In this paper, we employ elementary methods to investigate the reciprocal sums of the products of two Fibonacci numbers in several ways. First, we consider the sums of the reciprocals of the products of two Fibonacci numbers and establish five interesting families of identities. Then we extend such analysis to the alternating sums and obtain five analogous results. MSC: 11B39

No abstract

The aim of the present study was to transfect rat aortic smooth muscle cells with an early growth response factor-1 (Egr-1)-specific DNAzyme (ED5), to observe its effect on Egr-1 and proliferating cell nuclear antigen (PCNA) expression and to elucidate the mechanism of ED5-mediated inhibition of vascular smooth muscle cell (VSMC) proliferation. VSMCs in primary culture obtained by tissue block adhesion were identified by morphological observation and α smooth muscle actin (α-SM-actin) immunocytochemistry. The cells were then transfected with ED5 or scrambled ED5 (ED5SCR). The three groups of cells used in the present study were the control group, ED5 group and ED5SCR group. The expression levels of Egr-1 and PCNA protein were detected following transfection by analyzing and calculating the integral optical density value in each group. Primary culture of VSMCs and transfection of ED5 and ED5SCR were successfully accomplished. Following stimulation with 10% fetal calf serum, the Egr-1 protein was expressed most strongly at 1 h and demonstrated a declining trend over time; the expression of PCNA protein began at 4 h, peaked at 24 h and then demonstrated a slightly declining trend over time. Compared with the control group and the ED5SCR group, ED5 inhibited the expression of Egr-1 and PCNA (P<0.05). ED5 was able to inhibit the expression of Egr-1 and PCNA proteins in VSMCs to a certain extent and VSMC proliferation in vitro. DNAzyme gene therapy may be useful as a new method for treating vascular proliferative diseases, including atherosclerosis and restenosis.

Sodium-ion batteries (SIBs) demonstrate great application prospects for large-scale energy storage owing to the merits of low cost and abundant sodium resources. Nevertheless, the low initial Coulombic efficiency of anode...