ON LAGRANGE INTERPOLATION TO |x|α(1 ＜α＜ 2) WITH EQUALLY SPACED NODES

S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1, 1]. In 2000, M. Rever generalized S.M. Lozinskii's result to |x|α(0 ≤α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1 ＜α＜ 2)..     

NONDEGENERACY OF POSITIVE SOLUTIONS TO HOMOGENEOUS SECOND-ORDER DIFFERENTIAL SYSTEMS AND ITS APPLICATIONS

This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.     

禁用偶氮染料检测中假阳性结果的鉴别方法

全面比较了薄层色谱法、握相色谱法、液相色谱法（ＨＰＬＣ）、气相色谱－质谱联用法（ＧＣ／ＭＳ）在禁用偶氮染料检测中的优缺点。分析实际检测中假阳性结果产生的原因,研究了８种致癌芳香胺的１９种异构体在气相色谱和订色谱上的分离情况,提出取ＧＣ／ＭＳ和ＨＰＬＣ互为确证手段的阳性结果鉴别方法,可有效提高定性结果和准确性,避免假阳性结果。     

Structure of BaGd2（MoO4）4 Crystal

The title compound belongs to monoclinic,space group C2/c with a=5.2694(1),b=12.6659(4),c=19.4108(2) ,β=91.504(2)°,V=1295.06(5) 3,Z=4 and Dc=5.599 g/cm3. The structure of BaGd2(MoO4)4 contains a MoO4 tetrahedron,a distorted GdO8 polyhedron,and Ba2+ ions in a tenfold coordination. The GdO8 polyhedra are linked together through edge-sharing to give a two-dimensional Gd layer. The MoO4 tetrahedra connected to the Gd atoms are capped up and down the Gd layer through common oxygen apices,thus forming a new Gd-Mo layer. Finally,the Gd-Mo layers are held together through bridging BaO10 polyhedra to form a three-dimensional framework. Since the Ba-μ3-O bond has a large average distance of 2.888 ,this structural characteristic will result in a cleavage along the (001) plane.     

Synthesis and Crystal Structure of [{Cd(hmbdc)(H2O)3}·2H2O]n

A novel coordination polymer [{Cd(hmbdc)(H2O)3}·2H2O]n (hmbdc=5-hydroxy- isophthalic acid) has been synthesized and characterized by elemental analysis, IR spectra and single-crystal X-ray diffraction. The crystal belongs to monoclinic, space group P21/c, with a=9.599(3), b=18.699(5), c=7.557(2) (A), β= 108.198(4)°, V=1288.6(6) (A)3, Z=4, Mr=382.60, Dc=1.972 g/cm3, F(000)=760, μ=1.740, the final R=0.0555 and wR=0.0995 for 1732 observed reflections with Ⅰ ＞ 2σ(Ⅰ). The structural analysis shows that the intermolecular hydrogen bonds and π-π interactions result in a three-dimensional supramolecular framework.     

Studies on the Structure and Properties of Cordierite Synthesized by Talc-Magnesite

Homogeneous cordierite has been synthesized at low cost by talc-magnesite and coal gangue as the main raw materials. The mechanism of synthesizing cordierite under such a com- posing system of raw materials, and the effect of temperature on the crystal cell parameters and microstructure and thermal expansion coefficient of cordierite crystal have been studied via testing methods of XRD, SEM, etc. The result shows that the homogeneous cordierite can be synthesized by the systematic composing materials of “talc-magnesite—coal gangue—talc” with heat pre- servation at 1350 ℃ for 1 h; as the keeping time is prolonged, Al3+ and Mg2+ in cordierite crystal are replaced by a few impurity ions such as Fe3+, Fe2+, etc., and the crystal cell parameters of cordierite present an increase trend; as the high-temperature heat preservation is prolonged, the content of glassy phase in the sample is increased, its density is improved, and its thermal expansion coeffi- cient presents an increase trend.     

Study on the Dynamics of Blending of Glucomannan with Carrageenan and Guaran Gum

In order to prove up the interaction between konjac glucomannan (KGM) and other amyloses, by using KGM, guaran gum and carrageenan as materials, their blending in different external conditions was modeled by means of molecular dynamics (MD) method. The result showed that 323 K was a significant turning point for the formation of hydrogen bond, and KGM and guaran gum were just juxtaposed together via intermolecular hydrogen bond; but with the addition of carrageenan, KGM, guaran gum and carrageenan were spirally twisted together, and when their blending proportion is 3:2:9 the combination was the most compact. Moreover, the research result has provided the sequent studies afterwards on amyloses with some references.     

To the problem of a strong differentiability of integrals along different directions

It is proved that for any given sequence (σ _n ,n ∈ ℕ)=Γ₀ ⊂ Γ, where Γ is the set of all directions in ℝ² (i.e., pairs of orthogonal straight lines) there exists a locally integrable functionf on ℝ² such that: (1) for almost all directionsσ ∈ Γ\Γ₀ the integral ∫f is differentiable with respect to the familyB _2σ of open rectangles with sides parallel to the straight lines fromσ: (2) for every directionσ _n ∈ Γ₀ the upper derivative of ∫f with respect toB _{2σ n} equals +∞; (3) for every directionσ ∈ Γ the upper derivative of ∫ |f| with respect toB _2σ equals +∞.