On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

Photo-Controlled Macroscopic Self-Assembly Based on Photo-Switchable Hetero-Complementary Quadruple Hydrogen Bonds

A photo-switchable hetero-complementary quadruple H-bonding array, which consists of an azobenzene-derived ureidopyrimidinone (UPy) module ( Azo-UPy ) and a nonphotoactive diamidonaphthyridine (DAN) derivative ( Napy-1 ), is constructed based on a reversible photo-locking approach. Upon UV (390 nm)/Vis (460 nm) light irradiations, photo-switchable quadruple H-bonded dimerization between Azo-UPy and Napy-1 can be achieved with exhibiting 4.8×10⁴-fold differences in binding strength (ON/OFF ratios). Furthermore, smart polymeric gels with unique photo-controlled macroscopic self-assembly behavior can be fabricated by introducing such quadruple H-bonding array as photo-regulable noncovalent interfacial connections.     

Cobalt Based Nanoparticles Embedded Reduced Graphene Oxide Aerogel for Hydrogen Evolution Electrocatalyst

Efficient water electrolysis catalyst is highly demanded for the production of hydrogen as a sustainable energy fuel. It is reported that cobalt derived nanoparticle (CoS₂, CoP, CoS|P) decorated reduced graphene oxide (rGO) composite aerogel catalysts for highly active and reliable hydrogen evolution reaction electrocatalysts. 7 nm level cobalt derived nanoparticles are synthesized over graphene aerogel surfaces with excellent surface coverage and maximal expose of active sites. CoS|P/rGO hybrid aerogel composites show an excellent catalytic activity with overpotential of ≈169 mV at a current density of ≈10 mA cm^?2. Accordingly, efficient charge transfer is attained with Tafel slope of ≈52 mV dec^?1 and a charge transfer resistance (R_ct) of ≈12 Ω. This work suggests a viable route toward ultrasmall, uniform nanoparticles decorated graphene surfaces with well‐controlled chemical compositions, which can be generally useful for various applications commonly requiring large exposure of active surface area as well as robust interparticle charger transfer.     

Mixed-Metal MOF-74 Templated Catalysts for Efficient Carbon Dioxide Capture and Methanation

The vast chemical and structural tunability of metal–organic frameworks (MOFs) are beginning to be harnessed as functional supports for catalytic nanoparticles spanning a range of applications. However, a lack of straightforward methods for producing nanoparticle-encapsulated MOFs as efficient heterogeneous catalysts limits their usage. Herein, a mixed-metal MOF, NiMg-MOF-74, is utilized as a template to disperse small Ni nanoclusters throughout the parent MOF. By exploiting the difference in Ni O and Mg O coordination bond strength, Ni²⁺ is selectively reduced to form highly dispersed Ni nanoclusters constrained by the parent MOF pore diameter, while Mg²⁺ remains coordinated in the framework. By varying the ratio of Ni to Mg in the parent MOF, accessible surface area and crystallinity can be tuned upon thermal treatment, influencing CO₂ adsorption capacity and hydrogenation selectivity. The resulting Ni nanoclusters prove to be an active catalyst for CO₂ methanation and are examined using extended X-ray absorption fine structure and X-ray photoelectron spectroscopy. By preserving a segment of the Mg²⁺-containing MOF framework, the composite system retains a portion of its CO₂ adsorption capacity while continuing to deliver catalytic activity. The approach is thus critical for designing materials that can bridge the gap between carbon capture and CO₂ utilization.     

Rational Development of Remote C−H Functionalization of Biphenyl: Experimental and Computational Studies

A simple and efficient nitrile-directed meta-C−H olefination, acetoxylation, and iodination of biaryl compounds is reported. Compared to the previous approach of installing a complex U-shaped template to achieve a molecular U-turn and assemble the large-sized cyclophane transition state for the remote C−H activation, a synthetically useful phenyl nitrile functional group could also direct remote meta-C−H activation. This reaction provides a useful method for the modification of biaryl compounds because the nitrile group can be readily converted to amines, acids, amides, or other heterocycles. Notably, the remote meta-selectivity of biphenylnitriles could not be expected from previous results with a macrocyclophane nitrile template. DFT computational studies show that a ligand-containing Pd–Ag heterodimeric transition state (TS) favors the desired remote meta-selectivity. Control experiments demonstrate the directing effect of the nitrile group and exclude the possibility of non-directed meta-C−H activation. Substituted 2-pyridone ligands were found to be key in assisting the cleavage of the meta-C−H bond in the concerted metalation–deprotonation (CMD) process.     

Dimeric Manganese-Catalyzed Hydroarylation and Hydroalkenylation of Unsaturated Amides

An unprecedented Mn(I)-catalyzed selective hydroarylation and hydroalkenylation of unsaturated amides with commercially available organic boronic acids is reported. Alkenyl boronic acids have been successfully employed for the first time in Mn(I)-catalyzed carbon–carbon bond formation. A wide array of β-alkenylated amide products can be obtained in moderate to good yields, which offers practical access to five- and six-membered lactams. This protocol has predictable regio- and chemoselectivity, excellent functional group compatibility and ease of operation in air, representing a significant step-forward towards manganese-catalyzed C−C coupling.     

Nb(iPrNPMe2)3Fe–PMe3: A potential high reactivity heterobimetallic catalyst for acetylene cycloadditions

Alkynes cycloaddition reactions are powerful tools for constructing cyclic molecules with optimal atom efficiency, but these reactions cannot proceed at ambient temperature without transition-metal catalysts. In this work, a heterobimetallic complex featuring an Nb–Fe triple bond, Nb(ⁱPrNPMe₂)₃Fe–PMe₃, has been evaluated as the potential catalyst for acetylene cycloaddition, using density functional theory. The calculated results show that the singlet-state (i.e. ground-state) Nb(ⁱPrNPMe₂)₃Fe–PMe₃ can be applied to benzene synthesis, but is not suitable for cyclobutadiene. Benzene can be obtained easily at room temperature and is the unique product on the singlet potential surface. The irradiation of infrared-red light can drive the excitation of singlet Nb(ⁱPrNPMe₂)₃Fe–PMe₃ to its triplet state. Both benzene and cyclobutadiene can be formed on the triplet reaction potential surface due to their low energy barriers. Therefore, Nb(ⁱPrNPMe₂)₃Fe–PMe₃ is a potential high reactivity heterobimetallic catalyst for the cyclotrimerization of alkynes. In the reaction process, the catalytic active site of Nb(ⁱPrNPMe₂)₃Fe–PMe₃ moves from niobium to iron.     

A novel LC–MS/MS method for the determination of ziritaxestat in rat plasma and its pharmacokinetic study

Ziritaxestat is a first-in-class autotoxin inhibitor. The purpose of this study was to develop a liquid chromatography/electrospray ionization tandem mass spectrometric (LC–MS/MS) method for the determination of ziritaxestat in rat plasma. The plasma sample was deproteinated using acetonitrile and then separated on an Acquity BEH C₁₈ column with water containing 0.1% formic acid and acetonitrile as mobile phase, which was delivered at 0.4 ml/min. Ziritaxestat and the internal standard (crizotinib) were quantitatively monitored with precursor-to-product transitions of m/z 589.3 > 262.2 and m/z 450.1 > 260.2, respectively. The total running time was 2.5 min. The method showed excellent linearity over the concentration range 0.5–2000 ng/ml, with correlation coefficient >0.9987. The extraction recovery was >82.09% and the matrix effect was not significant. Inter- and intra-day precisions (RSD) were <11.20% and accuracies were in the range of −8.50–7.45%. Ziritaxestat was demonstrated to be stable in rat plasma under the tested conditions. The validated LC–MS/MS method was successfully applied to study the pharmacokinetic profiles of ziritaxestat in rat plasma after intravenous and oral administration. Pharmacokinetic results demonstrated that ziritaxestat displayed a short half-life (~3 h) and low bioavailability (20.52%).