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Minimal Estrada index of the trees without perfect matchings
No full textTrees possessing no Kekul ́e structures (i.e., perfect matching) with the minimal Estrada index are considered. Let T_n be the set of the trees having no perfect matchings with n vertices. When n is odd and n ≥ 5, the trees with the smallest and the second smallest Estrada indices among T_n are obtained. When n is even and n ≥ 6, the tree with the smallest Estrada index in T_n is deduced
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
Computing Kemeny\u27s constant for a barbell graph
No full textIn a graph theory setting, Kemeny\u27s constant is a graph parameter which measures a weighted average of the mean first passage times in a random walk on the vertices of the graph. In one sense, Kemeny\u27s constant is a measure of how well the graph is `connected\u27. An explicit computation for this parameter is given for graphs of order consisting of two large cliques joined by an arbitrary number of parallel paths of equal length, as well as for two cliques joined by two paths of different length. In each case, Kemeny\u27s constant is shown to be , which is the largest possible order of Kemeny\u27s constant for a graph on vertices. The approach used is based on interesting techniques in spectral graph theory and includes a generalization of using twin subgraphs to find the spectrum of a graph
Solving the Sylvester Equation AX-XB=C when
No full textThe method for solving the Sylvester equation in complex matrix case, when , by using Jordan normal form is given. Also, the approach via Schur decomposition is presented
Unions of a clique and a co-clique as star complements for non-main graph eigenvalues
No full textGraphs consisting of a clique and a co-clique, both of arbitrary size, are considered in the role of star complements for an arbitrary non-main eigenvalue. Among other results, the sign of such a eigenvalue is discussed, the neigbourhoods of star set vertices are described, and the parameters of all strongly regular extensions are determined. It is also proved that, unless in a specified special case, if the size of a co-clique is fixed then there is a finite number of possibilities for our star complement and the corresponding non-main eigenvalue. Numerical data on these possibilities is presented
Minute by Minute: An Assessment of the Environmental Flows Program for Restoration of the Colorado River Delta
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Impacts of Place-Based Professional Development on Teachers
No full textThe qualitative case study investigated the relationship between high-quality professional development for place-based education and long-term impacts on teacher practices. The case study focused on a small subset of teachers who attended all four years of the PLACE (Place-based Learning and Civic Engagement) program from 2011-2014. This study was built off a previous program evaluation of PLACE. The purpose of this research study was to evaluate the PLACE professional development\u27s long-term impact on teachers\u27 perceptions and practices and the teachers\u27 implementation of place-based education. The data collection methods for this study involved interviews, observations, and surveys. Based on the data collected from the small sample of teachers, the evidence suggested that the program impacted the teachers\u27 practices to various degrees and their implementation of place-based education varied by teachers. The results identified the continuous, experiential, and collaborative structure of the PLACE program as factors for the program\u27s long-term impact on teaching practices. Recommendations and limitations are included
NASA Microgravity: Internal Structure and Recovery Method Optimization
No full textMicrogravity is defined as a state of having very little gravity, such as that experienced in space. Research has been performed by NASA for over 25 years as a way to determine how space technologies are impacted by a microgravity environment. To simulate microgravity, an aerodynamic payload is dropped in a vacuum chamber or from high altitudes until a state of freefall is reached. NASA drop towers are the standard microgravity testing platforms used today. These towers can produce microgravity environments for 2.2-5.2 seconds; however, these platforms are expensive and require months of advanced planning. The University of Wyoming (UW) microgravity project aims to develop a low cost alternative, while also producing microgravity environments that are equal to or better than that of drop towers. For this project, microgravity is achieved by dropping an aerodynamic payload from a weather balloon from an altitude of 100,000 feet. If successful 15-20 seconds of microgravity can be achieved.
The first UW Microgravity drop occurred in August 2017. Shock force data from the drop revealed that the internal structure components were significantly over-designed. Incorrect stress analysis of the recovery method contributed to this over-design. The over-designed components add unnecessary mass to the payload. The drop also revealed poor integration between the electronic systems and internal frame. The main objective of this project was to optimize the recovery method to reduce shock force, decrease the mass of the internal structure, and provide enhanced integration between electronic systems and the internal frame