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Full-Text Articles in Physical Sciences and Mathematics
A Look At Multi-Decompositions Of Complete Graphs Into Graph Pairs Of Order 4, Yizhe Gao, Daniel Roberts, Faculty Advisor
A Look At Multi-Decompositions Of Complete Graphs Into Graph Pairs Of Order 4, Yizhe Gao, Daniel Roberts, Faculty Advisor
John Wesley Powell Student Research Conference
Firstly, a graph G consists of a vertex set V (G), and an edge set E (G) of endpoints which relate two vertices with each edge. Also, a decomposition of a graph is a list of subgraphs such that each edge appears in exactly one subgraph in the list. In the field ofgraph theory, graph decomposition is an active field of research. One type of decomposition is graph pairs. A graph pair is a pair of graphs on the same vertex set whose union is the complete graph. Abueida and Daven studieddecompositions of complete graphs into graph-pairs of order four. …
Frames And Spline Framelets, Tung Nguyen, Nahee Kim, Tian-Xiao He, Faculty Advisor
Frames And Spline Framelets, Tung Nguyen, Nahee Kim, Tian-Xiao He, Faculty Advisor
John Wesley Powell Student Research Conference
Frames can be seen as a generalization of orthonormal bases, which not only maintain useful characteristics of orthonormal bases but also allow more flexibility in applications. The applications of frames include communication and image processing, as its characteristic inherited from orthonormal bases helps speed up the transmitting and processing time while its additional flexibility adds to frames the ability to reconstruct lost information. In this project, we study the construction of a class of tight frames in Euclidean spaces. Also, we use Fourier transforms and the techniques of Multi-Resolution Analysis (MRA) in wavelet analysis to investigate a class of tight …