+publisher:"Vanderbilt University" +contributor:("Akram Aldroubi")

Vanderbilt University

1. Spaeth, Anneliese Heidi. A Determination of the Existence of Various Types of Positive Systems in L^p.

Degree: PhD, Mathematics, 2013, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07122013-163741/ ;

► We consider various types of generalized bases in spaces of the type L^p(T), where T=[0,1]. More specifically, we determine whether there exists a system {f_n}_n,… (more)

Subjects/Keywords: quasibasis; Schauder basis; pseudobasis; Walsh basis

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APA (6^th Edition):

Spaeth, A. H. (2013). A Determination of the Existence of Various Types of Positive Systems in L^p. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07122013-163741/ ;

Chicago Manual of Style (16^th Edition):

Spaeth, Anneliese Heidi. “A Determination of the Existence of Various Types of Positive Systems in L^p.” 2013. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07122013-163741/ ;.

MLA Handbook (7^th Edition):

Spaeth, Anneliese Heidi. “A Determination of the Existence of Various Types of Positive Systems in L^p.” 2013. Web. 24 Jan 2020.

Vancouver:

Spaeth AH. A Determination of the Existence of Various Types of Positive Systems in L^p. [Internet] [Doctoral dissertation]. Vanderbilt University; 2013. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07122013-163741/ ;.

Council of Science Editors:

Spaeth AH. A Determination of the Existence of Various Types of Positive Systems in L^p. [Doctoral Dissertation]. Vanderbilt University; 2013. Available from: http://etd.library.vanderbilt.edu/available/etd-07122013-163741/ ;

Vanderbilt University

2. Tang, Sui. Dynamical Sampling.

Degree: PhD, Mathematics, 2016, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ ;

► Let f â l²(I) be a signal at time t = 0 of an evolution process controlled by a bounded linear operator A that produces… (more)

Subjects/Keywords: Sampling theory; Frame theory; channel estimation

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APA (6^th Edition):

Tang, S. (2016). Dynamical Sampling. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ ;

Chicago Manual of Style (16^th Edition):

Tang, Sui. “Dynamical Sampling.” 2016. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ ;.

MLA Handbook (7^th Edition):

Tang, Sui. “Dynamical Sampling.” 2016. Web. 24 Jan 2020.

Vancouver:

Tang S. Dynamical Sampling. [Internet] [Doctoral dissertation]. Vanderbilt University; 2016. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ ;.

Council of Science Editors:

Tang S. Dynamical Sampling. [Doctoral Dissertation]. Vanderbilt University; 2016. Available from: http://etd.library.vanderbilt.edu/available/etd-05302016-212758/ ;

Vanderbilt University

3. Davis, Jacqueline Teresa Haines. Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems.

Degree: PhD, Mathematics, 2014, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07162014-173530/ ;

► Dynamical sampling is a new type of sampling problem that results from sampling an evolving signal at various times and asks the question: when do… (more)

Subjects/Keywords: spatio-temporal trade-off; sampling theory

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APA (6^th Edition):

Davis, J. T. H. (2014). Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07162014-173530/ ;

Chicago Manual of Style (16^th Edition):

Davis, Jacqueline Teresa Haines. “Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems.” 2014. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07162014-173530/ ;.

MLA Handbook (7^th Edition):

Davis, Jacqueline Teresa Haines. “Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems.” 2014. Web. 24 Jan 2020.

Vancouver:

Davis JTH. Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2014. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07162014-173530/ ;.

Council of Science Editors:

Davis JTH. Spatio-temporal trade-off for quasi-uniform sampling of signals in evolutionary systems. [Doctoral Dissertation]. Vanderbilt University; 2014. Available from: http://etd.library.vanderbilt.edu/available/etd-07162014-173530/ ;

Vanderbilt University

4. Tuo, Shengquan. Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector.

Degree: PhD, Physics, 2015, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03192015-152905/ ;

► The azimuthal correlations of charged particles produced in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV and proton-lead collisions at 5.02 TeV have… (more)

Subjects/Keywords: Heavy ion collision; Multiparticle Correlation; LHC; Flow; CMS

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APA (6^th Edition):

Tuo, S. (2015). Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03192015-152905/ ;

Chicago Manual of Style (16^th Edition):

Tuo, Shengquan. “Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector.” 2015. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03192015-152905/ ;.

MLA Handbook (7^th Edition):

Tuo, Shengquan. “Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector.” 2015. Web. 24 Jan 2020.

Vancouver:

Tuo S. Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector. [Internet] [Doctoral dissertation]. Vanderbilt University; 2015. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03192015-152905/ ;.

Council of Science Editors:

Tuo S. Multiparticle Azimuthal Correlation Measurements in Lead-Lead and Proton-Lead Collisions at LHC with the CMS Detector. [Doctoral Dissertation]. Vanderbilt University; 2015. Available from: http://etd.library.vanderbilt.edu/available/etd-03192015-152905/ ;

Vanderbilt University

5. Lee, Chang Hsin. Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints.

Degree: PhD, Mathematics, 2017, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-06152017-210945/ ;

► A fundamental problem in signal processing called signal reconstruction, or signal recovery, is the determination of a signal from a sequence of samples obtained from… (more)

Subjects/Keywords: digital signal processing; consistent reconstruction; Rangan-Goyal algorithm; signal reconstruction

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APA (6^th Edition):

Lee, C. H. (2017). Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-06152017-210945/ ;

Chicago Manual of Style (16^th Edition):

Lee, Chang Hsin. “Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints.” 2017. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-06152017-210945/ ;.

MLA Handbook (7^th Edition):

Lee, Chang Hsin. “Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints.” 2017. Web. 24 Jan 2020.

Vancouver:

Lee CH. Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints. [Internet] [Doctoral dissertation]. Vanderbilt University; 2017. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-06152017-210945/ ;.

Council of Science Editors:

Lee CH. Analysis of Signal Reconstruction Algorithms Based on Consistency Constraints. [Doctoral Dissertation]. Vanderbilt University; 2017. Available from: http://etd.library.vanderbilt.edu/available/etd-06152017-210945/ ;

Vanderbilt University

6. Michaels, Timothy Joseph. Node Generation on Surfaces and Bounds on Minimal Riesz Energy.

Degree: PhD, Mathematics, 2017, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-11072017-155807/ ;

► Discretizing a manifold is a far reaching subject throughout the mathematical and physical sciences. This thesis has two principal foci. We present and analyze a… (more)

Subjects/Keywords: spherical configurations; atmospheric modeling; minimal energy

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APA (6^th Edition):

Michaels, T. J. (2017). Node Generation on Surfaces and Bounds on Minimal Riesz Energy. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-11072017-155807/ ;

Chicago Manual of Style (16^th Edition):

Michaels, Timothy Joseph. “Node Generation on Surfaces and Bounds on Minimal Riesz Energy.” 2017. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-11072017-155807/ ;.

MLA Handbook (7^th Edition):

Michaels, Timothy Joseph. “Node Generation on Surfaces and Bounds on Minimal Riesz Energy.” 2017. Web. 24 Jan 2020.

Vancouver:

Michaels TJ. Node Generation on Surfaces and Bounds on Minimal Riesz Energy. [Internet] [Doctoral dissertation]. Vanderbilt University; 2017. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-11072017-155807/ ;.

Council of Science Editors:

Michaels TJ. Node Generation on Surfaces and Bounds on Minimal Riesz Energy. [Doctoral Dissertation]. Vanderbilt University; 2017. Available from: http://etd.library.vanderbilt.edu/available/etd-11072017-155807/ ;

Vanderbilt University

7. Gui, Bin. A unitary tensor product theory for unitary vertex operator algebra modules.

Degree: PhD, Mathematics, 2018, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-06272018-151541/ ;

► Let V be a unitary vertex operator algebra (VOA) satisfying the following conditions: (1) V is of CFT type. (2) Every N-gradable weak V -module… (more)

Subjects/Keywords: algebraic quantum field theory; tensor category; conformal field theory; Vertex operator algebra; unitary modular tensor category

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APA (6^th Edition):

Gui, B. (2018). A unitary tensor product theory for unitary vertex operator algebra modules. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-06272018-151541/ ;

Chicago Manual of Style (16^th Edition):

Gui, Bin. “A unitary tensor product theory for unitary vertex operator algebra modules.” 2018. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-06272018-151541/ ;.

MLA Handbook (7^th Edition):

Gui, Bin. “A unitary tensor product theory for unitary vertex operator algebra modules.” 2018. Web. 24 Jan 2020.

Vancouver:

Gui B. A unitary tensor product theory for unitary vertex operator algebra modules. [Internet] [Doctoral dissertation]. Vanderbilt University; 2018. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-06272018-151541/ ;.

Council of Science Editors:

Gui B. A unitary tensor product theory for unitary vertex operator algebra modules. [Doctoral Dissertation]. Vanderbilt University; 2018. Available from: http://etd.library.vanderbilt.edu/available/etd-06272018-151541/ ;

Vanderbilt University

8. Leshen, Sara. Balian-Low Type Results for Gabor Schauder Bases.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03202019-161148/ ;

► The uncertainty principle implies that a function and its Fourier transform cannot both be well-localized. The Balian-Low theorem is a version of the uncertainty principle… (more)

Subjects/Keywords: Schauder bases; uncertainty principle; time-frequency analysis

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APA (6^th Edition):

Leshen, S. (2019). Balian-Low Type Results for Gabor Schauder Bases. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03202019-161148/ ;

Chicago Manual of Style (16^th Edition):

Leshen, Sara. “Balian-Low Type Results for Gabor Schauder Bases.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03202019-161148/ ;.

MLA Handbook (7^th Edition):

Leshen, Sara. “Balian-Low Type Results for Gabor Schauder Bases.” 2019. Web. 24 Jan 2020.

Vancouver:

Leshen S. Balian-Low Type Results for Gabor Schauder Bases. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03202019-161148/ ;.

Council of Science Editors:

Leshen S. Balian-Low Type Results for Gabor Schauder Bases. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-03202019-161148/ ;

Vanderbilt University

9. Su, Yujian. Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2.

Degree: PhD, Mathematics, 2015, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-11122015-154408/ ;

► Let Λ be a lattice in R^d with positive co-volume. Among Λ-periodic N-point configurations, we consider the minimal renormalized Riesz s-energy mathcal{E}_s,Lambda(N). While the dominant… (more)

Subjects/Keywords: polarization; max-min problems; Epstein Hurwitz Zeta function; Ewald summation; periodic energy

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APA (6^th Edition):

Su, Y. (2015). Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-11122015-154408/ ;

Chicago Manual of Style (16^th Edition):

Su, Yujian. “Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2.” 2015. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-11122015-154408/ ;.

MLA Handbook (7^th Edition):

Su, Yujian. “Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2.” 2015. Web. 24 Jan 2020.

Vancouver:

Su Y. Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2. [Internet] [Doctoral dissertation]. Vanderbilt University; 2015. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-11122015-154408/ ;.

Council of Science Editors:

Su Y. Discrete Minimal Energy on Flat Tori and Four-Point Maximal Polarization on S^2. [Doctoral Dissertation]. Vanderbilt University; 2015. Available from: http://etd.library.vanderbilt.edu/available/etd-11122015-154408/ ;

Vanderbilt University

10. Jiang, Jiayi. Quantization in Signal Processing with Frame Theory.

Degree: PhD, Mathematics, 2016, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03252016-123616/ ;

► Quantization is an important part of signal processing. Several issues influence the performance of a quantization algorithm. One is the âbasisâ we choose to represent… (more)

Subjects/Keywords: Frame; Fusion Frame; Sigma-Delta Quantization; Sobolev Dual

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APA (6^th Edition):

Jiang, J. (2016). Quantization in Signal Processing with Frame Theory. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03252016-123616/ ;

Chicago Manual of Style (16^th Edition):

Jiang, Jiayi. “Quantization in Signal Processing with Frame Theory.” 2016. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03252016-123616/ ;.

MLA Handbook (7^th Edition):

Jiang, Jiayi. “Quantization in Signal Processing with Frame Theory.” 2016. Web. 24 Jan 2020.

Vancouver:

Jiang J. Quantization in Signal Processing with Frame Theory. [Internet] [Doctoral dissertation]. Vanderbilt University; 2016. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03252016-123616/ ;.

Council of Science Editors:

Jiang J. Quantization in Signal Processing with Frame Theory. [Doctoral Dissertation]. Vanderbilt University; 2016. Available from: http://etd.library.vanderbilt.edu/available/etd-03252016-123616/ ;

Vanderbilt University

11. Northington, Michael Carr V. Balian-Low Type Theorems for Shift-Invariant Spaces.

Degree: PhD, Mathematics, 2016, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03252016-124257/ ;

► Shift-invariant spaces and Gabor systems are frequently used in approximation theory and signal processing. In these settings, it is advantageous for the generators of such… (more)

Subjects/Keywords: sobolev spaces; time-frequency analysis; shift-invariant spaces

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APA (6^th Edition):

Northington, M. C. V. (2016). Balian-Low Type Theorems for Shift-Invariant Spaces. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03252016-124257/ ;

Chicago Manual of Style (16^th Edition):

Northington, Michael Carr V. “Balian-Low Type Theorems for Shift-Invariant Spaces.” 2016. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03252016-124257/ ;.

MLA Handbook (7^th Edition):

Northington, Michael Carr V. “Balian-Low Type Theorems for Shift-Invariant Spaces.” 2016. Web. 24 Jan 2020.

Vancouver:

Northington MCV. Balian-Low Type Theorems for Shift-Invariant Spaces. [Internet] [Doctoral dissertation]. Vanderbilt University; 2016. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03252016-124257/ ;.

Council of Science Editors:

Northington MCV. Balian-Low Type Theorems for Shift-Invariant Spaces. [Doctoral Dissertation]. Vanderbilt University; 2016. Available from: http://etd.library.vanderbilt.edu/available/etd-03252016-124257/ ;

Vanderbilt University

12. Li, Shiying. Adaptive Methods and Collocation by Splines for Solving Differential Equations.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07112019-130042/ ;

► Splines have been used to approximate the solutions of differential equations for a while. In the first part of this thesis, adaptive algorithms based on… (more)

Subjects/Keywords: Numerical Methods for Differential Equations; Collocation Methods; Splines; Approximation Theory; Adaptive Methods

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APA (6^th Edition):

Li, S. (2019). Adaptive Methods and Collocation by Splines for Solving Differential Equations. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07112019-130042/ ;

Chicago Manual of Style (16^th Edition):

Li, Shiying. “Adaptive Methods and Collocation by Splines for Solving Differential Equations.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07112019-130042/ ;.

MLA Handbook (7^th Edition):

Li, Shiying. “Adaptive Methods and Collocation by Splines for Solving Differential Equations.” 2019. Web. 24 Jan 2020.

Vancouver:

Li S. Adaptive Methods and Collocation by Splines for Solving Differential Equations. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07112019-130042/ ;.

Council of Science Editors:

Li S. Adaptive Methods and Collocation by Splines for Solving Differential Equations. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-07112019-130042/ ;

Vanderbilt University

13. Solava, Ryan William. On the fine structure of graphs avoiding certain complete bipartite minors.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-08182019-190904/ ;

► Avoiding complete bipartite graphs as minors, and in particular K_2,t as a minor, has been used to give sufficient conditions for Hamiltonicity. For this reason… (more)

Subjects/Keywords: Graph theory; Graph minors

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APA (6^th Edition):

Solava, R. W. (2019). On the fine structure of graphs avoiding certain complete bipartite minors. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-08182019-190904/ ;

Chicago Manual of Style (16^th Edition):

Solava, Ryan William. “On the fine structure of graphs avoiding certain complete bipartite minors.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-08182019-190904/ ;.

MLA Handbook (7^th Edition):

Solava, Ryan William. “On the fine structure of graphs avoiding certain complete bipartite minors.” 2019. Web. 24 Jan 2020.

Vancouver:

Solava RW. On the fine structure of graphs avoiding certain complete bipartite minors. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-08182019-190904/ ;.

Council of Science Editors:

Solava RW. On the fine structure of graphs avoiding certain complete bipartite minors. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-08182019-190904/ ;

Vanderbilt University

14. Tian, Yu. Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems.

Degree: PhD, Mechanical Engineering, 2010, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07182010-165646/ ;

► Effect of wheel slip in modeling and control of a nonholonomic Wheel Mobile Robot (WMR) subject to wheel slip is studied in this dissertation. First… (more)

Subjects/Keywords: nonholonomic wheeled mobile robot; under-actuated system; wheel slip effect; game -based pursuit-evasion

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APA (6^th Edition):

Tian, Y. (2010). Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07182010-165646/ ;

Chicago Manual of Style (16^th Edition):

Tian, Yu. “Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems.” 2010. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07182010-165646/ ;.

MLA Handbook (7^th Edition):

Tian, Yu. “Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems.” 2010. Web. 24 Jan 2020.

Vancouver:

Tian Y. Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2010. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07182010-165646/ ;.

Council of Science Editors:

Tian Y. Effect of wheel slip in modeling and control of wheeled mobile robots: applications to formation control and pursuit-evasion problems. [Doctoral Dissertation]. Vanderbilt University; 2010. Available from: http://etd.library.vanderbilt.edu/available/etd-07182010-165646/ ;

Vanderbilt University

15. Huang, Longxiu. Dynamical Sampling and its Applications.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03192019-114134/ ;

► Dynamical sampling is a new area in sampling theory that deals with signals that evolve over time under the action of a linear operator. There… (more)

Subjects/Keywords: Cadzow denoising algorithm; numerical linear algebra; continuous frames; dynamical sampling

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APA (6^th Edition):

Huang, L. (2019). Dynamical Sampling and its Applications. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03192019-114134/ ;

Chicago Manual of Style (16^th Edition):

Huang, Longxiu. “Dynamical Sampling and its Applications.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03192019-114134/ ;.

MLA Handbook (7^th Edition):

Huang, Longxiu. “Dynamical Sampling and its Applications.” 2019. Web. 24 Jan 2020.

Vancouver:

Huang L. Dynamical Sampling and its Applications. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03192019-114134/ ;.

Council of Science Editors:

Huang L. Dynamical Sampling and its Applications. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-03192019-114134/ ;

Vanderbilt University

16. Villalobos GuillÃ©n, CristÃ³bal. A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03262019-051041/ ;

► This work is motivated by the problem of recovering the magnetization M of a rock sample from a given set of measurements for the magnetic… (more)

Subjects/Keywords: geometric measure theory; BV fucntions; Inverse problems; Inverse problems in electromagnetism

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APA (6^th Edition):

Villalobos GuillÃ©n, C. (2019). A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03262019-051041/ ;

Chicago Manual of Style (16^th Edition):

Villalobos GuillÃ©n, CristÃ³bal. “A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03262019-051041/ ;.

MLA Handbook (7^th Edition):

Villalobos GuillÃ©n, CristÃ³bal. “A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.” 2019. Web. 24 Jan 2020.

Vancouver:

Villalobos GuillÃ©n C. A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03262019-051041/ ;.

Council of Science Editors:

Villalobos GuillÃ©n C. A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-03262019-051041/ ;

Vanderbilt University

17. Feigenbaum, Ahram Samuel. Applications of Modular Forms to Geometry and Interpolation Problems.

Degree: PhD, Mathematics, 2019, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-10172019-222828/ ;

► The sphere packing problem asks for the densest collection of non-overlapping con- gruent spheres in Rn. In 2016, Viazovska proved that the E8 lattice is… (more)

Subjects/Keywords: Modular Forms; Fourier Transform

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APA (6^th Edition):

Feigenbaum, A. S. (2019). Applications of Modular Forms to Geometry and Interpolation Problems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-10172019-222828/ ;

Chicago Manual of Style (16^th Edition):

Feigenbaum, Ahram Samuel. “Applications of Modular Forms to Geometry and Interpolation Problems.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-10172019-222828/ ;.

MLA Handbook (7^th Edition):

Feigenbaum, Ahram Samuel. “Applications of Modular Forms to Geometry and Interpolation Problems.” 2019. Web. 24 Jan 2020.

Vancouver:

Feigenbaum AS. Applications of Modular Forms to Geometry and Interpolation Problems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-10172019-222828/ ;.

Council of Science Editors:

Feigenbaum AS. Applications of Modular Forms to Geometry and Interpolation Problems. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://etd.library.vanderbilt.edu/available/etd-10172019-222828/ ;

18. Khorasgani, Hamed Ghazavi. Model- and data-driven approaches to fault detection and isolation in complex systems.

Degree: PhD, Electrical Engineering, 2018, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-01182018-134749/ ;

► Complex engineering systems pervade every aspect of our daily lives. The need for increased performance, safety, and reliability of these systems provide the motivation for… (more)

▼ Complex engineering systems pervade every aspect of our daily lives. The need for increased performance, safety, and reliability of these systems provide the motivation for developing system health monitoring methodologies for these systems. It is important to develop diagnosis for nonlinear systems that are robust to model uncertainties and noisy measurements. For greater applicability, it becomes essential to extend these diagnosis methods to cover hybrid behaviors, and to apply in a distributed manner to complex systems. On the other hand, the lack of sufficiently rich and complete models for these complex systems, but the availability of data collected from system operations may indicate the need to move toward data-driven diagnosis approaches. The contributions of this thesis research are primarily categorized into: 1) model-based, and 2) data-driven diagnosis. For robust model-based diagnosis, we have developed sensitivity analysis methods to quantify the performance of residuals generated for fault diagnosis in the presence of noise and uncertainty. We combine the robustness analysis with efficient residual selection algorithms to find a residual set that meets pre-specified diagnostic criteria. A second contribution of this thesis in the model-based diagnosis domain is developing two general approaches for distributed fault detection and isolation. The first method guarantees minimum communication of measurement values among subsystems. The second algorithm is computationally more efficient and it does not use the global system model for designing the local (distributed) diagnosers. However, it does not guarantee the minimum communication of measurement values. Our next contribution is developing model based methods that combine mode detection and diagnosis of faults in hybrid systems. Our approach does not require pre-enumeration of all possible modes and, therefore, it is feasible for hybrid systems with large number of switching elements. Finally, towards our contributions to data-driven diagnosis, we combine the use of unsupervised learning techniques with expert knowledge to develop an anomaly detection method to discover previously unknown faults in a complex system. Our clustering algorithm helps determine regions of nominal behavior, and by extension outliers and anomalous groups that are well-separated from the nominal clusters. We derive significant features associate for each outlier group, and then consult experts to identify and characterize these anomalies as faults in system behavior. Advisors/Committee Members: Gabor Karsai (committee member), Gautam Biswas (chair), Xenofon Koutsoukos (committee member), Akram Aldroubi (committee member), Don Wilkes (committee member).

Subjects/Keywords: Fault diagnosis; Fault detection and isolation; Unsupervised learning; Data-driven monitoring; Complex systems; Anomaly detection

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APA (6^th Edition):

Khorasgani, H. G. (2018). Model- and data-driven approaches to fault detection and isolation in complex systems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-01182018-134749/ ;

Chicago Manual of Style (16^th Edition):

Khorasgani, Hamed Ghazavi. “Model- and data-driven approaches to fault detection and isolation in complex systems.” 2018. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-01182018-134749/ ;.

MLA Handbook (7^th Edition):

Khorasgani, Hamed Ghazavi. “Model- and data-driven approaches to fault detection and isolation in complex systems.” 2018. Web. 24 Jan 2020.

Vancouver:

Khorasgani HG. Model- and data-driven approaches to fault detection and isolation in complex systems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2018. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-01182018-134749/ ;.

Council of Science Editors:

Khorasgani HG. Model- and data-driven approaches to fault detection and isolation in complex systems. [Doctoral Dissertation]. Vanderbilt University; 2018. Available from: http://etd.library.vanderbilt.edu/available/etd-01182018-134749/ ;

19. Calef, Matthew Thomas. Theoretical and Computational Investigations of Minimal Energy Problems.

Degree: PhD, Mathematics, 2009, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07152009-162919/ ;

► Let A be a d-dimensional compact subset of p-dimensional Euclidean space. For s in (0,d) the Riesz s-equilibrium measure is the unique Borel probability… (more)

Subjects/Keywords: potential theory; normalized d-energy; density

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APA (6^th Edition):

Calef, M. T. (2009). Theoretical and Computational Investigations of Minimal Energy Problems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07152009-162919/ ;

Chicago Manual of Style (16^th Edition):

Calef, Matthew Thomas. “Theoretical and Computational Investigations of Minimal Energy Problems.” 2009. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07152009-162919/ ;.

MLA Handbook (7^th Edition):

Calef, Matthew Thomas. “Theoretical and Computational Investigations of Minimal Energy Problems.” 2009. Web. 24 Jan 2020.

Vancouver:

Calef MT. Theoretical and Computational Investigations of Minimal Energy Problems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2009. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07152009-162919/ ;.

Council of Science Editors:

Calef MT. Theoretical and Computational Investigations of Minimal Energy Problems. [Doctoral Dissertation]. Vanderbilt University; 2009. Available from: http://etd.library.vanderbilt.edu/available/etd-07152009-162919/ ;

20. LeCrone, Jeremy. On the axisymmetric surface diffusion flow.

Degree: PhD, Mathematics, 2012, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-05222012-212749/ ;

► In this thesis, we establish analytic results for the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In the first part of the… (more)

Subjects/Keywords: fourier multipliers; nonlinear stability; maximal regularity; periodic boundary conditions; surface diffusion

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APA (6^th Edition):

LeCrone, J. (2012). On the axisymmetric surface diffusion flow. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-05222012-212749/ ;

Chicago Manual of Style (16^th Edition):

LeCrone, Jeremy. “On the axisymmetric surface diffusion flow.” 2012. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-05222012-212749/ ;.

MLA Handbook (7^th Edition):

LeCrone, Jeremy. “On the axisymmetric surface diffusion flow.” 2012. Web. 24 Jan 2020.

Vancouver:

LeCrone J. On the axisymmetric surface diffusion flow. [Internet] [Doctoral dissertation]. Vanderbilt University; 2012. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-05222012-212749/ ;.

Council of Science Editors:

LeCrone J. On the axisymmetric surface diffusion flow. [Doctoral Dissertation]. Vanderbilt University; 2012. Available from: http://etd.library.vanderbilt.edu/available/etd-05222012-212749/ ;

21. Chen, Xuemei. Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm.

Degree: PhD, Mathematics, 2012, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-06012012-105002/ ;

► This dissertation consists of two topics: compressed sensing and the Kaczmarz algorithm. Compressed sensing addresses the problem of recovering an unknown signal z_0in ℝ^d from… (more)

Subjects/Keywords: stability; compressed sensing; Kaczmarz Algorithm; randomization; null space property; dictionary

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APA (6^th Edition):

Chen, X. (2012). Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-06012012-105002/ ;

Chicago Manual of Style (16^th Edition):

Chen, Xuemei. “Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm.” 2012. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-06012012-105002/ ;.

MLA Handbook (7^th Edition):

Chen, Xuemei. “Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm.” 2012. Web. 24 Jan 2020.

Vancouver:

Chen X. Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm. [Internet] [Doctoral dissertation]. Vanderbilt University; 2012. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-06012012-105002/ ;.

Council of Science Editors:

Chen X. Stability of compressed sensing for dictionaries and almost sure convergence rate for the Kaczmarz algorithm. [Doctoral Dissertation]. Vanderbilt University; 2012. Available from: http://etd.library.vanderbilt.edu/available/etd-06012012-105002/ ;

22. Sekmen, Ali Safak. Subspace Segmentation and High-Dimensional Data Analysis.

Degree: PhD, Mathematics, 2012, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-04022012-093720/ ;

► This thesis developed theory and associated algorithms to solve subspace segmentation problem. Given a set of data W={w₁,...,w_N} in R^D that comes from a union… (more)

Subjects/Keywords: motion segmentation; subspace segmentation; union of subspaces

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APA (6^th Edition):

Sekmen, A. S. (2012). Subspace Segmentation and High-Dimensional Data Analysis. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-04022012-093720/ ;

Chicago Manual of Style (16^th Edition):

Sekmen, Ali Safak. “Subspace Segmentation and High-Dimensional Data Analysis.” 2012. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-04022012-093720/ ;.

MLA Handbook (7^th Edition):

Sekmen, Ali Safak. “Subspace Segmentation and High-Dimensional Data Analysis.” 2012. Web. 24 Jan 2020.

Vancouver:

Sekmen AS. Subspace Segmentation and High-Dimensional Data Analysis. [Internet] [Doctoral dissertation]. Vanderbilt University; 2012. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-04022012-093720/ ;.

Council of Science Editors:

Sekmen AS. Subspace Segmentation and High-Dimensional Data Analysis. [Doctoral Dissertation]. Vanderbilt University; 2012. Available from: http://etd.library.vanderbilt.edu/available/etd-04022012-093720/ ;

23. Petrosyan, Armenak. Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators.

Degree: PhD, Mathematics, 2017, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-05172017-130101/ ;

► The main problem in sampling theory is to reconstruct a function from its values (samples) on some discrete subset W of its domain. However, taking… (more)

Subjects/Keywords: Feichtinger conjecture; Reconstruction; Shift-Invariant Spaces; Sub-Sampling; Frames; Dynamical Sampling; Sampling Theory

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APA (6^th Edition):

Petrosyan, A. (2017). Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-05172017-130101/ ;

Chicago Manual of Style (16^th Edition):

Petrosyan, Armenak. “Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators.” 2017. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-05172017-130101/ ;.

MLA Handbook (7^th Edition):

Petrosyan, Armenak. “Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators.” 2017. Web. 24 Jan 2020.

Vancouver:

Petrosyan A. Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators. [Internet] [Doctoral dissertation]. Vanderbilt University; 2017. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-05172017-130101/ ;.

Council of Science Editors:

Petrosyan A. Dynamical Sampling and Systems of Vectors from Iterative Actions of Operators. [Doctoral Dissertation]. Vanderbilt University; 2017. Available from: http://etd.library.vanderbilt.edu/available/etd-05172017-130101/ ;

24. Wang, Lujun. Trivariate polynomial splines on 3D T-meshes.

Degree: PhD, Mathematics, 2012, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-05152012-224523/ ;

► Trivariate polynomial spline spaces deﬁned on three-dimensional (3D) T-meshes are useful tools for the ﬁnite element method. In addition to dimension formulae, explicit basis functions… (more)

Subjects/Keywords: 3D T-meshes; Hermite interpolation; splines; hanging vertices

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APA (6^th Edition):

Wang, L. (2012). Trivariate polynomial splines on 3D T-meshes. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-05152012-224523/ ;

Chicago Manual of Style (16^th Edition):

Wang, Lujun. “Trivariate polynomial splines on 3D T-meshes.” 2012. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-05152012-224523/ ;.

MLA Handbook (7^th Edition):

Wang, Lujun. “Trivariate polynomial splines on 3D T-meshes.” 2012. Web. 24 Jan 2020.

Vancouver:

Wang L. Trivariate polynomial splines on 3D T-meshes. [Internet] [Doctoral dissertation]. Vanderbilt University; 2012. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-05152012-224523/ ;.

Council of Science Editors:

Wang L. Trivariate polynomial splines on 3D T-meshes. [Doctoral Dissertation]. Vanderbilt University; 2012. Available from: http://etd.library.vanderbilt.edu/available/etd-05152012-224523/ ;

25. Das, Sayan. Poisson boundaries of finite von Neumann algebras.

Degree: PhD, Mathematics, 2017, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07202017-142037/ ;

► Poisson boundaries of groups plays a major role in the study of group actions on measure spaces. In this work, we study noncommmutative Poisson boundaries… (more)

Subjects/Keywords: property (T); amenability; hyperstate; entropy; rigidity; operator systems

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APA (6^th Edition):

Das, S. (2017). Poisson boundaries of finite von Neumann algebras. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07202017-142037/ ;

Chicago Manual of Style (16^th Edition):

Das, Sayan. “Poisson boundaries of finite von Neumann algebras.” 2017. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07202017-142037/ ;.

MLA Handbook (7^th Edition):

Das, Sayan. “Poisson boundaries of finite von Neumann algebras.” 2017. Web. 24 Jan 2020.

Vancouver:

Das S. Poisson boundaries of finite von Neumann algebras. [Internet] [Doctoral dissertation]. Vanderbilt University; 2017. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07202017-142037/ ;.

Council of Science Editors:

Das S. Poisson boundaries of finite von Neumann algebras. [Doctoral Dissertation]. Vanderbilt University; 2017. Available from: http://etd.library.vanderbilt.edu/available/etd-07202017-142037/ ;

Vanderbilt University

26. Borodachov, Sergiy Volodymyrovych. Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets.

Degree: PhD, Mathematics, 2006, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-06212006-125022/ ;

► This work studies the behavior of the minimal discrete Riesz s-energy and best-packing distance on rectifiable sets as the cardinality N of point configurations gets… (more)

Subjects/Keywords: best-packing; minimum energy; Riesz potential; rectifiable set

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APA (6^th Edition):

Borodachov, S. V. (2006). Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-06212006-125022/ ;

Chicago Manual of Style (16^th Edition):

Borodachov, Sergiy Volodymyrovych. “Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets.” 2006. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-06212006-125022/ ;.

MLA Handbook (7^th Edition):

Borodachov, Sergiy Volodymyrovych. “Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets.” 2006. Web. 24 Jan 2020.

Vancouver:

Borodachov SV. Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets. [Internet] [Doctoral dissertation]. Vanderbilt University; 2006. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-06212006-125022/ ;.

Council of Science Editors:

Borodachov SV. Asymptotic Results for the minimum energy and Best-Packing Problems on Rectifiable Sets. [Doctoral Dissertation]. Vanderbilt University; 2006. Available from: http://etd.library.vanderbilt.edu/available/etd-06212006-125022/ ;

Vanderbilt University

27. Halder, Bibhrajit. Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems.

Degree: PhD, Mechanical Engineering, 2006, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-10192006-122408/ ;

► The demand for automation in modern society has significantly increased during the last few decades. Robotic systems play an important role in automation industries that… (more)

▼ The demand for automation in modern society has significantly increased during the last few decades. Robotic systems play an important role in automation industries that include manufacturing, assembly, and biotechnology among others. In addition, there is a growing need for unmanned operation in different services and research sectors such as search and rescue operation, nuclear waste clean-up, and planetary exploration. Robots can perform repetitive tasks efficiently and can function in a harsh and unsafe environment. However, robots are susceptible to system faults. Faults may result in mission failures that are costly in mission critical enterprises. Therefore fault detection and isolation (FDI) is important for reliable and safe robot operations. In this dissertation, we present a new approach, called the robust nonlinear analytic redundancy (RNLAR) technique, to sensor and actuator FDI for input-affine nonlinear multivariable dynamic systems in the presence of model-plant-mismatch and process disturbances. Robust FDI is important because of the universal existence of model uncertainties and process disturbances in most systems. The new approach is based on analytic redundancy relation, which has primarily been used in the linear domain. The proposed RNLAR technique extends the current state-of-the-art in analytic redundancy relation-based FDI into the nonlinear domain. The RNLAR technique is used to design primary residual vectors (PRV) to detect actuator and sensor faults. Primary residual vectors are designed in such a manner that they are highly sensitive to the faults and less sensitive to model-plant-mismatch and process disturbances. The proposed methodology is applied to the actuator and sensor fault detection of a wheeled mobile robot as well as a robotic manipulator. The order of redundancy relation is used to characterize the robustness of the RNLAR technique. It is proved that an increase in the order of redundancy relation increases the robustness of the RNLAR technique. This result extends the existing relationship between the order of redundancy relation and robustness from the linear domain to the nonlinear domain. Finally, a robust fault isolation technique is presented in this work. The PRVs are transformed into a set of structured residual vectors (SRV) for fault isolation. Experimental results on a Pioneer 3-DX mobile robot and a PUMA 560 robotic manipulator are presented to justify the effectiveness of the RNLAR technique. Advisors/Committee Members: Nilanjan Sarkar (chair), Eric Barth (committee member), Michael Goldfarb (committee member), George E. Cook (committee member), Akram Aldroubi (committee member).

Subjects/Keywords: Fault location (Engineering); mobile robots; nonlinear systems; PUMA; order of redundancy; Fault detection; analytical redundancy; robustness; Robots – Error detection and recovery

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APA (6^th Edition):

Halder, B. (2006). Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-10192006-122408/ ;

Chicago Manual of Style (16^th Edition):

Halder, Bibhrajit. “Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems.” 2006. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-10192006-122408/ ;.

MLA Handbook (7^th Edition):

Halder, Bibhrajit. “Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems.” 2006. Web. 24 Jan 2020.

Vancouver:

Halder B. Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems. [Internet] [Doctoral dissertation]. Vanderbilt University; 2006. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-10192006-122408/ ;.

Council of Science Editors:

Halder B. Robust nonlinear analytic redundancy for fault detection and isolation of robotic systems. [Doctoral Dissertation]. Vanderbilt University; 2006. Available from: http://etd.library.vanderbilt.edu/available/etd-10192006-122408/ ;

Vanderbilt University

28. Leonetti, Casey Clark. Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces.

Degree: PhD, Mathematics, 2007, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-03292007-180005/ ;

► In the following chapters we provide error estimates for signals reconstructed from corrupt data. Two different types of error are considered. First, we address the… (more)

Subjects/Keywords: jitter; noise; sampling; shift-invariant space; frame; fourier

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APA (6^th Edition):

Leonetti, C. C. (2007). Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-03292007-180005/ ;

Chicago Manual of Style (16^th Edition):

Leonetti, Casey Clark. “Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces.” 2007. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-03292007-180005/ ;.

MLA Handbook (7^th Edition):

Leonetti, Casey Clark. “Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces.” 2007. Web. 24 Jan 2020.

Vancouver:

Leonetti CC. Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces. [Internet] [Doctoral dissertation]. Vanderbilt University; 2007. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-03292007-180005/ ;.

Council of Science Editors:

Leonetti CC. Reconstruction from Error-Affected Sampled Data in Shift-Invariant Spaces. [Doctoral Dissertation]. Vanderbilt University; 2007. Available from: http://etd.library.vanderbilt.edu/available/etd-03292007-180005/ ;

Vanderbilt University

29. Yattselev, Maxim L. Non-Hermitian Orthogonality and Meromorphic Approximation.

Degree: PhD, Mathematics, 2007, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07262007-180105/ ;

► In this thesis we consider the distribution of poles of meromorphic and multipoint Padé approximants to the sum of a rational function and a Cauchy… (more)

Subjects/Keywords: meromorphic; rational; Padé approximation; orthogonal polynomials

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APA (6^th Edition):

Yattselev, M. L. (2007). Non-Hermitian Orthogonality and Meromorphic Approximation. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07262007-180105/ ;

Chicago Manual of Style (16^th Edition):

Yattselev, Maxim L. “Non-Hermitian Orthogonality and Meromorphic Approximation.” 2007. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07262007-180105/ ;.

MLA Handbook (7^th Edition):

Yattselev, Maxim L. “Non-Hermitian Orthogonality and Meromorphic Approximation.” 2007. Web. 24 Jan 2020.

Vancouver:

Yattselev ML. Non-Hermitian Orthogonality and Meromorphic Approximation. [Internet] [Doctoral dissertation]. Vanderbilt University; 2007. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07262007-180105/ ;.

Council of Science Editors:

Yattselev ML. Non-Hermitian Orthogonality and Meromorphic Approximation. [Doctoral Dissertation]. Vanderbilt University; 2007. Available from: http://etd.library.vanderbilt.edu/available/etd-07262007-180105/ ;

Vanderbilt University

30. Bosuwan, Nattapong. Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations.

Degree: PhD, Mathematics, 2000, Vanderbilt University

URL: http://etd.library.vanderbilt.edu/available/etd-07012013-143520/ ;

► We investigate two subjects in asymptotic analysis. The first focuses on a class of rational functions called PadÃ©-orthogonal approximants. We study the relation of the… (more)

Subjects/Keywords: rational approximation; Pade approximants; Fabrys Theorem; Riesz polarization; Chebyshev constants Montessus de Ballore s Theorem; Riesz energy; rational approximation; Pade approximants; Riesz energy; Chebyshev constants Montessus de Ballore s Theorem; Riesz polarization; Fabrys Theorem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bosuwan, N. (2000). Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://etd.library.vanderbilt.edu/available/etd-07012013-143520/ ;

Chicago Manual of Style (16^th Edition):

Bosuwan, Nattapong. “Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations.” 2000. Doctoral Dissertation, Vanderbilt University. Accessed January 24, 2020. http://etd.library.vanderbilt.edu/available/etd-07012013-143520/ ;.

MLA Handbook (7^th Edition):

Bosuwan, Nattapong. “Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations.” 2000. Web. 24 Jan 2020.

Vancouver:

Bosuwan N. Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations. [Internet] [Doctoral dissertation]. Vanderbilt University; 2000. [cited 2020 Jan 24]. Available from: http://etd.library.vanderbilt.edu/available/etd-07012013-143520/ ;.

Council of Science Editors:

Bosuwan N. Two problems in asymptotic analysis PadÃ©-orthogonal approximation and Riesz polarization constants and configurations. [Doctoral Dissertation]. Vanderbilt University; 2000. Available from: http://etd.library.vanderbilt.edu/available/etd-07012013-143520/ ;

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