An asymptotic finite element method for improvement of solutions of boundary layer problems

Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(ⁿ⁺¹) (where is the small parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes.     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

Synthesis, crystal structure and magnetic properties of a novel complex [Cu(NIT2Py)(PDA)(H2O)]·(CH3OH)(H2O)

A novel complex [Cu(NIT2Py)(PDA)(H₂O)]·(CH₃OH)(H₂O) has been synthesized and structurally characterized by X-ray diffraction methods. It crystallizes in the monoclinic space group P2(1)/c. The structure consists of [Cu(NIT2Py)(PDA)(H₂O)] moiety, one solvent methanol molecule and one water molecule. The copper(II) ion is in a distorted octahedral environment: one nitrogen atom and one oxygen atom from the NIT2Py, one nitrogen atom from the PDA (2,6-pyridine dicarboxylic acid) and one oxygen atom from the aqueous in the basal plane; two oxygen atoms from the PDA in the axial position. The units of [Cu(NIT2Py)(PDA)(H₂O)] were connected as one dimension chain by the intermolecular hydrogen bonds. The complex exhibits intramolecular antiferromagnetic interactions between the Cu(II) ion and the NIT2Py.     

荧光法研究Ge-132对牛血清白蛋白Maillard反应的抑制作用

人体内氨基酸及蛋白质的非酶糖化反应(Maillard反应)与糖尿病及其并发症的关系已经引起广泛注意[1].有机锗化合物β-羧乙基锗倍半氧化物(Ge-132)具有预防糖尿病及调节糖代谢的作用[2].     

A Chiral Coordination Polymer of Silver(I) with Saccharinate and Pyridine: Synthesis,Spectral, Thermal,and Structural Characterization of [Ag(sac)(py)]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The first silver(I) complex of saccharinate (sac) with pyridine (py), [Ag(sac)(py)]_n has been synthesized and characterized by elemental analysis, IR spectroscopy and single crystal X-ray diffractometry. The complex crystallizes in chiral, trigonal space group P3₁21 (No. 152) with unit cell parameters of a = 11.2605(2) Å, c = 17.3300(4) Å, V = 1903.02(6) ų and Z = 6. [Ag(sac)(py)]_n contains monomeric [Ag(sac)(py)] units linked into infinite helices by way of Ag⋅sAg interactions [d(Ag⋅sAg) = 2.909(2) and 2.985(1) Å]. The distorted square-planar environment of Ag is completed by an N-bonded sac [Ag—N = 2.084(2) Å] and a py molecule [Ag—N = 2.116(2) Å]. The N_sac—Ag—N_py angle is 173.85(10)^∘. The one-dimensional chains are crosslinked by C—H⋅sO interactions involving the carbonyl and sulfonyl O atoms of sac and aromatic-ring hydrogen atoms of both sac and py. The thermal stability of the title complex was investigated using thermogravimetry and differential thermal analysis in a static atmosphere of air. The first decomposition stage between 90 and 160^∘C corresponds to removal of the py molecule in a single stage, while the degradation of the sac moiety occurs at two stages in the temperature range 370–515^∘C, giving an end product of metallic Ag.     

Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

Both the homometal cluster [P(ph₄)]₂[Mo₂O₂(μ-S)₂(S₂)₂] (1) and [Mo₂O₂(μ-S)₂(Et₂dtc)₂] (2) (Et₂dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145×10⁻³⁰ esu for (1) and 5.428×10⁻³⁰ esu for (2).     

Two-photon absorption in quadrupolar pi-conjugated molecules: influence of the nature of the conjugated bridge and the donor-acceptor separation

Quadrupolar-type substitution of pi-conjugated chromophores with donor and acceptor groups has been shown to increase their two-photon absorption (TPA) response by up to two orders of magnitude. Here, we apply highly correlated quantum-chemical calculations to evaluate the impact of the nature of conjugated bridge and the charge-transfer distance on that enhancement. We compare chromophores with phenylenevinylene-, thienylenevinylene-, polyene-, and indenofluorene-type backbones substituted by dimethylamino and cyano groups. In all compounds, we find a strongly TPA-active A(g) state (either 2A(g) or 3A(g)) in the low-energy region, as well as a higher lying TPA-active state (mA(g)) at close to twice the energy of the lowest lying one-photon allowed state; the smaller energy detuning in the mA(g) states results in very large TPA cross sections delta. We also investigate the influence of the degree of ground-state polarization on TPA. Independent of the nature of the backbone and the donor-acceptor separation, delta displays the same qualitative evolution with a maximum before the cyanine-like limit; the highest TPA cross sections are calculated for distirylbenzene- and polyene-based systems.