Recurrence Relations for Strongly q-Log-Convex Polynomials

We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly q-log-convex. We also prove that the Bessel transformation preserves log-convexity.Comment: 15 page

Crystal and Electronic Structures of LiNH₂

The crystal structure of LiNH2 was reinvestigated using powder neutron diffraction with high sensitivity. The compound crystallizes in the tetragonal space group I4 with lattice parameters α = b= 5.034 42 (24) Å, c = 10.255 58 (52) Å. It is found that H atoms occupy 8g1(0.2429, 0.1285, 0.1910) and 8g2 (0.3840, 0.3512, 0.1278) sites. The bond lengths between the nearest nitrogen and hydrogen atoms are 0.986 and 0.942 Å, respectively. The bond angle between H-N-H is about 99.97°. These results are significantly different from those of previous experiments. The electronic structure was calculated according to the revised structural data. The calculated density of states and charge density distribution show strong ionic characteristics between the ionic Li+ cation and the covalent bonded [NH2]- anion

Crystal and Electronic Structures of the Complex Hydride Li₄BN₃H₁₀

The crystal structure of Li4BN3H10 was investigated using powder neutron diffraction with high sensitivity. The compound crystallizes in the cubic space group 213 with lattice parameters a=10.645 19(52) Å with an ordered arrangement of [NH2]−1 and [BH4]−1 anions in a molar ratio of 3:1. The bond lengths between the nearest nitrogen and hydrogen atoms are 1.04(4) and 1.14(4) Å. The bond angle between H(1)-N-H(2) is about 126(6)°, while those between H(3)-B-H(3) and H(3)-B-H(4) are about 109(6)°-110(7)°. There are three different Li sites surrounded by [NH2]−1 and [BH4]−1 anions in distorted tetrahedral configurations. The Li(3)-B and Li(3)-N bond distances are about 1.72(3) and 2.32(2) Å, respectively, while the Li(1)-N and Li(2)-N distances are both around 2.09 Å. The strong bonding of Li(3) to the [BH4]−1 and the weaker Li(3)-[NH2]−1 bond are evidenced by the presence of the LiBH4 moiety in a projection of the crystal structure onto the a-b plane. First-principle calculations have been performed based on the structural data. Analyses of the density of states and charge density indicate that H(1) and H(2) strongly interact with N, and H(3) and H(4) interact with B to form [NH2]−1 and [BH4]−1, respectively. It is confirmed that Li(1) and Li(2) are strongly bonded to N and Li(3) is strongly bonded to B. These results are significantly different from some of the previous studies

Recurrence Relations for Strongly q-Log-Convex Polynomials

We consider a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly q-log-convex. We also prove that the Bessel transformation preserves log-convexity.Comment: 15 page

Large Scale Growth and Magnetic Properties of Fe and Fe₃O₄ Nanowires

Fe and Fe3O4 nanowires have been synthesized by thermal decomposition of Fe(CO)5, followed by heat treatments. The Fe wires are formed through the aggregation of nanoparticles generated by decomposition of Fe(CO)5. A core-shell structure with an iron oxide shell and Fe core is observed for the as-prepared Fe wires. Annealing in air leads to the formation of Fe2O3/Fe3O4 wires, which after heat treatment in a N2/alcohol atmosphere form Fe3O4 wires with a sharp Verwey [Nature (London) 144, 327 (1939)] transition at 125 K. The Fe3O4 wires have coercivities of 261 and 735 Oe along the wire axis at RT and 5 K, respectively. The large increase of coercivity at 5 K as compared to RT is due to the increase of anisotropy resulting from the Verwey transition