Effects of digestion,chemical separation,and deposition on Po-210 quantitative analysis

The purpose of this work was to determine polonium losses from a variety of sample types (soil, cotton fiber, and air filter) due to digestion technique, chemical separation, and deposition method for alpha energy analysis. Results demonstrated that yields from a perchloric acid wet-ash (87 ± 5 %) were similar to that from a microwave digestion (100 ± 7 %), but both were greater than the dry-ash procedure (38 ± 5 %). The polonium was separated from an SRM soil using an AG1X8 ion exchange column and deposited on a Ag disk with a recovery of 83 ± 7 % of polonium-209 (Po-209). Deposition yields without chemical separation averaged 90 ± 5 % of Po-209. The polonium-210 content was successfully measured in the three matrix types and quantitated using alpha spectroscopy.     

A Geometric Approach to the Existence of Orbits with Unbounded Energy in Generic Periodic Perturbations by a Potential of Generic Geodesic Flows of ?2}

We give a proof based in geometric perturbation theory of a result proved by J. N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a generic geodesic flow in IJ by a generic periodic potential.     

Exponentially Small Splitting of Separatrices Under Fast Quasiperiodic Forcing

We consider fast quasiperiodic perturbations with two frequencies (1/ɛ,γ/$epsiv;) of a pendulum, where γ is the golden mean number. The complete system has a two-dimensional invariant torus in a neighbourhood of the saddle point. We study the splitting of the three-dimensional invariant manifolds associated to this torus. Provided that the perturbation amplitude is small enough with respect to ɛ, and some of its Fourier coefficients (the ones associated to Fibonacci numbers), are separated from zero, it is proved that the invariant manifolds split and that the value of the splitting, which turns out to be exponentially small with respect to ɛ, is correctly predicted by the Melnikov function. Received: 19 February 1996 / Accepted: 14 February 1997     

Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations

A vector bundle morphism of a vector bundle with strongly ordered Banach spaces as fibers is studied. It is assumed that the fiber maps of this morphism are compact and strongly positive. The existence of two complementary, dimension-one and codimension-one, continuous subbundles invariant under the morphism is established. Each fiber of the first bundle is spanned by a positive vector (that is, a nonzero vector lying in the order cone), while the fibers of the other bundle do not contain a positive vector. Moreover, the ratio between the norms of the components (given by the splitting of the bundle) of iterated images of any vector in the bundle approaches zero exponentially (if the positive component is in the denominator). This is an extension of the Krein-Rutman theorem which deals with one compact strongly positive map only. The existence of invariant bundles with the above properties appears to be very useful in the investigation of asymptotic behavior of trajectories of strongly monotone discrete-time dynamical systems, as demonstrated by Poláik and Tereák (Arch. Ration. Math. Anal. 116, 339–360, 1991) and Hess and Poláik (preprint). The present paper also contains some new results on typical asymptotic behavior in scalar periodic parabolic equations.     

A Reinvestigation of the Dichlorination of Thymidine

The reaction of thymidine with thionyl chloride in HMPA, reported¹ to give pure 1-(3,5-dichloro-2,3,5-trideoxy-β-D-threo-pentofuranosyl)thymine, has been found to give a mixture of erythro and threo isomers. Upon reacting thymidine with thionyl chloride, according to the literature procedure,¹ a product was isolated which melted 138–141°C [reported¹ 138–140°C] and gave one spot in CHCl₃/ETOH (4:1) on Eastman silica gel sheets at R_f=0.6 [reported¹ one spot at R_f=0.7 on Baker silica gel sheets]. However, the TLC of the product in neat ethyl acetate or CHCl₃/MeOH (9:1) gave two spots. A sample was separated into pure components by flash chromatography².