Composition operators from large weighted Hardy spaces into the Dirichlet space

Given a large weighted Hardy space we show there exists a composition operatorC with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College.     

Thermodynamic Modeling of Actinide Complexation with Acetate and Lactate at High Ionic Strength

The stability constants of NpO ₂ ⁺ , UO ₂ ²⁺ Am³⁺, and Th⁴⁺ with acetate and lactate anions has been measured in 0.3–5.0m NaCl media at 25°C by the solvent extraction technique. For the 1:1 complexation, the values of the stability constants increased in the order: NpO ₂ ⁺ < Am³⁺ < ₂ ²⁺ < Th⁴⁺, in accordance with the actinide charge density and reflecting the strongly ionic bonding of the complexes. The Pitzer ionic interaction parameters were calculated and used to estimate the thermodynamic stability constants at I = 0. Because our data were collected mainly in the high ionic strength region values of ⁽¹⁾ were estimated from values reported in the literature. For all stability constants the Pitzer model gives an excellent representation of the data using three interaction parameters ⁽⁰⁾, ⁽¹⁾, and COn leave from Institute of     

A finiteness theorem for a class of exponential congruences

For given elements and belonging to the ring of integers of a number field we consider the set of all tuples in for which divides for any and prove under some reasonable assumptions that the set of solutions is finite.

     

A Lefschetz type result for Koszul cohomology

We study the behaviour of Koszul cohomology under restriction to a divisor, extending previous results of M. Green. Using our result we compare Greens canonical conjecture to the gonality conjecture of Green-Lazarsfeld.Revised version: 15 May 2003Acknowledgements. M. Aprodu was financed by a EC-Marie Curie Fellowship, contract no. HPMF-CT-2000-00895. We would like to thank the referee for some useful remarks on the first version of this paper.     

Intensity-related dynamics of femtosecond frequency combs

We have performed systematic studies of intensity-related dynamics of the pulse repetition and carrier-envelope offset frequencies in mode-locked Ti:sapphire lasers. We compared the results far two laser systems that have different intracavity dispersion-compensation schemes. We found that the carrier-envelope phase noise and its dynamic response depend critically on the mode-locking conditions. An intensity-related shift of the laser spectrum was found to be instrumental in interpretations.     

Strong topologies on vector-valued function spaces

Let be a real Banach space and let E be an ideal of L ⁰ over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function , defined by , belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.     

Chemoenzymatic synthesis of phosphocarnitine enantiomers

Racemic phosphocarnitine 3 has been synthesized starting from diethyl 3-chloro-2-oxopropanephosphonate 4 in three steps involving reduction of 4 to the corresponding 2-hydroxyphosphonate 5, conversion of the latter to phosphonic acid 6, and final reaction with trimethylamine, affording the trimethylammonium salt of 3. Baker's yeast reduction of 4 and enzymatic kinetic resolution of (+/-)-5 afforded the enantiomerically pure precursors of phosphocarnitine, (R)-(+)-5 and (S)-(-)-5, which were converted to (S)-(-)- and (R)-(+)-phosphocarnitine 3, respectively.     

A semi-empirical approach to determine gamma activities in environmental cylindrical samples

A semi-empirical method to determine radionuclide concentrations in large environmental samples without the use of reference material and avoiding the typical complexity of Monte-Carlo codes is proposed. The calculation of full-energy peak efficiencies was carried out from a relative efficiency curve (obtained from the gamma spectra data), and the geometric (simulated by Monte-Carlo), absorption, sample and intrinsic efficiencies for energies between 130 and 3000 keV. The absorption and sample efficiencies were determined from the mass absorption coefficients, whereas the intrinsic efficiency was approximated by an empirical function. The deviations between calculated and experimental efficiencies for a reference material in most cases are less than 10%. Radionuclide activities in marine sediment samples calculated by the proposed method and by the experimental comparative method were not significantly different. This new method can be used for routine environmental monitoring when uncertainties up to 10% are acceptable.