Curved π-conjugated molecules have attracted considerable interest because of the unique properties originating from their curved π surface. However, the synthesis of such distorted molecules requires harsh conditions, which hamper easy access to heteroatom-containing curved π systems. Here we report the synthesis of a π-extended azacorannulene with nitrogen in its centre. The oxidation of 9-aminophenanthrene provides tetrabenzocarbazole, which is converted to the azabuckybowl through palladium-catalysed intramolecular coupling. The electron-donating nature and curved π surface of the azabuckybowl enable its tight association with C60 in solution and solid states. High charge mobility is observed for the azabuckybowl/C60 assembly. This compound may be of interest in the fields of curved π systems as fullerene hosts, anisotropic π donors and precursors to nitrogen-containing nanocarbon materials.

We designed and synthesized molecular tweezers consisting of nitrogen-embedded buckybowl subunits. The judicious choice of the covalent linkers modulated their binding strength with C or C in solution. Titration studies by optical and H NMR analyses revealed a 1:1 composition of the resulting complexes. X-ray diffraction analysis elucidated their solid-state structures, in which two azabuckybowl units surround one fullerene molecule. The large association constants stabilize the complexes toward redox reactions and the purification process on silica-gel column chromatography. The linker enabled tuning of the cavity size for binding of fullerenes, achieving complementary fullerene hosts for C and C: the carbazole-bridged dimer preferentially associates with C over C, while the phenanthrene-bridged dimer interacts with C more strongly than C. Electrochemical analysis in combination with density functional theory calculations indicated the existence of intermolecular charge-transfer interactions between the buckybowl units and the fullerenes. Nonlinear optical measurements showed that the two-photon absorption cross sections of the molecular tweezers are enhanced upon association with fullerenes.

The reversible formation of σ-bonds between organic radicals has been widely investigated. However, reports on the formation of σ-dimers from delocalized π-radical cations are scarce. Herein, we report the reversible σ-dimerization behavior of a bowl-shaped π-radical cation generated from a nitrogen-embedded buckybowl, both in the crystalline state and in solution. The detailed structure of the σ-dimer in the crystalline state was determined by a single-crystal X-ray diffraction analysis. The monomeric radical cation exists predominantly in solution at room temperature, while dimerization of the radical cations occurs through carbon–carbon σ-bond formation upon reducing the temperature. 1H NMR and optical spectroscopy measurements confirmed the formation of a σ-dimer at low temperature. Comparative studies with a similar yet planar π-conjugated system suggested that the curved structure of the bowl-shaped π-radical cation facilitates the σ-dimerization at one of the internal sp2-hybridized carbon atoms. This trend was also observed for the nucleophilic addition reaction of methanol to the π-radical cations. The methoxylation reaction proceeded only for the curved π-radical cation. Theoretical calculations revealed that the large relief of structural strain at the α-carbon atom during the dimerization or nucleophilic addition reactions accelerated the bond formation at the internal carbon atom of the curved radical cation.

A directly connected azabuckybowl dimer forms a 1 : 1 complex with C60 in a diluted solution, while 1D chain supramolecular assemblies are obtained upon increasing the concentration.

A diazo-bridged BODIPY dimer and tetramer were prepared by the oxidative coupling reaction of β-amino-substituted BODIPYs. The structure of the dimer was elucidated by X-ray diffraction analysis, showing its coplanar orientation of two BODIPY units. Effective extension of π-conjugation was confirmed by optical and electrochemical investigations.

This paper investigates a class of viral infection models with a nonlinear infection rate and two discrete delays, one of which represents an intracellular latent period for the contacted target cell with virus to begin producing virions, the other of which represents the time needed in cytotoxic T cells (CTLs) response before immune becomes effective after a novel pathogen invades. Since immune system is a complex network of cells and signals that have evolved to respond to the presence of pathogens, we further assume two situations for immune activation delay. When both delays are ignored, the global stability for the ordinary differential equations model are established. While both delays are included, the positivity and boundedness of all solutions of the delay differential equations model are proved. Utilizing Lyapunov functionals and LaSalle invariance principle, the global dynamical properties are also studied. In particular, stability switch is shown to occur as immune delay increasing by bifurcation theory. Our results exhibit that the intracellular delay does not affect the stability of equilibria. However, the immune activation delay is able to destabilize the interior equilibrium and brings periodic solutions. Numerical simulations are performed to verify the theoretical results and display the different impacts of two type delays in two cases. Those analysis give us some useful suggestions on new drugs to fight against

Population growth rate, which depends on several biological parameters, is valuable information for the conservation and management of pelagic sharks, such as blue and shortfin mako sharks. However, reported biological parameters for estimating the population growth rates of these sharks differ by sex and display large variability. To estimate the appropriate population growth rate and clarify relationships between growth rate and relevant biological parameters, we developed a two-sex age-structured matrix population model and estimated the population growth rate using combinations of biological parameters. We addressed elasticity analysis and clarified the population growth rate sensitivity. For the blue shark, the estimated median population growth rate was 0.384 with a range of minimum and maximum values of 0.195–0.533, whereas those values of the shortfin mako shark were 0.102 and 0.007–0.318, respectively. The maturity age of male sharks had the largest impact for blue sharks, whereas that of female sharks had the largest impact for shortfin mako sharks. Hypotheses for the survival process of sharks also had a large impact on the population growth rate estimation. Both shark maturity age and survival rate were based on ageing validation data, indicating the importance of validating the quality of these data for the conservation and management of large pelagic sharks.

Oxidation of 2-amino-substituted BODIPYs afforded BODIPY trimers in a one-step operation. The trimer consists of a pyrazine-fused BODIPY dimer to which one BODIPY unit is connected through an NH linkage. Effective expansion of π-conjugation over the fused dimer was observed in optical and electrochemical measurements.