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Spectral Bounds for the Connectivity of Regular Graphs with Given Order
No full textThe second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results answer a question of Mohar
Bounded linear operators that preserve the weak supermajorization on
No full textLinear preservers of weak supermajorization which is defined on positive functions contained in the discrete Lebesgue space are characterized. Two different classes of operators that preserve the weak supermajorization are formed. It is shown that every linear preserver may be decomposed as sum of two operators from the above classes, and conversely, the sum of two operators which satisfy an additional condition is a linear preserver. Necessary and sufficient conditions under which a bounded linear operator is a linear preserver of the weak supermajorization are given. It is concluded that positive linear preservers of the weak supermajorization coincide with preservers of weak majorization and standard majorization on
Extremal octagonal chains with respect to the spectral radius
No full textOctagonal systems are tree-like graphs comprised of octagons that represent a class of polycyclic conjugated hydrocarbons. In this paper, a roll-attaching operation for the calculation of the characteristic polynomials of octagonal chain graphs is proposed. Based on these characteristic polynomials, the extremal octagonal chains with n octagons having the maximum and minimum spectral radii are identified
Bankruptcy Law -- A Battle of Two Acts: Midland Funding, LLC v Johnson, 137 S. Ct. 1407 (2017)
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Sensational Service Through Transformational Travel
No full textTravel and service are two fundamental activities for me. One way I have been able to combine these experiences and cultivate my love for them is through the University of Wyoming’s Alternative Breaks Program. The mission of this program is, “to engage the University of Wyoming community in service and experiential learning while promoting global citizenship”. The goals for students include, but are not limited to, “enact positive change through service, develop a stronger community between students, empower student leaders, becoming further educated on social justice issues, as well as encourage students to become active citizens”. It is through the Alternative Breaks program that I have been able to see positive changes in myself, as I have reached some of the goals outlined for students.
My first exposure to Alternative Breaks was during my sophomore year, when I went to Kanab, Utah. We worked with Best Friends Animal Sanctuary while focusing on animal wellness for this trip. One year later, I went to Matelot, Trinidad. The focus of this trip was community development and women’s education. The two trips were drastically different, while remaining equally impactful. This year, I have the tremendous opportunity to co-lead a trip to Arizona in March 2018. The goal for this trip is to learn about, and provide service for immigration rights and reform. To do so, we will work with non-profit organizations in Tucson and Phoenix, getting exposure to people whose lives are affected by immigration rights on a daily basis
The Perceptions of Principals Regarding the Formative Supervision of Teachers
No full textEducational scholars commonly identify teachers as the primary in-school influence for increasing student achievement therefore, principals need to focus on improving teacher effectiveness through formative supervision. The purpose of this study was to explore differences in perceptions towards the formative supervision of teachers between more experienced and less experienced principals. Formative supervision allows principals to monitor, assess, and systemically address teacher performance with the intent of improving their practice. Guided by current literature, different aspects of formative supervision were constructed, the analyses indicated that certain sets of formative supervision constructs had no significant differences when comparing the grouping variables of principal experience. However, principals with more than three years of experience had a significantly different perception about their abilities to improve teaching through formative supervision than principals with less than three years of experience. More experienced principals indicated a higher level of confidence in improving instruction, as well as a preference for written feedback typically found in performance evaluations and not necessarily in walkthroughs where the principal has the option for oral feedback