Isometries of Besov Type Spaces among Composition Operators

Let Bp,alpha for p \u3e1 and alpha \u3e1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by Martin, Vukotic and by Allen, Heller and Pons on certain Besov spaces

A Prison Education Counternarrative: “Mock Citizenship” in a Women’s Prison

In this article, we develop a perspective on the purposes and possibilities of education in prison through the stories of the first author, a prison educator and critical pedagogue. In the context of today’s prisons, we complicate universalist notions of citizenship by weaving theories of citizenship into the story of education. We share the daily concerns of a prison educator and explore the transformative possibilities that women convict students try on. We question how to shape educational practices in prison and contemplate the construction of a new “mock citizenship” informed by the realities of felony disenfranchisement. Our hope is to bring to the conversation something that has been lacking when discussions of incarceration occur: insight into the ways incarcerated students perform the role of citizen and how the purpose of prison education must extend beyond job readiness toward the creation of full citizens able to participate in the democratic process

Transitioning to an Active Learning Environment for Calculus at the University of Florida

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections

Transitioning to an Active Learning Environment for Calculus at the University of Florida

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections

Germ Granule Evolution Provides Mechanistic Insight into Drosophila Germline Development

The copackaging of mRNAs into biomolecular condensates called germ granules is a conserved strategy to posttranscriptionally regulate germline mRNAs. In Drosophila melanogaster, mRNAs accumulate in germ granules by forming homotypic clusters, aggregates containing multiple transcripts from the same gene. Nucleated by Oskar (Osk), homotypic clusters are generated through a stochastic seeding and self-recruitment process that requires the 3′ untranslated region (UTR) of germ granule mRNAs. Interestingly, the 3′ UTR belonging to germ granule mRNAs, such as nanos (nos), have considerable sequence variations among Drosophila species and we hypothesized that this diversity influences homotypic clustering. To test our hypothesis, we investigated the homotypic clustering of nos and polar granule component (pgc) in four Drosophila species and concluded that clustering is a conserved process used to enrich germ granule mRNAs. However, we discovered germ granule phenotypes that included significant changes in the abundance of transcripts present in species\u27 homotypic clusters, which also reflected diversity in the number of coalesced primordial germ cells within their embryonic gonads. By integrating biological data with computational modeling, we found that multiple mechanisms underlie naturally occurring germ granule diversity, including changes in nos, pgc, osk levels and/or homotypic clustering efficacy. Furthermore, we demonstrated how the nos 3′ UTR from different species influences nos clustering, causing granules to have ∼70% less nos and increasing the presence of defective primordial germ cells. Our results highlight the impact that evolution has on germ granules, which should provide broader insight into processes that modify compositions and activities of other classes of biomolecular condensate