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The k-th derivatives of the immanent and the chi-symmetric power of an operator
No full textIn recent papers, formulas are obtained for directional derivatives, of all orders, ofthe determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix
Water Flow and Beaver Habitat in Grand Teton National Park: Adaptation to Climate Change
No full textBeavers are a keystone species in Grand Teton National Park and are critical to the aquatic and terrestrial landscape. Modifications to their habitat by climate change impact multiple species. This study is designed to examine the current distribution and habitat of beavers in Grand Teton National Park and analyze the alterations to this distribution and habitat based on climate change. Field and aerial surveys were completed to determine the distribution of beaver colonies in Grand Teton National Park. Beaver habitat was constructed by integrating field surveys of vegetation, soils and hydrologic characteristics with satellite imagery classification. A model of climate change was utilized in an effort to distinguish potentially different rates of temperature and precipitation change into the 21st century. The results of the climate model were then integrated into a watershed assessment model to determine stream flow in the Snake River basin. The decreasing flow rates are critical to beaver habitat for cottonwoods and willow species and beaver settlement and movement and will limit their movement. In addition, the Snake River below Jackson Lake Dam is regulated for irrigation into Idaho and the decreasing flows on the Snake River below the Jackson Lake Dam will also impact water availability for beaver habitats. Decreases in precipitation availability will increase irrigation demand causing changes in the Snake River flow patterns. Management conflicts exist between preserving and maintaining beaver habitat in the national park and meeting the irrigatio
Archaeology and Social Geography in the Sunlight Basin, Wyoming
No full textPainter Cave (48PA3288) is a dry rockshelter in the foothills of the Absaroka Mountains of northwestern Wyoming that has deeply stratified deposits. Archaeological materials were disturbed several decades ago by looters, who reportedly took a number of perishable Native American artifacts including moccasins and a cradle board, as well as numerous other unidentified objects. Preliminary assessment by Shoshone National Forest Service personnel in 2011 suggested that the site might still be partially intact. Indiana Universityâs Bighorn Archaeology project conducted a pilot study at Painter Cave and the surrounding area in 2014 in an effort to identify and recover any additional cultural deposits. Artifact recovery addressed local landscape use, cultural chronology of the area, subsistence strategies, and environmental conditions. The looter activity unfortunately proved to be extensive. Although team members identified numerous archaeological signatures at different sites in the study area, primary deposits in the shelter itself were disturbed in such a way that investigation into the use of Painter Cave by past peoples was challenging
Shallow Seismic Investigation of the Teton Fault
No full textPreliminary results from seismic data collected at two sites on the Teton fault reveal shallow sub-surface fault structure and a basis for evaluating the post-glacial faulting record in greater detail. These new data include high-resolution shallow 2D seismic refraction and Interferometric Multi-Channel Analysis of Surface Waves (IMASW) (OâConnell and Turner 2010) depth-averaged shear wave velocity (Vs). The Teton fault, a down-to-the east normal fault, is expressed as a distinct topographic escarpment along the base of the eastern front of the Teton Range in Wyoming. The average fault scarp height cut into deglacial surfaces in several similar valleys and an assumed 14,000 yr BP deglaciation indicates an average postglacial offset rate of 0.82 m/ka (Thackray and Staley, in review). Because the fault is located almost entirely within Grand Teton National Park (GTNP), and in terrain that is remote and difficult to access, very few subsurface studies have been used to evaluate the fault. As a result, many uncertainties exist in the present characterization of along-strike slip rate, down-dip geometry, and rupture history, among other parameters. Additionally, questions remain about the fault dip at depth. Shallow seismic data were collected at two locations on the Teton fault scarp to (1) use a non-destructive, highly portable and cost-effective data collection system to image and characterize the Teton fault, (2) use the data to estimate vertical offsets of faulted bedrock and sediment, and (3) estimate fault dip in the shallow subsurface. Vs data were also collected at three GTNP facility structures to provide measured 30 m depth-averaged Vs (Vs30) for each site. Seismic data were collected using highly portable equipment packed into each site on foot. The system utilizes a sensor line 92 m long that includes 24 geophones (channels) at 4 m intervals. At both the Taggart Lake and String Lake sites, P-wave refraction data were collected spanning the fault scarp and perpendicular to local fault strike, as well as IMASW Vs seismic lines positioned on the hanging wall to provide Vs vs. Depth profiles crossing and perpendicular to the refraction survey lines. The Taggart Lake and String Lake 2D P-wave refraction profile and IMASW Vs plots reveal buried velocity structure that is vertically offset by the Teton fault. At Taggart Lake, we interpret the velocity horizon to be the top of dense glacial sediment (possibly compacted till), which is overlain by younger, slower, sediments. This surface is offset ~13 m (down-to-the-east) across the Teton fault. The vertical offset is in agreement with the measured height of the corresponding topographic scarp (~12 - 15 m). Geomorphic analysis of EarthScope (2008) LiDAR reveals small terraces, slope inflections and an abandoned channel on the footwall side of the scarp. At String Lake, the shallow buried velocity structure is inferred as unconsolidated alluvium (till, colluvium, alluvium); this relatively low velocity zone
Spectral characterizations of propeller graphs
No full textA propeller graph is obtained from an ∞-graph by attaching a path to the vertex of degree four, where an ∞-graph consists of two cycles with precisely one common vertex. In this paper, it is proved that all propeller graphs are determined by their Laplacian spectra as well as their signless Laplacian spectra
Simplifications of the Ostrowski upper bounds for the spectral
No full text A.M. Ostrowski in 1951 gave two well-known upper bounds for the spectral radius of nonnegative matrices. However, the bounds are not of much practical use because they all involve a parameter α in the interval [0, 1], and it is not easy to decide the optimum value of α. In this paper, their equivalent forms which can be computed with the entries of matrix and without having to minimize the expressions of the bounds over all possible values of α ∈ [0, 1], are given
A note on the convexity of the indefinite joint numerical range
No full textThis note investigates the convexity of the indefinite joint numerical range of a tuple of Hermitian matrices in the setting of Krein spaces. Its main result is a necessary and sufficient condition for convexity of this set. A new notion of âquasi-convexityâ is introduced as a refinement of pseudo-convexity
On the fixed-point type Sylvester matrix equations over complete commutative dioids
No full textThis paper extends the concept of tropical tensor product defined by Butkovic and Fiedler to general idempotent dioids. Then, it proposes an algorithm in order to solve the fixed-point type Sylvester matrix equations of the form X = A â X â X â B â C. An application is discussed in efficiently solving the minimum cardinality path problem in Cartesian product graphs
Eigenvalue localization for complex matrices
No full textLet be an complex matrix with . It is shown that at least of the eigenvalues of lie in the disk \begin{equation*}\left\vert z-\frac{\func{tr}A}{n}\right\vert \leq \sqrt{\frac{n-1}{n}\left(\sqrt{\left( \left\Vert A\right\Vert _{2}^{2}-\frac{\left\vert \func{tr} A\right\vert ^{2}}{n}\right) ^{2}-\frac{\left\Vert A^{\ast }A-AA^{\ast}\right\Vert _{2}^{2}}{2}}-\frac{\limfunc{spd}\nolimits^{2}(A)}{2}\right) },\end{equation*} where \func{tr}A, and \limfunc{spd}(A) denote the Frobenius norm, the trace, and the spread of , respectively. In particular, if is normal, then at least of the eigenvalues of lie in the disk {\small \begin{eqnarray*} & & \left\vert z-\frac{\func{tr}A}{n}\right\vert \\ & & \leq \sqrt{\frac{n-1}{n}\left( \frac{\left\Vert A\right\Vert _{2}^{2}}{2}-\frac{\left\vert \func{tr}A\right\vert ^{2}}{n}-\frac{3}{2}\max_{i,j=1,\dots,n} \left( \sum_{\substack{ k=1 \\ k\neq i}}^{n}\left\vert a_{ki}\right\vert ^{2}+\sum_{\substack{ k=1 \\ k\neq j}}^{n}\left\vert a_{kj}\right\vert ^{2}+\frac{\left\vert a_{ii}-a_{jj}\right\vert ^{2}}{2}\right) \right) }. \end{eqnarray*}} Moreover, the constant can be replaced by if the matrix is Hermitian