Flatness of differentiable functions along a subset of a real analytic set

The vanishing order of the value of a smooth function at a point along a subset is related to the order of its Taylor expansion there. To compare these vanishing orders the Spallek function is introduced. A number of properties of this function are developed.     

A regioselective enolate formation of trimethylsilylmethyl ketones application to the (E)-selective synthesis of α,β-unsaturated ketones

Two possible enolate anions of trimethylsilylmethyl ketones have been prepared regioselectively by the appropriate choice of base. The one directed to the silylmethyl site behaves as a highly reactive and (E)-selective condensation reagent to aldehydes.     

Mixed-valence states of 11, 1111-dialkyl- and 11, 1111-bis(methylbenzyl)biferrocenium triiodides

It was found that the packing of cations and anions influences the electronic structures of mixed-valence binuclear ferrocene derivatives. Temperature-dependence of the mixed-valence state of 1¹, 1¹¹¹-diisobutylbiferrocenium triiodide was observed in a crystalline state, whereas only a trapped-valence state was found in a dispersed state. The packing effect was also observed for a series of 1¹, 1¹¹¹-dialkyl- and 1¹, 1¹¹¹-bis(methylbenzyl)biferrocenium triiodides by means of ESR spectroscopy.     

Observables and quark confinement in the covariant canonical formalism of Yang-Mills theory

A concise criterion for observables in Yang-Mills theory is presented in the framework of covariant canonical field theory. As an example, the symmetric energy-momentum tensor θ_øν is proved to be an observable and its physically meaningful form is clarified. The validity of the “Maxwell-type” equation of motion is established in the physical subspace $\text{V}$_phys defined by the subsidiary condition $\text{Q}{}_{\mathrm{<mtext>B</mtext>}}\text{?}\text{phys}\text{〉 = 0}$ (Q_B: BRS charge). Its meaning and consequences are discussed in connection with the notion of observables: especially, all (quasi-) local observables in QCD are shown to be colour singlets and this fact paves the way to quark confinement.     

A regio- and stereo-controlled synthesis of α,β-unsaturated carbonyl compounds

α,β-Unsaturated carbonyl compounds and butenolides are readily prepared by the rhodium(I) catalyzed isomerization of 1,3-diene monoepoxides and α-alkylidene-γ-butyrolactones, respectively. The former transformation is formally regarded as the equivalent of a regiospecific aldol condensation of an unsymmetrical ketone.     

An oxidative route to α-trimethylsilyl ketones by means of rhodium catalyzed dehydrogenation of β-trimethylsilyl alcohols

The transfer hydrogenation of β-trimethylsilyl alcohols catalyzed by HRh(PPh₃)₄ has been successfully applied to the efficient synthesis of α-trimethylsilyl ketones.     

Observation of a soft phonon in linear chain compound (NbSe4)3I by Raman scattering

The phase transition of the linear chain compound (NbSe₄)₃I was studied by Raman scattering. At 78 K three new peaks were observed at 73 cm^?1, 205 cm^?1 and 261 cm^?1. The totally symmetric Raman peak at 73 cm^?1 shows anomalous temperature dependence. The frequency decreases with increasing temperature, and at high temperatures an anticrossing occurs with another peak observed at about 58 cm^?1. The Raman intensity decreases and the linewidth broadens remarkably as the temperature increases. These properties allow us to assign this peak to a soft phonon. This fact indicates clearly the existence of a structural phase transition of a displacive type below room temperature.     

Polymerisation von Propylen mit Tetrabenzylzirkonium

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