University of Wyoming Open Journals
Not a member yet
3193 research outputs found
Sort by
Moving Beyond 2D Covalent Bonding: Interactive 3D Experiences with Water and Carbon Dioxide Molecules
No full textThis three-lesson sequence is from a Bonding unit in a sophomore High School Chemistry class that focuses on the formation of covalent bonds in simple molecules. The purpose of these lessons is for students to apply their knowledge of atomic structure and electron arrangements, and understand, at an atomic level, why non-metal atoms share pairs of electrons to achieve electronic stability. Learning objectives are formatively assessed throughout the lessons, focused on addressing student misconceptions. This is done through drawing diagrams and simple 2D models, teacher-led question/answer and discussion, and an in-class worksheet. For this three-lesson sequence, eight 3D experiences were created to support the visualization of the covalent bond formation and minimize students’ misconceptions. This paper focuses on two 3D experiences, water and carbon dioxide
Rational solutions of the matrix equation
No full textWe extend Theorem 1 of R. Reams, A Galois approach to m-th roots of matrices with rational entries, LAA, 258:187-194, 1997. Let be any polynomial over , and let have irreducible characteristic polynomial with degree . We provide necessary and sufficient conditions for the existence of a solution of the polynomial matrix equation Specifically, we find necessary and sufficient conditions for to have a factor of degree over $\mathbb{Q}.
Symmetry and asymmetry between positive and negative square energies of graphs
No full textThe positive and negative square energies of a graph, and , are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between and . This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios and , as well as new examples of symmetry. Some questions previously asked about and are answered and several further avenues of research are suggested
Extremal spectral radii of uniform supertrees
No full textFor a hypergraph consisting of a nonempty vertex set and an edge set , its adjacency matrix is defined as , where . The spectral radius of a hypergraph , denoted by , is the maximum modulus among all eigenvalues of . In this paper, we represent some results on the spectral radius changing under some graphic structural perturbations. With these results, among all -uniform () supertrees with fixed number of vertices, the supertrees with the maximum, the second maximum, and the minimum spectral radius are completely determined, respectively
New properties of a special matrix related to positive-definite matrices
No full textLet be a real symmetric positive-definite matrix. Suppose that is a partitioned matrix, in which represents the Hadamard product and the block has order , . Several new properties on the matrix are derived including inequalities that involve the symplectic eigenvalues and the usual eigenvalues, where
Some symmetric sign patterns requiring unique inertia
No full textA sign pattern is a matrix whose entries are from the set . A sign pattern requires unique inertia if every matrix in its qualitative class has the same inertia. For symmetric tree sign patterns, several necessary and sufficient conditions to require unique inertia are known. In this paper, sufficient conditions for symmetric tree sign patterns to require unique inertia based on the sign and position of the loops in the underlying graph are given. Further, some sufficient conditions for a symmetric sign pattern to require unique inertia if the underlying graph contains cycles are determined
Commutators of skew-involutions
No full textLet be the group of all matrices over a field with determinant . Denote by () the () identity matrix. A matrix is called skew-involution if . It is proved that every matrix in is a product of at most three commutators of skew-involutions if and , and at most four commutators of skew-involutions if and n>1. Every complex symplectic matrix is a product of two commutators of complex symplectic skew-involutions, and every real symplectic matrix is a product of not more than four commutators of real symplectic skew-involutions
Preparing Educators to Navigate the Social-Emotional Terrain: A Game-Based Approach
No full textThe FIXIT Social-Emotional Learning (SEL) game was created by the authors as an analog card game to help educators prepare for social-emotional challenges in the classroom. In the game, players work together as a team to overcome obstacles and practice addressing challenging scenarios while thinking through support beyond academic needs. This game-based approach provides a low-risk environment for educators to practice and prepare for real-life situations. Learning assessment is completed through gameplay discussions, end-of-game debriefs, and personal learning reflections. This version of FIXIT is for educators, but the game can be adapted to fit any content that includes problem-solving for all ages and grades ECE-12+
Volume 2, Issue 2 Introduction
No full textWelcome to the fourth issue of the Journal of Technology-Integrated Lessons and Teaching (JTILT). This journal publishes international, peer-reviewed, technology-rich lessons, activities, and materials for teachers. These resources are freely available for adaptation, use, and dissemination through a Creative Commons, Attribution-NonCommercial-ShareAlike 4.0 International license (CC-BY-NC-SA 4.0). JTILT provides a venue for PK-12 teachers, media specialists, librarians, instructional coaches, administrators, teacher educators, and other relevant parties to highlight, reflect, and share teaching practices