Blow-up of semilinear pde's at the critical dimension. A probabilistic approach

We present a probabilistic approach which proves blow-up of solutions of the Fujita equation in the critical dimension . By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as . In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of -Laplacians with possibly different parameters .

     

A novel cacalolide from Psacalium decompositum

A new cacalolide sesquiterpenoid, named as Romo-A, was isolated from the roots of Psacalium decompositum, Asteraceae, a Mexican medicinal shrub with antidiabetic properties. Its structure was elucidated by NMR, MS, IR, UV, and confirmed by X-ray diffraction studies.     

Chaotic polynomials on Fréchet spaces

Contrary to the case of polynomials on Banach spaces, in which it is known that no hypercyclic homogeneous polynomial of degree exists on any Banach space, we construct for each a chaotic -homogeneous polynomial on the Fréchet space .

     

Drüsenfarbstoffe aus Labiaten: Die polaren Diterpenoide aus Plectranthus argentatus S. T. BLAKE

Polar Diterpenoids from Leaf-Glands of Plectranthus argentatus S. T. B_LAKE From the red leaf-glands of the Australian Plectranthus argentatus the following novel diterpenoids were isolated: coleon-U-quinone ( 1 ), 8α,9α-epoxycoleon-U-quinone ( 3 ), 6β-formyloxy-7α-hydroxyroyleanone ( 7 ), and 5,6-dihydrocoleon U ( 10 ), besides the already known compounds 6β, 7α-dihydroxyroyleanone ( 4 ), 7α-acetoxy-6β-hydroxyroyleanone ( 5 ), and 7α-formyloxy-6β-hydroxyroyleanone ( 6 ). Epoxydation of 1 by perborate led in 32% yield to the epoxyquinone 3 .     

Excitation of stable transverse wavepackets with quadratic and cubic susceptibilities

We have identified a family of (2+1)D spatial solitary waves which can stably propagate in bulk media in the presence of coexisting diffraction, self-focusing Kerr and quadratic nonlinearities. In a conspicuous range of excitation conditions close to the stationary solutions, the emerging wavepackets are immune to the detrimental occurrence of filamentation and collapse, typical of pure Kerr media. The presence of a second-order contribution to the cubic nonlinear response is, therefore, able to prevent optical damage in applications relying on self-guidance. We show that the cross-phase modulation plays an important effect on stability. Our estimate shows that the effects of the cubic susceptibility cannot be neglected below a certain beam size in realistic crystals (e.g. KTP or similar).     

Localized states in polymeric molecules III The electronic structure of polyacetylene

The Transfer Matrix approach is used to treat the relaxed defect problem in trans-polyacetylene. We use a particular choice of parametrization for the hopping integrals, which is related to the existence of solitons in this material, to discuss its electronic structure. We obtain closed expressions for the density of states and for the wavefunctions associated to the localized state at any site of the chain.     

Pulsed low-resolution nuclear magnetic resonance — an analytical tool in food science

Routine food analysis requires methods that are non-destructive, rapid and easy to use. Pulsed low-resolution NMR satisfies all these conditions and is increasingly being applied to determine the water, oil and protein content of a number of foodstuffs.