γ\gamma-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces

In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space \B. If we denote by $H$ the Hilbert space L^2((0,\infty),dt/t),\gamma(H,\B) represents the space of $\gamma$-radonifying operators from $H$ into \B. We prove that the Hermite square function defines bounded operators from BMO_\mathcal{L}(\R,\B) (respectively, H^1_\mathcal{L}(\R, \B)) into BMO_\mathcal{L}(\R,\gamma(H,\B)) (respectively, H^1_\mathcal{L}(\R, \gamma(H,\B))), where $BMO_\mathcal{L}$ and $H^1_\mathcal{L}$ denote $BMO$ and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMO_\mathcal{L}(\R, \B) and H^1_\mathcal{L}(\R,\B) by using Littlewood-Paley-Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces.Comment: 31 page

Modules with cosupport and injective functors

Several authors have studied the filtered colimit closure lim(B) of a class B of finitely presented modules. Lenzing called lim(B) the category of modules with support in B, and proved that it is equivalent to the category of flat objects in the functor category (B^{op},Ab). In this paper, we study the category (Mod-R)^B of modules with cosupport in B. We show that (Mod-R)^B is equivalent to the category of injective objects in (B,Ab), and thus recover a classical result by Jensen-Lenzing on pure injective modules. Works of Angeleri-Hugel, Enochs, Krause, Rada, and Saorin make it easy to discuss covering and enveloping properties of (Mod-R)^B, and furthermore we compare the naturally associated notions of B-coherence and B-noetherianness. Finally, we prove a number of stability results for lim(B) and (Mod-R)^B. Our applications include a generalization of a result by Gruson-Jensen and Enochs on pure injective envelopes of flat modules.Comment: 16 page

R. B. Flowers

R. B. Flowershttps://scholarsjunction.msstate.edu/ua-photo-collection/4627/thumbnail.jp

Representations and Discourses of Black Motherhood in Hip Hop and R&B over Time

This study will examine how representations and discourses regarding Black motherhood have changed in the Hip Hop and R&B genres over time. Specifically, this scholarly work will contextualize the lyrics of 79 songs (57 Hip Hop songs; 18 R&B songs; 2 songs represented the Hip Hop and R&B genre; 2 songs represented artists who produce music in 5 or 6 genres) from 1961-2015 to identify the ways that Black male and Black female artists described motherhood. Through the use of Black Feminist Theory, and by placing the production of these songs within a sociohistorical context, we provide an in-depth qualitative examination of song lyrics related to Black motherhood. Results gave evidence that representations and discourse of motherhood have been largely shaped by patriarchy as well as cultural, political, and racial politics whose primary aim was to decrease the amount of public support for poor, single Black mothers. In spite of the pathological framing of Black mothers, most notably through the welfare queen and baby mama stereotypes, a substantial number of Hip Hop and R&B artists have provided a strong counter narrative to Black motherhood by highlighting their positive qualities, acknowledging their individual and collective struggle, and demanding that these women be respected

Is Black Motherhood A Marker of Oppression or Empowerment? Hip-Hop and R&B Lessons about Mama

A qualitative content analysis was conducted on the lyrics of 59 songs (40 Hip Hop songs; 17 R&B songs; 2 songs that represented the Hip Hop and R&B genre) from 1961-2013 to identify the ways that Black male and Black female artists described motherhood. The songs were determined by Billboard Chart Research Services, and Black Feminist Theory provided the theoretical foundation on which the themes were identified. Qualitative analysis of the lyrics revealed Black motherhood in R&B and Hip Hop to be based on the following four typologies: (1) Motherhood as Source of Emotional Comfort and Support; (2) Motherhood as Source of Strength and Self-Confidence; (3) Motherhood as Superior to Fatherhood; (4) Motherhood as Teacher and Disciplinarian; and (5) Motherhood Instills Unconditional Endless Love. Supporting qualitative lyrics are provided to support each of the aforementioned themes

Is Black Motherhood A Marker of Oppression or Empowerment? Hip-Hop and R&B Lessons about Mama

A qualitative content analysis was conducted on the lyrics of 59 songs (40 Hip Hop songs; 17 R&B songs; 2 songs that represented the Hip Hop and R&B genre) from 1961-2013 to identify the ways that Black male and Black female artists described motherhood. The songs were determined by Billboard Chart Research Services, and Black Feminist Theory provided the theoretical foundation on which the themes were identified. Qualitative analysis of the lyrics revealed Black motherhood in R&B and Hip Hop to be based on the following four typologies: (1) Motherhood as Source of Emotional Comfort and Support; (2) Motherhood as Source of Strength and Self-Confidence; (3) Motherhood as Superior to Fatherhood; (4) Motherhood as Teacher and Disciplinarian; and (5) Motherhood Instills Unconditional Endless Love. Supporting qualitative lyrics are provided to support each of the aforementioned themes