Estimates for the eigenvalues of Hill's equation and applications for the eigenvalues of the laplacian on toroidal surfaces

In this paper we give upper and lower bounds for each eigenvalue λ _n of Hill's differential equation. We apply the results to toroidal surfaces of revolution in order to get estimates for the eigenvalues of the Laplacian in terms of curvature expressions; they are sharp for the flat torus. As an example, we investigate the standard torus in IR³; here, the bounds depend on the radii only.     

New epoxy thermosets modified with hyperbranched poly(ester-amide) of different molecular weight

The influence of hydroxy-functionalized hyperbranched poly(ester-amide) (HBP) of different molecular weight on the curing process of diglycidylether of bisphenol A (DGEBA) was studied using methyltetrahydrophthalic anhydride (MTHPA) as curing agent. By Differential Scanning Calorimetry (DSC) and Fourier Transform Infrared Spectroscopy (FTIR) the curing reaction was monitored and the covalent incorporation of the modifier in the matrix was proved. By thermomechanical analysis (TMA) the reduction of the contraction after gelation on changing the HBP proportion was observed. The incorporation of HBP increased the glass transition temperature (T_g) and reduced the overall shrinkage. The modified materials showed a higher thermal degradability than neat DGEBA thermosets allowing reworkability. Thermal expansion coefficient, Young’s modulus, impact strength and microhardness were improved. The water uptake behavior was also evaluated.     

Distribution of Chlorophyll- and Bacteriochlorophyll-derived Photosensitizers in Human Blood Plasma

Chlorophyll a and, in particular, bacteriochlorophyll a derivatives are promising candidates for photosensitizers in photodynamic therapy. The distribution of 21 (bacterio)chlorophyll derivatives among human blood plasma fractions was studied by iodixanol gradient ultracentrifugation and in situ absorption spectroscopy. Modifications of the natural pigments involved the central metal (Mg²⁺, Zn²⁺, Pd²⁺, none), the isocyclic ring (closed, open and taurinated), substituents at C-3 (vinyl, acetyl, 1-hydroxyethyl) and C-17³ (phytyl ester, free acid). Cellular blood components bound only a small fraction of the pigments. Distribution among low-density lipoproteins (LDL), high-density lipoproteins (HDL) and high-density proteins (HDP) of the plasma was influenced as follows: (1) application in Cremophor^® EL slightly altered pigment distribution by lipoprotein modification, (2) only very polar pigments with multiple hydrophilic substituents showed substantial HDP binding, (3) the presence of the esterifying alcohol at C-17³ caused enrichment in LDL, this was more pronounced with bacteriochlorophylls than with chlorophylls, (4) substituents at C-3 had only little influence on the distribution, (5) Zn²⁺-complexes were enriched in HDL compared to Mg²⁺ and Pd²⁺ complexes, indicating specific binding of the former. Equilibration of pigments among the different fractions was largely complete within 3 h.     

Stereochimie de l'hydrogenation des (±) Δ3(3a)-hydrindenones-4. Comparaison avec le cas de la (+) methyl-3 Δ3(3a)-hydrindenone-4 et de ses dioxolannes

We show that the four studied 4-hydrindenones (with or without a methyl substituant at C3 or C7a) give by hydrogenation on Raney nickel or on Pd/C, in various solvants, the cis 4-hydrindanones, by a kinetically controlled process. During the hydrogenation, the double bond can migrate only in the positions conjugated to the carbonyl group.In contrast, when the carbonyle is protected as a dioxolanne, the double bond is free to migrate around the five membered ring. In spite of this mobility the optical purity of the saturated dioxolannes formed is high. In the case of the (+)3-methyl Δ^3(3a) 4-hydrindenone, the enantiomeric hydrindanones $\text{9a}$ obtained by direct hydrogenation or with isomerization of the double bond are not the same. Therefore, the optical purity of the product is low, but its value allows an estimation of the relative importance of the two reaction pathways.     

Molecule-to-metal bonds: electrografting polymers on conducting surfaces.

Electrografting is a powerful and versatile technique for modifying and decorating conducting surfaces with organic matter. Mainly based on the electro-induced polymerization of dissolved electro-active monomers on metallic or semiconducting surfaces, it finds applications in various fields including biocompatibility, protection against corrosion, lubrication, soldering, functionalization, adhesion, and template chemistry. Starting from experimental observations, this Review highlights the mechanism of the formation of covalent metal-carbon bonds by electro-induced processes, together with major applications such as derivatization of conducting surfaces with biomolecules that can be used in biosensing, lubrication of low-level electrical contacts, reversible trapping of ionic waste on reactive electrografted surfaces as an alternative to ion-exchange resins, and localized modification of conducting surfaces, a one-step process providing submicrometer grafted areas and which is used in microelectronics.     

In-situ deactivation of packed columns for SFC

Residual adsorptive activity of reversed phase (RP) column packings used in supercritical fluid chromatography (SFC) can be significantly reduced by a dynamic in-situ silanization with diphenyltetramethyldisilazane (DPTMDS). RP-materials thus deactivated were characterized both chromatographically and by solid-phase ²⁹Si NMR.     

Synthesis of 2,3-anti-3,4-anti and 2,3-anti-3,4-syn propionate motifs: a diastereoselective tandem sequence of Mukaiyama and free-radical-based hydrogen transfer reactions

[reaction: see text] Reported herein is a strategy employing a Mukaiyama reaction in tandem with a hydrogen transfer reaction for the elaboration of 2,3-anti-3,4-anti and 2,3-anti-3,4-syn propionate motifs. The mode of complexation is controlled through monodentate or chelate pathways for the Mukaiyama reaction to give access to either syn or anti aldol products, precursors of the free-radical reduction reaction. Boron Lewis acid is used to control the free-radical reaction through the exocyclic pathway.