Bogdanov‐Takens bifurcations of codimensions 2 and 3 in a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting

The Bogdanov‐Takens bifurcations of a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting were studied. In the paper “Diff. Equ. Dyn. Syst. 20(2012), 339‐366,” Gupta et al proved that the Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting has rich dynamics. Some equilibria of codimension 1 and their bifurcations were discussed. In this paper, we find that the model has an equilibrium of codimensions 2 and 3. We also prove analytically that the model undergoes Bogdanov‐Takens bifurcations (cusp cases) of codimensions 2 and 3. Hence, the model can have 2 limit cycles, coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1 as the values of parameters vary. Moreover, several numerical simulations are conducted to illustrate the validity of our results.     

Hyperbolic Yamabe problem

In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.     

Positive piecewise pseudo-almost periodic solutions of first-order singular differential equations with impulses

This paper is concerned with a kind of first-order singular differential equations with impulses. The main purpose of this paper is to study the existence, uniqueness, and globally exponential stability of the positive piecewise pseudo-almost periodic solutions. The main tools utilized to establish our results consist of the contraction mapping principle and generalized Gronwall–Bellmain inequality. Two examples are given at the end of the paper to illustrate the main results.     

Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces

In this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtained in earlier work.     

Electrochromic Detection of Latent Fingermarks on Metal Surface Using 1,1′-Dibenzyl-4,4′-bipyridinium Dichloride

The electrochromic detection of latent fingermarks on polished or unpolished, flat or curved metal surfaces is described using electrochromic material, 1,1’-dibenzyl-4,4’-bipyridinium dichloride. The surface area covered by fingermarks acts as an insulating mask, causing 1,1’-dibenzyl-4,4’-bipyridinium dichloride to change color and produce inversed images of the fingermark. By changing the applied potential, the optical properties of 1,1’-dibenzyl-4,4’-bipyridinium dichloride can be continuously and reversibly adjusted to optimize the visual contrast of fingermarks, so as to realize the detection of latent fingermarks on stainless steel surface. It is demonstrated that the fabricated electrochromic devices can detect the fingermarks on these types of surfaces within twenty seconds at −1.0∼−2.0 V. This work can qualify as a tangible improvement in fingermark detection of the natural fingermarks on the never-cleaned (more than 3 years) and curved surfaces of daily-used container, e. g. cup, and the handle of cleaning tool, mop.     

Tuning C1/C2 Selectivity of CO2 Electrochemical Reduction over in-Situ Evolved CuO/SnO2 Heterostructure

Heterostructured oxides with versatile active sites, as a class of efficient catalysts for CO₂ electrochemical reduction (CO₂ER), are prone to undergo structure reconstruction under working conditions, thus bringing challenges to understanding the reaction mechanism and rationally designing catalysts. Herein, we for the first time elucidate the structural reconstruction of CuO/SnO₂ under electrochemical potentials and reveal the intrinsic relationship between CO₂ER product selectivity and the in situ evolved heterostructures. At −0.85 V_RHE, the CuO/SnO₂ evolves to Cu₂O/SnO₂ with high selectivity to HCOOH (Faradaic efficiency of 54.81 %). Mostly interestingly, it is reconstructed to Cu/SnO_2-x at −1.05 V_RHE with significantly improved Faradaic efficiency to ethanol of 39.8 %. In situ Raman spectra and density functional theory (DFT) calculations reveal that the synergetic absorption of *COOH and *CHOCO intermediates at the interface of Cu/SnO_2-x favors the formation of *CO and decreases the energy barrier of C−C coupling, leading to high selectivity to ethanol.     

Multiple Dynamic Bonds-Driven Integrated Cathode/Polymer Electrolyte for Stable All-Solid-State Lithium Metal Batteries

All-solid-state lithium metal batteries (LMBs) are considered as the promising higher-energy and improved-safety energy-storage systems. Nevertheless, the electrolyte-electrodes interfacial issues due to the limited solid physical contact lead to discontinuous interfacial charge transport and large interfacial resistance, thereby suffering from unsatisfactory electrochemical performance. Herein, we construct an integrated cathode/polymer electrolyte for all-solid-state LMBs under the action of polymer chains exchange and recombination originating from multiple dynamic bonds in our well-designed dynamic supramolecular ionic conductive elastomers (DSICE) molecular structure. The DSICE acts as polymer electrolytes with excellent electrochemical performance and mechanical properties, achieving the ultrathin pure polymer electrolyte thickness (12 μm). Notably, the DSICE also functions as lithium iron phosphate (LiFePO₄, LFP) cathode binders with enhanced adhesive capability. Such well-constructed Li|DSICE|LFP-DSICE cells generate delicate electrolyte-electrodes interfacial contact at the molecular level, providing continuous Li⁺ transport pathways and promoting uniform Li⁺ deposition, further delivering superior long-term charge/discharge stability (>600 cycles, Coulombic efficiency, >99.8 %) and high capacity retention (80 % after 400 cycles). More practically, the Li|DSICE|LFP-DSICE pouch cells show stable electrochemical performance, excellent flexibility and safety under abusive tests.     

[2+2+1+1] Cycloaddition for de novo Synthesis of Densely Functionalized Phenols

A unique benzannulation strategy for regioselective de novo synthesis of densely functionalized phenols is described. Through metal-mediated formal [2+2+1+1] cycloaddition of two different alkynes and two molecules of CO, a series of densely functionalized phenols were obtained. The benzannulation strategy allows efficient regioselective installation up to five different substituents on a phenol ring. The resulting phenols have a substitution pattern different from those obtained from Dötz and Danheiser benzannulations.     

Integrated Tandem Electrochemical-chemical-electrochemical Coupling of Biomass and Nitrate to Sustainable Alanine

Alanine is widely employed for synthesizing polymers, pharmaceuticals, and agrochemicals. Electrocatalytic coupling of biomass molecules and waste nitrate is attractive for the nitrate removal and alanine production under ambient conditions. However, the reaction efficiency is relatively low due to the activation of the stable substrates, and the coupling of two reactive intermediates remains challenging. Herein, we realize the integrated tandem electrochemical-chemical-electochemical synthesis of alanine from the biomass-derived pyruvic acid (PA) and waste nitrate (NO₃⁻) catalyzed by PdCu nano-bead-wires (PdCu NBWs). The overall reaction pathway is demonstrated as a multiple-step catalytic cascade process via coupling the reactive intermediates NH₂OH and PA on the catalyst surface. Interestingly, in this integrated tandem electrochemical-chemical-electrochemical catalytic cascade process, Cu facilitates the electrochemical reduction of nitrate to NH₂OH intermediates, which chemically couple with PA to form the pyruvic oxime, and Pd promotes the electrochemical reduction of pyruvic oxime to the desirable alanine. This work provides a green strategy to convert waste NO₃⁻ to wealth and enriches the substrate scope of renewable biomass feedstocks to produce high-value amino acids.     

A Semisynthetic Bioluminescence Sensor for Ratiometric Imaging of Metal Ions In Vivo Using DNAzymes Conjugated to An Engineered Nano-Luciferase

DNA-based probes have gained significant attention as versatile tools for biochemical analysis, benefiting from their programmability and biocompatibility. However, most existing DNA-based probes rely on fluorescence as the signal output, which can be problematic due to issues like autofluorescence and scattering when applied in complex biological materials such as living cells or tissues. Herein, we report the development of bioluminescent nucleic acid (bioLUNA) sensors that offer laser excitation-independent and ratiometric imaging of the target in vivo. The system is based on computational modelling and mutagenesis investigations of a genetic fusion between circular permutated Nano-luciferase (NLuc) and HaloTag, enabling the conjugation of the protein with a DNAzyme. In the presence of Zn²⁺, the DNAzyme sensor releases the fluorophore-labelled strand, leading to a reduction in bioluminescent resonance energy transfer (BRET) between the luciferase and fluorophore. Consequently, this process induces ratiometric changes in the bioluminescent signal. We demonstrated that this bioLUNA sensor enabled imaging of both exogenous Zn²⁺ in vivo and endogenous Zn²⁺ efflux in normal epithelial prostate and prostate tumors. This work expands the DNAzyme sensors to using bioluminescence and thus has enriched the toolbox of nucleic acid sensors for a broad range of biomedical applications.