Class numbers of definite binary quadratic lattices over algebraic function fields

Let k be an algebraic function field of one variable X having a finite field GF(q) of constants with q elements, q odd. Confined to imaginary quadratic extensions $\text{K}\text{k}$, class number formulas are developed for both the maximal and nonmaximal binary quadratic lattices L on (K, N), where N denotes the norm from K to k. The class numbers of L grow either with the genus g(k) of k (assuming the fields under consideration have bounded degree) or with the relative genus $\text{g(}\text{K}\text{k}\text{)}$ (assuming the lattices under consideration have bounded scale). In contrast to analogous theorems concerning positive definite binary quadratic lattices over totally real number fields, k is not necessarily totally real.     

Detecting exposure-dependent changes of liver detoxification capacity of children in a formerly high-loaded industrial area with a 15N-labelled diagnostic tool

The effect of remediation activities in formerly high-loaded industrial areas is measured conventionally in terms of decreased toxic loads. It is more difficult to investigate the effect on physiological parameters of the people living there. A non-invasive 15N-based organ function test, the [15N]methacetin urine test, was adapted to environmental-medical purposes for the detection of small deviations from the norm-range hepatic detoxification capacity. Parallel to the measurement of region-specific external exposure (especially by tri- and tetrachloro ethylene) and of the corresponding internal load (urinary trichloro acetic acid), the hepatic mono oxygenation capacity was determined. The study cohort consisted of 35 kindergarten children who were 3.3+/-0.5 years old at the beginning of the study. They lived in a high-polluted industrial village (n = 23) and in a non-polluted control village close by (n = 12), respectively. Children living in the polluted area were exposed a 2.3 times higher load and showed detoxification capacities 6% lower than the children in the control area. Improvement of the environmental situation led to exposure data decreasing by 70%, which is also reflected in smaller internal load and improved liver detoxification of the children in the polluted area. Then, between loaded and control area the mean hepatic detoxification was no longer significantly different (0.6%). The study shows that chronic low-dose exposure can disturb a hepatic function and that thereafter the capacity is recovered quickly in children. The stable isotope-based test is suited to characterize a health effect of multicomponent exposure by bioeffect monitoring within the framework of screening and testing the remediation efficiency.     

Greedy sums of distinct squares

When a positive integer is expressed as a sum of squares, with each successive summand as large as possible, the summands decrease rapidly in size until the very end, where one may find two 's, or several 's. We find that the set of integers for which the summands are distinct does not have a natural density but that the counting function oscillates in a predictable way.

     

Novel stabilization mechanism on polar surfaces: ZnO(0001)-Zn

The (1x1) terminated (0001)-Zn surface of wurtzite ZnO was investigated with scanning tunneling microscopy. The surface is characterized by the presence of nanosized islands with a size-dependent shape and triangular holes with single-height, O-terminated step edges. It is proposed that the resulting overall decrease of the surface Zn concentration stabilizes this polar surface. Ab initio calculations of test geometries predict triangularly shaped reconstructions over a wide range of oxygen and hydrogen chemical potentials. The formation of these reconstructions appears to be electrostatically driven.     

Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons

We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.