subject:(Laplacian)

Rice University

1. Buras, Eric. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.

Degree: MA, Engineering, 2016, Rice University

URL: http://hdl.handle.net/1911/96624

► The Laplacian matrix, L, of a graph, G, contains degree and edge information of a given network. Solving a Laplacian linear system Lx = b… (more)

Subjects/Keywords: Laplacian; Multigrid

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APA (6^th Edition):

Buras, E. (2016). A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/96624

Chicago Manual of Style (16^th Edition):

Buras, Eric. “A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.” 2016. Masters Thesis, Rice University. Accessed January 19, 2020. http://hdl.handle.net/1911/96624.

MLA Handbook (7^th Edition):

Buras, Eric. “A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs.” 2016. Web. 19 Jan 2020.

Vancouver:

Buras E. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. [Internet] [Masters thesis]. Rice University; 2016. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1911/96624.

Council of Science Editors:

Buras E. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. [Masters Thesis]. Rice University; 2016. Available from: http://hdl.handle.net/1911/96624

2. Kiral, Eren Mehmet. Spectral Theory and Shifted Convolution Sums in Analytic Number Theory.

Degree: PhD, Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386223/

► The spectrum of the hyperbolic Laplacian decomposes the space of square integrable functions on the hyperbolic plane invariant under a discrete subgroup of isometries. We… (more)

Subjects/Keywords: Hyperbolic Laplacian

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APA (6^th Edition):

Kiral, E. M. (2014). Spectral Theory and Shifted Convolution Sums in Analytic Number Theory. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386223/

Chicago Manual of Style (16^th Edition):

Kiral, Eren Mehmet. “Spectral Theory and Shifted Convolution Sums in Analytic Number Theory.” 2014. Doctoral Dissertation, Brown University. Accessed January 19, 2020. https://repository.library.brown.edu/studio/item/bdr:386223/.

MLA Handbook (7^th Edition):

Kiral, Eren Mehmet. “Spectral Theory and Shifted Convolution Sums in Analytic Number Theory.” 2014. Web. 19 Jan 2020.

Vancouver:

Kiral EM. Spectral Theory and Shifted Convolution Sums in Analytic Number Theory. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2020 Jan 19]. Available from: https://repository.library.brown.edu/studio/item/bdr:386223/.

Council of Science Editors:

Kiral EM. Spectral Theory and Shifted Convolution Sums in Analytic Number Theory. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386223/

3. Kahatapiti Kankanamalage Kissani Ridma, Perera. A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究.

Degree: 博士（機能数理学）, 2013, Kyushu University / 九州大学

URL: http://hdl.handle.net/2324/21705 ; http://dx.doi.org/10.15017/21705

► In the last decade important relationships between Laplacian eigenvalues and the eigenvectors of graphs and several other graph parameters were discovered. Spectral clustering uses eigenvalues… (more)

▼ In the last decade important relationships between Laplacian eigenvalues and the eigenvectors of graphs and several other graph parameters were discovered. Spectral clustering uses eigenvalues and eigenvectors of matrices associated with graphs to find clusters in the graphs and is widely used to analysis the social networks, web graphs, communication networks etc. In this thesis, we present some of the results and discuss their consequences in spectral clustering and graph energy. We mainly consider normalized Laplacian matrix to find the bipartitions of graphs. There is a close relationship between the second smallest eigenvalue of normalized Laplacian matrix and the normalized cut introduced by Shi and Malik. We compare these two clustering methods and discuss their performances. Several authors considered the applications of normalized cut for graph partitioning and less attention is paid for theoretical explanation of this measure compare with isoperimetric and Cheeger constant. Here we use the notation Mcut(G) to represent the minimum normalized cut and derive formula for Mcut(G) of some basic classes of graphs such as paths, cycles, complete graphs, double trees and cycle cross paths and some complex graphs such as lollipop type graphs LP_n_,_m and LP'_n_,_2, roach type graphs R_n_,_k, weighted paths P_n_,_k and double tree cross paths. Next we discuss three matrices associated with graphs called difference Laplacian matrix, normalized Laplacian matrix and signless Laplacian matrix and review some known results. Specially we discuss the boundary values of the second smallest eigenvalue of the difference and normalized Laplacian matrices using isoperimetric number and Cheeger constant. Next we address the problem of finding graphs which perform poorly on spectral methods. We use the term Lcut(G) to represent the minimum normalized cut of partitions produced by the second eigenvector of normalized Laplacian matrix. We give counter examples of graphs and conditions, where Mcut(G) and Lcut(G) produce different clusters on graphs. Next we address the problem of finding directed graphs with minimum Laplacian energy. First, we define Laplacian energy of a directed graph as the sum of squares of eigenvalues of a Laplacian matrix. Then we derive a formula for Laplacian energy of a simple directed graph using outdegrees of vertices. This motivates us to consider the problem of minimizing sum of squares of degrees in order to find the graphs with minimum Laplacian energy. Finally, we demonstrate the experimental results about spectral clustering on directed graphs. We extend the undirected spectral clustering algorithms to directed graphs using directed Laplacian matrix. Further we propose an algorithm based on merging techniques. Advisors/Committee Members: 溝口, 佳寛.

Subjects/Keywords: Laplacian; graph partitioning

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APA (6^th Edition):

Kahatapiti Kankanamalage Kissani Ridma, P. (2013). A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究. (Thesis). Kyushu University / 九州大学. Retrieved from http://hdl.handle.net/2324/21705 ; http://dx.doi.org/10.15017/21705

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kahatapiti Kankanamalage Kissani Ridma, Perera. “A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究.” 2013. Thesis, Kyushu University / 九州大学. Accessed January 19, 2020. http://hdl.handle.net/2324/21705 ; http://dx.doi.org/10.15017/21705.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kahatapiti Kankanamalage Kissani Ridma, Perera. “A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究.” 2013. Web. 19 Jan 2020.

Vancouver:

Kahatapiti Kankanamalage Kissani Ridma P. A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究. [Internet] [Thesis]. Kyushu University / 九州大学; 2013. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/2324/21705 ; http://dx.doi.org/10.15017/21705.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kahatapiti Kankanamalage Kissani Ridma P. A study on normalized Laplacian, normalized cut and graph partitioning : ラプラシアン行列と標準カットに基づくグラフ分割に関する研究. [Thesis]. Kyushu University / 九州大学; 2013. Available from: http://hdl.handle.net/2324/21705 ; http://dx.doi.org/10.15017/21705

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oklahoma

4. Qu, Hong. COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS.

Degree: PhD, 2014, University of Oklahoma

URL: http://hdl.handle.net/11244/13880

► From a geometric point of view, we use coordinates as the main tool to define the holomorphic gradient, the antiholomorphic gradient, and the complex gradient… (more)

Subjects/Keywords: Mathematics.; Holomorphic Gradient, Antiholomorphic Gradient, Complex Gradient.; Holomorphic Laplacian, Antiholomorphic Laplacian, Complex Laplacian.; Holomorphic p-Laplacian, Antiholomorphic p-Laplacian, Complex p-Laplacian.; Kahler Manifold.

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APA (6^th Edition):

Qu, H. (2014). COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS. (Doctoral Dissertation). University of Oklahoma. Retrieved from http://hdl.handle.net/11244/13880

Chicago Manual of Style (16^th Edition):

Qu, Hong. “COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS.” 2014. Doctoral Dissertation, University of Oklahoma. Accessed January 19, 2020. http://hdl.handle.net/11244/13880.

MLA Handbook (7^th Edition):

Qu, Hong. “COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS.” 2014. Web. 19 Jan 2020.

Vancouver:

Qu H. COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2014. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/11244/13880.

Council of Science Editors:

Qu H. COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS. [Doctoral Dissertation]. University of Oklahoma; 2014. Available from: http://hdl.handle.net/11244/13880

Texas A&M University

5. Garg, Deepak. Smoothing Wavelet Reconstruction.

Degree: 2013, Texas A&M University

URL: http://hdl.handle.net/1969.1/149509

► This thesis present a new algorithm for creating high quality surfaces from large data sets of oriented points, sampled using a laser range scanner. This… (more)

Subjects/Keywords: Surface reconstruction; Graphics; Wavelets; Laplacian

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APA (6^th Edition):

Garg, D. (2013). Smoothing Wavelet Reconstruction. (Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/149509

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Garg, Deepak. “Smoothing Wavelet Reconstruction.” 2013. Thesis, Texas A&M University. Accessed January 19, 2020. http://hdl.handle.net/1969.1/149509.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Garg, Deepak. “Smoothing Wavelet Reconstruction.” 2013. Web. 19 Jan 2020.

Vancouver:

Garg D. Smoothing Wavelet Reconstruction. [Internet] [Thesis]. Texas A&M University; 2013. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1969.1/149509.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Garg D. Smoothing Wavelet Reconstruction. [Thesis]. Texas A&M University; 2013. Available from: http://hdl.handle.net/1969.1/149509

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

NSYSU

6. Wang, Wei-Chuan. Direct and inverse problems for one-dimensional p-Laplacian operators.

Degree: PhD, Applied Mathematics, 2010, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414

► In this thesis, direct and inverse problems concerning nodal solutions associated with the one-dimensional p-Laplacian operators are studied. We first consider the eigenvalue problem on… (more)

Subjects/Keywords: p-Laplacian; inverse problems

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APA (6^th Edition):

Wang, W. (2010). Direct and inverse problems for one-dimensional p-Laplacian operators. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414

Chicago Manual of Style (16^th Edition):

Wang, Wei-Chuan. “Direct and inverse problems for one-dimensional p-Laplacian operators.” 2010. Doctoral Dissertation, NSYSU. Accessed January 19, 2020. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414.

MLA Handbook (7^th Edition):

Wang, Wei-Chuan. “Direct and inverse problems for one-dimensional p-Laplacian operators.” 2010. Web. 19 Jan 2020.

Vancouver:

Wang W. Direct and inverse problems for one-dimensional p-Laplacian operators. [Internet] [Doctoral dissertation]. NSYSU; 2010. [cited 2020 Jan 19]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414.

Council of Science Editors:

Wang W. Direct and inverse problems for one-dimensional p-Laplacian operators. [Doctoral Dissertation]. NSYSU; 2010. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414

Oregon State University

7. Kiser, Terry. Fractional powers of the Laplacian with application to small amplitude water waves.

Degree: PhD, in Mathematics, 1983, Oregon State University

URL: http://hdl.handle.net/1957/17417

See pdf Advisors/Committee Members: Bodvarsson, Gunnar (advisor).

Subjects/Keywords: Laplacian operator

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APA (6^th Edition):

Kiser, T. (1983). Fractional powers of the Laplacian with application to small amplitude water waves. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/17417

Chicago Manual of Style (16^th Edition):

Kiser, Terry. “Fractional powers of the Laplacian with application to small amplitude water waves.” 1983. Doctoral Dissertation, Oregon State University. Accessed January 19, 2020. http://hdl.handle.net/1957/17417.

MLA Handbook (7^th Edition):

Kiser, Terry. “Fractional powers of the Laplacian with application to small amplitude water waves.” 1983. Web. 19 Jan 2020.

Vancouver:

Kiser T. Fractional powers of the Laplacian with application to small amplitude water waves. [Internet] [Doctoral dissertation]. Oregon State University; 1983. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1957/17417.

Council of Science Editors:

Kiser T. Fractional powers of the Laplacian with application to small amplitude water waves. [Doctoral Dissertation]. Oregon State University; 1983. Available from: http://hdl.handle.net/1957/17417

Kansas State University

8. Alshammari, Bandar Saad. A nonlocal Laplacian in one dimension.

Degree: MS, Department of Mathematics, 2019, Kansas State University

URL: http://hdl.handle.net/2097/40245

► An overview on nonlocal Laplace operators acting on real-valued one-dimensional functions is presented. We provide a definition for nonlocal Laplace operators and present some basic… (more)

Subjects/Keywords: nonlocal Laplacian; Fourier multipliers.

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APA (6^th Edition):

Alshammari, B. S. (2019). A nonlocal Laplacian in one dimension. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/40245

Chicago Manual of Style (16^th Edition):

Alshammari, Bandar Saad. “A nonlocal Laplacian in one dimension.” 2019. Masters Thesis, Kansas State University. Accessed January 19, 2020. http://hdl.handle.net/2097/40245.

MLA Handbook (7^th Edition):

Alshammari, Bandar Saad. “A nonlocal Laplacian in one dimension.” 2019. Web. 19 Jan 2020.

Vancouver:

Alshammari BS. A nonlocal Laplacian in one dimension. [Internet] [Masters thesis]. Kansas State University; 2019. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/2097/40245.

Council of Science Editors:

Alshammari BS. A nonlocal Laplacian in one dimension. [Masters Thesis]. Kansas State University; 2019. Available from: http://hdl.handle.net/2097/40245

Cornell University

9. Kara, Yasemin. The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms .

Degree: 2015, Cornell University

URL: http://hdl.handle.net/1813/41048

► This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane… (more)

Subjects/Keywords: Laplacian; Rieamann surfaces; Maass forms

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APA (6^th Edition):

Kara, Y. (2015). The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/41048

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kara, Yasemin. “The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms .” 2015. Thesis, Cornell University. Accessed January 19, 2020. http://hdl.handle.net/1813/41048.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kara, Yasemin. “The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms .” 2015. Web. 19 Jan 2020.

Vancouver:

Kara Y. The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms . [Internet] [Thesis]. Cornell University; 2015. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1813/41048.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kara Y. The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms . [Thesis]. Cornell University; 2015. Available from: http://hdl.handle.net/1813/41048

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Louisville

10. Osborne, Christopher Hayward. An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials.

Degree: M. Eng., 2013, University of Louisville

URL: 10.18297/etd/1084 ; https://ir.library.louisville.edu/etd/1084

► The work outlined in this thesis expanded on previous work to improve a thin-film microfabricated electrode array intended for cardiac electrophysiology studies. A thin layer… (more)

Subjects/Keywords: Bio MEMS; MEMS; Microelectrodes; Cardiac; Surface laplacian

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APA (6^th Edition):

Osborne, C. H. (2013). An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials. (Masters Thesis). University of Louisville. Retrieved from 10.18297/etd/1084 ; https://ir.library.louisville.edu/etd/1084

Chicago Manual of Style (16^th Edition):

Osborne, Christopher Hayward. “An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials.” 2013. Masters Thesis, University of Louisville. Accessed January 19, 2020. 10.18297/etd/1084 ; https://ir.library.louisville.edu/etd/1084.

MLA Handbook (7^th Edition):

Osborne, Christopher Hayward. “An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials.” 2013. Web. 19 Jan 2020.

Vancouver:

Osborne CH. An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials. [Internet] [Masters thesis]. University of Louisville; 2013. [cited 2020 Jan 19]. Available from: 10.18297/etd/1084 ; https://ir.library.louisville.edu/etd/1084.

Council of Science Editors:

Osborne CH. An improved thin-film microelectrode array and signal conditioning board for measuring cardiac surface potentials. [Masters Thesis]. University of Louisville; 2013. Available from: 10.18297/etd/1084 ; https://ir.library.louisville.edu/etd/1084

11. Anoop, T V. On weighted eigenvalue problems and applications; -.

Degree: Mathematical Science, 2011, INFLIBNET

URL: http://shodhganga.inflibnet.ac.in/handle/10603/4696

►

The main objective of this thesis is to _nd a large class of weight functions that admits a positive principal eigenvalue for the weighted eigenvalue… (more)

▼

The main objective of this thesis is to _nd a large class of weight functions that admits a positive principal eigenvalue for the weighted eigenvalue problems for the Laplacian and the p-Laplacian. More speci_cally, for a connected domain in RN with N _ 2; we study su_cient conditions for a function g 2 L1 loc() to admit a pair (_; u); with _ 2 R+ and u gt 0 a.e. such that u is a weak solution of the following problem: _ _pu = _gjujp_2u; in ; (1) where 1 lt p lt N and _pu := div(jrujp_2ru) is the p-Laplace operator. Such a _; if exists, is called a principal eigenvalue of (1). In the literature, most of the su_cient conditions for the existence of a positive principal eigenvalue demand that the weight function g or its positive part g+ to be in L p (): However, in the _eld of applications one may need to consider weights that are not belonging to any of the Lebesgue spaces. We look for a weak solution of (1) in D1;p 0 (); where newlineD1;p 0 () := completion of C1c ()with respect to kr_kp norm : Now the existence of a positive principal eigenvalue for (1) is closely related with the existence of a minimizer for the functional J(u)= Z jrujp on the level set Mp=nu 2 D1;2 newline0 (): R gjujp=1o: If the map G; G(u) = R g+jujp; is compact, then a direct variational method ensures the existence of a minvii imizer for J on Mp: If g+ is in LN p (), the dual of Lp_ p (); then the map G is compact. This is mainly a consequence of three facts (i) the continuous embedding of D1;p 0 () into Lp_() (ii) the compactness of the embedding of D1;p 0 () into Lp loc() (iii) the density of C1c () in LN p (): The main novelty of our results is that we allow weights that are not in any of the Lebesgue spaces, but only in certain weak Lebesgue spaces. For this we make use of the _nest embedding of D1;p 0 () into the Lorentz space L(p_; p) = (u measurable : Z jj 0 [t1 p_ u_(t)]p dt t lt 1); where u_ denotes the one dimensional decreasing rearrangement of u: The Lorentz space L(p_; p) is a Banach space with a suitable norm and it is a proper subspace.

Bibilography p.155-160

Advisors/Committee Members: Kesavan, S, Ramaswamy, Mythily.

Subjects/Keywords: Laplacian; function spaces; Orlicz spaces; Degree Theory

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APA (6^th Edition):

Anoop, T. V. (2011). On weighted eigenvalue problems and applications; -. (Thesis). INFLIBNET. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/4696

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Anoop, T V. “On weighted eigenvalue problems and applications; -.” 2011. Thesis, INFLIBNET. Accessed January 19, 2020. http://shodhganga.inflibnet.ac.in/handle/10603/4696.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Anoop, T V. “On weighted eigenvalue problems and applications; -.” 2011. Web. 19 Jan 2020.

Vancouver:

Anoop TV. On weighted eigenvalue problems and applications; -. [Internet] [Thesis]. INFLIBNET; 2011. [cited 2020 Jan 19]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/4696.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Anoop TV. On weighted eigenvalue problems and applications; -. [Thesis]. INFLIBNET; 2011. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/4696

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Victoria

12. Bowles, Malcolm. Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow.

Degree: Department of Mathematics and Statistics, 2014, University of Victoria

URL: http://hdl.handle.net/1828/5591

► In this thesis, we study a linear fractional Fokker-Planck equation that models non-local (`fractional') diffusion in the presence of a potential field. The non-locality is… (more)

Subjects/Keywords: splitting; Fractional Laplacian; Wasserstein Gradient Flow

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APA (6^th Edition):

Bowles, M. (2014). Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow. (Masters Thesis). University of Victoria. Retrieved from http://hdl.handle.net/1828/5591

Chicago Manual of Style (16^th Edition):

Bowles, Malcolm. “Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow.” 2014. Masters Thesis, University of Victoria. Accessed January 19, 2020. http://hdl.handle.net/1828/5591.

MLA Handbook (7^th Edition):

Bowles, Malcolm. “Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow.” 2014. Web. 19 Jan 2020.

Vancouver:

Bowles M. Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow. [Internet] [Masters thesis]. University of Victoria; 2014. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1828/5591.

Council of Science Editors:

Bowles M. Weak Solutions to a Fractional Fokker-Planck Equation via Splitting and Wasserstein Gradient Flow. [Masters Thesis]. University of Victoria; 2014. Available from: http://hdl.handle.net/1828/5591

Virginia Tech

13. Lanz, Colleen B. The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances.

Degree: MS, Mathematics, 2010, Virginia Tech

URL: http://hdl.handle.net/10919/33933

► In this thesis, we set out to provide an enhanced set of techniques for determining the eigenvalues of the Laplacian in polygonal domains. Currently, finite-element… (more)

Subjects/Keywords: Laplacian; Eigenvalues; Schwarz-Christoffel Transformations; Polygons

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APA (6^th Edition):

Lanz, C. B. (2010). The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/33933

Chicago Manual of Style (16^th Edition):

Lanz, Colleen B. “The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances.” 2010. Masters Thesis, Virginia Tech. Accessed January 19, 2020. http://hdl.handle.net/10919/33933.

MLA Handbook (7^th Edition):

Lanz, Colleen B. “The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances.” 2010. Web. 19 Jan 2020.

Vancouver:

Lanz CB. The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances. [Internet] [Masters thesis]. Virginia Tech; 2010. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/10919/33933.

Council of Science Editors:

Lanz CB. The Use of Schwarz-Christoffel Transformations in Determining Acoustic Resonances. [Masters Thesis]. Virginia Tech; 2010. Available from: http://hdl.handle.net/10919/33933

Kansas State University

14. Almutairi, Fahad Hamoud. Nonlocal vector calculus.

Degree: MS, Department of Mathematics, 2018, Kansas State University

URL: http://hdl.handle.net/2097/38781

► Nonlocal vector calculus, introduced in generalizes differential operators' calculus to nonlocal calculus of integral operators. Nonlocal vector calculus has been applied to many fields including… (more)

Subjects/Keywords: Nonlocal; Divergence; Gradient; Laplacian; Adjoint; Operator

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APA (6^th Edition):

Almutairi, F. H. (2018). Nonlocal vector calculus. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/38781

Chicago Manual of Style (16^th Edition):

Almutairi, Fahad Hamoud. “Nonlocal vector calculus.” 2018. Masters Thesis, Kansas State University. Accessed January 19, 2020. http://hdl.handle.net/2097/38781.

MLA Handbook (7^th Edition):

Almutairi, Fahad Hamoud. “Nonlocal vector calculus.” 2018. Web. 19 Jan 2020.

Vancouver:

Almutairi FH. Nonlocal vector calculus. [Internet] [Masters thesis]. Kansas State University; 2018. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/2097/38781.

Council of Science Editors:

Almutairi FH. Nonlocal vector calculus. [Masters Thesis]. Kansas State University; 2018. Available from: http://hdl.handle.net/2097/38781

University of Ontario Institute of Technology

15. Falconer, Cory. Image super resolution via non-local normalized graph Laplacian regularization.

Degree: 2019, University of Ontario Institute of Technology

URL: http://hdl.handle.net/10155/1040

► Given we live in a digital age where images are regularly being viewed, posted, or utilized, spectators of such images on occasion could prefer a… (more)

Subjects/Keywords: Super resolution; Regularization; Image restoration; Graph Laplacian

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APA (6^th Edition):

Falconer, C. (2019). Image super resolution via non-local normalized graph Laplacian regularization. (Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/1040

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Falconer, Cory. “Image super resolution via non-local normalized graph Laplacian regularization.” 2019. Thesis, University of Ontario Institute of Technology. Accessed January 19, 2020. http://hdl.handle.net/10155/1040.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Falconer, Cory. “Image super resolution via non-local normalized graph Laplacian regularization.” 2019. Web. 19 Jan 2020.

Vancouver:

Falconer C. Image super resolution via non-local normalized graph Laplacian regularization. [Internet] [Thesis]. University of Ontario Institute of Technology; 2019. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/10155/1040.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Falconer C. Image super resolution via non-local normalized graph Laplacian regularization. [Thesis]. University of Ontario Institute of Technology; 2019. Available from: http://hdl.handle.net/10155/1040

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Sydney

16. Chang, Ting-Ying. On Singular Solutions of Weighted Divergence Operators .

Degree: 2017, University of Sydney

URL: http://hdl.handle.net/2123/16817

► We give a complete classification of the isolated singularities of positive solutions to a broad class of nonlinear elliptic equations involving a weighted p-Laplacian and… (more)

Subjects/Keywords: isolated singularity; regular variation; weighted p-Laplacian

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APA (6^th Edition):

Chang, T. (2017). On Singular Solutions of Weighted Divergence Operators . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/16817

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chang, Ting-Ying. “On Singular Solutions of Weighted Divergence Operators .” 2017. Thesis, University of Sydney. Accessed January 19, 2020. http://hdl.handle.net/2123/16817.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chang, Ting-Ying. “On Singular Solutions of Weighted Divergence Operators .” 2017. Web. 19 Jan 2020.

Vancouver:

Chang T. On Singular Solutions of Weighted Divergence Operators . [Internet] [Thesis]. University of Sydney; 2017. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/2123/16817.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chang T. On Singular Solutions of Weighted Divergence Operators . [Thesis]. University of Sydney; 2017. Available from: http://hdl.handle.net/2123/16817

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Hong Kong University of Science and Technology

17. Huang, Yufa. A lower bound for eigenvalue of Laplace operator on locally symmetric space.

Degree: 2010, Hong Kong University of Science and Technology

URL: http://repository.ust.hk/ir/Record/1783.1-6754 ; https://doi.org/10.14711/thesis-b1106709 ; http://repository.ust.hk/ir/bitstream/1783.1-6754/1/th_redirect.html

► This dissertation is concerned with the lower bound for the first eigenvalue λ1(T) of Laplace operator Δ on a locally symmetric space T G /… (more)

Subjects/Keywords: Eigenvalues ; Laplacian operator

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APA (6^th Edition):

Huang, Y. (2010). A lower bound for eigenvalue of Laplace operator on locally symmetric space. (Thesis). Hong Kong University of Science and Technology. Retrieved from http://repository.ust.hk/ir/Record/1783.1-6754 ; https://doi.org/10.14711/thesis-b1106709 ; http://repository.ust.hk/ir/bitstream/1783.1-6754/1/th_redirect.html

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Huang, Yufa. “A lower bound for eigenvalue of Laplace operator on locally symmetric space.” 2010. Thesis, Hong Kong University of Science and Technology. Accessed January 19, 2020. http://repository.ust.hk/ir/Record/1783.1-6754 ; https://doi.org/10.14711/thesis-b1106709 ; http://repository.ust.hk/ir/bitstream/1783.1-6754/1/th_redirect.html.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Huang, Yufa. “A lower bound for eigenvalue of Laplace operator on locally symmetric space.” 2010. Web. 19 Jan 2020.

Vancouver:

Huang Y. A lower bound for eigenvalue of Laplace operator on locally symmetric space. [Internet] [Thesis]. Hong Kong University of Science and Technology; 2010. [cited 2020 Jan 19]. Available from: http://repository.ust.hk/ir/Record/1783.1-6754 ; https://doi.org/10.14711/thesis-b1106709 ; http://repository.ust.hk/ir/bitstream/1783.1-6754/1/th_redirect.html.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Huang Y. A lower bound for eigenvalue of Laplace operator on locally symmetric space. [Thesis]. Hong Kong University of Science and Technology; 2010. Available from: http://repository.ust.hk/ir/Record/1783.1-6754 ; https://doi.org/10.14711/thesis-b1106709 ; http://repository.ust.hk/ir/bitstream/1783.1-6754/1/th_redirect.html

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Colorado State University

18. Mankovich, Nathan. Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data.

Degree: MS(M.S.), Mathematics, 2020, Colorado State University

URL: http://hdl.handle.net/10217/199775

► Feature selection is an essential step in many data analysis pipelines due to its ability to remove unimportant data. We will describe how to realize… (more)

Subjects/Keywords: Feature Selection; Laplacian; Spectral; Influenza; Centrality; Network

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APA (6^th Edition):

Mankovich, N. (2020). Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/199775

Chicago Manual of Style (16^th Edition):

Mankovich, Nathan. “Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data.” 2020. Masters Thesis, Colorado State University. Accessed January 19, 2020. http://hdl.handle.net/10217/199775.

MLA Handbook (7^th Edition):

Mankovich, Nathan. “Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data.” 2020. Web. 19 Jan 2020.

Vancouver:

Mankovich N. Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data. [Internet] [Masters thesis]. Colorado State University; 2020. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/10217/199775.

Council of Science Editors:

Mankovich N. Methods for Network Generation and Spectral Feature Selection: Especially on Gene Expression Data. [Masters Thesis]. Colorado State University; 2020. Available from: http://hdl.handle.net/10217/199775

19. Kempton, Louis. Distributed control and optimisation of complex networks via their Laplacian spectra.

Degree: PhD, 2018, University of Bristol

URL: http://hdl.handle.net/1983/655bf049-92e3-40d2-bc9b-7d4a75bccdb4

► In complex networked systems, the structure of the underlying communication between individual agents can have profound impacts on the performance and dynamics of the system… (more)

Subjects/Keywords: Distributed optimisation; Graph Laplacian; Complex networks

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APA (6^th Edition):

Kempton, L. (2018). Distributed control and optimisation of complex networks via their Laplacian spectra. (Doctoral Dissertation). University of Bristol. Retrieved from http://hdl.handle.net/1983/655bf049-92e3-40d2-bc9b-7d4a75bccdb4

Chicago Manual of Style (16^th Edition):

Kempton, Louis. “Distributed control and optimisation of complex networks via their Laplacian spectra.” 2018. Doctoral Dissertation, University of Bristol. Accessed January 19, 2020. http://hdl.handle.net/1983/655bf049-92e3-40d2-bc9b-7d4a75bccdb4.

MLA Handbook (7^th Edition):

Kempton, Louis. “Distributed control and optimisation of complex networks via their Laplacian spectra.” 2018. Web. 19 Jan 2020.

Vancouver:

Kempton L. Distributed control and optimisation of complex networks via their Laplacian spectra. [Internet] [Doctoral dissertation]. University of Bristol; 2018. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/1983/655bf049-92e3-40d2-bc9b-7d4a75bccdb4.

Council of Science Editors:

Kempton L. Distributed control and optimisation of complex networks via their Laplacian spectra. [Doctoral Dissertation]. University of Bristol; 2018. Available from: http://hdl.handle.net/1983/655bf049-92e3-40d2-bc9b-7d4a75bccdb4

University of Colorado

20. Taylor, Kye Malcolm. The Geometry of Signal and Image Patch-Sets.

Degree: PhD, Applied Mathematics, 2011, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/22

► In this thesis, we study the representation of local, or fine scale, snippets – or patches – that are extracted from a signal or… (more)

▼ In this thesis, we study the representation of local, or fine scale, snippets – or patches – that are extracted from a signal or image. We describe a method that characterizes the dimensionality that is observed in the set of patches when they are regarded as points in Euclidean space. Our approach is based on the assumption that the signal or image is composed of solutions to ordinary differential equations of a certain class. We also provide a theoretical interpretation – via graph models – that explains the success of analyzing signal and image patches using diffusion-based graph metrics. Our framework is built on the assumption that there exists a partition of the signal or image's patches. Specifically, we assume there are two subsets of patches. One set comprises patches that are connected through some type of coherence in the domain of the signal, such as temporal coherence in time series, or spatial coherence between patches in the image plane. The other set comprises patches whose edge connections are not so largely influenced by the aforementioned coherence. Instead, these connections are more sporadic, with little relationship between the locations in the signal or image domain from which the patches were extracted. Using the commute time metric – a diffusion-based graph metric – we prove that the average proximity between patches in the first set grows faster than the average proximity between patches in the second set, as the number of patches approaches infinity. Consequently, a parametrization of the patches based on commute times will relatively cluster the second set of patches, which is the first step toward solving a larger problem, such as classification or clustering of the patches, detection of anomalies, or segmentation of an image. In addition to our theoretical results, this thesis also evaluates numerical procedures designed to efficiently compute the spectral decomposition of large matrices. These procedures include the Nystrom extension, and a multilevel eigensolver. Finally, we benchmark a classifier that is trained on the commute time embedding of a dataset of seismic events, against a standard algorithm used to detect arrival-times. Advisors/Committee Members: Francois G. Meyer, James H. Curry, Juan G. Restrepo.

Subjects/Keywords: commute time; diffusion maps; graph Laplacian; image patch; Laplacian eigenmaps; Applied Mathematics

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APA (6^th Edition):

Taylor, K. M. (2011). The Geometry of Signal and Image Patch-Sets. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/22

Chicago Manual of Style (16^th Edition):

Taylor, Kye Malcolm. “The Geometry of Signal and Image Patch-Sets.” 2011. Doctoral Dissertation, University of Colorado. Accessed January 19, 2020. https://scholar.colorado.edu/appm_gradetds/22.

MLA Handbook (7^th Edition):

Taylor, Kye Malcolm. “The Geometry of Signal and Image Patch-Sets.” 2011. Web. 19 Jan 2020.

Vancouver:

Taylor KM. The Geometry of Signal and Image Patch-Sets. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2020 Jan 19]. Available from: https://scholar.colorado.edu/appm_gradetds/22.

Council of Science Editors:

Taylor KM. The Geometry of Signal and Image Patch-Sets. [Doctoral Dissertation]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/appm_gradetds/22

University of North Texas

21. Pudipeddi, Sridevi. Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN.

Degree: 2008, University of North Texas

URL: https://digital.library.unt.edu/ark:/67531/metadc6059/

► We establish the existence of radial solutions to the p-Laplacian equation ∆p u + f(u)=0 in RN, where f behaves like |u|q-1 u when u… (more)

Subjects/Keywords: Radial solutions; p-Laplacian; Laplacian; superlinear equations; eng; Laplacian operator.; Differential equations.

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APA (6^th Edition):

Pudipeddi, S. (2008). Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN. (Thesis). University of North Texas. Retrieved from https://digital.library.unt.edu/ark:/67531/metadc6059/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pudipeddi, Sridevi. “Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN.” 2008. Thesis, University of North Texas. Accessed January 19, 2020. https://digital.library.unt.edu/ark:/67531/metadc6059/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pudipeddi, Sridevi. “Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN.” 2008. Web. 19 Jan 2020.

Vancouver:

Pudipeddi S. Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN. [Internet] [Thesis]. University of North Texas; 2008. [cited 2020 Jan 19]. Available from: https://digital.library.unt.edu/ark:/67531/metadc6059/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pudipeddi S. Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN. [Thesis]. University of North Texas; 2008. Available from: https://digital.library.unt.edu/ark:/67531/metadc6059/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of South Carolina

22. Peng, Xing. Fractional Chromatic Numbers and Spectra of Graphs.

Degree: PhD, Mathematics, 2012, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/1610

► This dissertation mainly comes from my recent study of fractional chromatic numbers of graphs, spectra of edge-independent random graphs, Laplacian spectra of hypergraphs, and… (more)

▼ This dissertation mainly comes from my recent study of fractional chromatic numbers of graphs, spectra of edge-independent random graphs, Laplacian spectra of hypergraphs, and loose Laplacian spectra of random hypergraphs. For a graph G, let χ_f(G) be the fractional chromatic number of G. Based on the study of independence numbers of triangle-free graphs with maximum degree at most three, Heckman and Thomas conjectured that χ_f(G) ≤ 3-\frac{1}{5} if G is triangle-free and has maximum degree at most three. Since the fractional chromatic number of the generalized Peterson graph P(7,2) is 3-\frac{1}{5}, the conjecture is tight if it is true. The first result on this conjecture is due to Hatami and Zhu who proved χ_f(G) ≤ 3-\frac{3}{64}. We prove χ_f(G) ≤ 3-\frac{3}{43}. We also consider the following general question. What is the fractional chromatic number of a K_Δ-free graph with maximum degree Δ for Δ ≥ 3? Heckman and Thomas' conjecture is a special case of this question for Δ=3. We are able to prove that except for two graphs, the fractional chromatic number of each K_Δ-free graph with maximum degree Δ is at most Δ-\frac{2}{67}. There are a lot of literature addressing the spectra of random graphs. Recently, a new random graph model (edge-independent random graphs) attracted more and more attention. Let A(G) and L(G) be the adjacency matrix and the Laplacian matrix of an edge-independent graph G. Oliveira and Chung-Radcliffe showed eigenvalues of A(G) (and L(G)) can be approximated by those of the ``expectation'' of A (and the ``expectation'' of L) with some error term involving the maximum expected degree (and the minimum expected degree) and the number of vertices. We improve previous results by removing the √{\ln n}-factor from the error terms with a slightly stronger condition. Laplacians of graphs are studied extensively in the literature. There are some attempts to investigate the Laplacian matrices of hypergraphs. For an r-uniform hypergraph H, we will define the s-th Laplacian matrix L^(s)(H) for each 1 ≤ s ≤ r-1; we will also show some applications of Laplacians of hypergraphs. A natural question is: what are the Laplacian eigenvalues of a random hypergraph? Let H^r(n,p) be a random hypergraph. For each 1 ≤ s ≤ r/2, we prove that the eigenvalues of the s-th Laplacian L^(s)(H^r(n,p)) can be approximated by those of the complete hypergraph. Moreover, we show the distribution of eigenvalues of L^(s)(H^r(n,p)) satisfies the Semicircle Law for 1 ≤ s ≤ r/2. Advisors/Committee Members: Lu, Linyuan.

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; chromatic number; edge-independent random graph; fractional chromatic number; Generalized Laplacian matrix; Laplacian matrix

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

APA (6^th Edition):

Peng, X. (2012). Fractional Chromatic Numbers and Spectra of Graphs. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/1610

Chicago Manual of Style (16^th Edition):

Peng, Xing. “Fractional Chromatic Numbers and Spectra of Graphs.” 2012. Doctoral Dissertation, University of South Carolina. Accessed January 19, 2020. https://scholarcommons.sc.edu/etd/1610.

MLA Handbook (7^th Edition):

Peng, Xing. “Fractional Chromatic Numbers and Spectra of Graphs.” 2012. Web. 19 Jan 2020.

Vancouver:

Peng X. Fractional Chromatic Numbers and Spectra of Graphs. [Internet] [Doctoral dissertation]. University of South Carolina; 2012. [cited 2020 Jan 19]. Available from: https://scholarcommons.sc.edu/etd/1610.

Council of Science Editors:

Peng X. Fractional Chromatic Numbers and Spectra of Graphs. [Doctoral Dissertation]. University of South Carolina; 2012. Available from: https://scholarcommons.sc.edu/etd/1610

23. Hassannezhad, Asma. Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds.

Degree: Docteur es, Mathématiques, 2012, Université François-Rabelais de Tours

URL: http://www.theses.fr/2012TOUR4036

►

Le but de cette thèse est de trouver des bornes supérieures pour les valeurs propres des opérateurs naturels agissant sur les fonctions d’une variété compacte… (more)

▼

Le but de cette thèse est de trouver des bornes supérieures pour les valeurs propres des opérateurs naturels agissant sur les fonctions d’une variété compacte (M; g). Nous étudions l’opérateur de Laplace–Beltrami et des opérateurs du type laplacien. Dans le cas du laplacien, deux aspects sont étudiés. Le premier aspect est d’étudier des relations entre la géométrie intrinsèque et les valeurs propres du laplacien. Nous obtenons des bornes supérieures ne dépendant que de la dimension et d’un invariant conforme qui s’appelle le volume conforme minimal. Asymptotiquement, ces bornes sont consistantes avec la loi de Weyl. Elles améliorent également les résultats de Korevaar et de Yang et Yau. La méthode employée est intéressante en soi. Le deuxième aspect est d’étudier la relation entre la géométrie extrinsèque et les valeurs propres du laplacien agissant sur des sous-variétés compactes de RN et de CPN. Nous étudions un invariant extrinsèque qui s’appele l’indice d’intersection. Pour des sous-variétés compactes de RN, nous généralisons les résultats de Colbois, Dryden et El Soufi et obtenons des bornes supérieures qui sont stables par des petites perturbations. Pour des sous-variétés de CPN, nous obtenons une borne supérieure ne dépendant que du degré des sous-variétés. Pour des opérateur du type laplacien, une modification de notre méthode donne des bornes supérieures pour les valeurs propres des opérateurs de Schrödinger en termes du volume conforme minimal et de l’intégrale du potentiel. Nous obtenons également les bornes supérieures pour les valeurs propres du laplacien de Bakry–Émery dépendant d’invariants conformes.

The purpose of this thesis is to find upper bounds for the eigenvalues of natural operators acting on functions on a compact Riemannian manifold (M; g) such as the Laplace–Beltrami operator and Laplace-type operators. In the case of the Laplace-Beltrami operator, two aspects are investigated: The first aspect is to study relationships between the intrinsic geometry and eigenvalues of the Laplacian operator. In this regard, we obtain upper bounds depending only on the dimension and a conformal invariant called min-conformal volume. Asymptotically, these bounds are consistent with the Weyl law. They improve previous results by Korevaar and Yang and Yau. The method which is introduced to obtain the results, is powerful and interesting in itself. The second aspect is to study the interplay of the extrinsic geometry and eigenvalues of the Laplace–Beltrami operator acting on compact submanifolds of RN and of CPN. We investigate an extrinsic invariant called the intersection index studied by Colbois, Dryden and El Soufi. For compact submanifolds of RN, we extend their results and obtain upper bounds which are stable under small perturbation. For compact submanifolds of CPN, we obtain an upper bound depending only on the degree of submanifolds. For Laplace type operators, a modification of our method lead to have upper bounds for the eigenvalues of Schrödinger operators in terms of the min-conformal volume and…

Advisors/Committee Members: El Soufi, Ahmad (thesis director), Colbois, Bruno (thesis director), Ranjbar-Motlagh, Alireza (thesis director).

Subjects/Keywords: Laplacien; Opérateur de Schrödinger; Laplacien de Barky-Émery; Valeur propre; Borne suppérieure; Laplacian; Schrödinger operator; Bakry–Émery Laplacian; Eigenvalue; Upper bound

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

APA (6^th Edition):

Hassannezhad, A. (2012). Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds. (Doctoral Dissertation). Université François-Rabelais de Tours. Retrieved from http://www.theses.fr/2012TOUR4036

Chicago Manual of Style (16^th Edition):

Hassannezhad, Asma. “Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds.” 2012. Doctoral Dissertation, Université François-Rabelais de Tours. Accessed January 19, 2020. http://www.theses.fr/2012TOUR4036.

MLA Handbook (7^th Edition):

Hassannezhad, Asma. “Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds.” 2012. Web. 19 Jan 2020.

Vancouver:

Hassannezhad A. Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds. [Internet] [Doctoral dissertation]. Université François-Rabelais de Tours; 2012. [cited 2020 Jan 19]. Available from: http://www.theses.fr/2012TOUR4036.

Council of Science Editors:

Hassannezhad A. Bornes supérieures pour les valeurs propres d'opérateurs naturels sur les variétés riemanniennes compactes : Upper bounds for the eigenvalues of natural operators on compact Riemannian manifolds. [Doctoral Dissertation]. Université François-Rabelais de Tours; 2012. Available from: http://www.theses.fr/2012TOUR4036

Iowa State University

24. Hwang, Sukjung. Holder regularity of solutions of generalized p-Laplacian type parabolic equations.

Degree: 2012, Iowa State University

URL: https://lib.dr.iastate.edu/etd/12667

► Using ideas from the theory of Orlicz spaces, we discuss the Holder regularity of a bounded weak solution of a p-Laplacian type parabolic partial differential… (more)

Subjects/Keywords: generalized Laplacian equation; Holder regularity; Laplacian equation; Orlicz space; Parabolic equation; Partial differential equation; Applied Mathematics

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APA (6^th Edition):

Hwang, S. (2012). Holder regularity of solutions of generalized p-Laplacian type parabolic equations. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/12667

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hwang, Sukjung. “Holder regularity of solutions of generalized p-Laplacian type parabolic equations.” 2012. Thesis, Iowa State University. Accessed January 19, 2020. https://lib.dr.iastate.edu/etd/12667.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hwang, Sukjung. “Holder regularity of solutions of generalized p-Laplacian type parabolic equations.” 2012. Web. 19 Jan 2020.

Vancouver:

Hwang S. Holder regularity of solutions of generalized p-Laplacian type parabolic equations. [Internet] [Thesis]. Iowa State University; 2012. [cited 2020 Jan 19]. Available from: https://lib.dr.iastate.edu/etd/12667.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hwang S. Holder regularity of solutions of generalized p-Laplacian type parabolic equations. [Thesis]. Iowa State University; 2012. Available from: https://lib.dr.iastate.edu/etd/12667

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Loughborough University

25. Bironneau, Michael. Computational aspects of spectral invariants.

Degree: PhD, 2014, Loughborough University

URL: https://dspace.lboro.ac.uk/2134/15742 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.617948

► The spectral theory of the Laplace operator has long been studied in connection with physics. It appears in the wave equation, the heat equation, Schroedinger's… (more)

▼ The spectral theory of the Laplace operator has long been studied in connection with physics. It appears in the wave equation, the heat equation, Schroedinger's equation and in the expression of quantum effects such as the Casimir force. The Casimir effect can be studied in terms of spectral invariants computed entirely from the spectrum of the Laplace operator. It is these spectral invariants and their computation that are the object of study in the present work. The objective of this thesis is to present a computational framework for the spectral zeta function ζ(s) and its derivative on a Euclidean domain in ℝ², with rigorous theoretical error bounds when this domain is polygonal. To obtain error bounds that remain practical in applications an improvement to existing heat trace estimates is necessary. Our main result is an original estimate and proof of a heat trace estimate for polygons that improves the one of van den Berg and Srisatkunarajah, using finite propagation speed of the corresponding wave kernel. We then use this heat trace estimate to obtain a rigorous error bound for ζ(s) computations. We will provide numerous examples of our computational framework being used to calculate ζ(s) for a variety of situations involving a polygonal domain, including examples involving cutouts and extrusions that are interesting in applications. Our second result is the development a new eigenvalue solver for a planar polygonal domain using a partition of unity decomposition technique. Its advantages include multiple precision and ease of use, as well as reduced complexity compared to Finite Elemement Method. While we hoped that it would be able to contend with existing packages in terms of speed, our implementation was many times slower than MPSPack when dealing with the same problem (obtaining the first 5 digits of the principal eigenvalue of the regular unit hexagon). Finally, we present a collection of numerical examples where we compute the spectral determinant and Casimir energy of various polygonal domains. We also use our numerical tools to investigate extremal properties of these spectral invariants. For example, we consider a square with a small square cut out of the interior, which is allowed to rotate freely about its center.

Subjects/Keywords: 515; Casimir energi; Spectral determinant; Spectral theory; Laplacian; Heat equation

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APA (6^th Edition):

Bironneau, M. (2014). Computational aspects of spectral invariants. (Doctoral Dissertation). Loughborough University. Retrieved from https://dspace.lboro.ac.uk/2134/15742 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.617948

Chicago Manual of Style (16^th Edition):

Bironneau, Michael. “Computational aspects of spectral invariants.” 2014. Doctoral Dissertation, Loughborough University. Accessed January 19, 2020. https://dspace.lboro.ac.uk/2134/15742 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.617948.

MLA Handbook (7^th Edition):

Bironneau, Michael. “Computational aspects of spectral invariants.” 2014. Web. 19 Jan 2020.

Vancouver:

Bironneau M. Computational aspects of spectral invariants. [Internet] [Doctoral dissertation]. Loughborough University; 2014. [cited 2020 Jan 19]. Available from: https://dspace.lboro.ac.uk/2134/15742 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.617948.

Council of Science Editors:

Bironneau M. Computational aspects of spectral invariants. [Doctoral Dissertation]. Loughborough University; 2014. Available from: https://dspace.lboro.ac.uk/2134/15742 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.617948

University of Hong Kong

26. Cheung, Hok-man. On p-Laplacian equations with deviating arguments.

Degree: M. Phil., 2009, University of Hong Kong

URL: Cheung, H. [張學文]. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4370401 ; http://dx.doi.org/10.5353/th_b4370401 ; http://hdl.handle.net/10722/57556

published_or_final_version

Mathematics

Master

Master of Philosophy

Advisors/Committee Members: Cheung, WS.

Subjects/Keywords: Functional differential equations.; Laplacian operator.

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

APA (6^th Edition):

Cheung, H. (2009). On p-Laplacian equations with deviating arguments. (Masters Thesis). University of Hong Kong. Retrieved from Cheung, H. [張學文]. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4370401 ; http://dx.doi.org/10.5353/th_b4370401 ; http://hdl.handle.net/10722/57556

Chicago Manual of Style (16^th Edition):

Cheung, Hok-man. “On p-Laplacian equations with deviating arguments.” 2009. Masters Thesis, University of Hong Kong. Accessed January 19, 2020. Cheung, H. [張學文]. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4370401 ; http://dx.doi.org/10.5353/th_b4370401 ; http://hdl.handle.net/10722/57556.

MLA Handbook (7^th Edition):

Cheung, Hok-man. “On p-Laplacian equations with deviating arguments.” 2009. Web. 19 Jan 2020.

Vancouver:

Cheung H. On p-Laplacian equations with deviating arguments. [Internet] [Masters thesis]. University of Hong Kong; 2009. [cited 2020 Jan 19]. Available from: Cheung, H. [張學文]. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4370401 ; http://dx.doi.org/10.5353/th_b4370401 ; http://hdl.handle.net/10722/57556.

Council of Science Editors:

Cheung H. On p-Laplacian equations with deviating arguments. [Masters Thesis]. University of Hong Kong; 2009. Available from: Cheung, H. [張學文]. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4370401 ; http://dx.doi.org/10.5353/th_b4370401 ; http://hdl.handle.net/10722/57556

Baylor University

27. [No author]. Boundary condition dependence of spectral zeta functions.

Degree: 2015, Baylor University

URL: http://hdl.handle.net/2104/9459

► In this work, we provide the analytic continuation of the spectral zeta function associated with the one-dimensional regular Sturm-Liouville problem and the two-dimensional Laplacian on… (more)

Subjects/Keywords: Spectral zeta function. Sturm-Liouville. Laplacian. WKB. Functional determinant. Heat kernel.

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APA (6^th Edition):

author], [. (2015). Boundary condition dependence of spectral zeta functions. (Thesis). Baylor University. Retrieved from http://hdl.handle.net/2104/9459

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

author], [No. “Boundary condition dependence of spectral zeta functions. ” 2015. Thesis, Baylor University. Accessed January 19, 2020. http://hdl.handle.net/2104/9459.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

author], [No. “Boundary condition dependence of spectral zeta functions. ” 2015. Web. 19 Jan 2020.

Vancouver:

author] [. Boundary condition dependence of spectral zeta functions. [Internet] [Thesis]. Baylor University; 2015. [cited 2020 Jan 19]. Available from: http://hdl.handle.net/2104/9459.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

author] [. Boundary condition dependence of spectral zeta functions. [Thesis]. Baylor University; 2015. Available from: http://hdl.handle.net/2104/9459

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Anna University

28. Kurshid Jinna S. Some studies on data hiding using watermarking for authentication and security;.

Degree: 2013, Anna University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/13418

►

The proposed work addresses authentication by watermarking for security of digital images with no loss and minimum distortion constraints. The proposed algorithms enhance the signal… (more)

▼

The proposed work addresses authentication by watermarking for security of digital images with no loss and minimum distortion constraints. The proposed algorithms enhance the signal quality and embedding capacity. In this context, three new algorithms which embed watermark information in the cover image have been proposed. They can perform tamper detection and authentication as well as information hiding. All the three algorithms are implemented in frequency domain using integer wavelets. The first algorithm embeds data into a cover signal while inherently preserving the statistics of the image to some extent. The method is not reversible but is simple. The algorithm is neighbor correlation method which embeds watermark as bytes directly into the cover image as opposed to the existing bit oriented schemes. The second algorithm makes use of the bit planes of the image to embed the data. Bit plane coding and lossless compression method is used to create space for embedding the watermark data. Suitable headers are augmented to the watermark data for exact reconstruction of the cover image. Arithmetic coding is used for lossless compression. The third algorithm makes use of histogram shifting to embed the watermark data. Data is embedded by shifting the wavelet histograms of the image. The Laplacian distribution of the wavelet histogram is exploited in data hiding. The performances of the above algorithms are tested under the influence of noise. The noise may be unintentional or due to modification of the watermarked image by an unauthorized person. The proposed methods thoroughly analyse the embedding capacity of each algorithm for a given wavelet decomposition of the original image used for watermarking. Experiments are carried out to test all the proposed algorithms and they are successful in identifying the targeted attacks in a watermarked image while overcoming the limitations of the existing schemes. newline newline newline

Advisors/Committee Members: Ganesan, L..

Subjects/Keywords: Data hiding; watermarking; authentication; security; Laplacian; Bit plane coding

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APA (6^th Edition):

S, K. J. (2013). Some studies on data hiding using watermarking for authentication and security;. (Thesis). Anna University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/13418

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

S, Kurshid Jinna. “Some studies on data hiding using watermarking for authentication and security;.” 2013. Thesis, Anna University. Accessed January 19, 2020. http://shodhganga.inflibnet.ac.in/handle/10603/13418.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

S, Kurshid Jinna. “Some studies on data hiding using watermarking for authentication and security;.” 2013. Web. 19 Jan 2020.

Vancouver:

S KJ. Some studies on data hiding using watermarking for authentication and security;. [Internet] [Thesis]. Anna University; 2013. [cited 2020 Jan 19]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/13418.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

S KJ. Some studies on data hiding using watermarking for authentication and security;. [Thesis]. Anna University; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/13418

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

29. Sohani, Vijay Kumar. Nonlinear schrodinger equation and the twisted laplacian; -.

Degree: Mathematical Sciences, 2013, INFLIBNET

URL: http://shodhganga.inflibnet.ac.in/handle/10603/37405

None

Bibliograpgy p.103 - 106

Advisors/Committee Members: Ratankumar, P K.

Subjects/Keywords: equation; Nonlinear; schrodinger; twisted laplacian

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

APA (6^th Edition):

Sohani, V. K. (2013). Nonlinear schrodinger equation and the twisted laplacian; -. (Thesis). INFLIBNET. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/37405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sohani, Vijay Kumar. “Nonlinear schrodinger equation and the twisted laplacian; -.” 2013. Thesis, INFLIBNET. Accessed January 19, 2020. http://shodhganga.inflibnet.ac.in/handle/10603/37405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sohani, Vijay Kumar. “Nonlinear schrodinger equation and the twisted laplacian; -.” 2013. Web. 19 Jan 2020.

Vancouver:

Sohani VK. Nonlinear schrodinger equation and the twisted laplacian; -. [Internet] [Thesis]. INFLIBNET; 2013. [cited 2020 Jan 19]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/37405.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sohani VK. Nonlinear schrodinger equation and the twisted laplacian; -. [Thesis]. INFLIBNET; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/37405

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Toledo

30. Marinov, Petko I. Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity.

Degree: PhD, Mathematics, 2010, University of Toledo

URL: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

► We study stable capillary surfaces with planar or spherical boundary in the absence of gravity. If the boundary of the capillary surface is embedded in… (more)

Subjects/Keywords: Mathematics; capillarity; mean curvature; elliptic operators; Killing field; Laplacian; centroid

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APA (6^th Edition):

Marinov, P. I. (2010). Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity. (Doctoral Dissertation). University of Toledo. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

Chicago Manual of Style (16^th Edition):

Marinov, Petko I. “Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity.” 2010. Doctoral Dissertation, University of Toledo. Accessed January 19, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654.

MLA Handbook (7^th Edition):

Marinov, Petko I. “Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity.” 2010. Web. 19 Jan 2020.

Vancouver:

Marinov PI. Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity. [Internet] [Doctoral dissertation]. University of Toledo; 2010. [cited 2020 Jan 19]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654.

Council of Science Editors:

Marinov PI. Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity. [Doctoral Dissertation]. University of Toledo; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654

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