On vv--domains and star operations

Let $\ast$ be a star operation on an integral domain $D$. Let \f(D) be the set of all nonzero finitely generated fractional ideals of $D$. Call $D$ a $\ast$--Pr\"ufer (respectively, $(\ast, v)$--Pr\"ufer) domain if $(FF^{-1})^{\ast}=D$ (respectively, $(F^vF^{-1})^{\ast}=D$) for all F\in \f(D). We establish that $\ast$--Pr\"ufer domains (and $(\ast, v)$--Pr\"ufer domains) for various star operations $\ast$ span a major portion of the known generalizations of Pr\"{u}fer domains inside the class of $v$--domains. We also use Theorem 6.6 of the Larsen and McCarthy book [Multiplicative Theory of Ideals, Academic Press, New York--London, 1971], which gives several equivalent conditions for an integral domain to be a Pr\"ufer domain, as a model, and we show which statements of that theorem on Pr\"ufer domains can be generalized in a natural way and proved for $\ast$--Pr\"ufer domains, and which cannot be. We also show that in a $\ast$--Pr\"ufer domain, each pair of $\ast$-invertible $\ast$-ideals admits a GCD in the set of $\ast$-invertible $\ast$-ideals, obtaining a remarkable generalization of a property holding for the "classical" class of Pr\"ufer $v$--multiplication domains. We also link $D$ being $\ast$--Pr\"ufer (or $(\ast, v)$--Pr\"ufer) with the group Inv$^{\ast}(D)$ of $\ast$-invertible $\ast$-ideals (under $\ast$-multiplication) being lattice-ordered

Dicamptodon and D. ensatus

Number of Pages: 2Integrative BiologyGeological Science

A method for calculating the effects of design errors and measurement errors on pump performance

Technique has been developed for calculating effects of design errors and measurement errors on pump performance. Error equations and charts are utilized to relate amount of error in given performance parameter to amount of error in given design or measured variable. Error equations were derived primarily for axial flow pumps, but are not limited to axial flow

Systematics of the North American menhadens: molecular evolutionary reconstructions in the genus Brevoortia (Clupeiformes: Clupeidae)

Evolutionary associations among the four North American species of menhadens (Brevoortia spp.) have not been thoroughly investigated. In the present study, classifications separating the four species into small-scaled and large-scaled groups were evaluated by using DNA data, and genetic associations within these groups were explored. Specifically, data from the nuclear genome (microsatellites) and the mitochondrial genome (mtDNA sequences) were used to elicit patterns of recent and historical evolutionary associations. Nuclear DNA data indicated limited contemporary gene flow among the species, and also indicated higher relatedness within the small-scaled and large-scaled menhadens than between these groups. Mitochondrial DNA sequences of the large-scaled menhadens indicated the presence of two ancestral lineages, one of which contained members of both species. This result may indicate genetic diver-gence (reproductive isolation) followed by secondary contact (hybridization) between these species. In contrast, a single ancestral lineage indicated incomplete genetic divergence between the small-scaled menhaden. These results are discussed in the context of the biology and demographics of each species

Reaching DEEP in Math (Developing Educational Excellence and Proficiency in Mathematics)

This paper describes the DEEP in Math Program developed in the academic year 1998-1999 from a collaborative effort of the Louisiana Systemic lnitiative Program (LaSlP) and the Louisiana Department of Education (LDE). It includes evidence of impressive results in low achieving schools and in high-poverty districts targeted by the effort. The plan was for LaSlP to give intensive content and leadership training in Summer 1999 and academic year 1999-2000 to carefully selected. well-qualified math leaders. These leaders were then employed full-time in the 1999-2000 academic year and beyond by their local education authorities to work with all math teachers in a few designated schools at some cohesive subset of grades 3-8

Phase detector assembly Patent

Detector assembly for discriminating first signal with respect to presence or absence of second signal at time of occurrence of first signa

Ambystoma opacum

Number of Pages: 2Integrative BiologyGeological Science

Ambystoma ordinarium

Number of Pages: 2Integrative BiologyGeological Science

A Quest for Fair and Balanced: The Supreme Court, State Courts, and the Future of Same-Sex Marriage Review after Perry

Gay rights advocates and social conservatives alike have criticized the Supreme Court for its recent decisions concerning sexual orientation. An examination of those decisions reveals that, taken together, they represent a surprisingly careful balance. The result is a principle of neutrality in which the Court has effectively demanded that states refrain from taking either side in the culture war surrounding sexual orientation. The true test of that neutrality principle will arise when the Court considers the constitutionality of a same-sex marriage ban. Thus far, challenges have taken place in state courts under state constitutions; those judges appear to have been guided by their own assumptions and values rather than the Supreme Court\u27s balanced approach. The federal challenge in Perry v. Schwarzenegger may change the legal landscape. The district court ordered a full trial the first court to do so and held, based on the evidence, that the state constitutional amendment violated the U.S. Constitution because it served only to disapprove of gay persons and their relationships. This August 2010 decision provides an excellent application of the Supreme Court\u27s state-neutrality principle and will offer the Court the chance to weigh in on same-sex marriage