Uniqueness theorem for ordinary differential equations with Hölder continuity

We establish some uniqueness results near 0 for ordinary differential equations of the type u (n) (t) = f(u(t)) which satisfies u(0) = u 0 (0) = · · · = u (m−1)(0) = 0 and u (m) (0) 6= 0 with m ≥ n. We also show that although f is not Lipschitz near 0, it is always Holder ¨ continuous

The First Example of Tb-3-Containing Metallopolymer-Type Hybrid Materials with Efficient and High Color-Purity Green Luminescence

In the series of homo-leptic trinuclear complexes {[Ln(3)(L)(4)Cl-4(MeOH)(H2O)]center dot Cl} (Ln = La, 1; Ln = Eu, 2; Ln = Tb, 3 or Ln = Gd, 4) self-assembled from the allyl-modified benzimidazole-type ligand HL (4-allyl-2-(1H-benzo[d]imidazol-2-yl)-6-methoxyphenol) and LnCl(3)center dot 6H(2)O, a suitable energy level match endows efficient green luminescence (Phi(overall) = 72%) of Tb-3-arrayed complex 3. The copolymerization between each of these complex monomers 1-4 and C=C-containing MMA (methyl methacrylate) or NBE (norbornene) shows that degradative chain transfer of the terminal four flexible allyl groups within restrains their radical polymerization with MMA while it does not hinder their effective ring-opening metathesis polymerization (ROMP) with NBE. Thus, two kinds of PMMA-supported doping hybrid materials 1@PMMA, 2@PMMA, 3@PMMA and 4@PMMA and PNBE-supported metallopolymer-type hybrid materials Poly( NBE-1), Poly(NBE-2), Poly(NBE-3) and Poly(NBE-4) are obtained, respectively. Especially for both 3@PMMA and Poly(NBE-3) with high color-purity characteristic green emission of Tb3+ ions, improved physical properties including significantly enhanced luminescence (Phi(overall) = 76% or 83%) are observed, and covalent-bonding endows a higher-concentration self-quenching as compared to physical doping.National Natural Science Foundation 21373160, 91222201, 21173165Program for New Century Excellent Talents in University from the Ministry of Education of China NCET-10-0936Doctoral Program of Higher Education 20116101110003Science and Technology and Innovation Project of Shaanxi Province 2012KTCQ01-37Graduate Innovation and Creativity Fund (Visiting Learner) of Northwest University in P. R. ChinaChemistr

A New ZrCuSiAs-Type Superconductor: ThFeAsN

We report the first nitrogen-containing iron-pnictide superconductor ThFeAsN, which is synthesized by a solid-state reaction in an evacuated container. The compound crystallizes in a ZrCuSiAs-type structure with the space group P4/nmm and lattice parameters a=4.0367(1) {\AA} and c=8.5262(2) {\AA} at 300 K. The electrical resistivity and dc magnetic susceptibility measurements indicate superconductivity at 30 K for the nominally undoped ThFeAsN.Comment: 6 pages, 4 figures, 1 tabl