Produktintegration mit nicht-äquidistanten Stützstellen

Summary For the numerical evaluation of , 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.

     

Determination of the solubility of organic compounds. II

Summary In general, solid particles liquify when they are exposed to air laden with the vapor of a liquid in which they are soluble. There are exceptions, however, which may be explained by assuming the formation of a solvate.

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Zusammenfassung Feste Teilchen verflüssigen sich im allgemeinen, wenn sie Luft ausgesetzt sind, die mit dem Dampf einer Flüssigkeit geladen ist, in der sie löslich sind. Es wurden aber Ausnahmen gefunden, die möglicherweise durch die Bildung von Solvaten erklärt werden können.

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Résumé Généralement, les particules solides se liquéfient si elles sont exposées à l'air chargé de la vapeur d'un liquide dans lequel elles sont solubles. Il existe cependant des exceptions que l'on peut expliquer en supposant la formation de solvates.

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On the occasion of the hundredth return ofFriedrich Emich's birthday.

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The authors wish to express their appreciation to ProfessorO. F. Steinbach for his suggestions and advice.     

On the singular graph and the Weyr characteristic of anM-matrix

LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA _ii irreducible. LetS be the set of indices such that the diagonal blockA is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA _i, A_ij, , A_l.Let ₁ be the set of maximal elements ofS, and define thep-th level _p ,p = 2, 3, , inductively as the set of maximal elements ofS \( _{1 p-1}). Denote by _p the number of elements in _p . The Weyr characteristic (associated with 0) ofA is defined to be (A) = ( ₁, ₂,, _h ), where ₁ + + _p = dim KerA ^p ,p = 1, 2, , and _h > 0, _h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = ( ₁, , _h) if and only if certain submatricesD _p,p+1 ,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A. We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = ( ₁, , _h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02.     

Efficient nickel-mediated intramolecular amination of aryl chlorides

The use of an in situ generated Ni(0) catalyst associated with 2,2'-bipyridine or N,N'-bis(2,6-diisopropylphenyl)dihydroimidazol-2-ylidene (SIPr) as a ligand and NaO-t-Bu as the base for the intramolecular coupling of aryl chlorides with amines is described. The procedure has been applied to the formation of five-, six-, and seven-membered rings. [reaction: see text]     

An efficient synthetic route to glycoamino acid building blocks for glycopeptide synthesis

[reaction: see text] Chemical glycopeptide synthesis requires access to gram quantities of glycosylated amino acid building blocks. Hence, the efficiency of synthesis of such building blocks is of great importance. Here, we report a fast and highly efficient synthetic route to Fmoc-protected asparaginyl glycosides from unprotected sugars in three steps with high yields. The glycosylated amino acids were successfully incorporated into target glycopeptides 7 and 8 by standard Fmoc solid-phase peptide synthesis.     

Struktur-Reaktivitäts-Beziehungen bei koordinativ-ungesättigten Chelatkomplexen. VI. Synthese,Adduktbildung, Redoxpotentiale und photochrome lodderivate von Eisen(II)-Komplexen Schiffscher Basen mit elektronenziehenden Substituenten

Structure Reactivity Correlations in Coordinatively Unsaturated Chelate Complexes. VI. Synthesis, Adduct Formation, Redox Potentials, and Photochromic Iodine Derivatives of Iron(II) Complexes with Schiff Base Ligands Possessing Electron-Withdrawing Substituents Iron(II) complexes of the type 1 have been prepared by different synthetic methods. In contrast to similar chelates of the “saloph” and “salen” types, the high-spin complexes 1 form stable high-spin diadducts ( 1a – 1d ) and an unusual triadduct ( 1e ) with pyridine. The oxidation potentials of the Fe^II/Fe^III couple as measured by cyclic voltammetry are dependent on the solvent as well as the equatorial ligand substituents. The potentials are more positive in pyridine than in DMF, indicating a stabilization of Fe^II by pyridine. The redox potentials are discussed with respect to those of other metals in the same ligand environment. The complexes form iodine derivatives which show photochromic behaviour in THF solution. The rate of the reaction with dioxygen in the solid state as well as in pyridine solution decreases in the order 1f > 1a ≈ 1b > 1c ≈ 1d > 1e and correlates with the increasing oxidation potentials.     

Multiplexed hybridizations of positively charge-tagged peptide nucleic acids detected by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Peptide nucleic acid (PNA) is a novel class of DNA analogues in which the entire sugar-phosphate backbone is replaced by a pseudopeptide counterpart. Owing to its neutral character and the consequent lack of electrostatic repulsion, PNA exhibits very stable heteroduplex formation with complementary nucleic acid that is essentially ionic strength independent and enables hybridization under minimum salt conditions. This feature as well as its superior ion stability and easy ionization compared to DNA renders PNA very attractive for hybridization-based matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) applications. We have developed an approach to DNA characterization that takes advantage of multiplexed PNA hybridizations analyzed by MALDI-TOFMS. Our motivation was the further development of oligonucleotide fingerprinting, an efficient technique for cDNA and genomic DNA library characterization. Through positive 'charge-tagging' of PNA the efficiency of detection in MALDI-TOFMS was considerably enhanced permitting an unparalleled degree of multiplexing. Results from the simultaneous hybridization of 21 charge-tagged PNA hexamer oligonucleotides showed that genomic DNA and cDNA clones are successfully characterized on the basis of their hybridization profiles. The degree of multiplexing achieved may render a significant increase in throughput and hence efficiency of oligonucleotide fingerprinting possible.     

1H magic angle rotation NMR in polymer studies

The principles of the method of NMR line narrowing by measurement with spinning of the sample about the magic axis (MAR-NMR) are introduced, with particular emphasis on the effects of internal motion upon the possibilities and limitations of the method. The applications of the method in ¹H-NMR studies of polymer structure and dynamics are then reviewed. Due to both theoretical and experimental limitations, narrowing of dipolar broadened NMR lines by MAR can be observed in ¹H NMR spectra only in those cases where internal motion is anisotropic, or in heterogeneous systems where line width is limited by differences of magnetic susceptibility. In polymers, both solid and liquid, the method makes possible differentiation between isotropic and anisotropic internal motion. In systems with anisotropic internal motion, MAR-NMR makes possible a characterization of motional codes which normally are obscured by residual dipolar interactions, as well as of geometrical restrictions upon these motions.     

Poly(ethyleneimine) as reducing and stabilizing agent for the formation of gold nanoparticles in w/o microemulsions

This paper is focused on the use of branched poly(ethyleneimine) (PEI) as reducing as well as stabilizing agent for the formation of gold nanoparticles in different media. The process of nanoparticle formation was investigated, in the absence of any other reducing agents, in microemulsion template phase in comparison to the nucleation process in aqueous polymer solution.

On the one hand, it was shown that the polyelectrolyte can be used for the controlled single-step synthesis and stabilization of gold nanoparticles via a nucleation reaction and particles with an average diameter of 7.1 nm can be produced.

On the other hand, it was demonstrated that the polymer can also act as reducing and stabilizing agent in much more complex systems, i.e. in water-in-oil (w/o) microemulsion droplets. The reverse microemulsion droplets of the quaternary system sodium dodecylsulfate (SDS)/toluene–pentanol (1:1)/water were successfully used for the synthesis of gold nanoparticles. The polymer, incorporated in the droplets, exhibits reducing properties, adsorbs on the surface of the nanoparticles and prevents their aggregation. Consequently, nanoparticles of 8.6 nm can be redispersed after solvent evaporation without a change of their size.

Nevertheless, the polymer acts already as a “template” during the formation of the nanoparticles in water and in microemulsion, so that an additional template effect of the microemulsion is not observed.

The particle formation for both methods is checked by means of UV–vis spectroscopy and the particle size and size distribution are investigated via dynamic light scattering and transmission electron microscopy (TEM).     

The solubility of an hydroxyaluminosilicate

Hydroxyaluminosilicates (HAS) are critical secondary mineral phases in the biogeochemical cycle of aluminium. They are formed from the reaction of silicic acid (Si(OH)₄) with an aluminium hydroxide template and act as a geochemical control of the biological availability of Al. There are two main forms of HAS which we have called HAS_A and HAS_B and which of these will predominate will depend upon the Si(OH)₄ to Al ratio in any one environment. In all but the most heavily weathered environments or those undergoing a progressive acidification Si(OH)₄ will be present in significant excess to Al and HAS_B will be the dominant secondary mineral phase. We have tried to determine the solubility of HAS_B(s) so that its contribution to Al solubility control might be compared with other secondary minerals such as Al(OH)_3(gibbsite). In preliminary experiments, the dissolution of HAS_B(s) was found to be non-congruent with almost no Al being released during 18 months ageing. We then demonstrated that HAS_B(s) was significantly less soluble than Al(OH)_3(s) prepared under identical experimental conditions. We have used this information to describe a solubility expression for HAS_B(s) at a predefined quasi-equibrium and to calculate a solubility constant.

K^*Al₂Si₂O₅(OH)₄=[Al₂O⁴⁺][SiO₂]²[OH^-]⁴