University of Wyoming Open Journals
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Intercultural Competencies in Scholarship of Teaching and Learning
No full textIn an increasingly interconnected world, fostering intercultural competence is essential for both personal growth and professional effectiveness. The Fulbright-Hays Spanish Language Program, with its immersive approach, aims to transform participants into interculturally competent individuals.
This blog delves into a Scholarship of Teaching and Learning (SoTL) group study with a specific focus on intentional pedagogical practices in an intensive language and culture project in Costa Rica. By examining the experiences and reflections of participants, this study seeks to understand how such immersive programs enhance interactions across cultures and disciplines
Lyapunov-like transformations on the tensor product of nuclear pairs of proper cones
No full textLyapunov-like transformation/matrix on a cone appears in the theory of dynamical systems and linear complementarity problems. The set of all Lyapunov-like transformations on a proper cone in a finite dimensional inner product space is the Lie algebra of the automorphism group of that cone. The dimension of this Lie algebra is called the Lyapunov rank. A pair of proper cones is said to be a nuclear pair if one of them is simplicial. In this paper, we find the Lyapunov rank and Lyapunov-like transformations on the tensor product of nuclear pairs of cones. Further, we prove that the space of Lyapunov-like transformations on the tensor product of a nuclear pair is the tensor product of the spaces of Lyapunov-like transformations on the individual cones. As a consequence, given a nuclear pair , we describe the space of Lyapunov-like transformations on the cone of positive operators between and
Barycenter of the arithmetic-harmonic quantum divergence
No full textA notion of divergence is a very important and useful tool to measure the difference between probability distributions or between data (information). We consider a quantum divergence constructed by the difference of two-variable weighted arithmetic and harmonic means on the open convex cone of positive definite Hermitian matrices, called the arithmetic-harmonic quantum divergence. We see its invariance properties and study the barycenter minimizing the weighted sum of arithmetic-harmonic quantum divergences to given variables. We provide the lower bound for the barycenter of the arithmetic-harmonic quantum divergence in terms of Loewner order and its upper bound in terms of operator norm
New sufficient conditions for subdirect sums of Nekrasov matrices
No full textSome new sufficient conditions ensuring that the -subdirect sum of strictly diagonally dominant matrices and Nekrasov matrices is in the class of Nekrasov matrices are given. These sufficient conditions are different from those in [Electron. J. Linear Algebra, 38:339-346, 2022] and [Linear Multilinear Algebra, 64:208-218, 2016; 72:1044-1055, 2023]. In addition, some examples are given to illustrate the conditions presented
Improving the superadditivity of some determinantal matrix maps
No full textIn this note, a generalization by Yuan and Leng of Minkowski's determinant inequality is improved. An interpolation of the Yuan and Leng's inequality is shown by using the negativity of some related functional. Some refined versions of Minkowski's inequality and of Ky Fan's inequality are presented
Edge-disjoint spanning trees and balloons in (multi-)graphs from size or spectral radius
No full textA multigraph is a graph that may have multiple edges, but has no loops. The multiplicity of a multigraph is the maximum number of edges between any pair of vertices. The spanning tree packing number of a graph , denoted by , is the maximum number of edge-disjoint spanning trees contained in . A balloon of a graph is a maximal 2-edge-connected subgraph that is joined to the rest of by exactly one cut edge. By , , and , we denote the number of balloons, the size, and the vertex-connectivity of , respectively. In this paper, we show that for a positive integer and any multigraph of order with multiplicity and minimum degree , if then , where . This extends the result of Fan, Gu and Lin (J. Graph Theory, 2023). Analogous results involving the size to characterize or of a multigraph are also presented. In addition, we prove a tight sufficient condition to guarantee in terms of the spectral radius of a simple graph , with extremal graphs characterized
Puzzling Our Way into Computational Thinking
No full textThis unplugged activity is a brief, practical introduction to computational thinking that uses an accessible and decidedly low-tech approach: solving a jigsaw puzzle. The skills needed to collaboratively solve a jigsaw puzzle illustrate the key concepts of computational thinking in a straightforward way that makes the basics of decomposition, pattern recognition, abstraction, and algorithmic thinking come to life. The learning representation included here was taught as part of a professional development workshop for PK-12 teachers but could easily be adapted to use with learners from upper elementary grades through middle school, high school, or university
Probabilistic zero forcing with vertex reversion
No full textProbabilistic zero forcing is a graph coloring process in which blue vertices "infect" (color blue) white vertices with a probability proportional to the number of neighboring blue vertices. This paper introduces reversion probabilistic zero forcing (RPZF), which shares the same infection dynamics but also allows for blue vertices to revert to being white in each round. A threshold number of blue vertices is produced such that the complete graph is entirely blue in the next round of RPZF with high probability. Utilizing Markov chain theory, a tool is formulated which, given a graph's RPZF Markov transition matrix, calculates the probability of whether the graph becomes all white or all blue as well as the time at which this is expected to occur
Topics of Interest Formative Assessment, Single-Point Rubric
No full textFor some years, the need for deeper thought and personal reflection on the mission and purpose of formal education has become grist for the political mill. Germane here are issues related not only to what to teach, but how to teach it; thornier decisions must be grappled with in the wrestling rings of assessment and of equity.
Among other domains in education, critical thinking and formative assessment hold meaning for me. The scholarship of teaching and learning (SoTL) carries promise, at least possibly for the short term
A note on Lidskii's theorem for the directional derivatives of the eigenvalues of symmetric matrices
No full textLidskii's theorem is a classical perturbation result for the spectrum of symmetric matrices. It states that a change in the spectrum caused by a perturbation is majorized by the original spectrum. We present a generalization and a refinement of Lidskii's theorem involving the directional derivatives of the spectrum of a symmetric matrix