Unitals in Topological Affine Translation Planes Need Not Be Strictly Convex

We study the relationship of two incidence geometric convexity notions, namely, ovoids in real affine spaces and compact unitals of codimension 1 in topological affine translation planes. In [3] we showed that every ovoid in a translation plane is a unital, and we asked if the converse is true. Here we introduce the notion of a shell, which is distinctly weaker than that of an ovoid and still implies the unital property if the translation plane is properly chosen (and the shell is not too degenerate). We give an explicit example of a shell that is not an ovoid. The question remains whether or not conversely, every compact unital of codimension 1 in a translation plane is a shell.This paper was written while the third author was supported by a grant from DFG and TÜBITAK.Received March 12, 2002 Published online November 18, 2002     

Kernel polynomials for the solution of indefinite and ill-posed problems

We introduce a new family of semiiterative schemes for the solution of ill-posed linear equations with selfadjoint and indefinite operators. These schemes avoid the normal equation system and thus benefit directly from the structure of the problem. As input our method requires an enclosing interval of the spectrum of the indefinite operator, based on some a priori knowledge. In particular, for positive operators the schemes are mathematically equivalent to the so-called -methods of Brakhage. In a way, they can therefore be seen as appropriate extensions of the -methods to the indefinite case. This extension is achieved by substituting the orthogonal polynomials employed by Brakhage in the definition of the -methods by appropriate kernel polynomials. We determine the rate of convergence of the new methods and establish their regularizing properties.     

FeIII(tmdta)]--twist-boat/half-chair conformer ratio reliably deduced from DFT-calculated Raman spectra

The equilibrium between the twist-boat (tb) and half-chair (hc) conformers of the central diamine chelate ring of [Fe(III)(tmdta)]- in solids and aqueous solution has been studied by Raman spectroscopy, supported by calculated Raman spectra using Density Functional Theory.     

Diiodotetrasupersilylcyclotetrasilene (tBu3Si)4Si4I2—A Molecule Containing an Unsaturated Si4 Ring

The red-orange tetrasilacyclobutene 1 (R*=SitBu₃) is formed quantitatively by the reaction of tetrasilatetrahedrane 2 and iodine. Surprisingly, water and methanol do not react with 1 with addition to the Si−Si double bond, but instead with replacement of the silicon-bound iodine atoms with oxygen or the methoxy group, respectively. The substitutions possibly proceed by dissociative activation via intermediate 3 .     

P9]+ [Al(OR(F))4)]-, the salt of a homopolyatomic phosphorus cation

Positive at last: The first condensed-phase homopolyatomic phosphorus cation [P(9)](+) was prepared using a combination of the oxidant [NO](+) and weakly coordinating anion, [Al{OC(CF(3))(3)}(4)](-). [P(9)](+) consists of two P(5) cages linked by a phosphonium atom to give a D(2d)-symmetric Zintl cluster. NMR (see picture), Raman, and IR spectroscopy, mass spectrometry, and quantum-chemical calculations confirmed the structure.     

13C nuclear magnetic resonance spectra—VI: Stereochemical dependence of γanti,heterosubstituent effects on 13C chemical shifts of bridgehead substituted molecules

The ¹³C NMR data of some mono- and disubstituted adamantanes, homoadamantenes and homonoradamantenes are presented. A model of dependencies of the γ_anti substituent induced shifts on torsion angles and internuclear distances between substituents and the γ carbons is proposed. Furthermore, it is shown that for the α substituent induced shifts strain within the molecular frameworks of these compounds plays no significant part.     

Porous monodisperse poly(divinylbenzene) microspheres by precipitation polymerization

The precipitation polymerization of commercial divinylbenzene in acetonitrile containing up to 40 vol. % toluene or other cosolvents is shown to produce novel porous monodisperse poly(divinylbenzene) microspheres. These microspheres have diameters between 4 and 7 μm, total pore volumes of up to 0.52 cm³/g, and surface areas of up to 800 m²/g. As no surfactant nor stabilizer was used in the preparation of these particles, their surfaces are free of any such residues. The particles were slurry-packed into stainless steel columns for size exclusion chromatography evaluation, and the results show an exclusion limit at molecular weights of 500 g/mol. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1543–1551, 1998     

Monodisperse poly(chloromethylstyrene-co-divinylbenzene) microspheres by precipitation polymerization

Monodisperse poly(chloromethylstyrene-co-divinylbenzene-80) microspheres of 4–6-µm diameter were prepared by precipitation copolymerization in neat acetonitrile and in acetonitrile/toluene mixtures. These particles have clean surfaces due to the absence of any added stabilizer and up to 0.5 cm³/g pore volume, depending on the comonomer ratio and on the amount of toluene cosolvent. The effects of comonomer and cosolvent ratios on microsphere formation and morphology are described. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2295–2303, 1999     

Nuclear inelastic scattering studies on a dinuclear iron(II) spin crossover complex

The vibrational properties of the (high-spin)-(high-spin) and the (high-spin)- (low-spin) states of the dinuclear Fe(II) spin crossover complex[{Fe(L-N₄Me₂)}₂(BiBzIm)](ClO₄)₂·2EtCN¹ have been studied by means of nuclear inelastic scattering. At a temperature of 80 K typical low spin marker bands are detected in the region around 400 cm^?1, these bands almost completely disappear after increasing temperature to 190 K. Corresponding density functional theory calculations using the functional B3LYP* and the basis set CEP-31G reproduce the experimental data and thus allow a deeper understanding of the vibrational properties of dinuclear Fe(II) spin crossover complexes.