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We study the problem of efficiently constructing a curve C of genus 2 over a finite field F for which either the curve C itself or its Jacobian has a prescribed number N of F-rational points. In the case of the Jacobian, we show that any `CM-construction' to produce the required genus-2 curves necessarily takes time exponential in the size of its input. On the other hand, we provide an algorithm for producing a genus-2 curve with a given number of points that, heuristically, takes polynomial time for most input values. We illustrate the practical applicability of this algorithm by constructing a genus-2 curve having exactly 10^2014 + 9703 (prime) points, and two genus-2 curves each having exactly 10^2013 points. In an appendix we provide a complete parametrization, over an arbitrary base field k of characteristic neither 2 nor 3, of the family of genus-2 curves over k that have k-rational degree-3 maps to elliptic curves, including formulas for the genus-2 curves, the associated elliptic curves, and the degree-3 maps., Comment: Made a number of clarifications and corrected some typographical errors

1,4-Dioxane entered the environment as a result of historic leaks and spills in the production area at an industrial facility in the southeastern coastal plain. The areal extent of the 1,4-dioxane plume is several hundred acres and is largely contained on the site. Land use adjacent to the plant property is primarily undeveloped (wetlands or woods) or industrial, with a small area of mixed land use (commercial/residential) to the southwest and north. The surficial aquifer is a relatively simple hydrogeologic system with well-defined boundaries and is comprised of a 50- to 70-foot-thick deposit of alluvial/fluvial sand and gravel that overlies an aquitard in excess of 100 feet thick. A groundwater flow model, developed and calibrated using field-measured data, was used for the fate-and-transport modeling of 1,4-dioxane. The flow-and-transport model, combined with the evaluation of other site geochemical data, was used to support the selection of monitored natural attenuation (MNA) as the proposed groundwater remedy for the site. Since the active sources of contamination have been removed and the modeling/field data demonstrated that the plume was stable and not expanding, the proposed MNA approach was accepted and approved by the regulatory agency for implementation in 2004. Subsequent accumulated data confirm that concentrations in the 1,4-dioxane plume are declining as predicted by the fate-and-transport modeling. © 2008 Wiley Periodicals, Inc.

We present three families of pairs of geometrically non-isomorphic curves whose Jacobians are isomorphic to one another as unpolarized abelian varieties. Each family is parametrized by an open subset of P^1. The first family consists of pairs of genus-2 curves whose equations are given by simple expressions in the parameter; the curves in this family have reducible Jacobians. The second family also consists of pairs of genus-2 curves, but generically the curves in this family have absolutely simple Jacobians. The third family consists of pairs of genus-3 curves, one member of each pair being a hyperelliptic curve and the other a plane quartic. Examples from these families show that in general it is impossible to tell from the Jacobian of a genus-2 curve over Q whether or not the curve has rational points -- or indeed whether or not it has real points. Our constructions depend on earlier joint work with Franck Leprevost and Bjorn Poonen, and on Peter Bending's explicit description of the curves of genus 2 whose Jacobians have real multiplication by Z[\sqrt{2}]., LaTex, 20 pages. Excluded some degenerate cases from Theorem 2, improved the exposition, simplified some examples, added an application, and included links to Magma code

It is shown that the information contained in the complete set of eigenfunctions of a Hamiltonian is the same as the information contained in any member of the set, subject to certain restrictions.

Blood test results, using standard procedures, failed to exclude the alleged father as the biological father of a child in a case of disputed paternity. Using 21 different systems, the probability of exclusion for the man was 98.19%, and the probability of paternity was only 93.90% with a paternity index of 15.48. Chromosome heteromorphisms of all three individuals were studied. By comparison of fluorescent markers of chromosomes 13, 14, 15, 21, and 22, the child was shown to inherit one homologue of each of these chromosomes from the mother, but none were like the heteromorphisms of the alleged father. This excluded him as the biological father.

Under the assumption that benign ovarian teratomas in man arise parthenogenically from a germ cell by suppression of the second meiotic division, the distance of a gene from its centromere can be estimated from the observed proportion of heterozygous teratomas collected from heterozygous hosts. The frequency of heterozygous teratomas of heterozygous hosts is equivalent to the frequency of second division segregation at the gene locus which has been used for centromere-related mapping in fungal genetics for more than 40 years. Mapping functions useful for teratoma-based mapping in man are presented.

Sensory testing of cigarette smoke presents some unique problems to the sensory specialist. This is due to a variety of reasons including the high degree of similarity between blended cigarettes and a high degree of variability between individual cigarettes. In the cigarette industry, a large effort has been placed on adapting and developing new methods of collecting and analyzing sensory-data on both flavorants and cigarette smoke. These methods include odor profiling and multidimensional scaling based on attributes and acceptability scales. In addition, extensive research has been conducted to determine the number of relevent dimensions to smoking and the types of changes that could affect consumer acceptance or purchase behavior.

Two kindreds of lattice corneal dystrophy (LCD) [McKusick, 1983, catalog No. 12220] were studied for linkage. Fifty-one relatives were examined clinically, and 27 affected and 24 normal persons were ascertained. Tight linkage could be excluded for 15 informative markers with LOD scores of less than -2.0. The largest positive LOD score was 0.56 at 0 = 0.17 for linkage between haptoglobin and LCD. Combined with a previous study, the combined LOD score is 0.96.