Preconditioned Spectral Gradient Method

The spectral gradient method is a nonmonotone gradient method for large-scale unconstrained minimization. We strengthen the algorithm by modifications which globalize the method and present strategies to apply preconditioning techniques. The modified algorithm replaces a condition of uniform positive definitness of the preconditioning matrices, with mild conditions on the search directions. The result is a robust algorithm which is effective on very large problems. Encouraging numerical experiments are presented for a variety of standard test problems, for solving nonlinear Poisson-type equations, an also for finding molecular conformations by distance geometry.     

Polysubstituted oxygen heterocycles by a Reformatsky-type reaction/reductive cyclization approach from enantiopure beta-ketosulfoxides

The stereoselective synthesis of tetrasubstituted tetrahydrofurans and trisubstituted tetrahydropyrans bearing a sulfoxide was achieved by reductive cyclization (Et3SiH/TMSOTf) from the corresponding enantiopure hydroxy ketones protected as a dioxolane. These derivatives are easily accessible from a Reformatsky-type reaction between alpha-bromo-alpha'-sulfinyl ketones and protected alpha- or beta-ketoaldehydes, followed by diastereoselective reduction of the resulting beta-ketosulfoxide.     

An easy synthetic approach to pyridoporphyrins by domino reactions

Beta-amino-meso-tetraarylporphyrins react with cyclic enol ethers to yield pyrido[2,3-b]porphyrins bearing two vicinal hydroxyalkyl groups. These reactions are catalyzed by lanthanum triflate and occur under mild conditions. Esterification of the hydroxyalkyl groups with succinic anhydride and dodecanoyl chloride afforded the corresponding esters in almost quantitative yields. The crystal structure of the most hydrophobic derivative 7 was determined, and it shows that these porphyrinic macrocycles form one-dimensional supramolecular tapes in the solid state.     

Exact Controllability of a Koiter Shell by a Boundary Action

We consider a thin shell whose elastic deformations are described by the system of Koiter linear partial differential equations. The shell is controlled by functions acting along its boundary. We show, using the HUM method (Hilbert Uniqueness Method) of J.L. Lions, that when the middle surface of the shell satisfies specific geometrical assumptions, it is possible to obtain exact controllability which consists in driving the system to rest in finite time. In particular we identify the function spaces where the initial Cauchy data (initial displacement and velocity fields) have to be taken and the function space where the control can be chosen in order to get the exact controllability. This revised version was published online in August 2006 with corrections to the Cover Date.     

Generating series of classes of Hilbert schemes of points on orbifolds

The notion of power structure over the Grothendieck ring of complex quasi-projective varieties is used for describing generating series of classes of Hilbert schemes of zero-dimensional subschemes (“fat points”) on complex orbifolds.     

Unusual ligand-dependent chemoselective Suzuki-Miyaura cross-coupling reactions of 3-bromo-4-trifloyl-thiophenes

An unusual ligand-dependent chemoselective Suzuki-Miyaura cross-coupling reaction for 3-bromo-4-trifloyl-thiophenes was discovered. Pd(PPh₃)₄ showed selectivity for triflate over bromide, whereas the selectivity was reversed for Pd(^tBu₃P)₂.     

On the topology of a generic fibre of a polynomial function

In this work we study the topologies of the fibres of some families of complex polynomial functions with isolated critical points. We consider polynomials with some transversality conditions at infinity and compute explicitly its global Milnor number μ(f). the invariant λ(f) and therefore the Euler characteristic of its generic fibre. We show that under some mild ransversality condition (transversal at infinity) the behavior of f at infinity is good and the topology of the generic fibre is determined by the two homogeneous parts of higher degree of f Finally we study families of polynomials, called two-term polynomials. This polynomials may have atypical values at infinity. Given such a two-term polynomial f we characterize its atypical values by some invariants of f. These polynomials are a source of interesting examples.     

Butatrien durch Thermolyse von Propiolsäure-(2-propinyl)ester

Flow thermolysis of 2-propynyl propiolate (5) at 580° afforded butatriene (6) (ca. 50%) and, as by-products, 4-methylene-2-cyclobuten-1-one (7) , 2-ethynylpropenal (8) , 1-penten-4-yn-3-one (9) , 4-penten-2-ynal (10) (total ca. 10%), along with some propynal, acetylene, CO₂ and CO. In the same way, propiolic acid (1,1-D₂)-2-propynyl propiolate (11) led to (1,1-D₂)-butatriene (12) and a little 4-((D₂)methylene)-2-cyclobuten-1-one (13). A mechanism is proposed for the transformation of 5 into 6 and of 11 into 12 , which also accounts for the formation of 7,8,9 and 10 , as well as 13. The position of one of the published ¹³C-NMR signals of butatriene (6) must be revised. Thermolysis of methyl- (1) and ethyl propiolate (2) resulted in small yields of 2-buten-4-olide (3) and 2-penten-4-olide (4).     

Synthesis, chromatographic separation, vibrational circular dichroism spectroscopy, and ab initio DFT studies of chiral thiepane tetraol derivatives

Optically pure enantiomers of the chiral tetrahydroxythiepane derivative 3,6-dihydroxy-4,5-O-isopropylidene-thiepane (3) are obtained using a novel protocol in which a library of all possible stereoisomers of 3 is synthesized, followed by two-step stereoselective chromatography, using, first, conventional achiral and, then, chiral stationary phases. Configurational and conformational analysis of 3 are carried out using Vibrational Circular Dichroism (VCD) spectroscopy in conjunction with ab initio DFT calculations. The absolute configuration of 3 is shown to be 3R,4S,5R,6R-(+)/3S,4R,5S,6S-(-).     

Synthesis and structural characterization of pyrimidine bi- and tricyclic nucleosides with sugar puckers conformationally locked into the eastern region of the pseudorotational cycle

Reaction of 5'-O-tosyl TSAO-m(3)T (1) with amines has led to the synthesis of new classes of bi- and tricyclic nucleosides. Full details about the synthesis of these compounds and a plausible mechanism to explain their obtention are reported. In addition, we describe the development of a second, more efficient, and higher yielding synthetic route as a general approach for the synthesis of some of these bicyclic nucleosides. To study the conformational behavior of the bi- and tricyclic nucleosides described in this paper, intensive NMR investigations and molecular modeling studies were performed. Conformational analysis indicates that the furanose ring of the compounds described here prefers the eastern side of the pseudorotation cycle with the base substituents preferentially in the anti range. The torsion angle gamma describing the C-4'[bond]C-5' is found to prefer the +sc range. These compounds represent a novel class of E-type conformationally restricted bicyclic ribo-nucleosides containing a [3.3.0]-fused carbohydrate moiety. The bicyclic nucleosides described herein present an interesting potential for diverse and selective chemical treatments on the 2'-hydroxyl and/or the functionalities incorporated at the bridge between C-3' and C-5'.