University of Wyoming Open Journals
Not a member yet
3193 research outputs found
Sort by
Remarks on "Comparison between the Laplacian energy-like invariant and the Kirchhoff index''
No full textThe Laplacian-energy-like invariant and the Kirchhoff index of an -vertex simple connected graph are, respectively, defined to be and , where are the Laplacian eigenvalues of . In this paper, some results in the paper [Comparison between the Laplacian-energy-like invariant and the Kirchhoff index. Electron. J. Linear Algebra 31:27-41, 2016] are corrected and improved
On the banded Toeplitz structured distance to symmetric positive semidefiniteness
No full textThis paper is concerned with the determination of a close real banded positive definite Toeplitz matrix in the Frobenius norm to a given square real banded matrix. While it is straightforward to determine the closest banded Toeplitz matrix to a given square matrix, the additional requirement of positive definiteness makes the problem difficult. We review available theoretical results and provide a simple approach to determine a banded positive definite Toeplitz matrix
Group inverses of matrices associated with certain graph classes
No full textWe obtain formulae for group inverses of matrices that are associated with a new class of digraphs obtained from stars. This new class contains both bipartite and non-bipartite graphs. Expressions for the group inverse of matrices corresponding to double star digraphs and the adjacency matrix of certain undirected multi-star graphs are also proven. A blockwise representation of the inverse or group inverse of the adjacency matrix of the Dutch windmill graph is presented
Unicyclic 3-colored digraphs with bicyclic inverses
No full textThe class of unicyclic -colored digraphs with the cycle weight and with a unique perfect matching, denoted by , is considered in this article. Kalita \& Sarma [On the inverse of unicyclic 3-coloured digraphs, Linear and Multilinear Algebra, DOI: 10.1080/03081087.2021.1948956] introduced the notion of inverse of -colored digraphs. They characterized the unicyclic -colored digraphs in possessing unicyclic inverses. This article provides a complete characterization of the unicyclic -colored digraphs in possessing bicyclic inverses
Trees with maximum sum of the two largest Laplacian eigenvalues
No full textLet be a tree of order and be the sum of the two largest Laplacian eigenvalues of . Fritscher et al. proved that for any tree of order , . Guan et al. determined the tree with maximum among all trees of order . In this paper, we characterize the trees with among all trees of order except some trees. Moreover, among all trees of order , we also determine the first trees according to their . This extends the result of Guan et al
Sums of orthogonal, symmetric, and skew-symmetric matrices
No full textAn -by- matrix is called symmetric, skew-symmetric, and orthogonal if , , and , respectively. We give necessary and sufficient conditions on a complex matrix so that it is a sum of type ``"orthogonal symmetric" in terms of the Jordan form of . We also give necessary and sufficient conditions on a complex matrix so that it is a sum of type "orthogonal skew-symmetric" in terms of the Jordan form of
New results on -matrices, -matrices and their inverse classes
No full textIn this article, some new results on -matrices, -matrices and their inverse classes are proved. Specifically, we study when a singular -matrix is an -matrix, convex combinations of -matrices, almost monotone -matrices and Cholesky factorizations of -matrices
Eng, A. (2022). Our Laundry, Our Town: My Chinese American Life from Flushing to the Downtown Stage and Beyond. Fordham University Press.
No full text"We’re Coding A Drone?!”: Hands-on Drone Experiences for Online Students
No full textDrones are purchased for PK-12 schools with little thought to how they can be used to support learning (Carnahan et al., 2016). This activity introduces drones and coding to PK-12 teachers through a social constructivist design. Employed in an online setting, teachers can be exposed to coding and drones without individual access to the hardware to consider how drones could be used in their classrooms. During the activity, learners are introduced to block coding and code a drone flight which is then flown and videotaped by the instructor. Learners then view and reflect on their drone flights and discuss integration ideas that directly support their classroom and content
Micro:bit Hero: Using MakeCode to Replicate Popular Songs
No full textThis lesson opens with an introduction of how to program the Micro:bit using block code to play music using the piano keyboard embedded in the music section of Micro:bit Make Code. In this lesson, students explore how to make music using this feature and learn how to program the Micro:bit using MakeCode to incorporate rests and different notes (quarter, half, and full) to replicate nursery rhymes or popular songs. The lesson concludes with a discussion of the challenges/limitations of coding the Micro:bit to play music. Students also shared their musical creations with their peers through a “Name that Tune” game where they attempted to guess which popular song or nursery rhyme their peers had replicated in MakeCode.
Time: 30-45 minute