Self-oscillating gels based on novel catalyst for the Belousov–Zhabotinsky reaction

We report on the synthesis of new Ru(bpy)₂(phen) catalyst for the oscillatory Belousov–Zhabotinsky chemical reaction and on the preparation of novel Ru(bpy)₂(phen)-based self-oscillating gels. The synthesized gels exhibit high-amplitude autonomous mechanical oscillations when the Belousov–Zhabotinsky reaction proceeds inside these gels     

von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

Anti-fibrosis attributes: UHPLC-MS/MS-based pharmacokinetics profiling of a novel autotaxin inhibitor with excellent in vivo efficacy in rat

3,4-Difluorobenzyl(1-ethyl-5-(4-((4-hydroxypiperidin-1-yl)-methyl)thiazol-2-yl)-1H-indol-3-yl)carbamate (NAI59), a small molecule with outstanding therapeutic effectiveness to anti-pulmonary fibrosis, was developed as an autotaxin inhibitor candidate compound. To evaluate the pharmacokinetics and plasma protein binding of NAI59, a UPLC–MS/MS method was developed to quantify NAI59 in plasma and phosphate-buffered saline. The calibration curve linearity ranged from 9.95 to 1990.00 ng/mL in plasma. The accuracy was −6.8 to 5.9%, and the intra- and inter-day precision was within 15%. The matrix effect and recovery, as well as dilution integrity, were within the criteria. The chromatographic and mass spectrometric conditions were also feasible to determine phosphate-buffered saline samples, and it has been proved that this method exhibits good precision and accuracy in the range of 9.95–497.50 ng/mL in phosphate-buffered saline. This study is the first to determine the pharmacokinetics, absolute bioavailability, and plasma protein binding of NAI59 in rats using this established method. Therefore, the pharmacokinetic profiles of NAI59 showed a dose-dependent relationship after oral administration, and the absolute bioavailability in rats was 6.3%. In addition, the results of protein binding showed that the combining capacity of NAI59 with plasma protein attained 90% and increased with the increase in drug concentration.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Unconventional Secondary Structure Mimics: Ladder-Rungs

Secondary structures tend to be recognizable because they have repeating structural motifs, but mimicry of these does not have to follow such well-defined patterns. Bioinformatics studies to match side-chain orientations of a novel hydantoin triazole chemotype ( 1 ) to protein-protein interfaces revealed it tends to align well across parallel and antiparallel sheets, like rungs on a ladder. One set of these overlays was observed for the protein-protein interaction uPA⋅uPAR. Consequently, chemotype 1 was made with appropriate side-chains to mimic uPA at this interface. Biophysical assays indicate these compounds did in fact bind uPAR, and elicit cellular responses that affected invasion, migration, and wound healing.     

Sandwich-like Catalyst–Carbon–Catalyst Trilayer Structure as a Compact 2D Host for Highly Stable Lithium–Sulfur Batteries

Herein, we propose the construction of a sandwich-structured host filled with continuous 2D catalysis–conduction interfaces. This MoN-C-MoN trilayer architecture causes the strong conformal adsorption of S/Li₂S_x and its high-efficiency conversion on the two-sided nitride polar surfaces, which are supplied with high-flux electron transfer from the buried carbon interlayer. The 3D self-assembly of these 2D sandwich structures further reinforces the interconnection of conductive and catalytic networks. The maximized exposure of adsorptive/catalytic planes endows the MoN-C@S electrode with excellent cycling stability and high rate performance even under high S loading and low host surface area. The high conductivity of this trilayer texture does not compromise the capacity retention after the S content is increased. Such a job-synergistic mode between catalytic and conductive functions guarantees the homogeneous deposition of S/Li₂S_x, and avoids thick and devitalized accumulation (electrode passivation) even after high-rate and long-term cycling.     

Fabricating Dual-Atom Iron Catalysts for Efficient Oxygen Evolution Reaction: A Heteroatom Modulator Approach

Understanding the thermal aggregation behavior of metal atoms is important for the synthesis of supported metal clusters. Here, derived from a metal–organic framework encapsulating a trinuclear Fe^III₂Fe^II complex (denoted as Fe₃) within the channels, a well-defined nitrogen-doped carbon layer is fabricated as an ideal support for stabilizing the generated iron nanoclusters. Atomic replacement of Fe^II by other metal(II) ions (e.g., Zn^II/Co^II) via synthesizing isostructural trinuclear-complex precursors (Fe₂Zn/Fe₂Co), namely the “heteroatom modulator approach”, is inhibiting the aggregation of Fe atoms toward nanoclusters with formation of a stable iron dimer in an optimal metal–nitrogen moiety, clearly identified by direct transmission electron microscopy and X-ray absorption fine structure analysis. The supported iron dimer, serving as cooperative metal–metal site, acts as efficient oxygen evolution catalyst. Our findings offer an atomic insight to guide the future design of ultrasmall metal clusters bearing outstanding catalytic capabilities.     

A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.