Isoprene functionalization : E/Z-isomerism of 1-sulfonyl substituted 2-methylbutadienes

The isomeric chlorosulfones 3, 4 and 5 are prepared by 1,4-addition of sulfonyl chlorides to isoprene, Dehydrohalogenation affords the corresponding 2- and 3-methylbutadienyl sulfones in a configuration which is dependent on the configuration of the chlorosulfone. Pure Z-2-methylbutadienyl sulfones 1 are obtained by displacement of primary halides by the Z-sulfinate anion 2. The Z-sulfones 1 are isomerized to E/Z-mixtures. The E/Z-mixtures are separated into their components and the configuration of the isomers is established by the NMR-NOE technique.     

The Crystal Structure of Pb8FeIIFeF24: an ordered Fluorite-like Compound

Pb₈Fe^IIFeF₂₄ is triclinic: a = 20.118(3) Å, b = 5.597(1) Å, c = 9.440(2) Å, α = 89.75(2)°, β = 105.79(2)°, α = 89.38(2)°, Z = 2. The structure is solved in the unconventional space group C1 , from X-ray single crystal data using 1 641 independent reflections (R = 0.048, R_w = 0.051). It is built up from the stacking of two subnetworks along the a axis: fluorite-like [Pb₈F₁₀]_n⁶ⁿ⁺ layers and infinite dimetallic [Fe^IIFeF₁₄]_n^6n? double-chains of corner-sharing octahedra running along the b axis.     

A characterization of the Coxeter cap

Designs, Codes and Cryptography - In this paper, we complete the classification of the caps in $$\text{ PG }(n,q)$$ having the property that on every tangent line L, there exists a unique point...     

A Pollution Sensitive Marxian Production Inventory Model with Deterioration Under Fuzzy System

Journal of Optimization Theory and Applications - This article deals with an economic production quantity (EPQ) model with deterioration under the effect of environmental pollution in fuzzy...     

The inclusion of rhodium(II)α-methyl-cinnamate in β-cyclodextrin

The preparation and characterization of the 1:1 inclusion compound of rhodium(II) -methyl cinnamate in -cyclodextrin is reported. Evidence of inclusion was obtained from X-ray powder diffraction results, Raman, IR and UV-Vis spectroscopic studies and thermal analysis. Given the potential antitumor activity of the rhodium(II) carboxylate and its virtual insolubility in water, its inclusion in -cyclodextrin opens the possibility for its transference to the aqueous phase.     

Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space

LetE be a real Banach space andL(E) the family of all nonempty compact starshaped subsets ofE. Under the Hausdorff distance,L(E) is a complete metric space. The elements of the complement of a first Baire category subset ofL(E) are called typical elements ofL(E). ForXL(E) we denote by the metrical projection ontoX, i.e. the mapping which associates to eachaE the set of all points inX closest toa. In this note we prove that, ifE is strictly convex and separable with dimE2, then for a typicalXL(E) the map is not single valued at a dense set of points. Moreover, we show that a typical element ofL(E) has kernel consisting of one point and set of directions dense in the unit sphere ofE.     

Twistor holomorphic Lagrangian surfaces in the complex projective and hyperbolic planes

We completely classify all the twistor holomorphic Lagrangian immersions in the complex projective plane ², i.e. those Lagrangian immersions such that their twistor lifts to the twistor space over ² are holomorphic. This classification provides a one-parameter family of examples of Lagrangian spheres in ².Research partially supported by a DGICYT grant No. PB91-0731.