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Full-Text Articles in Other Mathematics
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Signings Of Graphs And Sign-Symmetric Signed Graphs, Ahmad Asiri
Theses and Dissertations
In this dissertation, we investigate various aspects of signed graphs, with a particular focus on signings and sign-symmetric signed graphs. We begin by examining the complete graph on six vertices with one edge deleted ($K_6$\textbackslash e) and explore the different ways of signing this graph up to switching isomorphism. We determine the frustration index (number) of these signings and investigate the existence of sign-symmetric signed graphs. We then extend our study to the $K_6$\textbackslash 2e graph and the McGee graph with exactly two negative edges. We investigate the distinct ways of signing these graphs up to switching isomorphism and demonstrate …
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki
Theses and Dissertations
Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L2(R) and the Hardy spaces Hp(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …