Xenon NMR: chemical shifts of a general anesthetic in common solvents, proteins, and membranes.

The rare gas xenon contains two NMR-sensitive isotopes in high natural abundance. The nuclide 129Xe has a spin of 1/2: 131Xe is quadrupolar with a spin of 3/2. The complementary NMR characteristics of these nuclei provide a unique opportunity for probing their environment. The method is widely applicable because xenon interacts with a useful range of condensed phases including pure liquids, protein solutions, and suspensions of lipid and biological membranes. Although xenon is chemically inert, it does interact with living systems; it is an effective general anesthetic. We have found that the range of chemical shifts of 129Xe dissolved in common solvents is ca. 200 ppm, which is 30 times larger than that found for 13C in methane dissolved in various solvents. Resonances were also observed for 131Xe in some systems; they were broader and exhibited much greater relaxation rates than did 129Xe. The use of 129Xe NMR as a probe of biological systems was investigated. Spectra were obtained from solutions of myoglobin, from suspensions of various lipid bilayers, and from suspensions of the membranes of erythrocytes and of the acetylcholine receptor-rich membranes of Torpedo californica. These systems exhibited a smaller range of chemical shifts. In most cases there was evidence of a fast exchange of xenon between the aqueous and organic environments, but the exchange was slow in suspensions of dimyristoyl lecithin vesicles

Orbital perturbations using geopotential coefficients up to high degree and order: Highly eccentric orbits

Several methods have been proposed for calculations of the eccentricity function for a high value of the eccentricity, however they cannot be used when the high degree and order coefficients of gravity fields are taken into account. The method proposed by Wnuk(1) is numerically stable in this case, but when is used. a large number of terms occurs in formulas for geopotential perturbations. In this paper we propose an application of expansions of some functions of the eccentric anomaly E as well as Hansen coefficients in power series of (e - e*), where e* is a fixed value of the eccentricity derived by da Silva Fernandes(2,3,4). These series are convergent for all e < 1

Partitioning procedure for polynomial optimization

Polynomial optimization, Positivstellensatz, Sum of squares, Benders decomposition,