Annual Report 1965 Short Staple Cotton Breeding

This item is part of the Agricultural Experiment Station archive. It was digitized from a physical copy provided by the University Libraries at the University of Arizona. For more information, please email CALS Publications at [email protected]

Social Support and Survival Strategies of Older African American Grandmother Caregivers

The effects of caring for grandchildren on grandparents’ emotional and physical well-being have become a significant area of focus in behavioral and medical research. Research suggests that African American grandmothers may experience increased mental and physical health challenges due to their caregiving stressors. To buffer the adverse influence of stress, caregivers often rely on informal social support from family and/or community members. In this study we explored older, African American caregivers’ management of their emotional well-being within the context and circumstances of available to minimal social support from family and community. During an 18-month period, seven caregiving grandmothers participated in three face-to-face, audiotaped, semi-structured interviews; eco-map and genogram data was included to understand the contextual complexities of caregivers’ social support and their strategies for survival. Using constant comparative analysis, six interrelated themes revealed grandmothers operated along a continuum of reliable to unreliable social support. In the context of these varying ranges of social support, four sub-themes depicting their survival strategies were identified: being strong, self-sacrificing, receiving help and self-compassion. Utilization of each survival strategy was dependent on grandmothers’ perception of where they fell on the continuum of reliable to unreliable social support. Grandmothers who engaged in being strong and self-sacrificing engaged in stress-related health behaviors, such as emotional eating, smoking nicotine, disruptive sleep patterns and postponement of self-care. We offer specific practice recommendations for addressing the emotional and physical health needs of grandmother caregivers

Vector Coherent State Realization of Representations of the Affine Lie Algebra sl^(2)\hat{sl}(2)

The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as special cases.Comment: 8 pages plain latex. To appear in J. Phys.

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Fractional Loop Group and Twisted K-Theory

We study the structure of abelian extensions of the group $L_qG$ of $q$-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on $G$ is discussed.Comment: Final version in Commun. Math. Phy

Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.Comment: 25 pages in AMS-LaTe

Loop groups and noncommutative geometry

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group $LG$. The construction is based on certain supersymmetric conformal field theory models associated with LG in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.Comment: Revised versio