On a conjecture of Vorst

Let k be an infinite perfect field of positive characteristic such that strong resolution of singularities holds over k. We prove that a localization of a d-dimensional commutative k-algebra R of finite type is K _d+1-regular if and only if it is regular. This partially affirms a conjecture of Vorst.     

Hopf algebroids and H-separable extensions

Since an H-separable extension is of depth two, we associate to it dual bialgebroids and over the centralizer as in Kadison-Szlachányi. We show that has an antipode and is a Hopf algebroid. is also Hopf algebroid under the condition that the centralizer is an Azumaya algebra over the center of . For depth two extension , we show that .

     

Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

A jump operator on honest subrecursive degrees

It is well known that the structure of honest elementary degrees is a lattice with rather strong density properties. Let and denote respectively the join and the meet of the degrees and . This paper introduces a jump operator () on the honest elementary degrees and defines canonical degrees and low and high degrees analogous to the corresponding concepts for the Turing degrees. Among others, the following results about the structure of the honest elementary degrees are shown: There exist low degrees, and there exist degrees which are neither low nor high. Every degree above is the jump of some degree, moreover, for every degree above there exist degrees such that . We have and . The jump operator is of course monotonic, i.e. . We prove that every situation compatible with is realized in the structure, e.g. we have incomparable degrees such that and incomparable degrees such that etcetera. We are able to prove all these results without the traditional recursion theoretic constructions. Our proof method relies on the fact that the growth of the functions in a degree is bounded. This technique also yields a very simple proof of an old result, namely that the structure is a lattice. Received October 4, 1995     

Preparation of a novel HALS polypropylene stabilizer

The radiation induced graft copolymerization of m-isopropenyl-α,α-dimethyl benzyl iso-cyanate (m-TMI) and styrene onto polypropylene was carried out. The extent of grafting increased with increasing amount of styrene and with increased radiation dose. A graft load of 180% was obtained by immersing a 50 kGy pre-irradiated film in a monomer solution containing 25 mol % m-TMI and 75 mol % styrene. The graft copolymer is suitable for covalently binding nonpolymerizable stabilizers with a suitable nucleophilic moiety. In this work the isocyanate moiety of the graft copolymer was allowed to react with 4-amino-2,2,6,6-tetramethyl piperidine, a hindered amine light stabilizer. Fourier trans-formed infrared spectroscopy confirmed the formation of an urea moiety. © 1995 John Wiley & Sons, Inc.     

Reactions of a Four-Membered Borete with Carbon,Silicon, and Gallium Donor Ligands: Fused and Spiro-Type Boracycles

Donor-acceptor cyclopropanes or cyclobutanes are dipolar reagents, which are widely used in the synthesis of complex organic (hetero)cycles in ring expansion reactions. Applying this concept to boron containing heterocycles, the four-membered borete cyclo-iPr₂N-BC₁₀H₆ reacted with the carbon donor ligands 2,6-xylylisonitrile and the carbene IMes :C(NMesCH)₂ with ring expansion and ring fusion, respectively. In particular, the tetracyclic structure formed with IMes displays zwitterionic character and absorption in the visible region. In contrast to the carbene IMes, the heavier carbenoids :Si(NDippCH)₂ and :Ga(AmIm) with a two-coordinate donor atom afford spiro-type bicyclic compounds, which display four-coordinate geometry at silicon or gallium. (TD-)DFT calculations provide deeper insight into the mechanism of formation and the absorption properties of these new compounds.     

Hollow Spheres of Iron Carbide Nanoparticles Encased in Graphitic Layers as Oxygen Reduction Catalysts

Nonprecious metal catalysts for the oxygen reduction reaction are the ultimate materials and the foremost subject for low‐temperature fuel cells. A novel type of catalysts prepared by high‐pressure pyrolysis is reported. The catalyst is featured by hollow spherical morphologies consisting of uniform iron carbide (Fe₃C) nanoparticles encased by graphitic layers, with little surface nitrogen or metallic functionalities. In acidic media the outer graphitic layers stabilize the carbide nanoparticles without depriving them of their catalytic activity towards the oxygen reduction reaction (ORR). As a result the catalyst is highly active and stable in both acid and alkaline electrolytes. The synthetic approach, the carbide‐based catalyst, the structure of the catalysts, and the proposed mechanism open new avenues for the development of ORR catalysts.