L^p boundedness of the wave operator for the one dimensional Schroedinger operator

Given a one dimensional perturbed Schroedinger operator H=-(d/dx)^2+V(x) we consider the associated wave operators W_+, W_- defined as the strong L^2 limits as s-> \pm\infty of the operators e^{isH} e^{-isH_0} We prove that the wave operators are bounded operators on L^p for all 1<p<\infty, provided (1+|x|)^2 V(x) is integrable, or else (1+|x|)V(x) is integrable and 0 is not a resonance. For p=\infty we obtain an estimate in terms of the Hilbert transform. Some applications to dispersive estimates for equations with variable rough coefficients are given.Comment: 26 page

Massive torsion modes, chiral gravity, and the Adler-Bell-Jackiw anomaly

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler-Bell-Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin 1/2 particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel-Jacobson-Smolin action of chiral gravity in four dimensions.Comment: 7 pages, RevTeX fil

Antimicrobial activity of Xylopia aethiopica, Aframomum melegueta and Piper guineense ethanolic extracts and the potential of using Xylopia aethiopica to preserve fresh orange juice

Antimicrobial activity of ethanolic extracts of Xylopia aethiopica, Aframomum melegueta and Piper guineense fruits were assayed against fourteen (14) microorganisms commonly associated with foodpoisoning and/or food spoilage. The microorganisms were Bacillus subtilis IAM1069, Bacillus cereus IFO 13494, Staphylococcus aureus FDA 209p, Escherichia coli NRIC 1023, Salmonella typhimurium IFO12529, Lactobacillus plantarum IAM 1041, Pediococcus acidilactici-M, Leuconostoc mesenteroides- M, Lactobacillus casei TISTR390, Saccharomyces cerevisiae OC-2, Hansenula anomala IFO 0140 (p), Pichia memb.IFO 0128, Penicillium funiclosum NBRC 6345 and Candida species. All the plant extracts exhibited selective antimicrobial activities on the test organisms. X. aethiopica extract exhibited the highest antimicrobial activity on the organisms with a minimum inhibitory concentration (MIC) of 50 ppm on Bacillus species and S. aureus. S. cerevisiae (MIC = 300 ppm), P. funiclosum NBRC 6345 and L. mesenteroides (MIC = 500 ppm) were also susceptible to X. aethiopica fruit extract but the MIC values for the other tested microorganisms were higher than 1000 ppm. This was followed by A. melegueta fruit extract with MIC of 100 ppm for B. cereus and S. aureus. Although P. guineense fruit extract inhibited the growth of B. cereus and S. aureus (MIC = 300 ppm); and B. subtilis (MIC = 1000), the MIC for the other microorganisms were higher than 5000 ppm. On the whole, all the plant extracts exhibited the least antimicrobial activities on Lactobacilli and fungi species. X. aethiopica fruit extract was used to preserve fresh orange juice. The ability of 100 and 1000 ppm extract to preserve the orange juice was significantly greater (p&lt;0.05) than 50 ppm. The microbial concentration in orange juice containing 100 ppm of X. aethiopica extract was 4 cfu/mL after 28 days of storage at room temperature.Keywords: Food spoilage, food poisoning, microorganisms, spices, ethanolic extract, natural preservatives, orange juiceAfrican Journal of Biotechnology Vol. 12(16), pp. 1993-199

Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time

We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.Comment: In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typo

WKB analysis for nonlinear Schr\"{o}dinger equations with potential

We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.Comment: 25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencie

Automated synthesis of radiopharmaceuticals for positron emission tomography: an apparatus for labelling with [11C] methyl iodide (MIASA)

A fully automated apparatus for the routine synthesis and formulation of short-lived 11C (t1/2 = 20 min) labelled radiopharmaceuticals for positron emission tomography (PET) has been developed. [11C]Carbon dioxide is converted to [11C]methyl iodide, which can be used to label a wide variety of substrates by methylation at C, N, O, or S electron rich centres. The apparatus, MIASA (methyl iodide automated synthesis apparatus), was designed to operate as part of an automated labelling system in a shielded ‘hot’ laboratory. The apparatus was designed without the size constraints of typical instrumentation used in hot cells, although it is compact where necessary. Ample use of indicators and sensors, together with compact design of the reaction flasks for small dead space and efficient evaporation, led to good reliability and performance. The design of the hardware and software is described in this paper, together with a preparation of 3-N-[11C]methylspiperone as a sterile injectable solution in physiological saline