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Nonlinear Approximation Using Blaschke Polynomials, Daniel Van Vliet
Nonlinear Approximation Using Blaschke Polynomials, Daniel Van Vliet
Graduate Theses, Dissertations, and Problem Reports
This dissertation, entitled Nonlinear Approximation Using Blaschke Polynomials, is motivated by questions arising from Empirical Mode Decomposition (EMD). EMD is a signal processing method which decomposes input signals into components called intrinsic mode functions (IMFs). These IMFs often have the desirable property that the instantaneous frequency of their analytic signals is positive. However, this is not always the case.;The first two chapters are introductions to approximation in general, and Empirical Mode Decomposition, respectively.;The third chapter presents a characterization of which analytic signals have the property of non-negative instantaneous frequency. These 'analytic signals with non-negative instantaneous frequency' (ASNIFs) are described using …
Integer Flow And Petersen Minor, Taoye Zhang
Integer Flow And Petersen Minor, Taoye Zhang
Graduate Theses, Dissertations, and Problem Reports
Tutte [45] conjectured that every bridgeless Petersen-minor free graph admits a nowhere-zero 4-flow. Let P10 m&d1; ) be the graph obtained from the Petersen graph by contracting mu edges from a perfect matching. In chapter 1 we prove that every bridgeless P10 3&d1; -minor free graph admits a nowhere-zero 4-flow.;Walton and Welsh [48] proved that if a coloopless regular matroid M does not have a minor in {lcub}M(K 3,3), M*(K5){rcub}, then M admits a nowhere zero 4-flow. Lai et al [27] proved that if M does not have a minor in {lcub}M( K5), M*(K5){rcub}, then M admits a nowhere zero …