Nonisomorphic curves that become isomorphic over extensions of coprime degrees

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field and let r and s be integers greater than 1 that are coprime to one another. We show that one can find a finite extension K of K_0, a degree-r extension L of K, a degree-s extension M of K, and two curves C and D over K such that C and D become isomorphic to one another over L and over M, but not over any proper subextensions of L/K or M/K. We show that such C and D can never have genus 0, and that if K is finite, C and D can have genus 1 if and only if {r,s} = {2,3} and K is an odd-degree extension of F_3. On the other hand, when {r,s}={2,3} we show that genus-2 examples occur in every characteristic other than 3. Our detailed analysis of the case {r,s} = {2,3} shows that over every finite field K there exist nonisomorphic curves C and D that become isomorphic to one another over the quadratic and cubic extensions of K. Most of our proofs rely on Galois cohomology. Without using Galois cohomology, we show that two nonisomorphic genus-0 curves over an arbitrary field remain nonisomorphic over every odd-degree extension of the base field.Comment: LaTeX, 32 pages. Further references added to the discussion in Section 1

Hedging in Field Theory Models of the Term Structure

We use path integrals to calculate hedge parameters and efficacy of hedging in a quantum field theory generalization of the Heath, Jarrow and Morton (HJM) term structure model which parsimoniously describes the evolution of imperfectly correlated forward rates. We also calculate, within the model specification, the effectiveness of hedging over finite periods of time. We use empirical estimates for the parameters of the model to show that a low dimensional hedge portfolio is quite effective.Comment: 18 figures, Invited Talk, International Econophysics Conference, Bali, 28-31 August 200

Interaction of amiodarone and desethylamiodarone with solubilized nuclear thyroid hormone receptors

The mechanisms of action of the potent antiarrhythmic drug amiodarone are unknown. However, amiodarone and its abundant metabolite, desethylamiodarone, bear a striking structural resemblance to thyroid hormones. In addition, certain cardiac electrophysiologic effects of amiodarone treatment are similar to those of hypothyroidism. These facts suggest that amiodarone or desethylamiodarone could be acting, in part, by blocking thyroid hormone action. Because thyroid hormones are known to act through nuclear receptor prqteins, the binding of amiodarone and desethylamiodarone was measured to nuclear extracts derived from human lymphocytes, bovine atrium and ventricle and rat liver.The capacity of increasing concentrations of amiodarone and desethylamiodarone nuclear extracts to block receptor binding of radiolabeled triiodothyronine (T3) in a standard in vitro competition assay was tested. Nuclear extracts demonstrated only minimal binding to amiodarone. However, all receptor preparations had substantial affinities (KD) for the desethyl analog: lymphocyte, 8.6 μM; atrium, 35.0 μM; ventricle, 26.9 μM and liver, 8.6 μM. Desethylamiodarone accumulates in very large quantities in parenchymatous organs during long-term amiodarone treatment. Taking its usual therapeutic serum level (about 4 μMor 2.7 μg/ml) as an estimate of intranuclear concentration, desethylamiodarone would partially saturate nuclear thyroid hormone receptors in several different tissues, including the heart.Thus, amiodarone treatment may exert some of its electrophysiologic effects by metabolic conversion to desethylamiodarone. This metabolite may then exclude thyroid hormone from nuclear receptor sites within the myocardium

Diagenetic responses to sea-level change: Integration of field, stable isotope, paleosol, paleokarst, fluid inclusion, and cement stratigraphy research to determine history and magnitude of sea-level fluctuation

Abstract Quantifying the history of changes in sea level is an important constraint for modeling sedimentary systems. Integration of diagenetic evidence for subaerial exposure with stratigraphic evidence of paleotopography is important for determining the history of relative changes in sea level. Surfaces of subaerial exposure can develop on marine strata from aggradation of sediment into the subaerial realm, from eustatic sea-level falls, or from uplift. Surfaces of subaerial exposure that result from aggradation alone can be distinguished from those that result from eustatic fall or uplift. If exposure surfaces directly overlie strata of subtidal origin or drape significant paleotopography, aggradation alone must be ruled out. The minimum relative fall in sea level can be quantified by tracing surfaces of subaerial exposure over reconstructed paleotopography or by determining the depth to which vadose-zone diagenesis occurred. Paleosols, paleokarst, trends in stable isotopes, calcite cement stratigraphy, calcite cement fabrics, and fluid inclusions provide diagenetic records that are useful in identifying ancient surfaces of subaerial exposure and determining the position of ancient vadose zones. Paleosols can be identified using the preserved records of desiccation and wetting, subaerial processes, and plant activity. Studies from the Pennsylvanian Holder Formation of New Mexico illustrate that paleosols can be laterally variable in nature and can be used to demonstrate a relative fall in sea level of at least 30 m (100 ft). Paleosol features can develop well below the subaerial surface, so caution must be used in applying this technique. Paleokarst is another useful record of subaerial exposure. Some karstification results in surface landforms, terra rossa paleosols, or vertical voids in which there is a clear relationship to an ancient surface of subaerial exposure. The depth of penetration of these karst features that developed in the vadose zone can be used as a minimum estimate of relative sea-level fall. For karst cavities that cannot be directly associated with a specific surface of subaerial exposure, the age of sediment fills or regional distribution of cavities can provide the most direct link to a particular surface of subaerial exposure. Whole-rock trends of relatively negative δ13C, relatively positive δ18O, and a baseline shift in δ18O can also reflect ancient surfaces of subaerial exposure. Variability of data from the Holder Formation shows that the trends predicted are not the result of stabilization in a homogeneous, relatively negative δ13C zone but the result of patchy cementation and replacement in a solution of heterogeneous carbon isotopic composition. Preservation of the most negative carbon signatures depends on sampling the highest volumes of soil-precipitated phases and those in closest proximity to organic structures in soils. Calcite cements with meniscus or pendant fabrics preserve a record of vadose diagenesis. Vertical pinchout of calcite-cement compositional zones may reflect surfaces of subaerial exposure. The lateral variability of such cements in the Pennsylvanian Holder Formation and the Lansing-Kansas City Groups of Kansas shows that such cements develop best in paleotopographically high settings. Fluid inclusions can provide a record of diagenesis in the vadose zone. Fluid inclusions trapped in the vadose zone are marked by variable ratios of vapor to liquid and all-liquid fluid inclusions. The distribution of such inclusions in Miocene rocks of Spain demonstrate a relative fall in sea level of at least 50-55 m (160-180 ft)

Diagenetic responses to sea-level change: Integration of field, stable isotope, paleosol, paleokarst, fluid inclusion, and cement stratigraphy research to determine history and magnitude of sea-level fluctuation

Abstract Quantifying the history of changes in sea level is an important constraint for modeling sedimentary systems. Integration of diagenetic evidence for subaerial exposure with stratigraphic evidence of paleotopography is important for determining the history of relative changes in sea level. Surfaces of subaerial exposure can develop on marine strata from aggradation of sediment into the subaerial realm, from eustatic sea-level falls, or from uplift. Surfaces of subaerial exposure that result from aggradation alone can be distinguished from those that result from eustatic fall or uplift. If exposure surfaces directly overlie strata of subtidal origin or drape significant paleotopography, aggradation alone must be ruled out. The minimum relative fall in sea level can be quantified by tracing surfaces of subaerial exposure over reconstructed paleotopography or by determining the depth to which vadose-zone diagenesis occurred. Paleosols, paleokarst, trends in stable isotopes, calcite cement stratigraphy, calcite cement fabrics, and fluid inclusions provide diagenetic records that are useful in identifying ancient surfaces of subaerial exposure and determining the position of ancient vadose zones. Paleosols can be identified using the preserved records of desiccation and wetting, subaerial processes, and plant activity. Studies from the Pennsylvanian Holder Formation of New Mexico illustrate that paleosols can be laterally variable in nature and can be used to demonstrate a relative fall in sea level of at least 30 m (100 ft). Paleosol features can develop well below the subaerial surface, so caution must be used in applying this technique. Paleokarst is another useful record of subaerial exposure. Some karstification results in surface landforms, terra rossa paleosols, or vertical voids in which there is a clear relationship to an ancient surface of subaerial exposure. The depth of penetration of these karst features that developed in the vadose zone can be used as a minimum estimate of relative sea-level fall. For karst cavities that cannot be directly associated with a specific surface of subaerial exposure, the age of sediment fills or regional distribution of cavities can provide the most direct link to a particular surface of subaerial exposure. Whole-rock trends of relatively negative δ13C, relatively positive δ18O, and a baseline shift in δ18O can also reflect ancient surfaces of subaerial exposure. Variability of data from the Holder Formation shows that the trends predicted are not the result of stabilization in a homogeneous, relatively negative δ13C zone but the result of patchy cementation and replacement in a solution of heterogeneous carbon isotopic composition. Preservation of the most negative carbon signatures depends on sampling the highest volumes of soil-precipitated phases and those in closest proximity to organic structures in soils. Calcite cements with meniscus or pendant fabrics preserve a record of vadose diagenesis. Vertical pinchout of calcite-cement compositional zones may reflect surfaces of subaerial exposure. The lateral variability of such cements in the Pennsylvanian Holder Formation and the Lansing-Kansas City Groups of Kansas shows that such cements develop best in paleotopographically high settings. Fluid inclusions can provide a record of diagenesis in the vadose zone. Fluid inclusions trapped in the vadose zone are marked by variable ratios of vapor to liquid and all-liquid fluid inclusions. The distribution of such inclusions in Miocene rocks of Spain demonstrate a relative fall in sea level of at least 50-55 m (160-180 ft)