Approximation of multi-scale elliptic problems using patches of finite elements

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439–456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1–21). However it is of much more flexible use in comparison to the latter. To cite this article: R. Glowinski et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

The phenomenon of conglomerate crystallization. Part 40: The crystallization behavior oftrans- Co(III) amines (+)546-trans-[Co(3,2,3-tet)(NO2)2]Cl·3H2O (I), (−)589 -trans-[Co(3,2,3-tet)Cl2]NO3 (II), and of (+)546-trans-[Co(3,2,3-tet)(NO2)2]NO3 (III)

A racemic solution of (I) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₄₆-trans-[Co(3,2,3-tet)(NO₂)₂]Cl·3H₂O (I), CoClO₇N₆C₈H₂₈. It crystallizes in the enantiomorphic space groupP2_l2_l2_l, with lattice constantsa=18.501(15) å,b=14.433(2) å, andc=6.441(3) å;V=1720.07 å³ andd(calc. M.W.=414.73,Z=4)=1.601 g cm^?3. A total of 2305 data were collected over the range of 4?≤2θ ≤55?; of these, 1724 (independent and withI > 3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.920 cm^?1), and the relative transmission coefficients ranged from 0.8258 to 0.9565. Refinement was carried out for both lattice enantiomorphs, and at this stage theR(F) andR _w (F) residuals were, respectively, 0.0381 and 0.0479 for (+ + +) and 0.0448 and 0.0532 for (? ? ?). Thus, the former was selected as correct for our specimen, and the final cycle of refinement with the (+ + +) model converged toR(F) andR _w (F) of 0.0315 and 0.0365. A racemic solution of (II) crystallizes as a conglomerate from which a crystal we selected was found to be (?)₅₈₉-trans-[Co(3,2,3-tet)Cl₂]NO₃ (II), CoCl₂O₃N₅C₈H₂₂. It crystallizes in the enantiomorphic space groujp,P2_l with lattice constantsa=6.395(2) å,b=8.886(2) å,c=13.185(2) å, andΒ=99.24(2)?;V=739.59 å³ andd(calc. M.W.=366.14,Z=2)=1.646 g cm ^?3. A total of 2912 data were collected over the range of 4?<2θ<64?; of these, 2147 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ =15.424 cm^?1), and the relative transmission coefficients ranged from 0.9632 to 0.9985. Refinement was carried out for both lattice enantiomorphs, and the finalR(F) andR _w (F) residuals were, respectively, 0.0326 and 0.0328 for (+ + +) and 0.0347 and 0.0348 for (? ? ?). Thus, the (+ + +) was selected as correct for our specimen. A racemic solution of (III) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₈₉-trans-[Co(3,2,3-tet)(NO₂)₂]NO₃ (III), CoO₇N₇C₈H₂₂. It crystallizes in the enantiomorphic space group,P2_l with lattice constantsa=6.295(1) å, b=15.108(3) å,c=8.029(1) å, andΒ=100.28(2)?;V=751.35 å³ andd(calc. M.W.=387.24,Z=2)=1.712 g cm^?3. A total of 2393 data were collected over the range of 4?≤2θ≤60?; of these, 1869 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.859 cm^?1), and the relative transmission coefficients ranged from 0.8814 to 0.9976. Refinement was carried out for both lattice enantiomorphs and the finalR(F) andR _w (F) residuals were, respectively, 0.0463 and 0.0482 for (+ + +) and 0.0441 and 0.0442 for (? ? ?). Thus, the latter was selected as correct for our specimen, and the final cycle of refinement with the (? ? ?) model converged toR(F) andR _w (F) of 0.0436 and 0.0421. For all three compounds, the six-membered rings are chairs; the secondary nitrogens are chiral centers, and the five-membered rings are ordered and conformationally dissymmetric, as expected. Coincidentally, in (I), (II), and (III) the central rings are right-handed helices withδ(+50.0?),δ(+53.3?), andδ(+48.3?), respectively. Thus, the secondary nitrogens of all three cations are (R), rendering the cations chiral. The incidence of conglomerate crystallization intrans coordination compounds is rare, and those known are asymmetrically substituted (see Ref. 4 for the four known cases). Thus, the incidence of such crystallization mode in a new series of [trans- Co(amine ligands)X₂]⁺ cations bearing symmetrical pairs oftrans ligands was an unexpected and welcomed event. In all three cases, the counteranions are bonded to the hydrogens of the terminal -NH₂ moieties, thus forming an overall entity which resembles a macrocycle. In fact, parallels between the crystallization behavior of our compounds and that of macrocycles bearing related fragments is discussed. Finally, in the three compounds, homochiral cations are linked into infinite strings by hydrogen bonds between the axial ligands and amino hydrogens on adjacent cations of the string. In turn, strings are stitched together by the counteranions which form bonds with amino hydrogens on cations of adjacent strings.     

Dinickel Complexes Bridged by Unusual (N,O,O′)-Coordinated α-Amino Acids: Syntheses,Structural Characterization and Magnetic Properties

Four novel dinickel complexes, coordinated by mixed ligands of tren and racemic amino acids, namely [Ni₂(tren)₂(dl-alaninato)(H₂O)]I₃·2H₂O (1), [Ni₂(tren)₂(dl-leucinato)(H₂O)]I₃·2.5H₂O (2), [Ni₂(tren)₂(dl-phenylalaninato)(H₂O)]I₃·H₂O (3), and {[Ni₂(tren)₂(dl-histinato)](ClO₄)₃·1.5H₂O} _n (4), have been synthesized and structurally characterized by X-ray crystallography, FTIR, u.v. and e.s. spectra. They represent the first series of dinickel(II) complexes bridged by the unusual (N,O,O)-coordinated -amino acids. In complexes (1–3), one of the nickel(II) centers is coordinated by four N-atoms of the tren ligand, one O-atom of the carboxylate group of the amino acidato ligand and one H₂O molecule. The other nickel(II) center is also coordinated by the four N-atoms of the tren ligand, one carboxylic O-atom and the amino N-atom of the amino acidato ligand, resulting in an asymmetric dinuclear core with chromophores of NiN₄O₂ and NiN₅O. In the polymeric {[Ni₂(tren)₂(dl-histinato)](ClO₄)₃·1.5H₂O} _n (4), the imidazole N-atom is also involved in ligation with nickel(II) and both nickel(II) centers have the same chromophore described as NiN₅O. The Ni...Ni distances are in the 5.5199(10)–5.5807(15)Å range. Analyses of the magnetic properties of complexes (1), (3) and (4) show that a weak ferromagnetic interaction exists between the two nickel(II) centers.     

Synthesis Optimization of Quaternized Chitosan and its Action as Reducing and Stabilizing Agent for Gold Nanoparticles

The optimal conditions for synthesizing quaternized chitosan (QCS) via microwave irradiation were explored. The microwave temperature, time, power, mole ratio between chitosan and 2,3-epoxypropyltrimethyl ammonium chloride (ETA), volume ratio between isopropanol and water, and pH value of the reaction system were studied to evaluate the effect on the degree of substitution (DS). The structure of QCS was characterized by means of FT-IR, NMR, XPS and XRD. TGA and DTG were used to measure its thermal stability. At last, QCS acted as a reducing and stabilizing agent to greenly synthesize gold nanoparticles without adding any other chemical reagent.     

Preparation and Characterization of Quaternized Chitosan Under Microwave Irradiation

For the first time, N-(2-hydroxyl) propyl-3-trimethyl ammonium chitosan chloride (HTCC) was prepared through a fast, easy and efficient method with the assistance of microwave irradiation, and the quaternized chitosan was also degraded via the microwave irradiation. A comparative study was performed by using the conventional heating method to prepare HTCC. The structure and property of the quaternized chitosan obtained by these two methods were characterized by GPC, XRD, FTIR, NMR, TG and elemental analysis. It was shown that quaternized chitosan was successfully prepared within 50 min via microwave irradiation method, while a much longer time of 6–7 h was needed with the conventional heating method. The substitutions both occurred on the C2 position of chitosan with the two different methods, and their HTCC products had weight average similar molecular weight (Mw), structure and thermal stability. The HTCC prepared by the microwave irradiation method had a little lower degree of substitution (DS) than those prepared via conventional heating with the same mole ratio (6:1) of the intermediate to chitosan. The degradation study showed that the Mw of HTCC decreased rapidly from 4.6 × 10⁵ to 1.1 × 10⁵ in 1 h under microwave irradiation, while it only decreased from 4.6 × 10⁵ to 2.1 × 10⁵in 1 h through conventional heating degradation. These results revealed that microwave irradiation is a more efficient and environment-friendly way to obtain the water-soluble chitosan derivatives and their degraded products.     

离子色谱法测定合成气制烯烃产物中的C_1~C_6有机酸

采用离子色谱建立了合成气制烯烃(SGTO)水相产物和油相产物中C1~C6有机酸的测定方法。对分离条件进行了优化,使用标准样品测定了线性范围和工作曲线,考察了方法的精密度和准确度,确定了SGTO油相产物样品的碱洗条件,并对SGTO水相产物和油相产物样品进行了测定。结果表明:C1~C6有机酸的质量浓度在各自配制的质量浓度范围内呈现良好的线性关系,相关系数均大于0.99。标准溶液的回收率测定表明回收率在95.6%~104.3%之间,5次重复测定的相对标准偏差(RSD)在0.4%~3.6%之间,表明该方法具有良好的准确性和精密度。SGTO油相产物中的加标回收率在91.1%~96.8%之间,5次重复测定的RSD为0.7%~2.3%,准确性可以满足实际分析的需要。实际SGTO水相产物和油相产物中C1~C6有机酸的分析结果表明,SGTO水相产物中C2~C4有机酸含量较高,而SGTO油相产物中C4~C6有机酸含量较高。本研究对SGTO反应研究、催化剂制备、工艺优化以及设备材料的选择具有重要意义。     

气相色谱法测定汽油中苯含量不确定度的评定

通过分析气相色谱法测定汽油中苯含量的操作流程对汽油中的苯含量测量结果的不确定度进行了评定,不确定度主要来源于相对定量校正因子、样品中添加内标物丁酮的体积、样品的体积、样品中苯与内标物丁酮面积的平均值之比、标准物质苯的纯度等参数引入的不确定度。其中相对校正因子引入的不确定度最大。当汽油样品中苯的体积分数为0.57%时,苯含量的扩展不确定度为0.02%(k=2)。     

氨基酸及杂环胺酰乙基锗倍半氧化物合成及对癌细胞的作用

β-羧乙基锗倍半氧化物(即Gc-132)是具广谱药理活性的水溶性有机锗化合物,但因其在体内代谢速度太快而影响药物利用度。因此,对它的各种衍生物的合成和生物活性研究受到重视。为提高Ge-132的亲脂性,增强药物活性,我们在分子中引入具有生物活性的氨基酸或杂环胺,合成了8种新型酰胺衍生物。合成路线如下:     

Rejection-free geometric cluster algorithm for complex fluids

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and nonlocal nature of the algorithm make it particularly suitable for the efficient simulation of complex fluids with components of widely varying size, such as colloidal mixtures. Compared to conventional simulation algorithms, typical efficiency improvements amount to several orders of magnitude.