Two-parameter differential calculus on the h-superplane

We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We also give a two-parameter deformation of the (1+1)-dimensional phase space algebra.Comment: 14 page

Cartan calculi on the quantum superplane

Cartan calculi on the extended quantum superplane are given. To this end, the noncommutative differential calculus on the extended quantum superplane is extended by introducing inner derivations and Lie derivatives

Two-parameter nonstandard deformation of 2x2 matrices

We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup $GL_{p,q}(1|1)$ by a transformation.Comment: 10 page

Screening by coral green fluorescent protein (GFP)-like chromoproteins supports a role in photoprotection of zooxanthellae

Green fluorescent protein (GFP)-like pigments are responsible for the vivid colouration of many reef-building corals and have been proposed to act as photoprotectants. Their role remains controversial because the functional mechanism has not been elucidated. We provide direct evidence to support a photoprotective role of the non-fluorescent chromoproteins (CPs) that form a biochemically and photophysically distinct group of GFP-like proteins. Based on observations of Acropora nobilis from the Great Barrier Reef, we explored the photoprotective role of CPs by analysing five coral species under controlled conditions. In vitro and in hospite analyses of chlorophyll excitation demonstrate that screening by CPs leads to a reduction in chlorophyll excitation corresponding to the spectral properties of the specific CPs present in the coral tissues. Between 562 and 586 nm, the CPs maximal absorption range, there was an up to 50 % reduction of chlorophyll excitation. The screening was consistent for established and regenerating tissue and amongst symbiont clades A, C and D. Moreover, among two differently pigmented morphs of Acropora valida grown under identical light conditions and hosting subclade type C3 symbionts, high CP expression correlated with reduced photodamage under acute light stress

Differential Geometry of the q-plane

Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.Comment: 9 page