subject:(Laplacian)

University of Florida

1. Pantangi, Venkata Raghutej. Smith and Critical Groups of Graphs.

Degree: PhD, Mathematics, 2019, University of Florida

► In this Dissertation, we compute the elementary divisors of the adjacency and Laplacian matrices of two families of strongly regular graphs: Polar graphs and van… (more)

Subjects/Keywords: laplacian

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APA (6^th Edition):

Pantangi, V. R. (2019). Smith and Critical Groups of Graphs. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0054289

Chicago Manual of Style (16^th Edition):

Pantangi, Venkata Raghutej. “Smith and Critical Groups of Graphs.” 2019. Doctoral Dissertation, University of Florida. Accessed January 23, 2021. https://ufdc.ufl.edu/UFE0054289.

MLA Handbook (7^th Edition):

Pantangi, Venkata Raghutej. “Smith and Critical Groups of Graphs.” 2019. Web. 23 Jan 2021.

Vancouver:

Pantangi VR. Smith and Critical Groups of Graphs. [Internet] [Doctoral dissertation]. University of Florida; 2019. [cited 2021 Jan 23]. Available from: https://ufdc.ufl.edu/UFE0054289.

Council of Science Editors:

Pantangi VR. Smith and Critical Groups of Graphs. [Doctoral Dissertation]. University of Florida; 2019. Available from: https://ufdc.ufl.edu/UFE0054289

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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Kiral EM. Spectral Theory and Shifted Convolution Sums in Analytic Number Theory. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2021 Jan 23]. 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/

Rice University

3. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Buras E. A Multigrid Solver for Graph Laplacian Linear Systems on Power-Law Graphs. [Internet] [Masters thesis]. Rice University; 2016. [cited 2021 Jan 23]. 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

4. 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 23, 2021. 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. 23 Jan 2021.

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 2021 Jan 23]. 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

5. 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 23, 2021. http://hdl.handle.net/11244/13880.

MLA Handbook (7^th Edition):

Qu, Hong. “COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS.” 2014. Web. 23 Jan 2021.

Vancouver:

Qu H. COMPLEX P-LAPLACIAN ON KAHLER MANIFOLDS AND ITS APPLICATIONS. [Internet] [Doctoral dissertation]. University of Oklahoma; 2014. [cited 2021 Jan 23]. 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

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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Wang W. Direct and inverse problems for one-dimensional p-Laplacian operators. [Internet] [Doctoral dissertation]. NSYSU; 2010. [cited 2021 Jan 23]. 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

Cornell University

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

Degree: PhD, Mathematics, 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. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/41048

Chicago Manual of Style (16^th Edition):

Kara, Yasemin. “The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms.” 2015. Doctoral Dissertation, Cornell University. Accessed January 23, 2021. http://hdl.handle.net/1813/41048.

MLA Handbook (7^th Edition):

Kara, Yasemin. “The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms.” 2015. Web. 23 Jan 2021.

Vancouver:

Kara Y. The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms. [Internet] [Doctoral dissertation]. Cornell University; 2015. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/1813/41048.

Council of Science Editors:

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

Texas A&M University

8. Garg, Deepak. Smoothing Wavelet Reconstruction.

Degree: MS, Computer Science, 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. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/149509

Chicago Manual of Style (16^th Edition):

Garg, Deepak. “Smoothing Wavelet Reconstruction.” 2013. Masters Thesis, Texas A&M University. Accessed January 23, 2021. http://hdl.handle.net/1969.1/149509.

MLA Handbook (7^th Edition):

Garg, Deepak. “Smoothing Wavelet Reconstruction.” 2013. Web. 23 Jan 2021.

Vancouver:

Garg D. Smoothing Wavelet Reconstruction. [Internet] [Masters thesis]. Texas A&M University; 2013. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/1969.1/149509.

Council of Science Editors:

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

Oregon State University

9. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Kiser T. Fractional powers of the Laplacian with application to small amplitude water waves. [Internet] [Doctoral dissertation]. Oregon State University; 1983. [cited 2021 Jan 23]. 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

10. 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 23, 2021. http://hdl.handle.net/2097/40245.

MLA Handbook (7^th Edition):

Alshammari, Bandar Saad. “A nonlocal Laplacian in one dimension.” 2019. Web. 23 Jan 2021.

Vancouver:

Alshammari BS. A nonlocal Laplacian in one dimension. [Internet] [Masters thesis]. Kansas State University; 2019. [cited 2021 Jan 23]. 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

Colorado School of Mines

11. Elbeleidy, Saad. Converting data from multi-instance to single-instance representations using p-Order Laplacian projections.

Degree: MS(M.S.), Computer Science, 2018, Colorado School of Mines

URL: http://hdl.handle.net/11124/172409

► Fields such as Computer Vision and Natural Language Processing have a high applicability of Machine Learning algorithms. With large amounts of complex data readily available,… (more)

▼ Fields such as Computer Vision and Natural Language Processing have a high applicability of Machine Learning algorithms. With large amounts of complex data readily available, there are two prominent approaches to handling data complexity using Machine Learning. First, dimensionality reduction methods such as Principal Component Analysis (PCA) or Laplacian Embeddings (LE) can minimize the number of features needed to accurately represent data. This approach is often effective but has two main drawbacks. First, the input to the dimensionality reduction method is a summary of all the components that make up the data and some valuable information may be lost. Second, dimensionality reduction methods are often sensitive to outliers. The second approach to dealing with complex data is Multi-Instance Learning (MIL). MIL introduces a new paradigm for data representation by viewing data as a grouping, called a bag, of instances. Each instance is modeled the same way the whole data would be represented but now the datum is represented as a bag of instances. Multi-Instance representation can be effective since they focus on modeling all the pieces that make up the whole datum. However, in order to use this representation in Machine Learning applications we must use MIL algorithms and cannot directly use traditional Machine Learning algorithms. In this work, we propose a method to tackle the issues that may arise in dimensionality reduction methods and MIL methods. We do this by learning a reduced-dimension, integrated, outlier resilient single instance representation for our data. We first propose a new dimensionality reduction method of p-Order Laplacian Embeddings (pOLE) that is less sensitive to outliers than traditional LE. We then use this method to learn a projection from the instances of each bag in a Multi-Instance representation of data. This projection, combined with the Single-Instance representation of the same data can produce a reduced-dimension, integrated, outlier resilient Single-Instance representation Advisors/Committee Members: Wang, Hua (advisor), Han, Qi (committee member), Williams, Thomas (committee member).

Subjects/Keywords: machine learning; Laplacian embedding

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

APA (6^th Edition):

Elbeleidy, S. (2018). Converting data from multi-instance to single-instance representations using p-Order Laplacian projections. (Masters Thesis). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/172409

Chicago Manual of Style (16^th Edition):

Elbeleidy, Saad. “Converting data from multi-instance to single-instance representations using p-Order Laplacian projections.” 2018. Masters Thesis, Colorado School of Mines. Accessed January 23, 2021. http://hdl.handle.net/11124/172409.

MLA Handbook (7^th Edition):

Elbeleidy, Saad. “Converting data from multi-instance to single-instance representations using p-Order Laplacian projections.” 2018. Web. 23 Jan 2021.

Vancouver:

Elbeleidy S. Converting data from multi-instance to single-instance representations using p-Order Laplacian projections. [Internet] [Masters thesis]. Colorado School of Mines; 2018. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/11124/172409.

Council of Science Editors:

Elbeleidy S. Converting data from multi-instance to single-instance representations using p-Order Laplacian projections. [Masters Thesis]. Colorado School of Mines; 2018. Available from: http://hdl.handle.net/11124/172409

12. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Anoop TV. On weighted eigenvalue problems and applications; -. [Internet] [Thesis]. INFLIBNET; 2011. [cited 2021 Jan 23]. 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 Bristol

13. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Kempton L. Distributed control and optimisation of complex networks via their Laplacian spectra. [Internet] [Doctoral dissertation]. University of Bristol; 2018. [cited 2021 Jan 23]. 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

Hong Kong University of Science and Technology

14. 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 23, 2021. 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. 23 Jan 2021.

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 2021 Jan 23]. 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

University of Victoria

15. 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 23, 2021. 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. 23 Jan 2021.

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 2021 Jan 23]. 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

University of Ontario Institute of Technology

16. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Falconer C. Image super resolution via non-local normalized graph Laplacian regularization. [Internet] [Thesis]. University of Ontario Institute of Technology; 2019. [cited 2021 Jan 23]. 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

Kansas State University

17. 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 23, 2021. http://hdl.handle.net/2097/38781.

MLA Handbook (7^th Edition):

Almutairi, Fahad Hamoud. “Nonlocal vector calculus.” 2018. Web. 23 Jan 2021.

Vancouver:

Almutairi FH. Nonlocal vector calculus. [Internet] [Masters thesis]. Kansas State University; 2018. [cited 2021 Jan 23]. 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 Louisville

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

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 23, 2021. 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. 23 Jan 2021.

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 2021 Jan 23]. 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

University of Sydney

19. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Chang T. On Singular Solutions of Weighted Divergence Operators . [Internet] [Thesis]. University of Sydney; 2017. [cited 2021 Jan 23]. 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

University of Bristol

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

Degree: PhD, 2018, University of Bristol

URL: https://research-information.bris.ac.uk/en/studentTheses/655bf049-92e3-40d2-bc9b-7d4a75bccdb4 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774414

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

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 https://research-information.bris.ac.uk/en/studentTheses/655bf049-92e3-40d2-bc9b-7d4a75bccdb4 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774414

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 23, 2021. https://research-information.bris.ac.uk/en/studentTheses/655bf049-92e3-40d2-bc9b-7d4a75bccdb4 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774414.

MLA Handbook (7^th Edition):

Kempton, Louis. “Distributed control and optimisation of complex networks via their Laplacian spectra.” 2018. Web. 23 Jan 2021.

Vancouver:

Kempton L. Distributed control and optimisation of complex networks via their Laplacian spectra. [Internet] [Doctoral dissertation]. University of Bristol; 2018. [cited 2021 Jan 23]. Available from: https://research-information.bris.ac.uk/en/studentTheses/655bf049-92e3-40d2-bc9b-7d4a75bccdb4 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774414.

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: https://research-information.bris.ac.uk/en/studentTheses/655bf049-92e3-40d2-bc9b-7d4a75bccdb4 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.774414

Colorado State University

21. Mankovich, Nathan. Methods for network generation and spectral feature selection: especially on gene expression data.

Degree: MS(M.S.), Mathematics, 2019, 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. (2019). 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.” 2019. Masters Thesis, Colorado State University. Accessed January 23, 2021. 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.” 2019. Web. 23 Jan 2021.

Vancouver:

Mankovich N. Methods for network generation and spectral feature selection: especially on gene expression data. [Internet] [Masters thesis]. Colorado State University; 2019. [cited 2021 Jan 23]. 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; 2019. Available from: http://hdl.handle.net/10217/199775

University of Colorado

22. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Taylor KM. The Geometry of Signal and Image Patch-Sets. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2021 Jan 23]. 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

23. 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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Pudipeddi S. Localized Radial Solutions for Nonlinear p-Laplacian Equation in RN. [Internet] [Thesis]. University of North Texas; 2008. [cited 2021 Jan 23]. 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

24. 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 23, 2021. 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. 23 Jan 2021.

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 2021 Jan 23]. 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

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

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 23, 2021. 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. 23 Jan 2021.

Vancouver:

Hwang S. Holder regularity of solutions of generalized p-Laplacian type parabolic equations. [Internet] [Thesis]. Iowa State University; 2012. [cited 2021 Jan 23]. 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

University of South Carolina

26. 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 23, 2021. https://scholarcommons.sc.edu/etd/1610.

MLA Handbook (7^th Edition):

Peng, Xing. “Fractional Chromatic Numbers and Spectra of Graphs.” 2012. Web. 23 Jan 2021.

Vancouver:

Peng X. Fractional Chromatic Numbers and Spectra of Graphs. [Internet] [Doctoral dissertation]. University of South Carolina; 2012. [cited 2021 Jan 23]. 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

NSYSU

27. Chen, Hui-yu. On generalized trigonometric functions.

Degree: Master, Applied Mathematics, 2010, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0625110-112752

► The function sin x as one of the six trigonometric functions is fundamental in nearly every branch of mathematics, and its applications. In this thesis,… (more)

Subjects/Keywords: generalized trigonometric functions; generalized sine function; identities; p-Laplacian

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

APA (6^th Edition):

Chen, H. (2010). On generalized trigonometric functions. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0625110-112752

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):

Chen, Hui-yu. “On generalized trigonometric functions.” 2010. Thesis, NSYSU. Accessed January 23, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0625110-112752.

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

MLA Handbook (7^th Edition):

Chen, Hui-yu. “On generalized trigonometric functions.” 2010. Web. 23 Jan 2021.

Vancouver:

Chen H. On generalized trigonometric functions. [Internet] [Thesis]. NSYSU; 2010. [cited 2021 Jan 23]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0625110-112752.

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

Council of Science Editors:

Chen H. On generalized trigonometric functions. [Thesis]. NSYSU; 2010. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0625110-112752

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

University of California – Berkeley

28. Lee, Minjae. Spectral Analysis on Point Interactions.

Degree: Mathematics, 2016, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/2vv215sj

► This thesis explores the spectral properties of Schrödinger-type operators on variousdomains such as R², rectangles, and metric graphs. In particular, we consider special types of… (more)

Subjects/Keywords: Mathematics; Quantum physics; Eigenvalue; Laplacian; Point Scatterer; Quantum Graph; Resonance; Scattering

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APA (6^th Edition):

Lee, M. (2016). Spectral Analysis on Point Interactions. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/2vv215sj

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):

Lee, Minjae. “Spectral Analysis on Point Interactions.” 2016. Thesis, University of California – Berkeley. Accessed January 23, 2021. http://www.escholarship.org/uc/item/2vv215sj.

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

MLA Handbook (7^th Edition):

Lee, Minjae. “Spectral Analysis on Point Interactions.” 2016. Web. 23 Jan 2021.

Vancouver:

Lee M. Spectral Analysis on Point Interactions. [Internet] [Thesis]. University of California – Berkeley; 2016. [cited 2021 Jan 23]. Available from: http://www.escholarship.org/uc/item/2vv215sj.

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

Council of Science Editors:

Lee M. Spectral Analysis on Point Interactions. [Thesis]. University of California – Berkeley; 2016. Available from: http://www.escholarship.org/uc/item/2vv215sj

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

UCLA

29. Kelly, Joshua Walter. Physics of Complex Polymeric Molecules.

Degree: Physics, 2017, UCLA

URL: http://www.escholarship.org/uc/item/9hk3m75p

► The statistical physics of complex polymers with branches and circuits is the topic of this dissertation. An important motivation are large, single-stranded (ss) RNA molecules.… (more)

Subjects/Keywords: Biophysics; Statistical physics; Branched Polymers; Folding; Laplacian; Quenched; RNA; Statistics

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APA (6^th Edition):

Kelly, J. W. (2017). Physics of Complex Polymeric Molecules. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/9hk3m75p

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):

Kelly, Joshua Walter. “Physics of Complex Polymeric Molecules.” 2017. Thesis, UCLA. Accessed January 23, 2021. http://www.escholarship.org/uc/item/9hk3m75p.

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

MLA Handbook (7^th Edition):

Kelly, Joshua Walter. “Physics of Complex Polymeric Molecules.” 2017. Web. 23 Jan 2021.

Vancouver:

Kelly JW. Physics of Complex Polymeric Molecules. [Internet] [Thesis]. UCLA; 2017. [cited 2021 Jan 23]. Available from: http://www.escholarship.org/uc/item/9hk3m75p.

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

Council of Science Editors:

Kelly JW. Physics of Complex Polymeric Molecules. [Thesis]. UCLA; 2017. Available from: http://www.escholarship.org/uc/item/9hk3m75p

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

University of Hong Kong

30. 張學文. On p-Laplacian equations with deviating arguments.

Degree: 2009, University of Hong Kong

URL: http://hdl.handle.net/10722/57556

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):

張學文. (2009). On p-Laplacian equations with deviating arguments. (Thesis). University of Hong Kong. Retrieved from http://hdl.handle.net/10722/57556

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

Chicago Manual of Style (16^th Edition):

張學文. “On p-Laplacian equations with deviating arguments.” 2009. Thesis, University of Hong Kong. Accessed January 23, 2021. http://hdl.handle.net/10722/57556.

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

MLA Handbook (7^th Edition):

張學文. “On p-Laplacian equations with deviating arguments.” 2009. Web. 23 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

張學文. On p-Laplacian equations with deviating arguments. [Internet] [Thesis]. University of Hong Kong; 2009. [cited 2021 Jan 23]. Available from: http://hdl.handle.net/10722/57556.

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

Council of Science Editors:

張學文. On p-Laplacian equations with deviating arguments. [Thesis]. University of Hong Kong; 2009. Available from: http://hdl.handle.net/10722/57556

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

Open Access Theses and Dissertations