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Georgia Tech

1. Li, Wuchen. A study of stochastic differential equations and Fokker-Planck equations with applications.

Degree: PhD, Mathematics, 2016, Georgia Tech

URL: http://hdl.handle.net/1853/54999

► Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis,…
(more)

Subjects/Keywords: Stochastic differential equations; Fokker-Planck equations; Gradient flow; Optimal control; Optimal transport

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

APA (6^{th} Edition):

Li, W. (2016). A study of stochastic differential equations and Fokker-Planck equations with applications. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/54999

Chicago Manual of Style (16^{th} Edition):

Li, Wuchen. “A study of stochastic differential equations and Fokker-Planck equations with applications.” 2016. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/54999.

MLA Handbook (7^{th} Edition):

Li, Wuchen. “A study of stochastic differential equations and Fokker-Planck equations with applications.” 2016. Web. 19 Nov 2019.

Vancouver:

Li W. A study of stochastic differential equations and Fokker-Planck equations with applications. [Internet] [Doctoral dissertation]. Georgia Tech; 2016. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/54999.

Council of Science Editors:

Li W. A study of stochastic differential equations and Fokker-Planck equations with applications. [Doctoral Dissertation]. Georgia Tech; 2016. Available from: http://hdl.handle.net/1853/54999

Georgia Tech

2. Liu, Jingfang. Adaptive iterative filtering methods for nonlinear signal analysis and applications.

Degree: PhD, Mathematics, 2013, Georgia Tech

URL: http://hdl.handle.net/1853/52169

► Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis…
(more)

Subjects/Keywords: Time-frequency analysis; EMD; Iterative filtering; ALIF; Instantaneous frequency

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APA (6^{th} Edition):

Liu, J. (2013). Adaptive iterative filtering methods for nonlinear signal analysis and applications. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/52169

Chicago Manual of Style (16^{th} Edition):

Liu, Jingfang. “Adaptive iterative filtering methods for nonlinear signal analysis and applications.” 2013. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/52169.

MLA Handbook (7^{th} Edition):

Liu, Jingfang. “Adaptive iterative filtering methods for nonlinear signal analysis and applications.” 2013. Web. 19 Nov 2019.

Vancouver:

Liu J. Adaptive iterative filtering methods for nonlinear signal analysis and applications. [Internet] [Doctoral dissertation]. Georgia Tech; 2013. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/52169.

Council of Science Editors:

Liu J. Adaptive iterative filtering methods for nonlinear signal analysis and applications. [Doctoral Dissertation]. Georgia Tech; 2013. Available from: http://hdl.handle.net/1853/52169

Georgia Tech

3. Lu, Jun. Method of evolving junctions: a new approach to path planning and optimal control.

Degree: PhD, Mathematics, 2014, Georgia Tech

URL: http://hdl.handle.net/1853/53428

► This thesis proposes a novel and efficient method (Method of Evolving Junctions) for solving optimal control problems with path constraints, and whose optimal paths are…
(more)

Subjects/Keywords: SDEs; Shortest path; Dynamic environment

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

APA (6^{th} Edition):

Lu, J. (2014). Method of evolving junctions: a new approach to path planning and optimal control. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/53428

Chicago Manual of Style (16^{th} Edition):

Lu, Jun. “Method of evolving junctions: a new approach to path planning and optimal control.” 2014. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/53428.

MLA Handbook (7^{th} Edition):

Lu, Jun. “Method of evolving junctions: a new approach to path planning and optimal control.” 2014. Web. 19 Nov 2019.

Vancouver:

Lu J. Method of evolving junctions: a new approach to path planning and optimal control. [Internet] [Doctoral dissertation]. Georgia Tech; 2014. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/53428.

Council of Science Editors:

Lu J. Method of evolving junctions: a new approach to path planning and optimal control. [Doctoral Dissertation]. Georgia Tech; 2014. Available from: http://hdl.handle.net/1853/53428

Georgia Tech

4. Yildirim Yolcu, Selma. Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian.

Degree: PhD, Mathematics, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/31649

► Some eigenvalue inequalities for Klein-Gordon operators and fractional Laplacians restricted to a bounded domain are proved. Such operators became very popular recently as they arise…
(more)

Subjects/Keywords: Fractional Laplacian; Klein-Gordon operator; Eigenvalue; Laplacian operator; Eigenvalues; Klein-Gordon equation; Spectral theory (Mathematics)

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APA (6^{th} Edition):

Yildirim Yolcu, S. (2009). Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/31649

Chicago Manual of Style (16^{th} Edition):

Yildirim Yolcu, Selma. “Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian.” 2009. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/31649.

MLA Handbook (7^{th} Edition):

Yildirim Yolcu, Selma. “Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian.” 2009. Web. 19 Nov 2019.

Vancouver:

Yildirim Yolcu S. Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/31649.

Council of Science Editors:

Yildirim Yolcu S. Eigenvalue inequalities for relativistic Hamiltonians and fractional Laplacian. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/31649

Georgia Tech

5. Grigo, Alexander. Billiards and statistical mechanics.

Degree: PhD, Mathematics, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/29610

► In this thesis we consider mathematical problems related to different aspects of hard sphere systems. In the first part we study planar billiards, which arise…
(more)

Subjects/Keywords: Billiards; Boltzmann equation; Hamiltonian systems; Statistical mechanics; Ergodic theory; Dynamics; Transport theory

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APA (6^{th} Edition):

Grigo, A. (2009). Billiards and statistical mechanics. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/29610

Chicago Manual of Style (16^{th} Edition):

Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/29610.

MLA Handbook (7^{th} Edition):

Grigo, Alexander. “Billiards and statistical mechanics.” 2009. Web. 19 Nov 2019.

Vancouver:

Grigo A. Billiards and statistical mechanics. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/29610.

Council of Science Editors:

Grigo A. Billiards and statistical mechanics. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/29610

Georgia Tech

6. Yolcu, Türkay. Parabolic systems and an underlying Lagrangian.

Degree: PhD, Mathematics, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/29760

► In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional…
(more)

Subjects/Keywords: Lagrangian; PDE; Parabolic equations; Variational method; De Giorgi; Optimization; Differential equations, Parabolic; Lagrangian functions; Interpolation; Algorithms

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

APA (6^{th} Edition):

Yolcu, T. (2009). Parabolic systems and an underlying Lagrangian. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/29760

Chicago Manual of Style (16^{th} Edition):

Yolcu, Türkay. “Parabolic systems and an underlying Lagrangian.” 2009. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/29760.

MLA Handbook (7^{th} Edition):

Yolcu, Türkay. “Parabolic systems and an underlying Lagrangian.” 2009. Web. 19 Nov 2019.

Vancouver:

Yolcu T. Parabolic systems and an underlying Lagrangian. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/29760.

Council of Science Editors:

Yolcu T. Parabolic systems and an underlying Lagrangian. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/29760

Georgia Tech

7. Zhao, Kun. Initial-boundary value problems in fluid dynamics modeling.

Degree: PhD, Mathematics, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/31778

► This thesis is devoted to studies of initial-boundary value problems (IBVPs) for systems of partial differential equations (PDEs) arising from fluid mechanics modeling, especially for…
(more)

Subjects/Keywords: Fluid dynamics; Partial differential equations; Initial-boundary value problem; Boundary value problems; Initial value problems; Fluid dynamics

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APA (6^{th} Edition):

Zhao, K. (2009). Initial-boundary value problems in fluid dynamics modeling. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/31778

Chicago Manual of Style (16^{th} Edition):

Zhao, Kun. “Initial-boundary value problems in fluid dynamics modeling.” 2009. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/31778.

MLA Handbook (7^{th} Edition):

Zhao, Kun. “Initial-boundary value problems in fluid dynamics modeling.” 2009. Web. 19 Nov 2019.

Vancouver:

Zhao K. Initial-boundary value problems in fluid dynamics modeling. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/31778.

Council of Science Editors:

Zhao K. Initial-boundary value problems in fluid dynamics modeling. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/31778

8. Li, Yao. Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks.

Degree: PhD, Mathematics, 2012, Georgia Tech

URL: http://hdl.handle.net/1853/49013

► The primary objective of this thesis is to make a quantitative study of complex biological networks. Our fundamental motivation is to obtain the statistical dependency…
(more)

Subjects/Keywords: Stochastic dynamical system; Fokker-Planck equation; Systematic measure; Systems biology; Bioinformatics; Fokker-Planck equation Numerical solutions; Stochastic differential equations

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

APA (6^{th} Edition):

Li, Y. (2012). Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/49013

Chicago Manual of Style (16^{th} Edition):

Li, Yao. “Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks.” 2012. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/49013.

MLA Handbook (7^{th} Edition):

Li, Yao. “Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks.” 2012. Web. 19 Nov 2019.

Vancouver:

Li Y. Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks. [Internet] [Doctoral dissertation]. Georgia Tech; 2012. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/49013.

Council of Science Editors:

Li Y. Stochastic perturbation theory and its application to complex biological networks – a quantification of systematic features of biological networks. [Doctoral Dissertation]. Georgia Tech; 2012. Available from: http://hdl.handle.net/1853/49013

9. Lu, Nan. Normally elliptic singular perturbation problems: local invariant manifolds and applications.

Degree: PhD, Mathematics, 2011, Georgia Tech

URL: http://hdl.handle.net/1853/41090

► In this thesis, we study the normally elliptic singular perturbation problems including both finite and infinite dimensional cases, which could also be non-autonomous. In particular,…
(more)

Subjects/Keywords: Dynamical system; Invariant manifold; Homoclinic orbit; Perturbation (Mathematics); Singular perturbations (Mathematics)

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

APA (6^{th} Edition):

Lu, N. (2011). Normally elliptic singular perturbation problems: local invariant manifolds and applications. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/41090

Chicago Manual of Style (16^{th} Edition):

Lu, Nan. “Normally elliptic singular perturbation problems: local invariant manifolds and applications.” 2011. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/41090.

MLA Handbook (7^{th} Edition):

Lu, Nan. “Normally elliptic singular perturbation problems: local invariant manifolds and applications.” 2011. Web. 19 Nov 2019.

Vancouver:

Lu N. Normally elliptic singular perturbation problems: local invariant manifolds and applications. [Internet] [Doctoral dissertation]. Georgia Tech; 2011. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/41090.

Council of Science Editors:

Lu N. Normally elliptic singular perturbation problems: local invariant manifolds and applications. [Doctoral Dissertation]. Georgia Tech; 2011. Available from: http://hdl.handle.net/1853/41090

10. Yin, Ke. New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography.

Degree: PhD, Mathematics, 2013, Georgia Tech

URL: http://hdl.handle.net/1853/48945

► This thesis is devoted to solving the inverse source problem arising in image reconstruction problems. In general, the solution is non-unique and the problem is…
(more)

Subjects/Keywords: Inverse problem; Tomography; Image reconstruction technique; Fluorescence tomography; Inverse problems (Differential equations); Inverse problems (Differential equations) Numerical solutions; Numerical analysis; Image reconstruction

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

APA (6^{th} Edition):

Yin, K. (2013). New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/48945

Chicago Manual of Style (16^{th} Edition):

Yin, Ke. “New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography.” 2013. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/48945.

MLA Handbook (7^{th} Edition):

Yin, Ke. “New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography.” 2013. Web. 19 Nov 2019.

Vancouver:

Yin K. New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography. [Internet] [Doctoral dissertation]. Georgia Tech; 2013. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/48945.

Council of Science Editors:

Yin K. New algorithms for solving inverse source problems in imaging techniques with applications in fluorescence tomography. [Doctoral Dissertation]. Georgia Tech; 2013. Available from: http://hdl.handle.net/1853/48945

11. Howard, Dustin F. Short-circuit currents in wind-turbine generator networks.

Degree: PhD, Electrical and Computer Engineering, 2013, Georgia Tech

URL: http://hdl.handle.net/1853/50361

► Protection of both the wind plant and the interconnecting transmission system during short-circuit faults is imperative for maintaining system structural integrity and reliability. The circuit…
(more)

Subjects/Keywords: Wind turbine; Power system protection; Power system transients; Short circuit currents; Power system modeling; Wind turbines; Short circuits

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APA (6^{th} Edition):

Howard, D. F. (2013). Short-circuit currents in wind-turbine generator networks. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/50361

Chicago Manual of Style (16^{th} Edition):

Howard, Dustin F. “Short-circuit currents in wind-turbine generator networks.” 2013. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/50361.

MLA Handbook (7^{th} Edition):

Howard, Dustin F. “Short-circuit currents in wind-turbine generator networks.” 2013. Web. 19 Nov 2019.

Vancouver:

Howard DF. Short-circuit currents in wind-turbine generator networks. [Internet] [Doctoral dissertation]. Georgia Tech; 2013. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/50361.

Council of Science Editors:

Howard DF. Short-circuit currents in wind-turbine generator networks. [Doctoral Dissertation]. Georgia Tech; 2013. Available from: http://hdl.handle.net/1853/50361

Georgia Tech

12. Li, Yongfeng. Nonlinear oscillation and control in the BZ chemical reaction.

Degree: PhD, Mathematics, 2008, Georgia Tech

URL: http://hdl.handle.net/1853/26565

► In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The…
(more)

Subjects/Keywords: Nonlinear oscillation; BZ chemical reaction; Geometric singular perturbation; Model reference control; Nonequilibrium thermodynamics; Singular perturbations (Mathematics)

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

APA (6^{th} Edition):

Li, Y. (2008). Nonlinear oscillation and control in the BZ chemical reaction. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/26565

Chicago Manual of Style (16^{th} Edition):

Li, Yongfeng. “Nonlinear oscillation and control in the BZ chemical reaction.” 2008. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/26565.

MLA Handbook (7^{th} Edition):

Li, Yongfeng. “Nonlinear oscillation and control in the BZ chemical reaction.” 2008. Web. 19 Nov 2019.

Vancouver:

Li Y. Nonlinear oscillation and control in the BZ chemical reaction. [Internet] [Doctoral dissertation]. Georgia Tech; 2008. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/26565.

Council of Science Editors:

Li Y. Nonlinear oscillation and control in the BZ chemical reaction. [Doctoral Dissertation]. Georgia Tech; 2008. Available from: http://hdl.handle.net/1853/26565

Georgia Tech

13. Chen, Jian. Bifurcations, Normal Forms and their Applications.

Degree: PhD, Mathematics, 2005, Georgia Tech

URL: http://hdl.handle.net/1853/7121

► The first part is a study of an ecological model with one herbivore and N plants. The system has a new type of functional response…
(more)

Subjects/Keywords: Functional response; Normal form; Bifurcation

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

APA (6^{th} Edition):

Chen, J. (2005). Bifurcations, Normal Forms and their Applications. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/7121

Chicago Manual of Style (16^{th} Edition):

Chen, Jian. “Bifurcations, Normal Forms and their Applications.” 2005. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/7121.

MLA Handbook (7^{th} Edition):

Chen, Jian. “Bifurcations, Normal Forms and their Applications.” 2005. Web. 19 Nov 2019.

Vancouver:

Chen J. Bifurcations, Normal Forms and their Applications. [Internet] [Doctoral dissertation]. Georgia Tech; 2005. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/7121.

Council of Science Editors:

Chen J. Bifurcations, Normal Forms and their Applications. [Doctoral Dissertation]. Georgia Tech; 2005. Available from: http://hdl.handle.net/1853/7121

Georgia Tech

14. Pugliese, Alessandro. Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices.

Degree: PhD, Mathematics, 2008, Georgia Tech

URL: http://hdl.handle.net/1853/24730

► In this thesis, we consider real matrix functions that depend on two parameters and study the problem of how to detect and approximate parameters' values…
(more)

Subjects/Keywords: Periodicity; Matrix function; Eigenvalues; Conical intersection; Singular values; Eigenvalues; Matrices; Decomposition (Mathematics); Algorithms; Eigenvectors; Differential operators

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

APA (6^{th} Edition):

Pugliese, A. (2008). Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/24730

Chicago Manual of Style (16^{th} Edition):

Pugliese, Alessandro. “Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices.” 2008. Doctoral Dissertation, Georgia Tech. Accessed November 19, 2019. http://hdl.handle.net/1853/24730.

MLA Handbook (7^{th} Edition):

Pugliese, Alessandro. “Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices.” 2008. Web. 19 Nov 2019.

Vancouver:

Pugliese A. Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices. [Internet] [Doctoral dissertation]. Georgia Tech; 2008. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/1853/24730.

Council of Science Editors:

Pugliese A. Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices. [Doctoral Dissertation]. Georgia Tech; 2008. Available from: http://hdl.handle.net/1853/24730