A new approach to reduction of the Neumann problem in acoustic scattering to a non-hypersingular integral equation

The Neumann problem for the propagative Helmholtz equation inthe exterior of several bodies (obstacles) is studied in twoand three dimensions by a special modification of the boundaryintegral equation method. This modification can be called the'method of interior boundaries', because additional boundariesare introduced inside scattering bodies. The solution of theproblem is obtained in the form of a single layer potentialon the whole boundary. The density in the potential satisfiesthe uniquely solvable Fredholm equation of the second kind andcan be computed by standard codes. In fact our method holdsfor any positive wave numbers.     

Amination of CF3-enones with nosyloxycarbamates

CF3-enones showed a different reactivity in amination reactions with nosyloxycarbamates. 4-Oxazolines or vinyl carbamates were obtained as unique products depending on the nature of double-bond substituents and on the choice of carbamates and bases. Starting from trans-trifluoroacetyl olefins carrying a heterocyclic residue or the p-methoxyphenyl group on the double bond, a rare loss of CF3CO was observed when the aminations were performed under heterogeneous conditions using CaO as the base.     

Parallel solution-phase synthesis of acrylonitrile scaffolds carrying L-alpha-amino acidic or D-glycosyl residues

A practical and straightforward protocol for the preparation of a solution-phase library of acrylonitrile scaffolds is reported. Target compounds were obtained in high yield, stereoselectivity, and purity by two simple and practical steps from cyanoacetic acid. Moreover, our study proposes a synthetic approach starting from the constructed library to obtain three-membered heterocycles.     

Ethoxycarbonylnitrene addition to vinyl chlorides. Synthesis and thermal rearrangement of α-chloroaziridines

The addition of ethoxycarbonylnitrene to vinyl chlorides gives N-ethoxycarbonyl-α-chloroaziridines which undergo an easy rearrangement mainly or exclusively to N-ethoxycarbonyl-2-chloro-2-alkenylamines.     

Sublattices of product spaces: Hulls, representations and counting

The Cartesian product of lattices is a lattice, called a product space, with componentwise meet and join operations. A sublattice of a lattice L is a subset closed for the join and meet operations of L. The sublattice hullLQ of a subset Q of a lattice is the smallest sublattice containing Q. We consider two types of representations of sublattices and sublattice hulls in product spaces: representation by projections and representation with proper boundary epigraphs. We give sufficient conditions, on the dimension of the product space and/or on the sublattice hull of a subset Q, for LQ to be entirely defined by the sublattice hulls of the two-dimensional projections of Q. This extends results of Topkis (1978) and of Veinott [Representation of general and polyhedral subsemilattices and sublattices of product spaces, Linear Algebra Appl. 114/115 (1989) 681-704]. We give similar sufficient conditions for the sublattice hull LQ to be representable using the epigraphs of certain isotone (i.e., nondecreasing) functions defined on the one-dimensional projections of Q. This also extends results of Topkis and Veinott. Using this representation we show that LQ is convex when Q is a convex subset in a vector lattice (Riesz space), and is a polyhedron when Q is a polyhedron in Rⁿ.We consider in greater detail the case of a finite product of finite chains (i.e., totally ordered sets). We use the representation with proper boundary epigraphs and provide upper and lower bounds on the number of sublattices, giving a partial answer to a problem posed by Birkhoff in 1937. These bounds are close to each other in a logarithmic sense. We define a corner representation of isotone functions and use it in conjunction with the representation with proper boundary epigraphs to define an encoding of sublattices. We show that this encoding is optimal (up to a constant factor) in terms of memory space. We also consider the sublattice hull membership problem of deciding whether a given point is in the sublattice hull LQ of a given subset Q. We present a good characterization and a polynomial time algorithm for this sublattice hull membership problem. We construct in polynomial time a data structure for the representation with proper boundary epigraphs, such that sublattice hull membership queries may be answered in time logarithmic in the size |Q| of the given subset.     

Diastereoselective aziridination of chiral alpha-carbonyl enoates

Nosyloxycarbamates very efficiently aziridinate optically active alpha-carbonyl enoates with high levels of diastereoselectivity under mild conditions and in a straightforward process.