Derivatives of (2R)-N-Glyoxylbornane-10,2-sultam and Their Use as auxiliaries in the diastereoselective spirocyclization of 2-substituted tryptamines

A crude hydrate 6 and a crystalline hemiacetal 7 of glyoxylamide 4 were prepared from crotonamide 5 (Scheme 2). Particularly hemiacetal 7 , but also 6 and the ‘dimer’ 8 (obtained from 7 ) may serve as homochiral auxiliaries. The structure of 8 was determined by X-ray analysis. By arenesulfonyl halides, tryptimines 12–14 of 4 were diastereoselectively transformed into spirotricycles 15–17 and 19 .     

Microwave-accelerated Claisen rearrangements of allyl tetronates and tetramates

[3,3]-Sigmatropic rearrangements of allyl tetronates and allyl tetramates to give 3-allyltetronic or -tetramic acids, respectively, proceed within 20-60 min under microwave irradiation (300 W, 130-190 °C). Consecutive (homo)sigmatropic [1,5] H-shifts such as oxa-ene reactions are promoted less effectively, which allows the isolation of Claisen intermediates of sigmatropic domino sequences, in contrast to conventional heating.     

Analysis of semiconducting materials by high-resolution radiofrequency glow discharge mass spectrometry

The analytical capabilities of a high-resolution mass spectrometer in combination with a 13.56 MHz glow discharge ion source for the analysis of semiconducting materials (silicon carbide and gallium arsenide) were studied. It was shown that single positively charged ions of sample material have about 10 eV higher average energy than the ions of the discharge and residual gas. Therefore effective energy separation of the ions of analyte from the ions of the discharge and residual gas was achieved by adjusting the ion transfer optics (breadth and position of energy slit), which improves the analytical capabilities of the developed method.Some analytical applications are presented to illustrate the performance of r.f. GDMS for the bulk analysis of semiconducting materials. The results of the trace element analysis of gallium arsenide and silicon carbide samples are compared with data of independent methods (LIMS, ICP-AES, SIMS).Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthdayOn leave from the Institute of Inorganic Chemistry, 630090 Novosibirsk, Russia     

Continuous spectral decompositions of Abelian group actions on -algebras

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual group of G as continuous spectral decompositions of G-actions on C^*-algebras. We classify such spectral decompositions using certain dense subspaces related to Marc Rieffel's theory of square-integrability. There is a unique continuous spectral decomposition if the group acts properly on the primitive ideal space of the C^*-algebra. But there are also examples of group actions without or with several inequivalent spectral decompositions.     

The nonobjectivity of past events in quantum mechanics

It is shown in this paper that a classical way of speaking about the past can be rejected when quantum systems without superselection rules are considered. To show this, use is made of a formal quantum language. The noncontextuality of quantum measurements is a presupposition of the quantum language. In addition, it is shown that introspective measurements, in contrast to the claims of Albert et al., do not violate the noncontextuality, and hence the result of rejecting the classical way of speaking remains still applicable to introspective measurements.     

On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems

We evaluate the practical relevance of two measures of conic convex problem complexity as applied to second-order cone problems solved using the homogeneous self-dual (HSD) embedding model in the software SeDuMi. The first measure we evaluate is Renegar's data-based condition measure C(d), and the second measure is a combined measure of the optimal solution size and the initial infeasibility/optimality residuals denoted by S (where the solution size is measured in a norm that is naturally associated with the HSD model). We constructed a set of 144 second-order cone test problems with widely distributed values of C(d) and S and solved these problems using SeDuMi. For each problem instance in the test set, we also computed estimates of C(d) (using Peña’s method) and computed S directly. Our computational experience indicates that SeDuMi iteration counts and log (C(d)) are fairly highly correlated (sample correlation R = 0.675), whereas SeDuMi iteration counts are not quite as highly correlated with S (R = 0.600). Furthermore, the experimental evidence indicates that the average rate of convergence of SeDuMi iterations is affected by the condition number C(d) of the problem instance, a phenomenon that makes some intuitive sense yet is not directly implied by existing theory.