On Friedrichs-Poincaré-type inequalities

Friedrichs- and Poincaré-type inequalities are important and widely used in the area of partial differential equations and numerical analysis. Most of their proofs appearing in references are the argument of reduction to absurdity. In this paper, we give direct proofs of Friedrichs-type inequalities in H¹(Ω) and Poincaré-type inequalities in some subspaces of W1,p(Ω). The dependencies of the inequality coefficients on the domain Ω and some sub-domains are illustrated explicitly.     

LaFe11.6Si1.4C0.5间隙化合物的磁性、磁相变和磁熵变

使用了约80％的廉价铁原料，制备了LaFe11．6Sil．4C0．5间隙化合物。研究表明：该间隙化合物仍保持了LaFe11．6Sil．4的NaZnl3立方晶体结构，间隙C原子的引入导致晶格膨胀了约0．35％，居里点提高了约50K；同时，仍然保持大的磁熵变，在0-2T磁场变化下，磁熵变达到Gd的2倍以上，大磁熵变源于磁场诱发的巡游电子变磁相变。该间隙化合物具有大磁熵变。     

La2-xKxCuO4类钙钛矿复合氧化物对柴油车排放碳颗粒物催化燃烧性能的研究

使用溶胶-凝胶法制备了纳米级不同K取代量的La2-xKxCuO4催化剂，通过H2-TPR，XRD，FT-IR和SEM等多种分析方法对催化剂进行了表征，利用程序升温氧化反应（TPO）就催化剂对碳颗粒物燃烧的催化活性进行了评价。结果表明：以K^＋部分取代La2CuO4中的La^3＋，La2-XKXuO4催化剂对soot催化燃烧的活性明显提高，其中K^＋的取代量对La2CuO4的晶形和活性都产生不同的影响；当x=0．2时，La1.8K0.2CuO4催化剂上呈四方晶相，soot的起燃温度下降到320℃。     

A new family of Padé-type approximants in

This paper gives the definition and some properties of a new family of Padé-type approximants (PTA) for k-variate formal power series (FPS). These PTA have the form P(t)/Q(t) where Q(t) = Π^r_{i = 0}(1 ? x(i)·t), {x(i), 0 ? i ? r} being a given set of points in

, and x·t is the scalar product of x and t in

. Some results about the approximation order, the unicity and some invariance properties of these PTA are proved together with a convergence result when the FPS is defined by a Stieltjes integral.     

Hybrid iodoperfluoroalkane-ferrocene supramolecular arrays: the shortest contacts iodine forms with nitrogen atoms and unsaturated moieties

α,ω-Diiodoperfluoralkanes self-assemble in solution and in the solid phase with (S)-(−)-N,N-dimethyl-1-ferrocenylethylamine. The formed adducts have been characterized by DSC, IR, Raman, and NMR techniques. Single crystal X-ray analysis of one of the obtained adducts shows that perfluorinated and organometallic modules alternate giving rise to infinite one-dimensional (1D) chains. The interacting modules are connected through strong n-type halogen bondings, involving nitrogen and iodine atoms, and weak π-type halogen bondings, involving Cp rings and iodine atoms. Both interactions are the shortest reported to now in their respective classes. Theoretical calculations have been performed to quantify the observed π-type halogen bonding. For the first time a metallocene-perfluorocarbon (PFC) hybrid material is described.     

H-type aggregation of functional metal ion sensing phthalocyanines: Synthesis,characterization and electrochemistry

We report, in this study, the preparation and physical characterization of the peripherally functionalized ionophore ligand, 4,5-bis(6-hydroxyhexan-3ylthio)-1,2-dicyanobenzene (1) and its branched thioalcohol-substituted phthalocyanines, 2,3,7,8,12,13,17,18-octakis{6-hydroxyhexan-3-ylthio)-metal (II) or (III) phthalocyanines {M{Pc[SCH(C₃H₇)(C₂H₅OH)]₈} {M = Pb(II) (2), Zn(II) (3), Cu(II) (4), Co(II) (5) and Mn(III), X = Cl⁻ (6)} which can selectively bind soft-metal ions such as silver (I) and palladium (II). It was observed by means of UV–Vis absorption spectrophotometry that the aggregates formed lead to a low solubility of the phthalocyanines in protic solvents, such as low molecular alcohols. However, the addition of AgNO₃ and Na₂PdCl₄ into a THF–MeOH solution of {M{Pc[SCH(C₃H₇)(C₂H₅OH)]₈X} {M = Pb(II) (2), Zn(II) (3), Cu(II) (4), Co(II) (5) and Mn(III), X = Cl⁻ (6)} induced optical changes, which indicated the formation of twisted H-type dimers (blue shift, face-to-face fashion) of {M{Pc[SCH(C₃H₇)(C₂H₅OH)]₈} complexes, bound by four PdCl₂ and AgNO₃ units in THF solution. Elemental analysis data, matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF/MS), FT-IR, ¹H, ¹³C NMR, and UV–Vis spectral data were used as complementary techniques. Voltammetry and in situ spectroelectrochemistry of the complexes were performed on Pt in DMSO/TBAP. The first reduction and oxidation processes of 5 were found to be split due to the presence of facile equilibria between the species coordinated differently at axial positions. The Mn(III)Pc(−2)X⁻ complex (6) displayed well-defined colour changes during its reduction processes. The redox behaviour of the Mn(III)Pc(−2)X⁻ complex was observed to be affected significantly by the existence of oxygen in solution due to the formation of μ-oxo MnPc species, Mn(III)Pc–O–PcMn(III). This effect was clarified well by in situ spectroelectrochemical measurements.     

Crystal structure and properties of the Na1−x Ru2O4 phase

Sodium ruthenium(III,IV) oxide Na_1−x Ru₂O₄ was synthesized by the solid state reaction of Na₂CO₃ and RuO₂ in inert atmosphere and characterized by X-ray powder diffraction, electron diffraction, and high-resolution transmission electron microscopy. The compound crystallizes in the CaFe₂O₄-type structure (space group Pnma, Z = 4, a = 9.2641(7) Å, b = 2.8249(3) Å, c = 11.1496(7) Å). Double rutile-like chains of the RuO₆ octahedra form a three-dimensional framework, whose tunnels contain sodium cations. The structure contains two crystallographically independent sites of ruthenium atoms randomly occupied by the Ru^III and Ru^IV cations. The superstructure with the doubled b parameter found for one of the samples under study using electron diffraction is caused, probably, by ordering of the Ru cations in the rutile-like chains. The Na_{1− x} Ru₂O₄ compound exhibits temperature-independent paramagnetism with χ₀ = 1.9·10⁻⁴ cm³ (mole of Ru⁻¹). Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1655–1660, October, 2006.     

Proximinal subspaces of 2-normed spaces

In 1965 Ga¨hler introduced 2-normed spaces and since then, this topic have been intensively studied and developed. We shall introduce the notion of 1-type proximinal subspaces of 2-normed spaces and give some results in this field.     

A classification of subgroups of odd unitary groups

In this paper, under the Λ-stable rank condition, we discuss the classification of subgroups of odd unitary groups and get an analogue of Sandwich Theorem.