Assignment of the 1H and 13C NMR of tocotrienols

Vitamin E is a family of chromanols that vary by the degree of methylation of the chroman ring as well as the nature of the hydrophobic side chain at C2 that serves to anchor these lipids in biological membranes. The tocopherols contain saturated side chains, whereas the tocotrienols contain three sites of unsaturation and are derived from geranylgeranyl diphosphate. A growing interest in the unique biological activities of the tocotrienols has led us to begin syntheses of isotopically substituted forms and other derivatives that will be useful for probing the metabolism and membrane behavior of the tocotrienols. In order to be certain of our ability to selectively modify sites on the parent molecules it was necessary to make as complete an assignment of the 1H and 13C NMR as possible. Herein we report multidimensional NMR data (HSQC, COSY, ADEQUATE(1,1), C--H HMBC, and NOESY) that have allowed us to assign the identity of almost all the resonances for alpha-, beta-, gamma-, and delta-tocotrienol.     

Self-similar Blow-Up Profiles for a Reaction–Diffusion Equation with Critically Strong Weighted Reaction

Journal of Dynamics and Differential Equations - We classify the self-similar blow-up profiles for the following reaction–diffusion equation with critical strong weighted reaction and...     

Stressed waveguides with tubular depressed-cladding inscribed in phosphate glasses by femtosecond hollow laser beams

We report on the single-step fabrication of stressed optical waveguides with tubular depressed-refractive-index cladding in phosphate glasses by the use of focused femtosecond hollow laser beams. Tubelike low index regions appear under direct exposure due to material rarefaction following expansion. Strained compacted zones emerged in domains neighboring the tubular track of lower refractive index, and waveguiding occurs mainly within the tube core fabricated by the engineered femtosecond laser beam. The refractive index profile of the optical waveguide was reconstructed from the measured transmitted near-field intensity.     

Microstructures and growth characteristics of polyelectrolytes on silicon using layer-by-layer assembly

Growth processes of nanocomposite layers obtained by polyelectrolytes, poly(sodium 4-styrenesulfonate) (PSS) and poly(diallyldimethylammonium chloride) (PDADMAC), self-assembled on silicon surface using layer-by-layer (LbL) technique were investigated, and theoretical and experimental data are herein reported. Complementary microstructural and compositional analyses techniques (scanning electron microscopy, ellipsometry, X-ray reflectivity, zeta (ξ) potential measurements and attenuated total reflection infrared spectroscopy) were used for deep characterization of the multilayer structure formation. Electrophoretic zeta (ξ) potential measurements indicated that the surface charge was either positive or negative, depending on the polyelectrolyte used (PDADMAC or PSS). ATR-IR spectra confirmed the successfully silanization process and then, the building up of the nanocomposite layer. Morphological investigation and X-ray reflectivity demonstrated the growth process and cross-section size of the bilayers. Ellipsometric measurements were in very good agreement with SEM and XRR, showing once again the successful deposition of polyelectrolyte multilayers.      

Renormalization of Non-Commutative \Phi^4_4 Field Theory in x Space

In this paper we provide a new proof that the Grosse–Wulkenhaarn on-commutative scalar theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler. It also allows direct interpretation in terms of the physical positions of the particles and should be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).     

A Voronovskaya Type Theorem for Poisson-Cauchy Type singular operators

In this article we continue with the study of approximation properties of smooth Poisson-Cauchy Type singular integral operators over the real line. We produce Voronovskaya Type results and give some quantitative results regarding the rate of convergence of these singular integral operators.     

Dynamical instabilities of ice X

Water ice X is stable in the 120-400 GPa pressure range, as obtained from lattice dynamical calculations performed using the density-functional theory. Below 120 GPa, it is characterized by one unstable flat phonon band, which generates the disordered ice X structure. Above 400 GPa, ice X has an unstable phonon mode in M, which leads to the Pbcm orthorhombic structure obtained in previous molecular-dynamics calculations [M. Benoit, M. Bernasconi, P. Focher, and M. Parrinello, Phys. Rev. Lett. 76, 2934 (1996)10.1103/PhysRevLett.76.2934]. Therefore, based on lattice dynamics, we propose that the high-pressure low-temperature phase-transition sequence in H2O ice is ice VIII-disordered ice X-ordered ice X-ice Pbcm.     

The Weyl Quantization and the Quantum Group Quantization of the Moduli Space of Flat <Emphasis Type="Italic">SU</Emphasis>(2)-Connections on the Torus are the Same

 We prove that, for the moduli space of flat SU(2)-connections on the 2-dimensional torus, the Weyl quantization and the quantization performed using the quantum group of SL(2,C) are the same. This is done by comparing the matrices of the operators associated through the two quantizations to cosine functions. We also discuss the *-product of the Weyl quantization and show that it satisfies the product-to-sum formula for noncommutative cosines on the noncommutative torus. Received: 27 January 2002 / Accepted: 9 September 2002 Published online: 19 December 2002 RID="*" ID="*" Research supported in part by the NSF, award No. DMS 0070690 Communicated by A. Connes     

Non-Commutative Complete Mellin Representation for Feynman Amplitudes

We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of space–time. In particular it paves the road for the dimensional renormalization of these theories. This complete Mellin representation also allows the study of asymptotic behavior under rescaling of arbitrary subsets of external invariants of any Feynman amplitude.