Two Types of Rubio de Francia Operators on Triebel–Lizorkin and Besov Spaces

Journal of Fourier Analysis and Applications - We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb...     

Biochemical evidence for the tyrosine involvement in cationic intermediate stabilization in mouse β-carotene 15, 15'-monooxygenase

Background  

β-carotene 15,15'-monooxygenase (BCMO1) catalyzes the crucial first step in vitamin A biosynthesis in animals. We wished to explore the possibility that a carbocation intermediate is formed during the cleavage reaction of BCMO1, as is seen for many isoprenoid biosynthesis enzymes, and to determine which residues in the substrate binding cleft are necessary for catalytic and substrate binding activity. To test this hypothesis, we replaced substrate cleft aromatic and acidic residues by site-directed mutagenesis. Enzymatic activity was measured in vitro using His-tag purified proteins and in vivo in a β-carotene-accumulating E. coli system.     

Asymptotics for models of non‐stationary diffusion in domains with a surface distribution of obstacles

We consider a time‐dependent model for the diffusion of a substance through an incompressible fluid in a perforated domain Ω_?, with n = 3,4. The fluid flows in a domain containing a periodical set of “obstacles” (Ω\Ω_?) placed along an inner (n ? 1)‐dimensional manifold . The size of the obstacles is much smaller than the size of the characteristic period ?. An advection term appears in the partial differential equation linking the fluid velocity with the concentration, while we assume a nonlinear adsorption law on the boundary of the obstacles. This law involves a monotone nonlinear function σ of the concentration and a large adsorption parameter. The “critical adsorption parameter” depends on the size of the obstacles , and, for different sizes, we derive the time‐dependent homogenized models. These models contain a “strange term” in the transmission conditions on Σ, which is a nonlinear function and inherits the properties of σ. The case in which the fluid velocity and the concentration do not interact is also considered for n ≥ 3.