Dynamic of Threshold Solutions for Energy-Critical NlS

We consider the energy-critical non-linear focusing Schr?dinger equation in dimension N = 3, 4, 5. An explicit stationary solution, W, of this equation is known. In [KeM], the energy E(W) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present article, we study the dynamics at the critical level E(u) = E(W) and classify the corresponding solutions. This gives in particular a dynamical characterization of W. Received: March 2007, Accepted: October 2007     

Model-independent separation of structure functions over an extended kinematical region

A method for the separation of structure functions in (e, e p) experiments is proposed, which is an extension of the traditional Rosenbluth-type techniques of [1,2]. In our approach, we use a very flexible Ansatz to describe the structure functions within an extended kinematical regionG and determine its free parameters with a x² minimization. The procedure is tested by pseudo data (¹²C(e, ep)¹¹B_g.s.) in the quasi-free region.Part of the doctorate-thesis of Thomas Veit     

Existence of self-similar blow-up solutions for Zakhrov equation in dimension two. Part I

We consider the Zakharov equation in space dimension two

A highly pyramidalized cage alkene formed via the double Diels-Alder cycloaddition of syn-4,5,13,14-bis(dehydro)octafluoroparacyclophane to anthracene

[reaction: see text] A double Diels-Alder reaction of the formal syn-bis(dehydro)octafluoroparacyclophane with anthracene leads to formation of a novel cage compound that contains a highly pyramidal double bond. The measures of pyramidality of this double bond constitute what appear to be the highest combined values of psi and phi (34.3 degrees and 33.5 degrees, respectively) yet reported to have been determined by X-ray crystallography. This cage compound, although stable indefinitely as a crystalline compound in air, exhibits the high reactivity with both triplet and singlet O2 in solution that is characteristic of such highly pyramidal pi systems.     

Polymerisation et copolymerisation de monophenyl et de diphenylethylenes amorcees par des graphitures de metaux alcalins

The bulk polymerization at -24° of α-methylstyrene initiated by the alkali metals and the graphitides LiC₁₂, KC₂₄ and KC₃₆ has been studied. The tacticities of polymers have been measured by [¹H] NMR. The alkali metals give polymers having the same tacticity and the propagation of the stereoconfiguration is bernouillian; LiC₁₂ yields more racemic diads while KC₂₄ and KC₃₆ yield more meso diads and show a penultimate effect. By measuring the growing of the thickness of KC₂₄ flakes, it appears that the more sterically hindered a monomer the more slowly it penetrates into the graphitide. The copolymerizations at 25° of styrene with 1-1 diphenylethylene or 1–2 diphenylethylene (trans stilbene) (comonomer ratio 1/1) initiated by KC₂₄ in tetrahydrofuran (THF), xylene (XL), decahydronaphthalene (decalin DL) and cyclohexane (CH) have been studied. The amount of styrene units in the copolymers depends on the nature of the solvent: it increases as the interaction solvent-graphitide decreases. All the results support the view that the polymerization proceeds between the graphite layers.     

Titanium catalysis in the Ugi reaction of alpha-amino acids with aromatic aldehydes

[reaction: see text] Ugi reaction between an (S)-alpha-amino acid, an aromatic aldehyde, and an isonitrile proceeds best under catalysis by TiCl(4) in MeOH. The sense of diastereoinduction is (S,S).     

Tuning phenoxyl-substituted diketopyrrolopyrroles from quinoidal to biradical ground states through (hetero-)aromatic linkers

Strongly fluorescent halochromic 2,6-di-tert-butyl-phenol-functionalised phenyl-, thienyl- and furyl-substituted diketopyrrolopyrrole (DPP) dyes were deprotonated and oxidised to give either phenylene-linked DPP1˙˙ biradical (y₀ = 0.75) with a singlet open shell ground state and a thermally populated triplet state (ΔE_ST = 19 meV; 1.8 kJ mol⁻¹; 0.43 kcal mol⁻¹) or thienylene/furylene-linked DPP2q and DPP3q compounds with closed shell quinoidal ground states. Accordingly, we identified the aromaticity of the conjugated (hetero-)aromatic bridge to be key for modulating the electronic character of these biradicaloid compounds and achieved a spin crossover from closed shell quinones DPP2q and DPP3q to open shell biradical DPP1˙˙ as confirmed by optical and magnetic spectroscopic studies (UV/vis/NIR, NMR, EPR) as well as computational investigations (spin-flip TD-DFT calculations in combination with CASSCF(4,4) and harmonic oscillator model of aromaticity (HOMA) analysis). Spectroelectrochemical studies and comproportionation experiments further prove the reversible formation of mixed-valent radical anions for the DPP2q and DPP3q quinoidal compounds with absorption bands edging into the NIR spectral region.

By variation of spacer aromaticity, a spin crossover from thienylene/furylene-linked quinones DPP2q/DPP3q to phenylene-bridged biradical DPP1˙˙ (y₀ = 0.75) with a singlet open shell ground state (ΔE_ST = 19 meV) was achieved.     

New trends in the chemistry of iron(III) citrate complexes: correlations between X-ray structures and solution species probed by electrospray mass spectrometry and kinetics of iron uptake from citrate by iron chelators

Despite the crucial role of "iron(III) citrate systems" in the iron metabolism of living organisms (bacteria as well as plants or mammals), the coordination chemistry of ferric citrate remains poorly defined. Variations in the experimental conditions used for the preparation of so-called ferric citrates (iron salt, Fe:cit molar ratio, base, pH, temperature, solvent) lead to several different species, which are in equilibrium in solution. To date, six different anionic complexes have been structurally characterized in the solid state, by ourselves or others. In the work described herein, we have established the experimental conditions leading to each of them. Five were obtained from aqueous solution. With the exception of a nonanuclear species (of which fragments have been detected), all were identified in aqueous solution on the basis of electrospray ionization mass spectrometry. In addition, the spectra revealed a new trinuclear species, which could not be crystallized. Kinetic studies of iron uptake from citrate species by iron chelators confirmed the results indicated by the ESI-MS studies. These studies also allowed the relative molar fraction of mononuclear versus polynuclear complexes to be determined, which depends on the Fe:cit molar ratio.