On the error-sum function of Pierce expansions

We introduce the error-sum function of Pierce expansions. Some basic properties of the error-sum function are analyzed. We also examine the fractal property of the graph of it by calculating the Hausdorff dimension, the box-counting dimension, and the covering dimension of the graph.Comment: 31 pages; typos correcte

Certain exceptional sets in Pierce expansions

In this paper, we are concerned with two exceptional sets arising in the Pierce expansion of numbers in the closed unit interval. One is the set of numbers having the divergent series of reciprocals of the digits and the other is the set of numbers having the divergent series of the $n$th iterates. Shallit (1986) showed that both sets have null Lebesgue measure and are uncountable and dense. We prove that the two exceptional sets are of null Hausdorff dimension and that both are dense $G_\delta$, both of which are stronger than Shallit's results.Comment: 11 page

Catalytic Mechanisms of Metmyoglobin on the Oxidation of Lipids in Liposome Model System

The catalytic mechanism of metmyoglobin (metMb) on the development of lipid oxidation in a phospholipid liposome model system was studied. Liposome model system was prepared with metMb solutions (2.0, 1.0, 0.5, and 0.25 mg metMb / mL) containing none, diethylenetriamine pentaacetic acid (DTPA), desferrioxamine (DFO), or ferric chloride and lipid oxidation was determined at 0, 15, 30, 60, and 90 min of incubation at 37 °C. Metmyoglobin catalyzed lipid oxidation in the liposome system, but the rate of lipid oxidation decreased as the concentration of metMb increased. The amount of free ionic iron in the liposome solution increased as the concentration of metMb increased, but the rate of metMb degradation was increased as the concentration of metMb decreased. The released free ionic iron was not involved in the lipid oxidation of model system because ferric iron has no catalytic effect without reducing agents. Both DFO and DTPA showed antioxidant effects, but DFO was more efficient than DTPA because of its multifunctional antioxidant ability as an iron and hematin chelator and an electron donor. The antioxidant activity of DTPA in liposome solution containing 0.25 mg metMb/mL was two times greater than that with 2 mg metMb/mL due to the increased prooxidant activity of DTPA-chelatable compounds. It was concluded that ferrylmyoglobin and DTPA-chelatable hematin generated from the interaction of metMb and LOOH, rather than free ionic iron, were the major catalysts in metMb-induced lipid oxidation in phospholipid liposome model system

Electron and phonon band-structure calculations for the antipolar SrPt3_{3}P antiperovskite superconductor: Evidence of low-energy two-dimensional phonons

SrPt3P has recently been reported to exhibit superconductivity with Tc = 8.4 K. To explore its superconducting mechanism, we have performed electron and phonon band calculations based on the density functional theory, and found that the superconductivity in SrPt3P is well described by the strong coupling phonon-mediated mechanism. We have demonstrated that superconducting charge carriers come from pd\pi-hybridized bands between Pt and P ions, which couple to low energy (~ 5 meV) phonon modes confined on the ab in-plane. These in-plane phonon modes, which do not break antipolar nature of SrPt3P, enhance both the electron-phonon coupling constant \lambda and the critical temperature Tc. There is no hint of a specific phonon softening feature in the phonon dispersion, and the effect of the spin-orbit coupling on the superconductivity is found to be negligible.Comment: 5 pages, 5 figures, 1 tabl

Current-driven dynamics of chiral ferromagnetic domain walls

In most ferromagnets the magnetization rotates from one domain to the next with no preferred handedness. However, broken inversion symmetry can lift the chiral degeneracy, leading to topologically-rich spin textures such as spin-spirals and skyrmions via the Dzyaloshinskii-Moriya interaction (DMI). Here we show that in ultrathin metallic ferromagnets sandwiched between a heavy metal and an oxide, the DMI stabilizes chiral domain walls (DWs) whose spin texture enables extremely efficient current-driven motion. We show that spin torque from the spin Hall effect drives DWs in opposite directions in Pt/CoFe/MgO and Ta/CoFe/MgO, which can be explained only if the DWs assume a N\'eel configuration with left-handed chirality. We directly confirm the DW chirality and rigidity by examining current-driven DW dynamics with magnetic fields applied perpendicular and parallel to the spin spiral. This work resolves the origin of controversial experimental results and highlights a new path towards interfacial design of spintronic devices

Dietary Cholesterol Affects Lipid Metabolism in Rabbits

Effects of dietary cholesterol (0 (control), 1, 2, 4 or 8 g cholesterol/kg diet for 12 wks) on lipid contents and fatty acid compositions in red blood cell (RBC) membranes and plasma of rabbits and pathological changes and lipid oxidation in their livers were determined. Contents of total lipid and unsaturated fatty acids in RBC membrane and plasma of rabbits fed ≥4 g and ≥2 g dosages, respectively, were significantly higher (P \u3c 0.05) than those of the control, and their increases were dosage-dependent. Accumulations of neutral lipids in centrolobular regions of livers in rabbits fed ≥ 2 g were dosage-dependent. Lipid oxidation in liver of rabbits fed 8 g was \u3e2 times higher (P \u3c 0.05) than those fed lower dosages. The results indicated that dietary cholesterol can modify lipid metabolisms of rabbits, including biosynthesis and transportation of lipids and fatty acids and incorporation of fatty acid into RBC membranes