Capillary gas chromatographic separation of C10–C12 secondary phenylalkanes on modified cyclodextrin stationary phases

The separation of isomers and enantiomers of branched C₁₀-C₁₂ phenylalkanes by gas chromatography on fused silica capillary columns coated with some modified β- and γ-cyclodextrins was studied. It was shown that the separation of positional isomers of C₁₀-C₁₂ phynylalkanes on modified cyclodextrin capillary columns is not better than that on a column coated with modified polyethylene glycol. Differences were found in the enantioselectivity of modified β- and γ-cyclodextrins for the separation of C₁₀-C₁₂ secondary phenylalkane enantiomers. While alkylderivatives of β-CDs resolve enantiomers of 3-phenylalkanes, alkyl derivatives of γ-CD resolve enantiomers of 2-phenylalkanes. Since shape selectivity factors of modified cyclodextrins have indicated no inclusion of the considered solutes in cyclodextrin cavities, enantioselective interactions most probably occur on the outer sphere of cyclodextrins.     

A hydrogen-1, nitrogen-15, and chlorine-35 NMR coordination study of Lu(ClO4)3 and Lu(NO3)3 in aqueous solvent mixtures

A coordination study of Lu(III) has been carried out for the nitrate and perchlorate salts in aqueous mixtures of acetone-d₆ and Freon-12 by¹H,¹⁵N and³⁵Cl NMR spectroscopy. At temperatures lower than –90°C, proton and ligand exchange are slow enough to permit the direct observation of¹H resonance signals for coordinated and free water molecules, leading to an accurate measure of the Lu(III) hydration number. In perchlorate solution, in the absence of inner-shell ion-pairing, Lu(III) exhibits a maximum coordination number of six over the allowable concentration range of study, contrasting markedly with the report of values of six to nine or greater as determined by a similar NMR method. The absence of contact ion-pairing was confirmed by³⁵Cl NMR chemical shift and linewidth measurements. Extensive ion-pairing was observed in the nitrate solutions as reflected by the lower Lu(III) hydration numbers of two to three in these systems, the observation of two coordinated water signals, and¹⁵N NMR signals for two complexes. The¹H and¹⁵N NMR spectra and the hydration number could be accounted for by the presence of (H₂O)₄Lu(NO₃)²⁺ and (H₂O)₂Lu(NO₃) ₂ ¹⁺ .     

H, C, N NMR, ESI mass spectral and single crystal X-ray structural characterization of three spiro[pyrrolidine-2,3′-oxindoles]

Three spiro[pyrrolidine-2,3′-oxindoles], 1,1′,2,2′,5′,6′,7′,7′a-octahydro-2-oxo-1′-phenyl-spiro[3H-indole-3,3′-[3H]-pyrrolizine]-2′-carboxylic acid methyl ester (1), 1,1′,2,2′,5′,6′,7′,7′a-octahydro-2-oxo-1′-nitro-2′-phenyl-spiro[3H-indole-3, 3′-[3H]-pyrrolizine] (2) and 1,1′,2,2′,5′,6′,7′,7′a-octahydro-2-oxo-1′-nitro-2′-(4″-chlorophenyl)-spiro[3H-indole-3,3′-[3H]-pyrrolizine] (3) have been synthesized and their ¹H, ¹³C and ¹⁵N spectra assigned. The chemical shift assignments are based on Pulsed Field Gradient (PFG) Double Quantum Filter (DQF) ¹H, ¹H correlation spectroscopy (COSY), PFG ¹H, ¹³C Heteronuclear Multiple Quantum Coherence (HMQC) and PFG ¹H,X (X = ¹³C and ¹⁵N) Heteronuclear Multiple Bond Correlation (HMBC) experiments. The single crystal X-ray structures of 1–3 have been determined. Compounds 1 and 2 crystallized in monoclinic space group C2/c and compound 3 in monoclinic space group P2₁/c, respectively. Also the ESI-TOF MS data of 1–3 are given.     

Triterpene Glycosides of Astragalus and Their Genins. LXVI. Cycloorbicoside C, a New Bisdesmoside

The new triterpene glycoside cycloorbicoside C was isolated from the aerial parts of Astragalus orbiculatus Ledeb. (Leguminosae) and was identified as (23R,24S)-16,23;16,24-diepoxycycloartan-3,25-diol 3-O--D-xylopyranoside 25-O--D-glucopyranoside.     

Regioselective Borylation of Porphyrins by C?H Bond Activation under Iridium Catalysis to Afford Useful Building Blocks for Porphyrin Assemblies

Highly regioselective and efficient borylation of a variety of porphyrins has been achieved by reaction with bis(pinacolato)diboron through C? H bond activation under iridium catalysis on the basis of the synthetic protocol developed by Miyaura, Hartwig, and Smith. A boryl group can be selectively introduced at sterically uncongested positions in the peripheral aryl groups of porphyrin substrates whose peripheral β‐positions are sterically hindered. Curiously, β substituents adjacent to the aryl group to be borylated have unexpectedly large effects on the regioselectivity, because the iridium catalyst can discriminate between subtle steric differences. Chemoselective borylation was also achieved for several functionalized porphyrins. This borylation protocol can be applied to various monomeric and oligomeric functional porphyrins, hence offering an efficient route to elaborate multiporphyrin‐based molecular constructs.     

Affine Ebenen und Tupelsysteme

Zusammenfassung Es werden zwei neue Koordinatisierungsmethoden für affine Ebenen gegeben, und zwar durch homogene bzw. stark balancierte Tupelsysteme. Ihre Brauchbarkeit wird u.a. demonstriert an einer Charakterisierung der Kollineationsgruppen einer affinen Ebene mit der Eigenschaft (R) Für alle i l enthält der Stabilisator von i nur Perspektivitäten mit Zentrum i. Außerdem wird der Satz bewiesen: Für eine Elation der geraden Ordnung d in einer projektiven Ebene der Ordnung v gilt 2d|v. Dieses Resultat impliziert schon bekannte Ergebnisse von Hughes (d=2) und Hall.

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We give two new coordinatization methods for affine planes by means of homogeneous (resp. strong balanced) tuple systems. Their usefulness is demonstrated by proving a characterization of collineation groups of an affine plane with the property (R): The stabilizer of every i l contains only perspectivities with centre i. Besides, we prove: If a projective plane of order v contains an elation of even order d then 2d|v. This implies known results of Hughes (d=2) and Hall.

     

On the homogeneity of additive mappings

LetK be a ring with an identity 1 0 andM, L two unitaryK-modules. Then, for any additive mappingf:M L, the setH _f :={ K f(x)=f(x) for allx M} forms a subring ofK, the homogeneity ring off. It is shown that, forM {0},L {0} and any subringS ofK for whichM is a freeS-module, there exists an additive mappingf:ML such thatH _f =S. This result is applied to the four Cauchy functional equations, and it leads also to an answer to the question as to whether it is possible to introduce onM a multiplication ·:M × M M makingM into a ring but not into aK-algebra.     

Matrix summability and a generalized Gibbs phenomenon

Letf be a real-valued function sequence {f _k } that converges to on a deleted neighborhoodD of . If there is a subsequence {f _k(j) } and a number sequencex such that lim _j x _j = and either lim _j f _k(j) (x _j )>lim sup _x (x) or lim _j f _k(j) (x _j ) x (x), thenf is said to display theGibbs phenomenon at . IfA is a (real) summability matrix, thenAf is a function sequence given by(Af) _n (x)= _k=0 a _n,k f _k (x). IfAf displays the Gibbs phenomenon wheneverf does, thenA is said to beGP-preserving. By replacingf _k (x) withf _k (x _j )F _k,j , the Gibbs phenomenon is viewed as a property of the matrixF, andGP-preserving matrices are determined by properties of the matrix productAF. The general results give explicit conditions on the entries {a _n,k } that are necessary and/or sufficient forA to beGP-preserving. For example: if(x)0 thenF displaysGP iff lim _k,j F _k,j 0, and ifA isGP-preserving then lim _n,k A _n,k 0. IfA is a triangular matrix that is stronger than convergence, thenA is notGP-preserving. The general results are used to study the preservation of the Gibbs phenomenon by matrix methods of Nörlund, Hausdorff, and others.     

The complete figure for second order multiple integral problems in the calculus of variations

Notation Throughout this paper Greek indices, , , and Latin indicesi, j, h, k, assume the values 1, ,m, and 1, ,n respectively. The summation convention is operative in respect of both sets of indices.This work was supported by the South African Council for Scientific and Industrial Research.At time of writing Professor Grässer was Visiting Scholar at the University of Arizona, Tucson, Arizona.     

Banach空间半线性发展方程的周期解

把上、下解方法引入到有序Ｂａｎａｃｈ空间中的半线性发展方程周期解问题，利用正算子半群特征与单调迭代程序，获得了最大周期解与最小周期解的存在性．所得的结果概括和推广了常微分方程与偏微分方程中的有关结论