Flatness Properties of S-Posets

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomology group vanishes.     

Compact and subelliptic estimates for the $${\overline{\partial}}$$-Neumann operator on C2 pseudoconvex domains

In this paper, we will show that Catlin’s property (P) implies regularity for the -Neumann operator in W ¹ on C ² domains. We will also look at the subelliptic case and derive the natural generalization to C ^k domains when k ≥  2.     

Non-equivalence Magnetique en Resonance Nucleaire—IV. Influence de Plusieurs Types de Dissymetries sur les Deplacements Chimiques et les Couplages Relatifs a des Systemes ?O?CH2?CH3 et ?S?CH2?CH3

Magnetic non-equivalence of methylenic protons in A? CH₂? CH₃ groups were studied for several types of compounds. Results are compared with respect (1) to the nature of heteroatom A:A = O and A = S and (2) to the structure of the local dissymmetry element: asymmetric carbon, ketal group and allenic system. Influence of substitution is discussed in relation to conformational problems. Furthermore a variation of the methylene geminal coupling constant with substituents of carbon α to OEt is observed.     

Monotone norms and tensor products

Various refinements of orthant monotonicity for norms are studied. A partial order is induced in the tensor product of two partially ordered vector spaces. The induced norm in the tensor product is shown to be orthant monotone in certain cases.     

Carbaporphyrinoid chemistry has a silver lining! silver(III) oxybenzi-, oxynaphthi-, tropi-, and benzocarbaporphyrins

[structure: see text] Carbaporphyrinoid systems with semiquinone, cycloheptatriene, or indene subunits react under mild conditions with silver(I) acetate to give stable silver(III) organometallic derivatives.     

Hodge Theory and Geometry

Hodge theory for a smooth algebraic curve includes both theHodge structure (period matrix) on cohomology and the use ofthat Hodge structure to study the geometry of the curve, viathe Jacobian variety. Hodge extended the theory of the periodmatrix to smooth algebraic varieties of any dimension, definingin general a Hodge structure on the cohomology of the variety.He gave a few applications to the geometry of the variety, butthese did not attain the richness of the Jacobian variety. Inrecent years, Hodge theory has been successfully extended toarbitrary varieties, and to families of varieties. In this expositorypaper, some of these developments are reviewed, with specialemphasis on instances where these extensions can be used tostudy the geometry – especially the algebraic cycles –on the variety. 2000 Mathematics Subject Classification 14CDFJ.     

Sweet success: Ionic liquids derived from non-nutritive sweeteners

The anions of the sweeteners saccharin and acesulfame form ionic liquids when paired with a variety of organic cations.