Tensor product of dualizing complexes over a field

Let $k$ be a field, and let $X,Y$ be two locally noetherian $k$-schemes (respectively $k$-formal schemes) with dualizing complexes $R_X$ and $R_Y$ respectively. We show that $R_X \boxtimes_{k} R_Y$ (respectively its derived completion) is a dualizing complex over $X\times_{k} Y$ if and only if $X\times_{k} Y$ is locally noetherian of finite Krull dimension.Comment: 13 pages, final version, to appear in the Journal of Commutative Algebr

Coarsening of graded local cohomology

Some criteria for graded local cohomology to commute with coarsening functors are proven, and an example is given where graded local cohomology does not commute with coarsening.Comment: minor correction

Heat Treated NiP–SiC Composite Coatings: Elaboration and Tribocorrosion Behaviour in NaCl Solution

Tribocorrosion behaviour of heat-treated NiP and NiP–SiC composite coatings was investigated in a 0.6 M NaCl solution. The tribocorrosion tests were performed in a linear sliding tribometer with an electrochemical cell interface. It was analyzed the influence of SiC particles dispersion in the NiP matrix on current density developed, on coefficient of friction and on wear volume loss. The results showed that NiP–SiC composite coatings had a lower wear volume loss compared to NiP coatings. However, the incorporation of SiC particles into the metallic matrix affects the current density developed by the system during the tribocorrosion test. It was verified that not only the volume of co-deposited particles (SiC vol.%) but also the number of SiC particles per coating area unit (and consequently the SiC particles size) have made influence on the tribocorrosion behaviour of NiP–SiC composite coatings

Catalytic transesterification of cellulose in ionic liquids: Sustainable access to cellulose esters

Catalytic transesterifications of cellulose were studied under homogeneous conditions using the ionic liquid 1-butyl-3-methylimidazolium chloride (BMIMCl) as a solvent. Cellulose was thus efficiently converted into cellulose esters employing various methyl esters and 10 mol% of 1,5,7-triazabicyclo[4.4.0]dec-5- ene (TBD) as catalyst. 1H NMR analysis of the products revealed up to 2.3 turnovers of the methyl esters per catalyst molecule, leading to degrees of substitution (DS) of up to 0.69. Although a comparatively low turnover number (TON) is observed, the developed methodology represents the first successful homogeneous catalytic reaction on cellulose. Furthermore, the new method is an important step forward in terms of sustainability, since the BMIMCl-DMSO mixture can be recycled and reused for the reaction, and toxic and corrosive chemicals commonly employed for cellulose esterification (such as anhydrides, acid chlorides and bromides, organic bases, all in overstoichiometric amounts) are avoided. To demonstrate the versatility of this transesterification, an aromatic (cellulose benzoate), an aliphatic (cellulose butyrate), and a fatty acid containing cellulose ester (cellulose 10-undecenoate) were prepared. Additionally, cellulose 10-undecenoate was successfully used for thiol-ene grafting onto reactions employing two thiols for efficient thiol-ene addition reactions. This journal is © the Partner Organisations 2014