Modules over\mathfrak{U}_q (\mathfrak{s}\mathfrak{l}_2 )

The restricted quantum universal enveloping algebra decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple . The indecomposable finite-dimensional are classified and located in the Auslander-Reiten quiver.     

Preparation of muscovite with ultrahigh specific surface area by chemical cleavage

The specific surface area of a muscovite sample increases drastically after exposure to a LiNO₃ solution, e.g., from 3.4 m²/g, corresponding to platelets of ca. 200 silicate layers, to 295 m²/g (platelets of ca. 2–3 silicate layers) after treatment at 180°C under atmospheric pressure for 46 h. The efficiency of the cleavage process decreases with decreasing temperature (down to 50°C). The LiNO₃/H₂O weight ratio is also very important: at 130°C and a reaction time of 46 h, for instance, a value in the range of 1.7–1.8 leads to the highest specific surfaces. The cleaved products have the form of strong papers that disperse readily in water. During the cleaving procedure, not only the particle thickness, but also the diameter decreases. There is no evidence of damage or partial dissolution of the silicate structure after cleavage, by IR spectroscopy and yield. The use of LiCl also leads to an increase in specific surface area, but the effect is weaker than in the case of LiNO₃. Treatment with some other alkaline and alkaline earth nitrates and chlorides did not increase the specific surface area of muscovite significantly.     

Adsorption of polymers with crown ether substituents on muscovite mica

Ultrahigh specific surface area muscovite with different ions at the surface (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺, Ca²⁺, Sr²⁺, Ba²⁺, Cu²⁺) was treated with aqueous solutions of low molecular weight crown ethers and polymers with crown ether substituents. The adsorption was assessed by UV analysis of the supernatant solution, and with TGA and IR spectroscopy of the mica solids. In contrast to other layered silicates, the low molecular weight crown ethers show no affinity to any of the muscovite surfaces. The polymers can adsorb, however, depending on the type of surface cation. The results indicate that at least some of the crown ether moieties are complexed to surface cations and that the diameter of the ions at the surface plays an important role in the adsorption process.     

Synthesis and Diels-Alder Reactions of a New Kind of Chiral Dienophiles: Cyclic Vinyl-p-tolylsulfilimines

A new kind of chiral dienophiles, cyclic vinyl-p-tolylsulfilimines (2a and 2b), were obtained from the corresponding (Z)-sulfinylacrylonitriles with HBF(4) and methanol. The asymmetric Diels-Alder reaction of optically pure 2a with cyclopentadiene under mild thermal or catalyzed conditions afforded only the endo-4a adduct with complete endo and pi-facial selectivities. The ability of the sulfilimine moiety to enhance the dienophilic reactivity of the double bond is similar to that of the sulfinyl group.     

Angular distributions of muon pairs produced by 194 GeV/c negative pions

We present the angular distributions of muon pairs obtained in a high-statistics experiment using a 194-GeV/c π^- impinging on a tungsten target. Our results are based on the analysis of 145,000 events with positive Feynmanx and mass above 4.07 GeV/c², excluding the ? region. Simple first-order QCD relations allow us to determine the ratio of annihilation with hard-gluon emission to the sum of annihilation with hard-gluon emission and hard-gluon Compton scattering, which is found to be about 58% to 75%. We determine the parton square intrinsic transverse momenta to be of the order of 0.6 (GeV/c)², and about 30% larger in the pion than in the nucleon. At largex ₁, our data agree with the higher-twist hypothesis, and support the interpretation of the relevant scale parameter as the dimuon square transverse momentum.     

Die Nicht-Existenz von Schnittflächen komplexer Stiefel-Mannigfaltigkeiten

Ohne Zusammenfassung