Subgroup separability of graphs of abelian groups

In the present paper we give necessary and sufficient conditions for the subgroup separability of the fundamental group of a finite graph of groups with finitely generated abelian vertex groups.

     

A new microtensile tester for the study of MEMS materials with the aid of atomic force microscopy

An apparatus has been designed and implemented to measure the elastic tensile properties (Young's modulus and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are “dog-bone” shaped ending in a large “paddle” for convenient electrostatic or, in the improved apparatus, ultraviolet (UV) light curable adhesive gripping deposited with electrostatically controlled manipulation. The typical test section of the specimens is 400 μm long with 2 μm×50 μm cross section. The new device supports a nanomechanics method developed in our laboratory to acquire surface topologies of deforming specimens by means of Atomic Force Microscopy (AFM) to determine (fields of) strains via Digital Image Correlation (DIC). With this tool, high strength or non-linearly behaving materials can be tested under different environmental conditions by measuring the strains directly on the surface of the film with nanometer resolution.     

Photooxidation of aryl alkanes by a decatungstate/triethylsilane system in the presence of molecular oxygen

Decatungstate photocatalyzes the oxidation of aryl alkanes to the corresponding tertiary hydroperoxides and alcohols, in the presence of molecular oxygen. The addition of triethylsilane to the reaction mixture substantially increases the proportion of hydroperoxide formed.     

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

A 1,8-naphthalenediol-based unsymmetrical dinucleating ligand

A facile synthesis of 2-formyl-1,8-naphthalenediol is reported. Its potential as a general precursor for the preparation of unsymmetrical multidentate chelating ligand systems based on 1,8-naphthalenediol is demonstrated by the synthesis of the dinucleating ligand L(4-)(H(4)L=N,N'-bis(2-(1,8-naphthalenediol)methylidene)propylenediamine). Reaction of H(4) L with copper acetate results in the formation of the unsymmetrical dinuclear Cu(II) complex [LCu(2)](3), which has been structurally characterized by single-crystal X-ray diffraction. One Cu(II) ion is coordinated by a N(2)O(2) compartment of L(4-) and the other Cu(II) ion is coordinated by an O(4) compartment of L(4-) while they are bridged by two aryloxide functions of L(4-). A dimerization of two molecules of 3 to a tetranuclear entity 3(2) occurs through formation of weak apical Cu--O interactions. Analysis of the temperature dependent magnetic susceptibility measurements (2--290 K) established a strong intradimer exchange coupling J(12)=-371 cm(-1). This strong superexchange interaction fits nicely in a magneto-structural correlation which has been established for dinuclear bis(phenoxide)-bridged Cu(II) complexes demonstrating the electronic equivalence of the aryloxides of a phenol and 1,8-naphthalenediol.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

Intrazeolite photooxygenation of chiral alkenes. Control of facial selectivity by confinement and cation-π interactions

Depending on the nature of the substituents on the stereogenic carbon atom, the ene reaction of singlet oxygen with several chiral alkenes by confinement within thionin-supported zeolite NaY, may exhibit significant changes on facial selectivity by comparison to their photooxygenation reaction in solution. It is proposed that, apart from the conformational consequences as a result of the alkene confinement within the zeolite cavities, a synergism between Na⁺-π interactions and singlet oxygen-Na⁺ interactions plays a significant role in the transition states of ene hydroperoxidation. Within NaY, the diastereoselectivity may significantly depend on the site selectivity, as probed through specific deuterium labelling of trisubstituted alkenes bearing a gem-dimethyl group. In certain cases, a remote stereogenic centre relative to the reacting double bond may induce enhanced diastereoselection and regioselectivity.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors     

A novel and facile synthesis of 7,8-diacylcoumarins

Oxidation of N-carbonylhydrazones of 7-hydroxy-8-acetylcoumarin with lead tetraacetate results in the synthesis of 7,8-diacylcoumarins in good yields. The reaction proceeds via the transformation of a hydroxy into an acyl group reported for the first time in heterocyclic chemistry.