The microalga Haematococcus pluvialis Flotow is one of the natural sources of astaxanthin, a pigment widely used in salmon feed. This study was made to discover optimal conditions for biomass and astaxanthin production in H. pluvialis from Steptoe, Nevada (USA), cultured in batch mode. Growth was carried out under autotrophic (with NaNO 3 , NH 4 Cl and urea) and mixotrophic conditions (with 4, 8, 12 mM sodium acetate) under two photon flux densities (PFD) (35 and 85 µmol m -2 s -1 ). The carotenogenesis was induced by 1) addition of NaCl (0.2 and 0.8 %), 2) N-deprivation and 3) high PFD (150 µmol m -2 s -1 ). Total carotenoids were estimated by spectrophotometry and total astaxanthin by HPLC. Ammonium chloride was the best N-source for growth (k=0.7 div day -1 , 228-258 mg l -1 and 2.0 x 10 5 -2.5 x 10 5 cells ml -1 at both PFD, respectively). With increasing acetate concentration, a slight increment in growth occurred only at 85 µmol m -2 s -1 . Light was the best inductive carotenogenic factor, and the highest carotenoid production (4.9 mg l -1 , 25.0 pg cell -1 ) was obtained in cultures pre-grown in nitrate at low light. The NaCl caused an increase in carotenoid content per cell at increasing salt concentrations, but resulted in a high cell mortality and did not produce any increment in carotenoid content per volume compared to cultures grown at 150 µmol m -2 s -1 . The highest carotenoid content per cell (22 pg) and astaxanthin content per dry weight (10.3 mg g -1 ) (1% w/w) were obtained at 85 µmol m -2 s -1 with 0.8% NaCl.

We propose a modification to the Lie algebra S-expansion method. The modification is carried out by imposing a condition on the S-expansion procedure, when the semigroup is given by a cyclic group of even order. The S-expanded algebras are called SH -expanded algebras where S = Z2n. The invariant tensors for SH -expanded algebras are calculated and the dual formulation of SH -expansion procedure is proposed. We consider the SH -expansion of the five-dimensional AdS algebra and its corresponding invariants tensors are found. Then a Chern-Simons Lagrangian invariant under the five-dimensional AdS algebra SH -expanded is constructed and its relationship to the general relativity is studied. †

The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by GB n and GL n respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB 5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref.[1] allow us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

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