Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Fabrication of Microporous Metal–Organic Frameworks in Uninterrupted Mesoporous Tunnels: Hierarchical Structure for Efficient Trypsin Immobilization and Stabilization

Hierarchically porous metal–organic frameworks (HP-MOFs) are promising in various applications. Most reported HP-MOFs are prepared based on the generation of mesopores in microporous frameworks, and the formed mesopores are connected by microporous channels, limiting the accessibility of mesopores for bulky molecules. A hierarchical structure is formed by constructing microporous MOFs in uninterrupted mesoporous tunnels. Using the confined space in as-prepared mesoporous silica, highly dispersed metal precursors for MOFs are coated on the internal surface of mesoporous tunnels. Ligand vapor-induced crystallization is employed to enable quantitative formation of MOFs in situ, in which sublimated ligands diffuse into mesoporous tunnels and react with metal precursors. The obtained hierarchically porous composites exhibit record-high adsorption capacity for the bulky molecule trypsin. The thermal and storage stability of trypsin is improved upon immobilization on the composites.     

Recent Advances of Freestanding Cathodes for Li-S Batteries

Lithium-sulfur batteries (LSBs) with high energy density and low cost have been recognized as one of the most promising next-generation energy storage systems. Although it has taken decades of development, the practical application of LSBs has been hindered by several inherent obstacles, particularly the severe shuttle effect and sluggish reaction kinetics in the sulfur cathode. Various strategies have been proposed to address these problems via rational design of electrode materials and configurations. Freestanding sulfur cathode could be a promising strategy to improve the sulfur mass loading at the cathode level and energy density of LSBs. This minireview will briefly summary the recent advances in freestanding cathodes for LSBs. The advantages and disadvantages of various freestanding cathodes are discussed and the prospects for the development of flexible cathodes are envisioned.     

A Ru(II)-Based Nanoassembly Exhibiting Theranostic PACT Activity in NIR Region

Photoactivated chemotherapy (PACT) has appealing merits over traditional chemotherapy as well as photodynamic therapy (PDT) by virtue of its spatial and temporal control on drug activity and oxygen-independent mechanisms of action. However, the short photoactivation wavelengths, e.g., visible light–activated Ru(II)-based PACT agents, limit the clinical application severely. In this work, a facile construction of supramolecular nanoparticles from a poly(ethylene glycol) (PEG)-modified [Ru(dip)₂(py-SO₃)]⁺ (abbreviated as Ru-PEG, dip = 4,7-diphenyl-1,10-phenanthroline, py-SO₃ = pyridine-2-sulfonate) and 1,3-phenylenebis(pyren-1-ylmethanone) (BP) is shown. While Ru-PEG may undergo photoinduced ligand dissociation and release anticancer species of [Ru(dip)₂(H₂O)₂]²⁺, BP has extremely large two-photon absorption cross sections (δ₂) in the NIR region and intense fluorescence over the wavelengths where Ru-PEG has strong absorption. Thus, two-photon excitation of BP followed by an efficient Förster resonance energy transfer (FRET) from BP to Ru-PEG may lead to a potent inactivation against cisplatin-resistant cancer cells and 3D multicellular tumor spheroids (MCTSs). The residue fluorescence of BP also allows the cellular uptake of the particles to be visualized. This work provides a universal and convenient strategy to realize theranostic PACT in the ideal phototherapeutic window of 650–900 nm.     

Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model

Nonlinear Dynamics - Oblique collisions are more likely to happen in the realistic translational joint with clearance, compared to the full front impacts. It can be a quite demanding task to...