Asymptotic equivalence of nonlinear evolution equations in Banach spaces

We show how the approach of Yosida Approximation of the derivative serves to obtain new results for evolution systems. We give criteria for the asymptotic equivalence of two different evolution systems, i.e., $$\lim_{t \to \infty} \|U_A(t, s)x - U_B(t, s)x\| =0,$$ where the evolution systems are generated by two different families of nonlinear and multivalued time-dependent operators A(t), and B(t).     

Temperature distribution in growing semi-transparent crystals (III). Conical liquid/solid interface

Temperature distribution in Al₂O₃ and YAG crystals grown by Czochralski method and in the melt layer adjacent to the liquid/solid interface of the conical shape was computed. The results were compared with the quality of the crystals. Using a highly absorbing material, temperature difference near the deeply submerged sharp interface decreases from the edge to the centre of a crystal and it is relatively great and unalterable in the case of a shallowly submerged blunt interface. Sharp interface show the crystals grown from the melt of the same composition (Al₂O₃ or accurately “stoichiometric” YAG), whereas the blunt one is typical of YAG grown from the melt of the “non-stoichiometric” composition, because its solidifying point is below the melting point of YAG phase.     

Ln(III) methyl and methylidene complexes stabilized by a bulky hydrotris(pyrazolyl)borate ligand

The reaction of Ln(AlMe(4))(3) with bulky hydrotris(pyrazolyl)borate (Tp(t)(Bu,Me))H proceeds via a sequence of methane elimination and C-H bond activation, affording unprecedented rare-earth metal ligand moieties including Ln(Me)[(micro-Me)AlMe(3)] and X-ray structurally characterized "Tebbe-like" Ln[(micro-CH(2))(2)AlMe(2)].     

Three‐Dimensional Protein Networks Assembled by Two‐Photon Activation

Spatial and temporal control over chemical and biological processes plays a key role in life and material sciences. Here we synthesized a two‐photon‐activatable glutathione (GSH) to trigger the interaction with glutathione S‐transferase (GST) by light at superior spatiotemporal resolution. The compound shows fast and well‐confined photoconversion into the bioactive GSH, which is free to interact with GST‐tagged proteins. The GSH/GST interaction can be phototriggered, changing its affinity over several orders of magnitude into the nanomolar range. Multiplexed three‐dimensional (3D) protein networks are simultaneously generated in situ through two‐photon fs‐pulsed laser‐scanning excitation. The two‐photon activation facilitates the three‐dimensional assembly of protein structures in real time at hitherto unseen resolution in time and space, thus opening up new applications far beyond the presented examples.     

Self‐Assembly of a Trinuclear Luminescent Europium Complex

Triangular luminescent box : Self‐assembly of a new multidentate receptor with europium cations results in the formation of trinuclear discrete complexes. X‐ray crystallography shows that nine‐coordinate cations are linked by ligands to provide a triangular complex in the solid state and in solution. Despite the coordinated solvent molecules, this topologically unusual complex exhibits remarkable luminescent properties.