In this article, we present the definitive transformation formulae of the mass aspect and angular momentum aspect under BMS transformations. Two different approaches that lead to the same formulae are taken. In the first approach, the formulae are derived by reading off the aspect functions from the curvature tensor. While in the second and more traditional approach, we read them off from the metric coefficients. As an application of the angular momentum aspect transformation formula, we directly verify a relation concerning the Dray-Streubel angular momentum. It also enables us to reinterpret our calculations in terms of differential forms on null infinity, and leads to an exact expression of the Drey-Streubel angular momentum of a general section. The formulae we obtained played crucial roles in our recent work on supertranslation invariant charges, and resolved some inconsistencies in the literature.

Abstract. The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal KillingYano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimensiontwo submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is introduced to highlight the special null geometry of the submanifold. Finally, Alexandrov type theorems are established for spacelike submanifolds with constant mixed higher order mean curvature, which are generalizations of hypersurfaces of constant Weingarten curvature in the Euclidean space.

Nicotine is not only a major component in tobacco but is also a survival agonist that inhibits apoptosis induced by certain agents including chemotherapeutic drugs. Here, we first showed that nicotine inhibits cisplatin-induced apoptosis in NCI-H446 cells. An MTT assay, Annexin V-FITC staining, RT-PCR, and Western blot were applied to identify the viability of cells, stages of apoptosis, mRNA and signaling proteins expression, respectively. First, we observed that nicotine induced no significant apoptosis when used alone and promoted cell proliferation at a low concentration or for a short time, but the opposite was observed at a high concentration or for a long time. In addition, an increase in XIAP and Survivin mRNA or protein was observed. Next, when combined with cisplatin, growth inhibition rates were concentration dependent, decreased to the lowest level at first, but later climbed to the highest point. Furthermore, nicotine inhibited apoptosis induced by cisplatin and caused a concentration-dependent increase in both XIAP and Survivin mRNA or protein. Moreover, the apoptotic effect of the combination group was obviously higher than that of nicotine used alone at the same nicotine concentration and lower than that of cisplatin used alone at the same cisplatin concentration. These studies suggest that exposure to nicotine might negatively impact the apoptotic potential of chemotherapeutics.