Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach

In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and quasi-derivatives.     

Construction of Cyclobutanes by Multicomponent Cascade Reactions in Homogeneous Solution through Visible-Light Catalysis

[2+2] Photocycloaddition of two olefins is a general method to assemble the core scaffold, cyclobutane, found in numerous bioactive molecules. A new approach to synthesize cyclobutanes through multicomponent cascade reactions by merging aldol reaction and Witting reaction with visible-light-induced [2+2] cycloaddition is reported. An array of cyclobutanes with high selectivity has been achieved from commercially available aldehydes, ketones (or phosphorus ylide), and olefins with visible-light irradiation of a catalytic amount of (fac-tris(2-phenylpyridinato-C₂,N)iridium) ([Ir(ppy)₃]) at room temperature. Control experiments and spectroscopic studies revealed that the triplet–triplet energy transfer from the excited [Ir(ppy)₃]* to enones, generated in situ from aldehyde and ketone or aldehyde and phosphorus ylide, is responsible for these simple and efficient muticomponent transformations.     

Hexanuclear 3d − 4f metal–organic cages assembled from a carboxylic acid‐functionalized tris‐triazamacrocycle for highly selective fluorescent sensing of picric acid

Two Ln^III ions are sandwiched by dinuclear Co^II building blocks derived from a tris‐triazamacrocyclic ligand bearing pendant carboxylic acid functionality, 1,3,5‐tris((4,7‐bis(2‐carboxyethyl)‐1,4,7‐triazacyclonon‐1‐yl)methyl)‐benzene (H₆L), giving rising to two nanoscale heterometallic metal–organic cages formulated as [Co₄Ln₂(LH_2.5)₂(H₂O)₄]·(ClO₄)₆·NO₃·nH₂O [Ln = Dy, n = 12 ( 1 ); Ln = Yb, n = 9 ( 2 )], whose internal cavity accommodates a guest NO₃^? anion. Their hexanuclear cage‐like architectures are maintained both in solution and solid states as confirmed by mass spectrum as well as X‐ray diffraction experiments. These two cages display ligand‐based fluorescence emissions and therefore both were chosen to be operated as fluorescent chemosensors for the detection of nitroaromatic compounds. Attractively, these metal–organic cages allow highly selective and sensitive detection of picric acid (PA) over other nitroaromatics in solution and suspension, and the fluorescence resonance energy transfer (FRET) between the cage probes and PA is mainly responsible for the remarkable detection efficiency.     

Synthesis,characterization, and electrochemistry of monophosphine‐containing diiron propane‐1,2‐dithiolate complexes related to the active site of [FeFe]‐hydrogenases

Five monophosphine‐substituted diiron propane‐1,2‐dithiolate complexes as the active site models of [FeFe]‐hydrogenases have been synthesized and characterized. Reactions of complex [Fe₂(CO)₆{μ‐SCH₂CH(CH₃)S}] ( 1 ) with a monophosphine ligand tris(4‐methylphenyl)phosphine, diphenyl‐2‐pyridylphosphine, tris(4‐chlorophenyl)phosphine, triphenylphosphine, or tris(4‐fluorophenyl)phosphine in the presence of the oxidative agent Me₃NO·2H₂O gave the monophosphine‐substituted diiron complexes [Fe₂(CO)₅(L){μ‐SCH₂CH(CH₃)S}] [L = P(4‐C₆H₄CH₃)₃, 2 ; Ph₂P(2‐C₅H₄N), 3 ; P(4‐C₆H₄Cl)₃, 4 ; PPh₃, 5 ; P(4‐C₆H₄F)₃, 6 ] in 81%–94% yields. Complexes 2 – 6 have been characterized by elemental analysis, spectroscopy, and X‐ray crystallography. In addition, electrochemical studies revealed that these complexes can catalyze the reduction of protons to H₂ in the presence of HOAc.     

Novel thionin-functionalised core shell magnetic nanoparticles for dispersive solid-phase extraction of Hg(II) in food and water samples

To develop an accurate and precise method for separation and pre-concentration of Hg(II), a novel thionin functionalised core shell structure magnetic material has been prepared and characterised. The extraction ability of the material was evaluated by magnetic solid-phase extraction coupled with inductively coupled plasma mass spectrometry determination of Hg(II) in food and water samples. Combining the advantages of magnetic separation with selective extraction of thionin towards Hg(II), the material exhibits enhanced enrich selectivity and efficiency for Hg(II). The experimental parameters influencing Hg(II) extraction efficiency, including pH of the aqueous solution, the dosage of the adsorbent, extraction time and sample volume, were systematically investigated. Under the optimised conditions, concentration of Hg(II) at 1.0 μg L^?1 can be successfully enriched by the material without the interference of the common co-existing ions. The enrichment factor and adsorption capacity were 250 and 75.2 mg g^?1, and precise of the method was confirmed by analysing the spiked food, water samples and standard water reference samples with the recoveries of 92.5–101.8%.     

1,10-Phenanthroline: A versatile ligand to promote copper-catalyzed cascade reactions

Ligand-promoted copper-catalyzed cascade reactions have become a robust tool for the synthesis of cyclic compounds. Although numerous ligands have been developed, this review focuses on the introduction of commercially available 1,10-phenanthroline-promoted copper-catalyzed cascade reactions in recent years. Moreover, based on original articles, this review highlights product yields in the presence and absence of the ligand, and the possible mechanistic role of the ‘copper/1,10-phenanthroline’ catalytic system.     

Salen–Mg-doped NH2–MIL-101(Cr) for effective CO2 adsorption under ambient conditions

A novel metal-doped metal–organic framework (MOF) was developed by incorporating salen–Mg into NH₂–MIL-101(Cr) structure under ambient conditions. The Schiff base complex was successfully prepared by condensing salicylaldehyde with a free amino group and then coordinating metal ions. Such a structure can endow the sample with higher CO₂ adsorption performance. At 0°C and 1 bar, the salen–Mg-modified sample achieves the maximum adsorption capacity of 2.18 mmol g⁻¹ for CO₂, which was 5.8% higher than the pristine salen–MOF under the same conditions. Notably, the Freundlich model indicates that the CO₂ adsorption process of all samples conforms to reversible adsorption. However, the correlation coefficients (R²) of the Mg-doped sample are lower than that of the pristine sample. Besides, the CO₂/N₂ adsorption selectivity and isosteric heat also show a similar trend. These results indicate that the salen–Mg can enhance the interaction between the material and CO₂ molecules.     

Optical vortices in the Ginzburg–Landau equation with cubic–quintic nonlinearity

In a dissipative system with cubic–quintic nonlinearity, the curious evolution of optical vortex beams characterized by different topological charges (TCs) is simulated numerically and presented their evolution profiles. We find that new vortices will be induced during propagation, and the behavior of vortices, as affected by the TC and the number of beads of the incident beam, as well as its size, is also discussed. Common rules associated with the initial conditions coming from various incident beams are developed to determine the number of induced vortices and the corresponding rotation direction. Attributed to the nonlinearity, during propagation we see the beams slowly expand to induce new vortices, which commonly appear in oppositely charged pairs, while the net topological charge of the vortex is conserved. Our results not only deepen the understanding of optical vortices, but also widen their potential applications.