Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Performance Analysis of Two Quantum Reaction Dynamics Codes: Time-Dependent and Time-Independent Strategies

The computer simulation of reaction dynamics has nowadays reached a remarkable degree of accuracy. Triatomic elementary reactions are rigorously studied with great detail on a straightforward basis using a considerable variety of Quantum Dynamics computational tools available to the scientific community. In our contribution we compare the performance of two quantum scattering codes in the computation of reaction cross sections of a triatomic benchmark reaction such as the gas phase reaction Ne + H2+ %12. NeH++ H. The computational codes are selected as representative of time-dependent (Real Wave Packet [ ]) and time-independent (ABC [ ]) methodologies. The main conclusion to be drawn from our study is that both strategies are, to a great extent, not competing but rather complementary. While time-dependent calculations advantages with respect to the energy range that can be covered in a single simulation, time-independent approaches offer much more detailed information from each single energy calculation. Further details such as the calculation of reactivity at very low collision energies or the computational effort related to account for the Coriolis couplings are analyzed in this paper.

Fly Ash Soil Stabilization for Non-Uniform Subgrade Soils, Volume I: Engineering Properties and Construction Guidelines, TR-461, 2005

Soil treated with self-cementing fly ash is increasingly being used in Iowa to stabilize fine-grained pavement subgrades, but without a complete understanding of the short- and long-term behavior. To develop a broader understanding of fly ash engineering properties, mixtures of five different soil types, ranging from ML to CH, and several different fly ash sources (including hydrated and conditioned fly ashes) were evaluated. Results show that soil compaction characteristics, compressive strength, wet/dry durability, freeze/thaw durability, hydration characteristics, rate of strength gain, and plasticity characteristics are all affected by the addition of fly ash. Specifically, Iowa selfcementing fly ashes are effective at stabilizing fine-grained Iowa soils for earthwork and paving operations; fly ash increases compacted dry density and reduces the optimum moisture content; strength gain in soil-fly ash mixtures depends on cure time and temperature, compaction energy, and compaction delay; sulfur contents can form expansive minerals in soil–fly ash mixtures, which severely reduces the long-term strength and durability; fly ash increases the California bearing ratio of fine-grained soil–fly ash effectively dries wet soils and provides an initial rapid strength gain; fly ash decreases swell potential of expansive soils; soil-fly ash mixtures cured below freezing temperatures and then soaked in water are highly susceptible to slaking and strength loss; soil stabilized with fly ash exhibits increased freeze-thaw durability; soil strength can be increased with the addition of hydrated fly ash and conditioned fly ash, but at higher rates and not as effectively as self-cementing fly ash. Based on the results of this study, three proposed specifications were developed for the use of self-cementing fly ash, hydrated fly ash, and conditioned fly ash. The specifications describe laboratory evaluation, field placement, moisture conditioning, compaction, quality control testing procedures, and basis of payment.

Fly Ash Soil Stabilization for Non-Uniform Subgrade Soils, Volume II: Influence of Subgrade Non-Uniformity on PCC Pavement Performance, TR-461, 2005

To provide insight into subgrade non-uniformity and its effects on pavement performance, this study investigated the influence of non-uniform subgrade support on pavement responses (stress and deflection) that affect pavement performance. Several reconstructed PCC pavement projects in Iowa were studied to document and evaluate the influence of subgrade/subbase non-uniformity on pavement performance. In situ field tests were performed at 12 sites to determine the subgrade/subbase engineering properties and develop a database of engineering parameter values for statistical and numerical analysis. Results of stiffness, moisture and density, strength, and soil classification were used to determine the spatial variability of a given property. Natural subgrade soils, fly ash-stabilized subgrade, reclaimed hydrated fly ash subbase, and granular subbase were studied. The influence of the spatial variability of subgrade/subbase on pavement performance was then evaluated by modeling the elastic properties of the pavement and subgrade using the ISLAB2000 finite element analysis program. A major conclusion from this study is that non-uniform subgrade/subbase stiffness increases localized deflections and causes principal stress concentrations in the pavement, which can lead to fatigue cracking and other types of pavement distresses. Field data show that hydrated fly ash, self-cementing fly ash-stabilized subgrade, and granular subbases exhibit lower variability than natural subgrade soils. Pavement life should be increased through the use of more uniform subgrade support. Subgrade/subbase construction in the future should consider uniformity as a key to long-term pavement performance.