Recent documents in Wyoming Scholars Repository
Updated: 17 hours 24 min ago

### Teaching the Teachers: Summer School at the University of Wyoming 1905-1950

Thu, 2018-04-12 10:45

This paper is a historical case study that examines the teacher education opportunities presented via the University of Wyoming Summer School from 1905 to 1950 and how the state’s teacher population was affected by these opportunities. It contextualizes UW Summer School in the broader movements of teacher education at the time, from teacher institutes to normal schools. UW Summer School is remarkable considering that when it started, the University had only been in existence for 17 years. The UW Summer School was a successful model, bringing in students for 110 years. This case study fills in gaps in the literature pertaining to the educational history of the west and the institutional history of the University.

### Fast verified computation for the solvent of the quadratic matrix equation

Mon, 2018-04-02 22:57

Two fast algorithms for numerically computing an interval matrix containing the solvent of the quadratic matrix equation \$AX^2 + BX + C = 0\$ with square matrices \$A\$, \$B\$, \$C\$ and \$X\$ are proposed. These algorithms require only cubic complexity, verify the uniqueness of the contained solvent, and do not involve iterative process. Let \$\ap{X}\$ be a numerical approximation to the solvent. The first and second algorithms are applicable when \$A\$ and \$A\ap{X}+B\$ are nonsingular and numerically computed eigenvector matrices of \$\ap{X}^T\$ and \$\ap{X} + \inv{A}B\$, and \$\ap{X}^T\$ and \$\inv{(A\ap{X}+B)}A\$ are not ill-conditioned, respectively. The first algorithm moreover verifies the dominance and minimality of the contained solvent. Numerical results show efficiency of the algorithms.

### Determinantal representations of elliptic curves via Weierstrass elliptic functions

Mon, 2018-04-02 22:56

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass \$\wp\$-functions in place of Riemann theta functions. An example of this approach is given.

### Upper Bound for the Number of Distinct Eigenvalues of a Perturbed Matrix

Mon, 2018-04-02 22:56

In 2016, Farrell presented an upper bound for the number of distinct eigenvalues of a perturbed matrix. Xu (2017), and Wang and Wu (2016) introduced upper bounds which are sharper than Farrell's bound. In this paper, the upper bounds given by Xu, and Wang and Wu are improved.

### Range-compatible homomorphisms over the field with two elements

Mon, 2018-04-02 08:04

Let U and V be finite-dimensional vector spaces over a field K, and S be a linear subspace of the space L(U, V ) of all linear operators from U to V. A map F : S → V is called range-compatible when F(s) ∈ Im s for all s ∈ S. Previous work has classified all the range-compatible group homomorphisms provided that codimL(U,V )S ≤ 2 dim V − 3, except in the special case when K has only two elements and codimL(U,V )S = 2 dim V − 3. This article gives a thorough treatment of that special case. The results are partly based upon the recent classification of vector spaces of matrices with rank at most 2 over F2. As an application, the 2-dimensional non-reflexive operator spaces are classified over any field, and so do the affine subspaces of Mn,p(K) with lower-rank at least 2 and codimension 3.

### Characterizing Graphs Of Maximum Principal Ratio

Mon, 2018-04-02 08:03

The principal ratio of a connected graph, denoted γ(G), is the ratio of the maximum and minimum entries of its Perron eigenvector. Cioaba and Gregory (2007) conjectured that the graph on n vertices maximizing γ(G) is a kite graph, that is, a complete graph with a pendant path. In this paper, their conjecture is proved

### Observations of Notable Parental Behaviours of Northern Spotted Owls (Strix occidentalis caurina)

Fri, 2018-03-30 13:15

Northern Spotted Owl (Strix occidentalis caurina) is a medium-sized forest owl of conservation concern in the Pacific Northwest of North America. We report two sightings of previously unreported parental behaviour: a Northern Spotted Owl feeding avian nestlings to its young and a Northern Spotted Owl defending a fledgling against a Black Bear (Ursus americanus). Further research may be warranted on the influence of brood size and habitat quality on dietary breadth. Although Black Bears have not been previously documented as Northern Spotted Owl predators, we suggest that they should be considered potential predators of nestling and fledgling owls.