Cheung Sing Leung = 頻散耗散系統中的本征矢量展開式 / 張承亮. / Thesis submitted in: October 2003. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves [141]-[144]). / Text in English; abstracts in English and Chinese. / Cheung Sing Leung = Pin san hao san xi tong zhong de ben zheng shi liang zhan kai shi / Zhang Chengliang. / Abstract --- p.i / Acknowledgments --- p.iv / Contents --- p.v / List of Figures --- p.ix / List of Tables --- p.xiii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Physical Motivation --- p.1 / Chapter 1.2 --- Review of Ohmic Damping Formalism --- p.3 / Chapter 1.3 --- Outline of Thesis --- p.11 / Chapter Chapter 2. --- Critical Point and Perturbation around Critical Points --- p.13 / Chapter 2.1 --- Introduction and Example --- p.13 / Chapter 2.2 --- Basis Vectors near and at Critical Point --- p.16 / Chapter 2.2.1 --- Properties of Jordan block basis --- p.20 / Chapter 2.3 --- Example of Damped Oscillator --- p.24 / Chapter 2.4 --- Perturbation around Critical Points --- p.25 / Chapter 2.4.1 --- Behavior of other Jordan blocks --- p.27 / Chapter 2.4.2 --- Summary on generic and non-generic behaviors around the critical point --- p.28 / Chapter Chapter 3. --- Fast Mode and Constrained Systems --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Model A: Damped System with Special Mass --- p.36 / Chapter 3.2.1 --- Limiting case ε= 0 --- p.38 / Chapter 3.2.2 --- Eigenvalue convergence --- p.40 / Chapter 3.3 --- Model B: Damped System with Outgoing-wave Condition --- p.44 / Chapter 3.3.1 --- Matching criteria --- p.46 / Chapter 3.4 --- Model C: Discrete Wave Equation with Outgoing-wave Condition --- p.46 / Chapter 3.4.1 --- Matching criteria in the N →∞ limit in wave element example --- p.48 / Chapter Chapter 4. --- Dispersive Dissipative Systems --- p.56 / Chapter 4.1 --- Introduction --- p.56 / Chapter 4.1.1 --- Relation between dispersion and dissipation --- p.58 / Chapter 4.2 --- Previous Works on Dispersive Dissipative Systems --- p.59 / Chapter 4.3 --- Damped Systems with Dispersion --- p.62 / Chapter 4.4 --- Initial-value Problem --- p.65 / Chapter Chapter 5. --- Dispersive Linear-space Formalism --- p.72 / Chapter 5.1 --- Low-dimensional System --- p.72 / Chapter 5.1.1 --- State space and evolution --- p.72 / Chapter 5.1.2 --- Inner product and bilinear map --- p.76 / Chapter 5.1.3 --- Metric --- p.78 / Chapter 5.2 --- Generalization of Metric for N = 1 and Arbitrary M --- p.81 / Chapter 5.3 --- Generalization of the Formalism to Arbitrary N and M --- p.82 / Chapter Chapter 6. --- Properties of Dispersive Systems --- p.86 / Chapter 6.1 --- Initial-value Problem Revisited --- p.86 / Chapter 6.1.1 --- Worked example --- p.88 / Chapter 6.2 --- Weak Dispersion --- p.91 / Chapter 6.2.1 --- Eigenvalues --- p.91 / Chapter 6.2.2 --- Decoupling --- p.93 / Chapter 6.2.3 --- Perturbation around the decoupling limit --- p.94 / Chapter 6.3 --- Connection between Dispersive and Ohmic Systems --- p.96 / Chapter 6.3.1 --- Illustrative example --- p.97 / Chapter 6.3.2 --- Conditions --- p.99 / Chapter 6.3.3 --- "Illustration of N =1, M = 2 case" --- p.100 / Chapter 6.3.4 --- Numerical example --- p.101 / Chapter Chapter 7. --- Conclusion --- p.105 / Chapter Appendix A. --- Perturbation Around Critical Points --- p.107 / Chapter A.1 --- Genericity --- p.107 / Chapter A.1.1 --- Example --- p.110 / Chapter A.2 --- Non-genericity --- p.111 / Chapter A.2.1 --- First-order non-genericity --- p.111 / Chapter A.2.1.1 --- Example --- p.113 / Chapter A.2.1.2 --- Special case --- p.114 / Chapter A.2.2 --- Second-order non-genericity --- p.117 / Chapter A.2.2.1 --- Example --- p.118 / Chapter A.2.2.2 --- Special case --- p.120 / Chapter A.2.3 --- Third-order non-genericity --- p.123 / Chapter A.2.3.1 --- Example --- p.125 / Chapter A.2.3.2 --- Special case --- p.128 / Chapter Appendix B. --- Numerical Detail of Initial-value Problem --- p.134 / Chapter B.1 --- Numerical Algorithm --- p.134 / Chapter B.2 --- Description of Extracted Components --- p.135 / Chapter Appendix C. --- Vandermonde Matrix --- p.137 / Chapter C.1 --- Introduction --- p.137 / Chapter C.2 --- Algorithm --- p.138 / Chapter C.3 --- Example --- p.138 / Chapter C.4 --- Proof of Alogrithm --- p.139 / Bibliography --- p.141

In the numerous problems of matrix algebra, one finds the problem of determining the eigenvalues of eigenvectors of a matrix quite frequently. The theory and methods leading to the solution of the eigenvalue and eigenvector problem are of considerable interest. The relation between vector spaces, matrices, eigenvalues, and eigenvectors is to be considered in this chapter, with particular concentration directed toward the eigenvalues and eigenvectors shall be developed in the following chapters with detailed examples of the methods.

Thesis (Ph.D.)--Brown University, 2008. / Vita. Advisor : Sergei Treil. Includes bibliographical references (leaves 19-20).

Thesis (M.S.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (December 19, 2006) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Queensland, 2002. / Includes bibliographical references.

Thesis (M.A.)--Boston University

The sensing technique described in this dissertation produces modal coordinates for monitoring and active control of structural vibration. The sensor array is constructed from strain-sensing segments. The segment outputs are transformed into modal coordinates by a sensor gain matrix. An adaptive algorithm for computing the sensor gain matrix with minimal knowledge of the structure's modal properties is proposed. It is shown that the sensor gain matrix is the modal matrix of the segment output correlation matrix. This modal matrix is computed using new algorithms based on Jacobi rotations. The procedure is relatively simple and can be performed gradually to keep computation requirements low. The sensor system can also identify the mode shapes of the structure in real time using Lagrange polynomial interpolation formula. An experiment is done with an array of piezoelectric polyvinylidene fluoride (PVDF) film segments on a beam to obtain the segment outputs. The results from the experiment are used to verify a computer simulation routine. Then a series of simulations are done to test the adaptive modal sensing algorithms. Simulation results verify that the sensor gain matrix obtained by the adaptive algorithm transforms the segment outputs into modal coordinates. / Ph. D.

No description available.

In this report we study the Aizawa field by first computing a Taylor series expansion for the solution of an initial value problem. We then look for singularities (equilibrium points) of the field and plot the set of solutions which lie in the linear subspace spanned by the eigenvectors. Finally, we use the Parameterization Method to compute one and two dimensional stable and unstable manifolds of equilibria for the system. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy