The constants of the Volterra derivation

The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.     

On positive solutions for a class of quasilinear elliptic systems

We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.     

A study of accelerated Newton methods for multiple polynomial roots

We analyze and compare several accelerated Newton methods with built in multiplicity estimates. We also introduce the concept of indicator functions and discuss the Crouse-Putt method. It is shown that many of the accelerated Newton methods not only derive from Schröder’s classic approach but are equivalent. The related computational experiments show that the built in multiplicity estimates can significantly decrease the number of Newton iterations, while the error of these estimates may significantly increase.     

M?ssbauer analysis of high-energy mechanical-milled sand fraction of a magnetic soil developing on basalt

A sample of the coarse sand fraction from the soil material of the A-horizon (0?C0.2 m from the soil surface) of a dusky red magnetic Oxisol was submitted to high-energy mechanical milling for different times. This assay aimed mainly at (a) monitoring the individualization of strongly aggregated mineral particles, and (b) measuring the effect of the milling pressure on the mineralogy changes of the material. These data are also intended to experimentally subside any physical model describing the mechanical behavior of the superficial soil layer that is subjected to intensive machine management, in agriculture fields. Powder X-ray data reveal that some mineralogical phases, notably gibbsite, disappear soon after the first few hours milling. The 298 K-transmission Mössbauer spectrum for the non-milled sand sample shows a qualitatively typical pattern for the sand fraction of basalt derived soils, with magnetically ordered sextets, assignable mainly to hematite and maghemite, and an intense central (super)paramagnetic Fe^3?+? doublet. For the milled samples, spectra revealed progressive spectral reduction of the magnetic hyperfine structure, with concomitant increase of relative subspectral areas due to (super)paramagnetic phases, as the milling time increased. This result is consistent with the reduction of measured saturation magnetization, from 4.96(8) J T^???1 kg^???1, for the non-milled sample, to 3.26(7) J T^???1 kg^???1, for the sample milled for 8 hours.     

Reactions of 2-Deoxy-4, 5-O-Isopropylidene-D-Erythro- and D-Threo-Pent-1-Enose Derivatives

ABSTRACT

The reactivity of the title compounds has been studied toward different nucleophiles and electrophiles. Unlike other ketene dithioacetals, compounds 3-5 did not add nucleophiles to the double bond. Instead, in the presence of Lewis acids they underwent substitution reaction at position 3. If the nucleophile was not strong enough, formation of 6 and 7 were observed. With 2,3,4,6-tetra-O-acetyl-1-thio-β-D-glucopyranose (18), a 3:1 mixture of 11 and 12 was formed from 4. These observations may be interpreted in terms of easy formation of the allylic carbocation I which gives diastereomers with nucleophiles. However, this allylic ether-like behaviour was ruled out by the fact that compounds 9 and 10 did not undergo [2,3] sigmatropic rearrangement with lithium diisopropylamide. With N-bromosuccinimide compound 3 gave the 2-bromo derivative 8. Compounds 3 and 8 resisted common mercury salt assisted demercaptalization procedures.     

Synthesis of linear and hyperbranched sugar‐grafted polysiloxanes using N‐hydroxysuccinimide‐activated esters

A straightforward method for the preparation of polysiloxanes grafted with carbohydrate side groups is described. Two kinds of backbones have been functionalized, namely one‐dimensional, linear polysiloxanes, and hyperbranched poly(siloxysilane)s based on cyclotetrasiloxanes. The method enables us to keep a good integrity of the polysiloxane backbone. The introduction of intermediate activated esters as side groups on the polysiloxane backbone ensures a complete homogeneity of the reaction medium during sugar grafting in dimethyl sulfoxide, and consequently an easy grafting with the unprotected amino sugar. Solubility of the resulting polysiloxanes has been tested in various solvents. The sugar‐grafted polysiloxanes are good candidates for applications such as silicone formulations, hydrophilic silicone elastomers, interactions with metallic nanoparticles, and suspension stabilization, or as starting point for the design of more complex polysiloxanes for molecular recognition. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3607–3618