On Polygonal Square Triangular Numbers

A pentagonal square triangular number is a number which is a pentagonal number P5(ℓ), a square y2 and a triangular number P3(m) at the same time. It would be well known for the specialists that there exists no pentagonal square triangular number except for P3(1) = 12 = P5(1) = 1. But we don’t know any simple reference of the proof of this fact in print. The object of this note is to provide a such reference. Here we shall present three independent proofs of this fact one of which was already referred in the net article [24]

ホウカゴ ノ コウコウセイ ゲンダイ ノ コウコウセイ ノ イシキ コウドウ ヲ キテイ スル ヨウイン ノ コウサツ

論

ゲンダイ コウコウセイ ノ ストレス ト ガッコウヨウイン

論

Crystalline maricite NaFePO₄ as a positive electrode material for sodium secondary batteries operating at intermediate temperature

Maricite NaFePO₄ (m-NaFePO₄) was investigated as a positive electrode material for intermediate-temperature operation of sodium secondary batteries using ionic liquid electrolytes. Powdered m-NaFePO₄ was prepared by a conventional solid-state method at 873 K and subsequently fabricated in two different conditions; one is ball-milled in acetone and the other is re-calcined at 873 K after the ball-milling. Electrochemical properties of the electrodes prepared with the as-synthesized m-NaFePO₄, the ball-milled m-NaFePO₄, and the re-calcined m-NaFePO₄ were investigated in Na[FSA]-[C₂C₁im][FSA] (C₂C₁im⁺ = 1-ethyl-3-methylimidazolium, FSA⁻ = bis(fluorosulfonyl)amide) ionic liquid electrolytes at 298 K and 363 K to assess the effects of temperature and particle size on their electrochemical properties. A reversible charge-discharge capacity of 107 mAh g⁻¹ was achieved with a coulombic efficiency >98% from the 2nd cycle using the ball-milled m-NaFePO₄ electrode at a C–rate of 0.1 C and 363 K. Electrochemical impedance spectroscopy using m-NaFePO₄/m-NaFePO₄ symmetric cells indicated that inactive m-NaFePO₄ becomes an active material through ball-milling treatment and elevation of operating temperature. X-ray diffraction analysis of crystalline m-NaFePO₄ confirmed the lattice contraction and expansion upon charging and discharging, respectively. These results indicate that the desodiation-sodiation process in m-NaFePO₄ is reversible in the intermediate-temperature range

Isolation and characterization of cancer stem cells derived from human glioblastoma

Cancer stem cell (CSC) is considered as a cause of cancer recurrence and metastasis. Simultaneously CSCs are responsible for the heterogeneous population in tumor tissues due to their differentiation potential. However, the characterizations of CSCs are still not enough and cancer stem cell lines widely available is desired to be established for the advancement of cancer research. In this study, we tried to isolate and characterize stem like cells from human glioblastoma cell line U-251MG cells. U-251MG P1 cells, which was previously condensed in the presence of hyaluronic acid as CD44 positive population were subjected to single cell isolation procedure. Although 5 clones were isolated, only one clone exhibited high expression of CD44, Nanog, OCT3/4 and SOX2, and named U-251MGSC1. The sphere forming ability of U-251MGSC1 cell was significantly higher than the parental U-251MG cells. Tumorigenicity of U-251MG-SC1 cells were higher than that of U-251MG cells. U-251MGSC1 cells exhibited higher expression of CD44, SOX2, Nestin and A2B5 than U-251MG cells in vitro and in vivo. The expression of GFAP and NF-M was enhanced when the cells were treated with the conditioned medium of U-251MG cells indicating the potential of differentiation. Sphere forming ability was more efficient than that of U-251MG cells and was enhanced in the presence of hyaluronic acid, which enhanced the cell growth as well. U-251MGSC1 cells exhibited rapid growth tumor in nude mice and efficient metastatic ability in transmembrane assay when compared with U-251MG cells. As the result, we concluded U-251MGSC1 cell was a glioblastoma CSC line derived from the parental U-251MG cells. U-251MGSC1 cells will be a good tool to develop effective therapeutic agents against CSCs and to elucidate the properties of glioma derived CSCs and the mechanism of tumor development in brain