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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 王振男 | |
dc.contributor.author | Ming-En Yang | en |
dc.contributor.author | 楊銘恩 | zh_TW |
dc.date.accessioned | 2021-06-17T07:26:04Z | - |
dc.date.available | 2019-07-11 | |
dc.date.copyright | 2019-07-11 | |
dc.date.issued | 2019 | |
dc.date.submitted | 2019-06-26 | |
dc.identifier.citation | [1] A.A. Grigor’yan. Heat kernel upper bounds on a complete non-compact manifold. Revista matemática iberoamericana, 1994, Vol.10(2), 395-452.
[2] A.A. Grigor’yan. Heat kernels on manifolds, graphs and fractals. PM, volume 201. [3] W. Hebisch and L. Saloff-Coste. Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21, no. 2 (1993), 673-709. [4] Thierry Coulhon and Adam Sikora. Gaussian heat kernel upper bounds via the Phragm ́en–Lindel ̈of theorem. Proc. London Math. Soc. (3) 96 (2008) 507–544. [5] N.Th. Varopoulos. Isoperimetric inequalities and Markov chains. Journal of Functional Analysis, 1985, Vol.63(2), pp.215-239. [6] Martin T. Barlow. Random Walks and Heat Kernels on Graphs. 2017. London Mathematical Society lecture note series. 438. [7] Dodziuk, J. Maximum principle for parabolic inequalities and the heat flow on open manifolds. Indiana Math. J. 32 (1983), 703–716. [8] Chavel, I. Eigenvealues in Riemannian geometry. 1984. Pure and applied mathematics (Academic Press). 115. [9] J. Nash. Continuity of solutions of parabolic and elliptic equations. American Journal of Mathematics, 10/1958, Vol.80(4), 931. [10] Richard F. Bass. On Aronson’s Upper Bounds for Heat Kernels. Bull. London Math. Soc.34 (2002) 415–419. [11] T. Coulhon and A. Grigoryan. Random Walks on Graphs with Regular Volume Growth. GAFA, Geom. funct. anal. Vol. 8 (1998) 656-701. [12] L. Saloff-Coste. A note on Poincar ́e, Sobolev, and Harnack inequalitie. International Mathematics Research Notices, Volume 1992, Issue 2, 1992, Pages 27–38. [13] Fabes, E. and Stroock, D. A new proof of Moser’s parabolic harnack inequality using the old ideas of Nash. Archive for Rational Mechanics and Analysis, 1986, Vol.96(4), pp.327-338. [14] Lawrence C. Evans. Partial Differential Equations. ISBN-13: 978-0821849743. [15] Thierry Delmotte. Parab olic Harnack inequality and estimates of Markov chains on graphs. Revista Matem ́atica Iberoamericana, Vol 15, no.1, 1999. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/73278 | - |
dc.description.abstract | 本文討論了歐氏空間與流形上之熱核估計,研究圖上相應條件下之離散熱核估計,並引進連續時間之熱核,藉此引導出離散熱核估計。方便起見,第二章收錄了常用的術語、符號、估計及重要的不等式與條件。文章最後介紹了一些高斯估計的成立條件與推導過程。 | zh_TW |
dc.description.abstract | The presenting work investigates into the heat kernel bounds in Euclidean spaces and on manifolds, and studies discrete heat kernel bounds on graphs under corresponding conditions. We introduce continuous time heat kernels and derive discrete heat kernel bounds from the its result. For convenience, we collect some common terminology and symbols in this topic in chapter two, and introduce some type of heat kernel bounds and some conditions and inequalities. Finally,
we introduce some conditions for the Gaussian bounds and how they can be proved. | en |
dc.description.provenance | Made available in DSpace on 2021-06-17T07:26:04Z (GMT). No. of bitstreams: 1 ntu-108-R05221010-1.pdf: 514654 bytes, checksum: 5f02aaf33cda321d422bd0cba98892fb (MD5) Previous issue date: 2019 | en |
dc.description.tableofcontents | 口試委員會審定書 i
誌謝 ii 中文摘要 iii 英文摘要 iv 1 Introduction 1 2 Notations and Conventions 3 2.1 Heat Kernels on Graphs................................3 2.2 Notations........................................4 2.3 Discrete Time Heat Kernel Bounds..........................5 2.4 Inequalities and Conditions..............................6 3 Heat Kernel Bounds in Different Spaces 8 4 BasicProperties 10 4.1 On-diagonal Upper Bounds..............................11 4.2 Carne-Varopoulos Bound...............................13 4.3 Conditions for Upper Bounds.............................15 4.4 Conditions for Lower Bounds.............................17 5 Continuous Time Random Walks 20 5.1 Continuous Time Heat Kernel Bounds........................21 5.2 Equivalence of the Heat Kernel Bounds.......................22 6 Gaussian Bounds 27 6.1 Gaussian Upper Bounds................................27 6.2 Conditions for Gaussian Bounds...........................31 參考文獻 33 | |
dc.language.iso | en | |
dc.title | 圖上的熱核估計 | zh_TW |
dc.title | Bounds of the Heat Kernels on Graphs | en |
dc.type | Thesis | |
dc.date.schoolyear | 107-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 林景隆,劉聚仁 | |
dc.subject.keyword | 熱核, | zh_TW |
dc.subject.keyword | heat kernel, | en |
dc.relation.page | 33 | |
dc.identifier.doi | 10.6342/NTU201901080 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2019-06-27 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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