moli1901, generated at Apotex Fermentation Inc., the purification process supplied by Molichem Medicines will be verified in the chemistry lab.
Purification. The purification of Moli1901 will be conducted by use of HPLC, followed by treatment with ion exchange resin, decolourization, concentration and freeze-drying in accordance with the pre-approved master batch record.
Purification. All compounds delivered to Pfizer will be purified via at least one of the following methods 1) *, 2) * or 3) *. The purity of the final compounds must be determined as detailed in section above. On rare occasions, and only with the agreement of Pfizer, the * and not the * compounds will be purified, however the purity of the * compounds delivered to Pfizer must still be determined and meet the above purity criteria.
Purification. 2.1. List of raw materials and specifications (e.g. resin identification, column loads)
Purification. A Suppose that LA→BE is degraded. To prove that a union over pure states is sufficient, we show that for every achievable rate pair (R0, R1), there exists a rate pair (R0j , R1j ), where Rjj ≥ Rj for j = 0, 1, that can be achieved with pure states. Fix pT,X (t, x) and {ϕt,x}. Let R0 ≤ min (I(T ; B)ρ , I(T ; E)ρ) (121) R1 ≤ min (I(X; B|T )ρ − I(X; E|T )ρ + RK , I(X; B|T )ρ) (122) and consider the spectral decomposition, A A ϕt,x = Σ pZ|T,X (z|t, x)φt,x,z z∈Z A where pZ|T,X (z|t, x) is a conditional probability distribution, and φt,x,z are pure. Consider the extended state A ρT XZA = Σ pT,X (t, x)pZ|T,X (z|t, x)|t)(t| ⊗ |x)(x| ⊗ |z)(z| ⊗ φt,x,z . (124) t,x,z Now, observe that the union in the RHS of (26) includes the rate pair (R0j , R1j ) that is given by R0j = R0 (125) R1j = min (I(X, Z; B|T )ρ − I(X, Z; E|T )ρ + RK , I(X, Z; B|T )ρ) (126) which is obtained by plugging Xj = (X, Z) instead of X, and the pure states φt,(x,z) instead of ϕt,x. That is, (Rj , Rj ) ∈ Ck-a(L). By the chain rule, I(X, Z; B|T )ρ = I(X; B|T )ρ + I(Z; B|T, X)ρ ≥ I(X; B|T )ρ . (127) | − | | − | | − | Furthermore, I(X, Z; B T )ρ I(X, Z; E T )ρ = [I(X; B T )ρ I(X; E T )ρ] + [I(Z; B X, T )ρ I(X; E X, T )ρ]. Assuming | ≥ | that the channel is degraded, we have I(Z; B X, T )ρ I(Z; E X, T )ρ, by the quantum data processing inequality [97, Theorem 11.5]. Hence, I(X, Z; B|T )ρ − I(X, Z; E|T )ρ ≥ I(X; B|T )ρ − I(X; E|T )ρ (128) and it follows that R1j ≥ R1. Thereby, the union can be restricted to pure states. APPENDIX B PROOF OF THEOREM 3 Consider the broadcast channel LA→BE with confidential messages and key assistance, with a key of rate RK.
