On nonuniform exponential dichotomy of evolution operators in Banach spaces

The problem of nonuniform exponential dichotomy of evolution operators in Banach spaces is considered. Connections between this concept and admissibility of the pair (C ₀,C ₀) are established. Generalizations to the nonuniform case of some results of Van Min, Räbiger and Schnaubelt ([MRS]) are obtained. It is shown that an implication from the uniform case is not true for nonuniform exponential dichotomy. The results are applicable for general time-varying linear equations with unbounded coefficients in Banach spaces.     

Nuclear magnetic triple resonance studies on formamide-14N

The magnitudes of the two spin-spin coupling constants J(N¹H …? ¹³C), and all relatives signs of the couplings J(¹H …? ¹H) and J(¹H …? ¹³C) of formamide-¹⁴N, were determined by triple resonance experiments of the types ¹H—{¹³C}—{¹⁴N} and ¹H—{¹H}—{¹⁴N}.     

Pseudocompact Whyburn spaces need not be Fréchet

We prove in ZFC that there exists a Tychonoff pseudocompact scattered AP-space of uncountable tightness. We give some sufficient and necessary conditions for a -space to be AP as well as a characterization of AP-property in linearly ordered topological spaces.

     

On a problem of Turán about positive definite functions

We study the following question posed by Turán. Suppose is a convex body in Euclidean space which is symmetric in and with value at the origin; which one has the largest integral? It is probably the case that the extremal function is the indicator of the half-body convolved with itself and properly scaled, but this has been proved only for a small class of domains so far. We add to this class of known Turán domains the class of all spectral convex domains. These are all convex domains which have an orthogonal basis of exponentials , . As a corollary we obtain that all convex domains which tile space by translation are Turán domains.

We also give a new proof that the Euclidean ball is a Turán domain.

     

Anhydrous Amorphous Calcium Oxalate Nanoparticles from Ionic Liquids: Stable Crystallization Intermediates in the Formation of Whewellite

The mechanisms by which amorphous intermediates transform into crystalline materials are not well understood. To test the viability and the limits of the classical crystallization, new model systems for crystallization are needed. With a view to elucidating the formation of an amorphous precursor and its subsequent crystallization, the crystallization of calcium oxalate, a biomineral widely occurring in plants, is investigated. Amorphous calcium oxalate (ACO) precipitated from an aqueous solution is described as a hydrated metastable phase, as often observed during low‐temperature inorganic synthesis and biomineralization. In the presence of water, ACO rapidly transforms into hydrated whewellite (monohydrate, CaC₂O₄ ? H₂O, COM). The problem of fast crystallization kinetics is circumvented by synthesizing anhydrous ACO from a pure ionic liquid (IL‐ACO) for the first time. IL‐ACO is stable in the absence of water at ambient temperature. It is obtained as well‐defined, non‐agglomerated particles with diameters of 15–20 nm. When exposed to water, it crystallizes to give (hydrated) COM through a dissolution/recrystallization mechanism.     

1,2,4-triazolium-ylures—V: Réactions des triazolium-phénacylures avec les alcynes dis-symétriques

4-Aryl-1,2,4-triazolium-phenacylides and ethyl propiolate give 3-substituted 4-aryl-1,2,4-triazoles via cycloadducts.     

Fluorocarbon‐ended polymers: Metal catalyzed radical and living radical polymerizations initiated by perfluoroalkylsulfonyl halides

Perfluoroalkylsulfonyl chlorides and bromides initiate metal catalyzed free radical polymerization of both hydrocarbon and fluorocarbon monomers affording polymers with perfluoroalkyl end groups. In the case of styrene (S) and methyl methacrylate (MMA) with Cu‐based catalysts the process affords polymers with a relatively narrow molecular weight distribution and linear dependence of molecular weight on conversion, suggesting that a living radical polymerization mechanism occurs. The orders of reaction in monomer, initiator and catalyst for these polymerizations were determined. In the case of PMMA, the detailed structure of a perfluorobutane chain‐end was determined by NMR analysis. Perfluoroalkylsulfonyl chlorides are stable in neutral aqueous media. This permits their use as initators for fluoroolefin polymerizations in H₂O. Poly(tetrafluoroethylene‐co‐hexafluoropropylene) was obtained in good yield with few ionic end groups. The aqueous fluoroolefin polymerization appears to be catalyzed by metal zero species from the reactor walls. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3313–3335, 2000     

Designing functional aromatic multisulfonyl chloride initiators for complex organic synthesis by living radical polymerization

The similarities and differences between sulfonyl chloride and alkyl halide initiators for metal‐catalyzed living radical polymerizations are discussed. The differences in the rates of formation, reactivities, and reactions of primary radicals derived from sulfonyl halides and alkyl halides demonstrated the design principles for monosulfonyl and multisulfonyl chlorides that provided quantitative initiation and higher rates of initiation than of propagation. Multifunctional initiators with two, three, four, six, and eight sulfonyl chloride groups that produced perfect star polymers in 95% conversions were designed and synthesized on the basis of these principles. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4776–4791, 2000