A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Identification of Rabbiteye Blueberry Cultivars (Vaccinium ashei Reade) and Analysis of Genetic Relationships Using Amplified Fragment Length Polymorphism (AFLP)

Proper cultivar identification is a requisite for commercial planting and breeding nurseries of cross-pollinated blueberry (Vaccinium ashei Reade) cultivars to insure high crop yields and optimize germplasm maintenance and utilization. Fourteen rabbiteye blueberry cultivars and three non-identified clones were screened with amplified fragment length polymorphism (AFLP) analysis with the aim of developing a fast and reliable identification technique. The selective primer pair applied (M-CTG/ E-ACC), which was previously tested, resulted in a large number of reproducible polymorphic fragments for cultivar identification. After comparison of the AFLP fingerprints, the Jaccard similarity indexes were calculated, and an UPGMA dendrogram was constructed. It was revealed that the three non-identified clones belong to the Tifblue' cultivar. Moreover, AFLP technique proved to be a fast, successful and reliable way in rabbiteye blueberry identification

Identification of Rabbiteye Blueberry Cultivars (Vaccinium ashei Reade) and Analysis of Genetic Relationships Using Amplified Fragment Length Polymorphism (AFLP)

Proper cultivar identification is a requisite for commercial planting and breeding nurseries of cross-pollinated blueberry (Vaccinium ashei Reade) cultivars to insure high crop yields and optimize germplasm maintenance and utilization. Fourteen rabbiteye blueberry cultivars and three non-identified clones were screened with amplified fragment length polymorphism (AFLP) analysis with the aim of developing a fast and reliable identification technique. The selective primer pair applied (M-CTG/ E-ACC), which was previously tested, resulted in a large number of reproducible polymorphic fragments for cultivar identification. After comparison of the AFLP fingerprints, the Jaccard similarity indexes were calculated, and an UPGMA dendrogram was constructed. It was revealed that the three non-identified clones belong to the Tifblue' cultivar. Moreover, AFLP technique proved to be a fast, successful and reliable way in rabbiteye blueberry identification