University of Wyoming Open Journals
Not a member yet
3193 research outputs found
Sort by
On oriented graphs with minimal skew energy
No full textLet S(G^Ï) be the skew-adjacency matrix of an oriented graph GÏ. The skew energy of G^Ï is the sum of all singular values of its skew-adjacency matrix S(G^Ï). This paper first establishes an integral formula for the skew energy of an oriented graph. Then, it determines all oriented graphs with minimal skew energy among all connected oriented graphs on n vertices with m (n ⤠m < 2(n â 2)) arcs, which is analogous to the conjecture for the energy of undirected graphs proposed by Caporossi et al. [G. Caporossi, D. Cvetkovic, I. Gutman, and P. Hansen. Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy. J. Chem. Inf. Comput. Sci., 39:984â996, 1999]
Exact results for perturbation to total positivity and to total nonsingularity
No full textA study of the maximum number of equal entries in totally positive and totally nonsingular m-by-n, matrices for small values of m and n, is presented. Equal entries correspond to entries of the totally nonnegative matrix J that are not changed in producing a TP or TNS matrix. It is shown that the maximum number of equal entries in a 7-by-7 totally positive matrix is strictly smaller than that for a 7-by-7 totally non-singular matrix, but, this is the first pair (m; n) for which these maximum numbers differ. Using point-line geometry in the projective plane, a family of values for (m; n) for which these maximum numbers differ is presented. Generalization to the Hadamard core, as well as larger projective planes is also established. Finally, the relationship with C4 free graphs, along with a method for producing symmetric TP matrices with maximal symmetric arrangements of equal entries is discussed
On the Estrada index of cacti
No full textLet G be a simple connected graph on n vertices and λ_1, λ_2, . . . , λ_n be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = \sum_{i=1}^n e^{λi}. A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cut edges was determined
Measuring the Morphology and Dynamics of the Snake River by Remote Sensing
No full textThe Snake River is a prominent, central feature of Grand Teton National Park, and this dynamic fluvial system maintains diverse habitats while actively shaping the landscape. Although the riparian corridor is relatively pristine, the Snake River is by no means free from anthropogenic influences: streamflows have been regulated since 1907 by Jackson Lake Dam. Among dam-controlled rivers in the western U.S., the Snake River is unique in that tributaries entering below the dam supply sufficient coarse bed material to produce a braided morphology. As a result of tributary inputs, sediment flux along the Snake River has been relatively unaffected by Jackson Lake Dam, but flow regulation has reduced the magnitude and altered the timing of streamflows. In this study we are coupling an annual image time series with extensive field surveys to document channel changes occurring on the Snake River. Our objective is to quantify how snowmelt runoff events and flow management strategies influence patterns of sediment transfer and storage throughout the river system, with a particular focus on tributary junctions. More specifically, we are using the image sequence to identify areas of erosion and deposition and hence infer the sediment flux associated with the observed changes in channel morphology. This analysis will improve our understanding of the riverâs response to flow management and enable us to generate hypotheses as to how the system might adapt to future anthropogenic and/or climate-driven alterations in streamflow and sediment supply. In addition, our research on the Snake River involves an ongoing assessment of the potential to measure the morphology and dynamics of large, complex rivers via remote sensing. A new aspect of this investigation involves estimating flow velocities from hyperspectral images that capture the texture of the water surface. Extensive field measurements of velocity and water surface roughness are being used to develop this innovative approach and thus increase the amount of river information that can be inferred via remote sensing
Inquiry-Based Geology Field Course for In-Service Educators
No full textEight in-service teachers and two instructors engaged in an inquiry-based geology field course from June 14 to 29, 2014 through Wyoming, South Dakota, and Nebraska. This team of learners spent three days in mid-June working in the Grand Teton National Park area. The UW-NPS facilities provide an excellent opportunity for participants to discover the natural history of the Teton Range, as well as close-out a few projects while sitting in a real chair, at a real table, a welcome change from our usual campground setting
Commutators from a hyperplane of matrices
No full textDenote by Mn(K) the algebra of n by n matrices with entries in the field K. A theorem of Albert and Muckenhoupt states that every trace zero matrix of Mn(K) can be expressed as AB − BA for some pair (A, B) ∈ Mn(K)2 . Assuming that n > 2 and that K has more than 3 elements, it is proved that the matrices A and B can be required to belong to an arbitrary given hyperplane of Mn(K)
A note on characterization of the shorted operation
No full textIn this article, an alternative characterization of the shorted operation defined on the class of all positive operators on a Hilbert space is presented