Ternäre intermetallische Phasen des Lithiums mit Elementen der 4. Neben- und 5. Hauptgruppe mit statistischer Metallverteilung im „Kationen”︁-Teilgitter

Ternary Intermetallic Phases of Lithium, Transition Metals of the 4^th Group and Elements of the 5^th Maingroup with Statistical Metal Distribution in the ?Cation”?-Substructure The results of X-ray investigations and neutron diffraction on new and in some cases already known [1, 2] ternary intermetallic phases of Lithium with transition metals of the 4^th group (b) and those of the 5^th main group (X = P, As, Sb, Bi) will be reported. They crystallize in a partly ?filled”? antifluorite type structure with a statistical Li/B-distribution in the tetrahedral sites. The structures are obviously stabilized by small amounts of enclosed d-elements.     

A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s ₁ψ₁ summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33D15 B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency. A. J. Yee: Research partially supported by a grant from The Number Theory Foundation.     

Matrix Elements in Analytic Form for Displaced Linear Oscillators

Analytic expressions of matrix elements of x^″, exp(-2cx) and exp(-cx²/2) for displaced linear oscillators with unequal vibrational frequencies are evaluated.     

Synthesis, structural characterization and properties of a 3D infinitely extended structural rare earth coordination compound of K3{[Sm(H2O)7]2Na[α-SiW11O39Sm(H2O)4]2}·14 H2O

A 3D infinitely extended structural rare earth coordination compound with a formula of K3{[Sm(H2O)7]2Na[α-SiW11O39Sm(H2O)4]2}·14H2O has been synthesized by reaction of Sm2O3, HClO4, NaOH with α-K8SiW11O39·nH2O, and characterized by IR,UV spectra, ICP, TG-DTA, cyclic voltammetry, variable-temperature magnetic susceptibility and X-ray single-crystal diffraction.X-ray single-crystal diffraction indicates that the title compound crystallizes in a triclinic lattice, Pī space group, with a=1.2462(3) nm, b=1.2652(3) nm,c=1.8420(4) nm,α=87.45(3)°,β=79.91(3)°,γ=82.57(3)°,Z=1, R1=0.0778,wR2=0.1610.Structural analysis reveals that Sm3+(1) coordination cation has incorporated into the vacant site of [α-SiW11O39]8- entity,forming the [α-SiW11O39Sm(H2O)4]5- subunit.The two adjacent [α-SiW11O39Sm(H2O)4]5- subunits are combined with each other through two Sm(1)-O-W bridges accompanying the formation of dimmer structural unit [α-SiW11O39Sm(H2O)4]210- of the title compound.The neighboring dimmer structural units [α-SiW11O39Sm(H2O)4]210- are linked to form the 1D chainlike structure by means of two Sm3+(2) and a Na+(1) coordination cations.The K+(1) cations connect the 1D packing chains constructing the 2D netlike structure, and adjacent netlike layers are also grafted by K+(2) cations to build the novel 3D infinitely extended structure.The result of TG-DTA curves manifests that the decomposition temperature of the title polyanionic framework is 554℃.The cyclic voltammetry measurements show that the title polyanion has the two-step redox processes in aqueous solution with pH=3.1.Variable temperature magnetic susceptibility indicates the title compound obeys the Cruie-Weiss Law in the higher temperature range from 110 to 300 K, while in the lower temperature range from 2 to 110 K the comparatively strong antiferromagnetism interactions can be observed.     

儿童神经过敏与血清中6种无机元素含量相关性研究

测定了1261名儿童(其中包括73名神经过敏儿童)血清中Zn、Fe、Cu、Ca、Mn和Pb的含量。研究发现,神经过敏患儿血清Zn含量(0.95±0.20μg/mL)显著低于对照组儿童(0.97±0.23μg/mL),P<0.05;Mn含量(0.03±0.01μg/mL)非常显著低于对照组儿童(0.04±0.02μg/mL),P<0.01。     

迭代目标转换因子分析法及其在光度分析中的应用——轻稀土元素多组份同时测定的研究

本文提出一种新的因子分析计算方法,即迭代目标转换因子分析法,避免了对转换矩阵求逆的运算过程,降低了实验误差在计算过程中放大的可能性,从而提高了浓度计算的准确度。用本文方法对La、Ce、Pr、Nd、Sm、Eu、Gd等稀土元素7组份混合物合成样品进行了分析,获得了满意的结果。     

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption linings are modeled as a bulk media with a complex speed of sound and mean density. Domain decomposition and parallel processing techniques are applied to address the high computational and memory requirements. The comparison of the computationally predicted and the experimentally measured transmission loss shows a good agreement.     

Spectroscopic properties as a function of fluorine content in Eu3+:PMMA

In this work europium was used as a spectroscopic probe of the local environment about a lanthanide dopant in a fluorinated copolymer of poly(methyl methacrylate) (PMMA). Fluorination of PMMA was achieved through copolymerization with heptafluorobutyl methacrylate (HFBMA). Samples were characterized for their refractive index, glass transition temperature (T_g), and optical emissions via prism coupling, differential scanning calorimetry, and fluorescence spectroscopy respectively. The refractive index and T_gs were found to decrease linearly with fluorine content. The hypersensitivity ratio, which is defined as the ratio of integrated emission intensity between the ⁵D₀ → ⁷F₂ hypersensitive transition and ⁵D₀ → ⁷F₁ magnetic dipole transition in Eu³⁺, was found to decrease by ～60% when the HFBMA copolymer content exceeded about 75% by weight. This implies a change in the local environment about the rare earth dopant that is dependent on the copolymer concentration and is likely due to changes in solubility between the ligand and host environment. The results show that fluorination of PMMA can be useful to tailor refractive index, glass transition, and the spectroscopic properties of active dopants. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1592–1596, 2006     

A two‐grid stabilization method for solving the steady‐state Navier‐Stokes equations

We formulate a subgrid eddy viscosity method for solving the steady‐state incompressible flow problem. The eddy viscosity does not act on the large flow structures. Optimal error estimates are obtained for velocity and pressure. The numerical illustrations agree completely with the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005