Coarse topological transitivity on open cones and coarsely J-class and D-class operators

We generalize the concept of coarse hypercyclicity, introduced by Feldman in [13], to that of coarse topological transitivity on open cones. We show that a bounded linear operator acting on an infinite dimensional Banach space with a coarsely dense orbit on an open cone is hypercyclic and a coarsely topologically transitive (mixing) operator on an open cone is topologically transitive (mixing resp.). We also “localize” these concepts by introducing two new classes of operators called coarsely J-class and coarsely D  -class operators and we establish some results that may make these classes of operators potentially interesting for further studying. Namely, we show that if a backward unilateral weighted shift on l²(N)$l^2(\mathbb{N})$ is coarsely J-class (or D  -class) on an open cone then it is hypercyclic. Then we give an example of a bilateral weighted shift on l^∞(Z)$l^{\infty }(\mathbb{Z})$ which is coarsely J-class, hence it is coarsely D-class, and not J  -class. Note that, concerning the previous result, it is well known that the space l^∞(Z)$l^{\infty }(\mathbb{Z})$ does not support J-class bilateral weighted shifts, see [10]. Finally, we show that there exists a non-separable Banach space which supports no coarsely D-class operators on open cones. Some open problems are added.     

In Vitro and In Vivo Enzyme‐Mediated Biomineralization of Oligo(poly(ethylene glycol) Fumarate Hydrogels

The enzyme alkaline phosphatase (ALP) is added at different concentrations (i.e., 0, 2.5, and 10 mg · ml^?1) to oligo(poly(ethylene glycol)fumarate) (OPF) hydrogels. The scaffolds are either incubated in 10 mM calcium glycerophosphate (Ca–GP) solution for 2 weeks or implanted in a rat subcutaneous model for 4 weeks. Fourier transform infrared (FTIR) spectroscopy, X‐ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and alizarin red staining show a strong ability to form minerals exclusively in ALP‐containing hydrogels in vitro. Additionally, the calcium content increases with increasing ALP concentration. Similarly, only ALP‐containing hydrogels induce mineralization in vivo. Specifically, small (≈5–20 µm) mineral deposits are observed at the periphery of the hydrogels near the dermis/scaffold interface using Von Kossa and alizarin red staining.

     

All-optical modulation based on electromagnetically induced transparency

We numerically investigate the implementation of all-optical absorption modulation of electromagnetic pulses by a medium that exhibits electromagnetically induced transparency. The quantum system is modelled as a three-level Λ-type system that interacts with two electromagnetic pulses, a probe pulse and a coupling pulse. The dynamics of the system is described by the coupled Maxwell-density matrix equations, and we explore the dependence of the optical modulation efficiency on the parameters of the system.