The facial skin of 354 women, aged 18-80, living in Shanghai, was investigated over two successive 6-month periods, summer and winter. Results from clinical assessments indicate that aging signs, such as wrinkling and sagging, are unaffected over such period. However, physical measurements revealed alterations in some functional criteria of the skin, such as sebum output, skin colour, melanin content of pigmented spots, skin hydration, all being increased during summer. The relationships between all criteria, as well as technical or applied inferences/consequences from this study, are discussed.

Abstract. Let H and K be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from B(H) into B(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is give which shows that a state ρ on H ⊗ K is separable if and only if (Φ ⊗ I)ρ ≥ 0 for all positive finite rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

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Abstract. In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain new indecomposable optimal witnesses which have no spanning property. These also provide new examples which support a recent conjecture saying that the so-called structural physical approximations to optimal positive maps (optimal entanglement witnesses) give entanglement breaking maps (separable states).

In this paper, a class of indecomposable positive finite rank elementary operators of order (n, n) are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2, 2) and get some new mixed entangled states that can not be detected by the positive partial transpose (PPT) criterion and the realignment criterion. PACS. 03.65.Ud, 03.65.Db, 03.67.-a.