Ammonium chiral borate salt catalyzed asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals

In the presence of a catalytic amount of ammonium chiral borate salt, asymmetric Friedel-Crafts alkylation of indoles with α,β-disubstituted enals proceeded to give the corresponding 1,4-addition products with moderate enantioselectivities.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.     

On the Hyers–Ulam stabilities of functional equations on ‐Banach spaces

The purpose of this article is to generalize the theory of stability of functional equations to the case of n‐Banach spaces. In this article, we prove the generalized Hyers–Ulam stabilities of the Cauchy functional equations, Jensen functional equations and quadratic functional equations on n‐Banach spaces.     

Cokriging for spatial functional data

This work proposes to generalize the method of kriging when data are spatially sampled curves. A spatial functional linear model is constructed including spatial dependencies between curves. Under some regularity conditions of the curves, an ordinary kriging system is established in the infinite dimensional case. From a practical point-of-view, the decomposition of the curves into a functional basis boils down the problem of kriging in infinite dimension to a standard cokriging on basis coefficients. The methodological developments are illustrated with temperature profiles sampled with dives of elephant seals in the Antarctic Ocean. The projection of sampled profiles into a Legendre polynomial basis is performed with a regularization procedure based on spline smoothing which uses the variance of the sampling devices in order to estimate coefficients by quadrature.     

ADSORPTION OF CAFFEINE BY HYDROGEN DONATING ADSORBENTS BASED ON HYDROGEN BONDING

1. INTRODUCTIONHydrogen bonding is a useful mechanism for adsorptive separation. The low enemy of thisbond ensures reversibility, while the directionality and the short range of this bond conferselectivity. The adsorption of hydrogen donating solutes onto an adsorbent capable of acceptinghydrogenedmberlite XAD-7, an adsorbent consisted of polycarboxylic ester--based onhydrogen bonding has been examined in detail 11-41. However, the adsorption of hydrogenaccepting solutes onto polymeric a…     

Eigenfunctions of transfer operators and cohomology

The eigenfunctions with eigenvalues 1 or −1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with coefficients in certain principal series representations.     

Four applications of majorization to convexity in the calculus of variations

The resemblance between the Horn-Thompson theorem and a recent theorem by Dacorogna-Marcellini-Tanteri indicates that Schur-convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity, such as rank one convexity or quasiconvexity. In Theorem 6.6, we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant.Majorization is used in order to give a very short proof of a theorem of Thompson and Freede [R.C. Thompson, L.J. Freede, Eigenvalues of sums of Hermitian matrices III, J. Res. Nat. Bur. Standards B 75B (1971) 115-120], Ball [J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, in: R.J. Knops (Ed.), Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, vol. 1, Res. Notes Math., 17, Pitman, 1977, pp. 187-241], or Le Dret [H. Le Dret, Sur les fonctions de matrices convexes et isotropes, CR Acad. Sci. Paris, Série I 310 (1990) 617-620], concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity.Next we prove (Theorem 7.3) a lower semicontinuity result for functionals with the form _∫Ωw(D?(x))dx, with w(F)=h(lnV_F). Here F=R_FU_F=V_FR_F is the usual polar decomposition of F∈gl(n,R), and lnV_F is Hencky’s logarithmic strain.We close this paper with a compact proof of Dacorogna-Marcellini-Tanteri theorem, based only on classical results about majorization. The mentioned resemblance of this theorem with the Horn-Thompson theorem is thus explained.     

Nombres de Tamagawa des groupes réductifs quasi-connexes

We define Tamagawa numbers for quasi-connected linear algebraic groups. This category of non-connected linear algebraic groups occurs naturally in the stabilization of the Arthur-Selberg trace formula. An expression for their Tamagawa numbers, needed for the stabilization process, is given in term of cohomological invariants generalizing results of Ono, Sansuc, Kottwitz and Kottwitz & Shestad. Received: 7 March 2000     

Paraloid文物保护材料光老化的红外光谱研究

Paraloid(乳胶粘合剂)是一系列丙烯酸树脂的商品名称,是文物保护领域中最常用的保护材料之一,主要用于文物的加固、封护和粘接,适用文物材质范围非常广泛。其中以Paraloid B-72最具代表性,在国内外的文物保护中被大量使用,相关的应用案例、性能评价及其老化机理研究都有较多报道,而Paraloid系列的其他产品却鲜有关注,在国内应用较少,老化性能研究尚未开展工作。该研究系统评价了Paraloid B-72,Paraloid B-44,Paraloid B-48N和Paraloid B-67的光老化性能,采用红外光谱跟踪紫外辐照3 864 h过程中Paraloid材料分子结构变化,对光老化机理进行了深入解析和半定量评测。结果显示,4种Paraloid系列丙烯酸树脂材料中,B-72老化前后颜色和光泽度均没有发生明显变化,B-48N和B-67老化前后色差较大,B-44光泽度降低最多。丙烯酸树脂老化过程中高分子材料内部发生断链反应以及一定程度的交联反应,表现在主要官能团吸收的减弱和羰基指数（CI）的增加。根据主要官能团吸收峰C═O相对强度的半定量分析结果反映出,B-72的光稳定性最好,B-48N和B-44略优于B-67,但与B-72相比差距较大。B-67可能是由于异丁基上的叔氢键能较低,易吸收光能量后产生自由基氧化反应,因此耐光老化性最差。综合评定4种Paraloid系列丙烯酸树脂的光老化性能,B-72在4种材料中光稳定性最好,其次是B-44和B-48N,最不适宜作为户外文物保护材料的是B-67。研究结论有望为一线文物保护工作者在选择Paraloid丙烯酸树脂作为保护材料时提供一定的科学参考。