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There has been an upsurge of research on complex networks in recent years. The purpose of this paper is to study the mathematical properties of the random pentagonal chain networks PECn with the help of graph theory. Based on the networks PECn, we first obtain the expected value expressions of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index, and additive degree-Kirchhoff index, and then, we get the explicit expression formulas of their variances. Finally, we find that their limiting distributions all have the probabilistic and statistical significance of normal distribution.

It is well known that many topological indices have widespread use in lots of fields about scientific research, and the Kirchhoff index plays a major role in many different sectors over the years. Recently, Li et al. (Appl. Math. Comput. 382 (2020) 125335) proposed the problem of determining the Kirchhoff index and multiplicative degree-Kirchhoff index of graphs derived from Sn×K2, the Cartesian product of the star Sn, and the complete graph K2. In the present study, we completely solve this problem, that is, the explicit closed-form formulae of the Kirchhoff index, multiplicative degree-Kirchhoff index, and number of spanning trees are obtained for some graphs derived from Sn×K2.

The investigation on the structures, stabilities, and magnetism of NimAln (m=1–3, n=1–9) clusters has been made by using first principles. We found some new ground-state structures which had not been found before. These mixed species prefer to adopt three-dimensional (3D) structures starting from four atoms. All the ground-state structures for the Ni-Al clusters are different from those of the corresponding pure Al clusters with the same number of atoms except for three atoms. The Mulliken population analysis shows that some charges transfer from the Al atoms to the Ni atoms. NiAln (n = odd number) cations, Ni2Al6 neutral, Ni2Al1 and Ni3Al cations and anions, and Ni3Al5 anion have the magnetic moments of 2 μB. The magnetic moments of NiAl4 and NiAl6 cluster neutrals and cations are 2 μB and 3 μB, respectively. All the other cluster neutrals and ions do not have any nontrivial magnetic moments. The 3d electrons in Ni atoms are mainly responsible for the magnetism of the mixed Ni-Al clusters.

Our previous studies showed that α7 nicotinic acetylcholine receptor (nAchR) agonist nicotine has stimulatory effects on murine bone marrow-derived semimature DCs, but the effect of nicotine on peripheral blood mononuclear cell- (PBMC-) derived human semimature dendritic cells (hu-imDCs) is still to be clarified. In the present study, hu-imDCs (cultured 4 days) were conferred with ex vivo lower dose nicotine stimulation and the effect of nicotine on surface molecules expression, the ability of cross-presentation, DCs-mediated PBMC priming, and activated signaling pathways were determined. We could demonstrate that the treatment with nicotine resulted in increased surface molecules expression, enhanced hu-imDCs-mediated PBMC proliferation, upregulated release of IL-12 in the supernatant of cocultured DCs-PBMC, and augmented phosphorylation of Akt and ribosomal protein S6. Nicotine associated with traces of LPS efficiently enhanced endosomal translocation of internalized ovalbumin (OVA) and increased TAP-OVA colocalization. Importantly, the upregulation of nicotine-increased surface molecules upregulation was significantly abrogated by the inhibition of Akt kinase. These findings demonstrate that ex vivo nicotine stimulation augments hu-imDCs surface molecules expression via Akt-S6 pathway, combined with increased Ag-presentation result in augmented efficacy of DCs-mediated PBMC proliferation and Th1 polarization.