Finite Group Schemes over Bases with Low Ramification

Let A be a complete characteristic (0,p) discrete valuation ring with absolute ramification degree e and a perfect residue field. We are interested in studying the category FF _A' of finite flat commutative group schemes over A withp-power order. When e= 1, Fontaine formulated the purely linear algebra notion of a finite Honda system over A and constructed an anti-equivalence of categories betweenineFF _A'> and the category of finite Honda systems over A when p> 2. We generalize this theory to the case e – 1.     

STOPPING RULES AND THE CONTROL OF STOCK POLLUTANTS

A stock pollutant is defined as a residual waste that might accumulate over time. This paper examines some of the important distinctions between degradable and nondegradable stock pollutants and between nondegradable stock pollutants with known versus uncertain environmental cost. The latter case is examined using the more recent literature on stochastic control with Brownian motion. The presence of irreversibility and uncertainty is known to lead to more conservative investment rules and places a value on the preservation of options. In the case of a nondegradable stock pollutant with Brownian environmental cost, options are preserved by stopping accumulation at a lower level than in the corresponding certainty-equivalent problem. The model presented in this paper permits the derivation of closed-form stopping rules. For a simple numerical problem, the optimal nondegradable stock with Brownian environmental cost was 20 to 45 percent lower than the optimal level with known environmental cost. The empirical study of an actual nondegradable stock pollutant will require time series data on private and social cost in order to estimate drift and variance parameters which will influence the actual extent to which the optimal stock is less than the certainty-equivalent stock.     

Synthesen von Dibenzo[b,e][1,4]dioxin-2,3-chinonen,einschliesslich der Ecklonochinone A und B sowie der Isoecklonochinone A und B

Syntheses of Dibenzo[b,e][1,4]dioxin-2,3-quinones Including the Ecklonoquinones A and B and the Isoecklonoquinones A and B Oxidation of monomesyloxy-substituted pyrocatechols with MnO₂ in toluene using phase-transfer conditions leads in high yield to monomesyloxy-substituted dibenzo[b,e][1,4]dioxin-2,3-quinones with loss of one mesyloxy group. In this way, ecklonoquinone A ( 2 ), ecklonoquinone B ( 3 ), isoecklonoquinone A ( 43 ), and isoecklonoquinone B ( 44 ) were prepared. Their structures are based on X-ray analyses of ecklonoquinone-A leucoacetate ( 45 ) and the mesyloxy-substituted quinone 20 . The reddish-violet dibenzodioxin-diquinone 49 was prepared from an intermediate of the iso-series. The parent compound 1 has been synthesized in yields better than 50% from pyrocatechol and methyl 2,5-dioxo-2,5-dihydrobenzoate as oxidant and 2-methoxypyridin as catalyst. To rationalize the specific effect on the dimerisation step of the mesyloxy group, the intermediacy of 1,4-quinone monoacetals is proposed. This also applies to a proposed biogenetic scheme.     

Measurements of F2 and xF(nu)(3) - xF(nu;)(3) from CCFR nu(mu)-Fe and nu;(mu)-Fe Data in a Physics Model-Independent Way

We report on the extraction of the structure functions F2 and DeltaxF(3) = xF(nu)(3)-xF(nu;)(3) from CCFR nu(mu)-Fe and nu;(mu)-Fe differential cross sections. The extraction is performed in a physics model-independent (PMI) way. This first measurement of DeltaxF(3), which is useful in testing models of heavy charm production, is higher than current theoretical predictions. The ratio of the F2 (PMI) values measured in nu(mu) and mu scattering is in agreement (within 5%) with the predictions of next-to-leading-order parton distribution functions using massive charm production schemes, thus resolving the long-standing discrepancy between the two sets of data.     

Uptake and release kinetics of 22 polar organic chemicals in the Chemcatcher passive sampler

The Chemcatcher passive sampler, which uses Empore? disks as sampling phase, is frequently used to monitor polar organic chemicals in river water and effluents. Uptake kinetics need to be quantified to calculate time-weighted average concentrations from Chemcatcher field deployments. Information on release kinetics is needed if performance reference compounds (PRCs) are used to quantify the influence of environmental conditions on the uptake. In a series of uptake and elimination experiments, we used Empore? SDB disks (poly(styrenedivinylbenzene) copolymer modified with sulfonic acid groups) as a sampling phase and 22 compounds with a logK _ow (octanol–water partitioning coefficient) range from ?2.6 to 3.8. Uptake experiments were conducted in river water or tap water and lasted up to 25 days. Only 1 of 22 compounds (sulfamethoxazole) approached equilibrium in the uptake trials. Other compounds showed continuing non-linear uptake, even after 25 days. All compounds could be released from SDB disks, and desorption was proportionally higher in disks loaded for shorter periods. Desorption showed two-phase characteristics, and desorption was proportionally higher for passively sorbed compounds compared to actively loaded compounds (active loading was performed by pulling spiked river water over SDB disks using vacuum). We hypothesise that the two-phase kinetics and better retention of actively loaded compounds—and compounds loaded for a longer period—may be caused by slow diffusion of chemicals within the polymer. As sorption and desorption did not show isotropic kinetics, it is not possible to develop robust PRCs for adsorbent material like SDB disks.     

Morse Theory and Central Configurations in the Spatial N-body Problem

In the spirit of Palmore and Pacella, Morse Theory is used to obtain a lower bound for the number of central configurations in the spatial N-body problem. The homology of the configuration ellipsoid with the collision and collinear manifolds removed and the SO(3) symmetry quotiented out is calculated. As intermediate steps, homology calculations are carried out for several additional manifolds naturally arising in the N-body problem.