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Consistency of Quaternion Matrix Equations and
No full textFor a given ordered units triple , the solutions to the quaternion matrix equations and , , where is the conjugate transpose of , and , , are discussed. Some new real representations of quaternion matrices are used, which enable one to convert -conjugate (transpose) matrix equations into some real matrix equations. By using this idea, conditions for the existence and uniqueness of solutions to the above quaternion matrix equations are derived. Also, methods to construct the solutions from some related real matrix equations are presented
A Note on Variants of Zero Forcing
No full textA small improvement is made to the zero-forcing variants defined by Butler, Grout, and Hall (2015) for matrices with a given number of negative eigenvalues, resulting in a better value for the Barioli-Fallat tree and one negative eigenvalue
On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices
No full textMv−matrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mv−matrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mv−matrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B ≤ 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mv−matrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mv−matrices are presented. Various numerical examples are given to support our theoretical findings
Lights, bats, and buildings: investigating the factors influencing roosting sites and habitat use by bats in Grand Teton National Park
No full textFree-flying bats are highly affected by artificial night lighting, causing individuals to either 1) gather in unnaturally high densities around the light sources to exploit insects, or 2) travel increased distances to avoid light exposure. Similarly, nocturnal insects are disproportionately attracted to night lighting, trapping them until they die of exhaustion. The advent of new lighting technology which may decrease the impacts of night lighting on bats and insects by primarily producing light at wavelengths these animals are not sensitive to (i.e. in the red portion of the spectrum) is promising, however no studies have shown this at a large scale, and not in North America. Similarly, many studies on the effects of lights on bats, in general, have been on European species, and thus our overall understanding of how North American species are affected is low. Grand Teton National Park, Wyoming, provides an excellent natural system to study the effects of lights on bat behavior, as well as to test possible mitigation methods, as the park supports a large community of over a dozen species, as well as sizeable human infrastructure that generates night light. From June through September, 2019, we undertook a large-scale, blocked experiment examining bat activity and space use in Colter Bay Village under both traditional street-lighting, as well as new “bat friendly” street lighting. Using both passive echolocation records and radiotelemetry, we collected data that will allow us to examine the ability of red LED streetlights to mitigate artificial light’s negative impacts on bats and insects.
Featured photo from figure 2 in report
A LiDAR-based landslide inventory and associated map portal (story map) for Grand Teton National Park
No full textFunding has enabled the design and implementation of a preliminary landslide inventory including roughly 500 deposits throughout GTNP. The three most common mass movement deposits were related to debris flows, translational earth slides and translational rock slides. More than 10% of the features were field-verified during campaigns mapping along the Teton Fault and in areas across varying lithology and relief including Steamboat Mountain, Paintbrush Canyon, Cascade Canyon, Two Ocean Lake, Open Canyon and lower Granite Canyon. Features were mapped according to protocols established by the Oregon Department of Geology and Mineral Industries (DOGAMI) and supported by the USGS. The Story Map remains under development, awaiting revised mapping and feedback from GTNP staff.
Featured photo taken from the AMK Ranch photo collection. https://flic.kr/p/RdWTq
Performing horizontal to vertical ratio testing in stiff soils in and around Grand Teton National Park
No full textHorizontal to vertical spectral ratio (HVSR) testing was completed at two cross sections in and around GTNP. The HVSR testing produced reliable estimates of the fundamental frequencies for many of the sites tested. The goal of the testing was to determine a depth of soil above competent bedrock. However the fundamental frequencies recorded yielded predicted depths that are much shallower than expected. Also the predicted depths did not increase at greater distance from the Teton Range, which would be expected at these sites. Based on these predictions the authors do not believe the frequencies recorded are a good indication of the depth of the soil above bedrock but instead it is believed that the depths correspond with a layer of softer topsoil/overburden above a stiffer gravel layer. Although the goal of measuring the depth of soil above bedrock was not met, HVSR produced results that may be useful to others for determination of a fundamental frequency of resonance at our testing locations.
Featured photo by Anna Cressman, taken from the AMK Ranch photo collection. https://flic.kr/p/2jjWZG
