Minkowski type theorems for convex sets in cones

Acta Mathematica Hungarica - Minkowski’s classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface...     

Intramolecular Hydroamination of Selenoalkynes to 2-Selenylindoles in the Absence of Catalyst

In this work, a series of 2-chalcogenylindoles was synthesized by an efficient methodology, starting from chalcogenoalkynes, including a previously unreported tellurium indole derivative. For the first time, these 2-substituted chalcogenylindoles were obtained in the absence of metal catalyst or base, under thermal conditions only. In addition, the results described herein represent a methodology with inverse regioselectivity for the chalcogen functionalization of indoles.     

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 .     

Non-linear Stability of Modulated Fronts¶for the Swift–Hohenberg Equation

We consider front solutions of the Swift–Hohenberg equation ∂ _t u= -(1+ ∂ _x ²)² u + ɛ² u -u ³. These are traveling waves which leave in their wake a periodic pattern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non-linear stability of these solutions. It turns out that this problem is closely related to the question of stability of the trivial solution for the model problem ∂ _t u(x,t) = ∂ _x ² u (x,t)+(1+tanh(x-ct))u(x,t)+u(x,t) ^p with p>3. In particular, we show that the instability of the perturbation ahead of the front is entirely compensated by a diffusive stabilization which sets in once the perturbation has hit the bulk behind the front. Received: 23 February 2001 / Accepted: 27 August 2001     

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.     

Crystal structures of two ancylite modifications

The crystal structures of two ancylite specimens from Khibiny massif (the Kola Peninsula, Russia)—ancylite-(Ce) from alkali hydrothermalites (Sr_1.01Ca_0.02Ba_0.01)_Σ1.04(Ce_0.52La_0.28Nd_0.11Pr_0.04 Sm_0.01)_Σ0.96(CO₃)₂(OH_0.83F_0.13)_Σ0.96 · 0.9H₂O and ancylite-(Ce) from carbonatites—have (Sr_0.80Ca_0.05Ba_0.01)_Σ0.86(Ce_0.62La_0.40Nd_0.09Pr_0.03) _Σ1.14(CO₃)₂(OH_0.99F_0.15)_Σ1.14 · 1.0H₂O been refined by the Rietveld method. A focusing STOE-STADIP diffractometer with a bent Ge(111) primary monochromator was used (λ MoK _{α 1} radiation, 2.16° < 2θ < 54.98°; reflection number 237–437). All the computations for ancylite from alkali hydrothermalites were performed within the sp. gr. Pmc2₁, a = 5.0634(1) Å, b = 8.5898(1) Å, c = 7.2781(1) Å, V = 316.55(1) ų, R _wp = 1.90; the computations for ancylite from carbonatites were performed within the sp. gr. Pmcn, a = 5.0577(1) Å, b = 8.5665(2) Å, c = 7.3151(2) Å, V = 316.94(1) ų, R _wp = 2.38 in the anisotropic approximation of thermal vibrations of cations and oxygen atoms.     

Magnetic resonance imaging of rigid polymers at elevated temperatures with SPRITE

Magnetic resonance imaging has rarely been applied to rigid polymeric materials, due primarily to the strong dipolar coupling and short signal lifetimes inherent in these materials. SPRITE (single point ramped imaging withT ₁ enhancement) (B. J. Balcom, R. P. MacGregor, S. D. Beyea, D. P. Green, R. L. Armstrong, T. W. Bremner: J. Magn. Reson. A123, 131–134, 1996) is particularly well suited to imaging solid materials. With SPRITE, the only requirement is thatT ₂^* be long enough so that the signal can be phase-encoded. The minimum phase encoding time is limited by the maximum gradient strength available and by the instrument deadtime. At present this is usually tens of microseconds and will only improve with refinements in technology. We have used the SPRITE sequence in conjunction with raising the sample temperature to obtain images of rigid polymers that have largely frustrated conventional imaging methods. This approach provides a straightforward and reliable method for imaging a class of samples that, up until now, have been very difficult to image.