subject:(Heat kernel)

Cornell University

1. Liu, Jingbo. HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS .

Degree: 2019, Cornell University

► In this thesis we study the properties of the Schrodinger operator L=−∆+q on a Harnack-type Dirichlet space for q belonging to Kato class K or… (more)

Subjects/Keywords: Mathematics; Dirichlet; Heat Kernel Estimate; Uniform Domain

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APA (6^th Edition):

Liu, J. (2019). HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/67362

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):

Liu, Jingbo. “HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS .” 2019. Thesis, Cornell University. Accessed January 17, 2020. http://hdl.handle.net/1813/67362.

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

MLA Handbook (7^th Edition):

Liu, Jingbo. “HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS .” 2019. Web. 17 Jan 2020.

Vancouver:

Liu J. HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS . [Internet] [Thesis]. Cornell University; 2019. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1813/67362.

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

Council of Science Editors:

Liu J. HEAT KERNEL ESTIMATE OF THE SCHRODINGER OPERATOR IN UNIFORM DOMAINS . [Thesis]. Cornell University; 2019. Available from: http://hdl.handle.net/1813/67362

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

Cornell University

2. Hou, Qi. Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces .

Degree: 2019, Cornell University

URL: http://hdl.handle.net/1813/67578

► This thesis studies some qualitative properties of local weak solutions of the heat equation in Dirichlet spaces. Let ≤ ft(X,𝓔,𝓕)) be a Dirichlet space where X… (more)

▼ This thesis studies some qualitative properties of local weak solutions of the heat equation in Dirichlet spaces. Let ≤ ft(X,𝓔,𝓕)) be a Dirichlet space where X is a metric measure space, and ≤ ft(𝓔,𝓕)) is a symmetric, local, regular Dirichlet form on L² ≤ ft(X)). Let -P and ≤ ft(H_t))_t>0 denote the corresponding generator and semigroup. Consider the heat equation ≤ ft(\partial_t+P))u=f in ℝ × X. Examples of such heat equations include the ones associated with (i) Dirichlet forms associated with uniformly elliptic, second order differential operators with measurable coefficients on ℝⁿ, and Dirichlet forms on fractal spaces;\ (ii) Dirichlet forms associated with product diffusions and product anomalous diffusions on infinite products of compact metric measure spaces, including the infinite dimensional torus, and the infinite product of fractal spaces like the Sierpinski gaskets.\ We ask the following qualitative questions about local weak solutions to the above heat equations, which in spirit are generalizations of the notion of hypoellipticity: Are they locally bounded? Are they continuous? Is the time derivative of a local weak solution still a local weak solution? Under some hypotheses on existence of cutoff functions with either bounded gradient or bounded energy, and sometimes additional hypotheses on the semigroup, we give (partially) affirmative answers to the above questions. Some of our key results are as follows. Let u be a local weak solution to ≤ ft(\partial_t+P))u=f on some time-space cylinder I × Ω.\ (i) If the time derivative of f is locally in L² ≤ ft(I × Ω)), then the time derivative of u is a local weak solution to ≤ ft(\partial_t+P))\partial_t u=\partial_t f.\ (ii) If the semigroup H_t is locally ultracontractive, and satisfies some Gaussian type upper bound, and if f is locally bounded, then u is locally bounded.\ (iii) Besides satisfying local contractivity and some Gaussian type upper bound, if the semigroup H_t further admits a locally continuous kernel h ≤ ft(t,x,y)), then u is locally continuous.\ (iv) If the semigroup is locally ultracontractive and satisfies some Gaussian type upper bound, then it admits a locally bounded function kernel h ≤ ft(t,x,y)). As a special case, on the infinite torus \mathbb{T}^∞, local boundedness of h ≤ ft(t,x,y)) implies automatically the continuity of h ≤ ft(t,x,y)), and hence of all local weak solutions.\ (v) The needed Gaussian type upper bounds can often be derived from the ultracontractivity conditions. We also discuss such implications under existence of cutoff functions with bounded gradient or bounded energy.\ The results presented in this thesis are joint work with Laurent Saloff-Coste. Advisors/Committee Members: Healey, Timothy James (committeeMember), Cao, Xiaodong (committeeMember).

Subjects/Keywords: Dirichlet space; heat equation; heat kernel; heat semigroup; local weak solution; Mathematics

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APA (6^th Edition):

Hou, Q. (2019). Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/67578

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):

Hou, Qi. “Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces .” 2019. Thesis, Cornell University. Accessed January 17, 2020. http://hdl.handle.net/1813/67578.

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

MLA Handbook (7^th Edition):

Hou, Qi. “Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces .” 2019. Web. 17 Jan 2020.

Vancouver:

Hou Q. Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces . [Internet] [Thesis]. Cornell University; 2019. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1813/67578.

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

Council of Science Editors:

Hou Q. Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces . [Thesis]. Cornell University; 2019. Available from: http://hdl.handle.net/1813/67578

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

Baylor University

3. [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 17, 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. 17 Jan 2020.

Vancouver:

author] [. Boundary condition dependence of spectral zeta functions. [Internet] [Thesis]. Baylor University; 2015. [cited 2020 Jan 17]. 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

Cornell University

4. Randles, Evan. Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations .

Degree: 2016, Cornell University

URL: http://hdl.handle.net/1813/44301

► The study of convolution powers of a finitely supported probability distribution [phi] on the d-dimensional square lattice is central to random walk theory. For instance,… (more)

▼ The study of convolution powers of a finitely supported probability distribution [phi] on the d-dimensional square lattice is central to random walk theory. For instance, the nth convolution power [phi](n) is the distribution of the nth step of the associated random walk. In the case that the random walk is aperiodic and irreducible, [phi](n) is well approximated by a single and appropriately scaled Gaussian density; this is the local (central) limit theorem. When such functions are allowed to be complex-valued, their convolution powers are seen to exhibit rich and disparate behavior, much of which never appears in the probabilistic setting. In the first half of this thesis, we study the asymptotic behavior of the convolution powers of complex-valued functions on Zd . This problem, originally motivated by the problem of Erastus L. De Forest in data smoothing, has found applications to the theory of stability of numerical difference schemes in partial differential equations. For a complex-valued function [phi] on Zd , we ask and address four basic and fundamental questions about the convolution powers [phi](n) which concern sup-norm estimates, generalized local limit theorems, pointwise estimates, and stability. In one dimension, we give a complete theory of sup-norm estimates and local limit theorems for the entire class of finitely supported complex-valued functions. This work extends results of I. J. Schoenberg, T. N. E. Greville, P. Diaconis and L. Saloff-Coste and, in the context of stability theory, results by V. Thom´ e and M. V. Fedoryuk. e In the second half of this thesis, we consider a class of "higher order" homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting objects of the convolution powers of complex-valued functions on the square lattice in the way that the classical heat kernel arises in the (local) central limit theorem. These socalled positive-homogeneous operators generalize the class of semi-elliptic operators in the sense that the definition is coordinate-free. We then introduce a class of variable-coefficient operators, each of which is uniformly comparable to a positive-homogeneous operator, and we study the corresponding Cauchy problem for the heat equation. Under the assumption that such an operator has ¨ Holder continuous coefficients, we construct a fundamental solution to its heat equation by the method of E. E. Levi, adapted to parabolic systems by A. Friedman and S. D. Eidelman. Though our results in this direction are implied by the long-known results of S. D. Eidelman for 2b-parabolic systems, our focus is to highlight the role played by the Legendre-Fenchel transform in heat kernel estimates. Specifically, we show that the fundamental solution satisfies an offdiagonal estimate, i.e., a heat kernel estimate, written in terms of the LegendreFenchel transform of the operator's principal symbol - an estimate which is seen to… Advisors/Committee Members: Elser,Veit (committeeMember), Gross,Leonard (committeeMember).

Subjects/Keywords: convolution powers; local limit theorems; heat kernel estimates

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APA (6^th Edition):

Randles, E. (2016). Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/44301

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):

Randles, Evan. “Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations .” 2016. Thesis, Cornell University. Accessed January 17, 2020. http://hdl.handle.net/1813/44301.

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

MLA Handbook (7^th Edition):

Randles, Evan. “Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations .” 2016. Web. 17 Jan 2020.

Vancouver:

Randles E. Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations . [Internet] [Thesis]. Cornell University; 2016. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1813/44301.

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

Council of Science Editors:

Randles E. Convolution Powers Of Complex-Valued Functions And Related Topics In Partial Differential Equations . [Thesis]. Cornell University; 2016. Available from: http://hdl.handle.net/1813/44301

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

Queens University

5. Seguin, Caroline. Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups .

Degree: Mathematics and Statistics, 2011, Queens University

URL: http://hdl.handle.net/1974/6834

► This thesis suggests an approach to compute the short-time behaviour of the hypoelliptic heat kernel corresponding to sub-Riemannian structures on unimodular Lie groups of type… (more)

Subjects/Keywords: Non-commutative Harmonic Analysis; Hypoelliptic heat kernel; Sub-Riemannian geometry

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APA (6^th Edition):

Seguin, C. (2011). Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/6834

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):

Seguin, Caroline. “Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups .” 2011. Thesis, Queens University. Accessed January 17, 2020. http://hdl.handle.net/1974/6834.

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

MLA Handbook (7^th Edition):

Seguin, Caroline. “Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups .” 2011. Web. 17 Jan 2020.

Vancouver:

Seguin C. Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups . [Internet] [Thesis]. Queens University; 2011. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1974/6834.

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

Council of Science Editors:

Seguin C. Short-time asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups . [Thesis]. Queens University; 2011. Available from: http://hdl.handle.net/1974/6834

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

University of Manchester

6. Yang, Xue. Neumann problems for second order elliptic operators with singular coefficients.

Degree: PhD, 2012, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553550

► In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients,… (more)

Subjects/Keywords: 536.2; Dirichlet form; Neumann boundary problem; Heat kernel; Fukushima's decomposition; Mixed boundary condition; Reflecting diffusion

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APA (6^th Edition):

Yang, X. (2012). Neumann problems for second order elliptic operators with singular coefficients. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553550

Chicago Manual of Style (16^th Edition):

Yang, Xue. “Neumann problems for second order elliptic operators with singular coefficients.” 2012. Doctoral Dissertation, University of Manchester. Accessed January 17, 2020. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553550.

MLA Handbook (7^th Edition):

Yang, Xue. “Neumann problems for second order elliptic operators with singular coefficients.” 2012. Web. 17 Jan 2020.

Vancouver:

Yang X. Neumann problems for second order elliptic operators with singular coefficients. [Internet] [Doctoral dissertation]. University of Manchester; 2012. [cited 2020 Jan 17]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553550.

Council of Science Editors:

Yang X. Neumann problems for second order elliptic operators with singular coefficients. [Doctoral Dissertation]. University of Manchester; 2012. Available from: https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.553550

7. Huang, Binbin. On a Pseudodifferential Calculus with Modest Boundary Decay Condition.

Degree: PhD, Mathematical Sciences, 2018, Binghamton University

URL: https://orb.binghamton.edu/dissertation_and_theses/36

► A boundary decay condition, called vanishing to infinite logarithmic order is introduced. A pseudodifferential calculus, extending the b-calculus of Melrose, is proposed based… (more)

Subjects/Keywords: Pure sciences; B-calculus; Dirac operator; Heat kernel; Index theory; Pseudodifferential operator; Mathematics

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APA (6^th Edition):

Huang, B. (2018). On a Pseudodifferential Calculus with Modest Boundary Decay Condition. (Doctoral Dissertation). Binghamton University. Retrieved from https://orb.binghamton.edu/dissertation_and_theses/36

Chicago Manual of Style (16^th Edition):

Huang, Binbin. “On a Pseudodifferential Calculus with Modest Boundary Decay Condition.” 2018. Doctoral Dissertation, Binghamton University. Accessed January 17, 2020. https://orb.binghamton.edu/dissertation_and_theses/36.

MLA Handbook (7^th Edition):

Huang, Binbin. “On a Pseudodifferential Calculus with Modest Boundary Decay Condition.” 2018. Web. 17 Jan 2020.

Vancouver:

Huang B. On a Pseudodifferential Calculus with Modest Boundary Decay Condition. [Internet] [Doctoral dissertation]. Binghamton University; 2018. [cited 2020 Jan 17]. Available from: https://orb.binghamton.edu/dissertation_and_theses/36.

Council of Science Editors:

Huang B. On a Pseudodifferential Calculus with Modest Boundary Decay Condition. [Doctoral Dissertation]. Binghamton University; 2018. Available from: https://orb.binghamton.edu/dissertation_and_theses/36

Purdue University

8. Rotz, Kevin L. Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups.

Degree: PhD, Mathematics, 2016, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/700

► The contents of this thesis are an assortment of results in analysis and subRiemannian geometry, with a special focus on the Heisenberg group Hn,… (more)

▼ The contents of this thesis are an assortment of results in analysis and subRiemannian geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups. As we wish for this thesis to be relatively self-contained, the main definitions and background are covered in Chapter 1. This includes basic information about Carnot groups, Hn, H-type groups, diffusion operators, and the curvature dimension inequality. Chapter 2 incorporates excerpts from a paper by N. Garofalo and the author, [42]. In it, we propose a generalization of Almgren’s frequency function N : (0, 1) → R for solutions to the sub-elliptic Laplace equation ΔHu = 0 in the unit ball of a Carnot group of arbitrary step. If the function u has vanishing discrepancy, then the frequency is monotonically non-decreasing, and we are able to prove a form of strong unique continuation for such functions. Chapter 3 grew out of the author seeking parabolic montonicity formulas in the same vein as Almgren’s frequency. These include two types of monotonicity formulas, those of Struwe- and Poon-type [72], [67]. If a diffusion operator L on a complete manifold M satisfies the curvature dimension inequality CD(ρ, n), then we are able to prove that for solutions to L u = ut in M × (0, T), Struwe’s energy monotonicity holds, at least for time values close enough to T. We introduce a new condition, C(ω) where ω ∈ C1(0, T), related to the Hessian of the heat kernel, and are able to prove a Poon-type frequency monotonicity formula when taking into account a weighting factor depending on ω. We also give examples of manifolds satisfying C(ω), the most interesting of which includes the Ornstein-Uhlenbeck operator. Monotonicity of the weighted frequency also implies a form of strong-unique continuation. In Chapter 4, we derive asymptotics for the heat kernel on H-type groups and generalize a gradient bound from a paper of Garofalo and Segala [43] to these groups. This gradient bound in turn implies a strong Harnack inequality and Wiener criterion similar to those found in [31] and [43]. Advisors/Committee Members: Nicola Garofalo, Donatella Danielli, Nicola Garofalo, Fabrice Baudoin, Nung Kwan Yip.

Subjects/Keywords: Pure sciences; Carnot groups; Heat kernel; Monotonicity formulas; Unique continuation; Wiener's criterion; Mathematics

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APA (6^th Edition):

Rotz, K. L. (2016). Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/700

Chicago Manual of Style (16^th Edition):

Rotz, Kevin L. “Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups.” 2016. Doctoral Dissertation, Purdue University. Accessed January 17, 2020. https://docs.lib.purdue.edu/open_access_dissertations/700.

MLA Handbook (7^th Edition):

Rotz, Kevin L. “Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups.” 2016. Web. 17 Jan 2020.

Vancouver:

Rotz KL. Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2020 Jan 17]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/700.

Council of Science Editors:

Rotz KL. Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/700

University of Washington

9. Rudnick, Christian. Boundary Harnack Principle for Stable-Like Processes.

Degree: PhD, 2016, University of Washington

URL: http://hdl.handle.net/1773/36756

► We establish the boundary Harnack principle for certain classes of symmetric stable-like processes in \mathbf{R}^d on arbitrary open sets as well as censored stable-like processes… (more)

Subjects/Keywords: boundary Harnack principle; Dirichlet heat kernel estimates; stable-like processes; Mathematics; mathematics

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APA (6^th Edition):

Rudnick, C. (2016). Boundary Harnack Principle for Stable-Like Processes. (Doctoral Dissertation). University of Washington. Retrieved from http://hdl.handle.net/1773/36756

Chicago Manual of Style (16^th Edition):

Rudnick, Christian. “Boundary Harnack Principle for Stable-Like Processes.” 2016. Doctoral Dissertation, University of Washington. Accessed January 17, 2020. http://hdl.handle.net/1773/36756.

MLA Handbook (7^th Edition):

Rudnick, Christian. “Boundary Harnack Principle for Stable-Like Processes.” 2016. Web. 17 Jan 2020.

Vancouver:

Rudnick C. Boundary Harnack Principle for Stable-Like Processes. [Internet] [Doctoral dissertation]. University of Washington; 2016. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1773/36756.

Council of Science Editors:

Rudnick C. Boundary Harnack Principle for Stable-Like Processes. [Doctoral Dissertation]. University of Washington; 2016. Available from: http://hdl.handle.net/1773/36756

Texas A&M University

10. Mohammed, Suheb. The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat.

Degree: 2014, Texas A&M University

URL: http://hdl.handle.net/1969.1/152620

► Water deficiency is the primary reason for decreasing wheat (Triticum aestivum) yields globally, causing a nearly 50-90% yield reduction on at least 60 Mha of… (more)

▼ Water deficiency is the primary reason for decreasing wheat (Triticum aestivum) yields globally, causing a nearly 50-90% yield reduction on at least 60 Mha of land in developing countries Previous studies have identified associations in genomic regions for cooler canopies, heat susceptible index, and grain yield components in winter wheat. This project aims to define the role that leaf epicuticular wax (EW) plays as a drought adaptive trait in terms of yield stability. A spring wheat Len/Halberd recombinant inbred line population was used to test this question. The RIL population exhibits significant segregation for leaf EW, canopy temperature (CT), awns, and drought susceptible index (DSI) yet has been selected. An alpha lattice design with 180 recombinants and 2 replications was used with two distinct treatments (water deficit and control conditions) at each of 5 environments. The inheritance of leaf EW was low (15%) due to a high environmental influence. The RILs grown under water deficit produced significantly higher EW content (19 to 30%) when compared to control. The leaf EW load significantly correlated with plot yield (r=32%), DSI (r=-40%), and leaf CT (r=-32%) under water deficit conditions. In addition, EW and CT correlated with higher yield stability using DSI and across environments using Eberhart stability under water deficit. Novel and robust co-localized QTLs for the leaf EW, cooler canopies, DSI, and grain attributes were detected on 2B, 3B, 5A, 5B, 6B, 7A, and 7B. High LOD scores and colocalization of CT and DSI along with independent EW loci explaining 35%, 41%, and 31% phenotypic variation respectively were detected on chromosome 4A. Chromosome 3B was investigated with closed association of leaf EW and canopy temperature all across the chromosomal length. Chromosome 6B had significant SNPs associated with cooler canopies in Halberd (2.4??) compared to Len. The Halberd parent played a role in donating major alleles for moisture stress tolerance whereas, Len donates major yield allelic variants. Many novel and robust QTLs were identified to dissect the crop performance under moisture stress conditions. These identified genetic loci conducive potential tools in strategic breeding approaches. Advisors/Committee Members: Hays, Dirk B (advisor), Ibrahim, Amir (advisor), Rooney, William L (committee member), Jessup, Russell W (committee member).

Subjects/Keywords: Drought susceptible index; Heat susceptible index; Epicuticular wax; Canopy temperature; Mean single head weight; Kernel number per spike; Thousand kernel weight; Quantitative trait loci; Recombinant inbred lines

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APA (6^th Edition):

Mohammed, S. (2014). The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat. (Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/152620

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):

Mohammed, Suheb. “The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat.” 2014. Thesis, Texas A&M University. Accessed January 17, 2020. http://hdl.handle.net/1969.1/152620.

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

MLA Handbook (7^th Edition):

Mohammed, Suheb. “The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat.” 2014. Web. 17 Jan 2020.

Vancouver:

Mohammed S. The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat. [Internet] [Thesis]. Texas A&M University; 2014. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1969.1/152620.

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

Council of Science Editors:

Mohammed S. The Role of Leaf Epicuticular Wax an Improved Adaptation to Moisture Deficit Environments in Wheat. [Thesis]. Texas A&M University; 2014. Available from: http://hdl.handle.net/1969.1/152620

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

Johannes Gutenberg Universität Mainz

11. Groh, Kai. Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies.

Degree: 2012, Johannes Gutenberg Universität Mainz

URL: http://ubm.opus.hbz-nrw.de/volltexte/2013/3333/

►

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this… (more)

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The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Das Konzept der Asymptotischen Sicherheit ermöglicht die Konstruktion einer konsistenten Theorie der Quantengravitation in Form einer Quantenfeldtheorie. Die zentrale Annahme ist hierbei die Existenz eines nicht-Gauß'schen Fixpunktes des Renormierungsgruppenflusses, der es erlaubt Renormierungsbedingungen zu formulieren. Zur Untersuchung dieses Szenarios findet eine nicht-störungstheoretische exakte Renormierungsgruppengleichung Anwendung. Diese beschreibt Wilsonsche Renormierungsgruppentransformationen und stellt eine äquivalente Formulierung einer Quantenfeldtheorie im Pfadintegralzugang dar.rnDie vorliegende Arbeit entwickelt einen algebraischen Algorithmus zur systematischen Konstruktion der Renormierungsgruppenflüsse von Eichtheorien und Quantengravitation. Dieser verwendet die nicht-diagonale…

Subjects/Keywords: Quantengravitation; Renormierungsgruppe; assymptotische Sicherheit; Wärmekern-Entwicklung; Quantum gravity; Renormalization group; asymptotic safety; heat kernel expansion; Physics

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APA (6^th Edition):

Groh, K. (2012). Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2013/3333/

Chicago Manual of Style (16^th Edition):

Groh, Kai. “Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies.” 2012. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed January 17, 2020. http://ubm.opus.hbz-nrw.de/volltexte/2013/3333/.

MLA Handbook (7^th Edition):

Groh, Kai. “Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies.” 2012. Web. 17 Jan 2020.

Vancouver:

Groh K. Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2012. [cited 2020 Jan 17]. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2013/3333/.

Council of Science Editors:

Groh K. Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2012. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2013/3333/

Louisiana State University

12. Yang, Yunyun. A New Method In Distribution Theory With A Non-Smooth Framework.

Degree: PhD, Applied Mathematics, 2015, Louisiana State University

URL: etd-04132015-160154 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1751

► In this work, we present a complete treatment of the theory of thick distributions and its asymptotic expansion. We also present several applications of thick… (more)

Subjects/Keywords: spectral theory; heat kernel; thick delta functions; thick distributions; regularization; Hadamard finite parts; mathematical physics; asymptotic expansion

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

APA (6^th Edition):

Yang, Y. (2015). A New Method In Distribution Theory With A Non-Smooth Framework. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-04132015-160154 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1751

Chicago Manual of Style (16^th Edition):

Yang, Yunyun. “A New Method In Distribution Theory With A Non-Smooth Framework.” 2015. Doctoral Dissertation, Louisiana State University. Accessed January 17, 2020. etd-04132015-160154 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1751.

MLA Handbook (7^th Edition):

Yang, Yunyun. “A New Method In Distribution Theory With A Non-Smooth Framework.” 2015. Web. 17 Jan 2020.

Vancouver:

Yang Y. A New Method In Distribution Theory With A Non-Smooth Framework. [Internet] [Doctoral dissertation]. Louisiana State University; 2015. [cited 2020 Jan 17]. Available from: etd-04132015-160154 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1751.

Council of Science Editors:

Yang Y. A New Method In Distribution Theory With A Non-Smooth Framework. [Doctoral Dissertation]. Louisiana State University; 2015. Available from: etd-04132015-160154 ; https://digitalcommons.lsu.edu/gradschool_dissertations/1751

Cornell University

13. Gyrya, Pavel. Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space .

Degree: 2007, Cornell University

URL: http://hdl.handle.net/1813/7729

► The main result of this thesis is the two-sided heat kernel estimates for both Dirichlet and Neumann problem in any inner uniform domain of the… (more)

Subjects/Keywords: heat kernel estimates; Harnack; inner uniform set; Dirichlet form

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APA (6^th Edition):

Gyrya, P. (2007). Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space . (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/7729

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):

Gyrya, Pavel. “Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space .” 2007. Thesis, Cornell University. Accessed January 17, 2020. http://hdl.handle.net/1813/7729.

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

MLA Handbook (7^th Edition):

Gyrya, Pavel. “Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space .” 2007. Web. 17 Jan 2020.

Vancouver:

Gyrya P. Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space . [Internet] [Thesis]. Cornell University; 2007. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/1813/7729.

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

Council of Science Editors:

Gyrya P. Heat kernel estimates for inner uniform subsets of Harnack-type Dirichlet space . [Thesis]. Cornell University; 2007. Available from: http://hdl.handle.net/1813/7729

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

14. Francisco Pereira Chaves. Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes.

Degree: PhD, 2016, Universidade Federal do Ceará

URL: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17332 ;

►

No presente trabalho, provaremos resultados de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas de variedades Riemannianas com curvatura seccional limitada superiormente pela curvatura… (more)

Subjects/Keywords: GEOMETRIA DIFERENCIAL; nÃcleo do calor; subvariedades mÃnimas; propriedade L1-Liouville; tom fundamental; curvatura mÃdia; heat kernel; minimal submanifolds; L1-Liouville property; fundamental tone; mean curvature; Variedades riemanianas; Riemannian manifolds

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APA (6^th Edition):

Chaves, F. P. (2016). Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes. (Doctoral Dissertation). Universidade Federal do Ceará. Retrieved from http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17332 ;

Chicago Manual of Style (16^th Edition):

Chaves, Francisco Pereira. “Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes.” 2016. Doctoral Dissertation, Universidade Federal do Ceará. Accessed January 17, 2020. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17332 ;.

MLA Handbook (7^th Edition):

Chaves, Francisco Pereira. “Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes.” 2016. Web. 17 Jan 2020.

Vancouver:

Chaves FP. Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes. [Internet] [Doctoral dissertation]. Universidade Federal do Ceará 2016. [cited 2020 Jan 17]. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17332 ;.

Council of Science Editors:

Chaves FP. Teoremas de comparaÃÃo para o nÃcleo do calor de subvariedades mÃnimas e aplicaÃÃes. [Doctoral Dissertation]. Universidade Federal do Ceará 2016. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17332 ;

Loughborough University

15. Li, Liangpan. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.

Degree: PhD, 2016, Loughborough University

URL: https://dspace.lboro.ac.uk/2134/23004 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706209

► In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact,… (more)

▼ In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method. In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle, we obtain certain asymptotic estimates about the integral kernel of heat operators. As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel. Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.

Subjects/Keywords: 515; Local spectral asymptotics; Heat kernel; Dirac operators; Laplace operators; Pseudo-differential operators; Fourier integral operators; Wodzicki residue; Finite propagation speed; Spectral determinant

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

APA (6^th Edition):

Li, L. (2016). Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. (Doctoral Dissertation). Loughborough University. Retrieved from https://dspace.lboro.ac.uk/2134/23004 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706209

Chicago Manual of Style (16^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Doctoral Dissertation, Loughborough University. Accessed January 17, 2020. https://dspace.lboro.ac.uk/2134/23004 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706209.

MLA Handbook (7^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Web. 17 Jan 2020.

Vancouver:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Internet] [Doctoral dissertation]. Loughborough University; 2016. [cited 2020 Jan 17]. Available from: https://dspace.lboro.ac.uk/2134/23004 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706209.

Council of Science Editors:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Doctoral Dissertation]. Loughborough University; 2016. Available from: https://dspace.lboro.ac.uk/2134/23004 ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.706209

16. Lazzarini, Giovanni. Sur la hauteur de tores plats : On the height of Flat Tori.

Degree: Docteur es, Mathématiques pures, 2015, Bordeaux

URL: http://www.theses.fr/2015BORD0018

►

Nous considérons la fonction zêta d’Epstein des réseaux euclidiens pour étudier le problème des minima de la hauteur du tore plat associé à un réseau.… (more)

▼

Nous considérons la fonction zêta d’Epstein des réseaux euclidiens pour étudier le problème des minima de la hauteur du tore plat associé à un réseau. La hauteur est définie comme la dérivée au point s = 0 de la fonction zêta spectrale du tore, fonction qui coïncide, à un facteur près, avec la fonction zêta d’Epstein du réseau dual du réseau donné. Nous donnons dans cette dissertation une condition suffisante pour qu’un réseau donné soit un point critique de la hauteur. En particulier, en utilisant la théorie des designs sphériques, nous montrons qu’un réseau qui a des 2-designs sphériques sur toutes ses couches est un point critique de la hauteur. Nous donnons un algorithme pour tester si un réseau donné satisfait cette condition de 2-designs, et nous donnons des tables de résultats en dimension jusqu’à 7. Ensuite, nous montrons qu’un réseau qui réalise un minimum local de la hauteur est nécessairement irréductible. Enfin, nous nous intéressons à certains tores définis sur les corps de nombres quadratiques imaginaires, et nous prouvons une formule qui donne leur hauteur comme limite d’une suite de hauteurs de tores complexes discrets.

In this thesis we consider the Epstein zeta function of Euclidean lattices, in order to study the problem of the minima of the height of the flat torus associated to a lattice. The height is defined as the first derivative at the point s = 0 of the spectral zeta function of the torus ; this function coincides, up to a factor, with the Epstein zeta function of the dual lattice of the given lattice. We describe a sufficient condition for a given lattice to be a stationary point of the height. In particular, by means of the theory of spherical designs, we show that a lattice which has a spherical 2-design on every shell is a stationary point of the height. We give an algorithm to check whether a given lattice satisfies this 2-design condition or not, and we give some tables of results in dimension up to 7. Then, we show that a lattice which realises a local minimum of the height is necessarily irreducible. Finally, we deal with some tori defined over the imaginary quadratic number fields, and we show a formula which gives their height as a limit of a sequence of heights of discrete complex tori.

Advisors/Committee Members: Coulangeon, Renaud (thesis director).

Subjects/Keywords: Réseau euclidien; Noyau de la chaleur.; Laplacien; Design sphérique; Hauteur; Fonction zêta d’Epstein; Tore plat; Euclidean lattice; Heat kernel; Laplacian; Spherical design; Height; Epstein’s zeta function; Flat torus

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

APA (6^th Edition):

Lazzarini, G. (2015). Sur la hauteur de tores plats : On the height of Flat Tori. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2015BORD0018

Chicago Manual of Style (16^th Edition):

Lazzarini, Giovanni. “Sur la hauteur de tores plats : On the height of Flat Tori.” 2015. Doctoral Dissertation, Bordeaux. Accessed January 17, 2020. http://www.theses.fr/2015BORD0018.

MLA Handbook (7^th Edition):

Lazzarini, Giovanni. “Sur la hauteur de tores plats : On the height of Flat Tori.” 2015. Web. 17 Jan 2020.

Vancouver:

Lazzarini G. Sur la hauteur de tores plats : On the height of Flat Tori. [Internet] [Doctoral dissertation]. Bordeaux; 2015. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2015BORD0018.

Council of Science Editors:

Lazzarini G. Sur la hauteur de tores plats : On the height of Flat Tori. [Doctoral Dissertation]. Bordeaux; 2015. Available from: http://www.theses.fr/2015BORD0018

INP Toulouse

17. Mouysset, Sandrine. Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications.

Degree: Docteur es, Signal, Image, Acoustique et Optimisation, 2010, INP Toulouse

URL: http://www.theses.fr/2010INPT0088

►

La classification spectrale consiste à créer, à partir des éléments spectraux d'une matrice d'affinité gaussienne, un espace de dimension réduite dans lequel les données sont… (more)

▼

La classification spectrale consiste à créer, à partir des éléments spectraux d'une matrice d'affinité gaussienne, un espace de dimension réduite dans lequel les données sont regroupées en classes. Cette méthode non supervisée est principalement basée sur la mesure d'affinité gaussienne, son paramètre et ses éléments spectraux. Cependant, les questions sur la séparabilité des classes dans l'espace de projection spectral et sur le choix du paramètre restent ouvertes. Dans un premier temps, le rôle du paramètre de l'affinité gaussienne sera étudié à travers des mesures de qualités et deux heuristiques pour le choix de ce paramètre seront proposées puis testées. Ensuite, le fonctionnement même de la méthode est étudié à travers les éléments spectraux de la matrice d'affinité gaussienne. En interprétant cette matrice comme la discrétisation du noyau de la chaleur définie sur l'espace entier et en utilisant les éléments finis, les vecteurs propres de la matrice affinité sont la représentation asymptotique de fonctions dont le support est inclus dans une seule composante connexe. Ces résultats permettent de définir des propriétés de classification et des conditions sur le paramètre gaussien. A partir de ces éléments théoriques, deux stratégies de parallélisation par décomposition en sous-domaines sont formulées et testées sur des exemples géométriques et de traitement d'images. Enfin dans le cadre non supervisé, le classification spectrale est appliquée, d'une part, dans le domaine de la génomique pour déterminer différents profils d'expression de gènes d'une légumineuse et, d'autre part dans le domaine de l'imagerie fonctionnelle TEP, pour segmenter des régions du cerveau présentant les mêmes courbes d'activités temporelles.

The Spectral Clustering consists in creating, from the spectral elements of a Gaussian affinity matrix, a low-dimension space in which data are grouped into clusters. This unsupervised method is mainly based on Gaussian affinity measure, its parameter and its spectral elements. However, questions about the separability of clusters in the projection space and the spectral parameter choices remain open. First, the rule of the parameter of Gaussian affinity will be investigated through quality measures and two heuristics for choosing this setting will be proposed and tested. Then, the method is studied through the spectral element of the Gaussian affinity matrix. By interpreting this matrix as the discretization of the heat kernel defined on the whole space and using finite elements, the eigenvectors of the affinity matrix are asymptotic representation of functions whose support is included in one connected component. These results help define the properties of clustering and conditions on the Gaussian parameter. From these theoretical elements, two parallelization strategies by decomposition into sub-domains are formulated and tested on geometrical examples and images. Finally, as unsupervised applications, the spectral clustering is applied, first in the field of genomics to identify different gene…

Advisors/Committee Members: Noailles, Joseph (thesis director), Ruiz, Daniel (thesis director).

Subjects/Keywords: Classification non supervisée; Classification spectrale; Noyau gaussien; Equation de la chaleur; Éléments finis; Parallélisation; Imagerie médicale; Clustering; Spectral clustering; Gaussian kernel; Heat equation; Finite elements; Parallelization; Medical imaging

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

APA (6^th Edition):

Mouysset, S. (2010). Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2010INPT0088

Chicago Manual of Style (16^th Edition):

Mouysset, Sandrine. “Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications.” 2010. Doctoral Dissertation, INP Toulouse. Accessed January 17, 2020. http://www.theses.fr/2010INPT0088.

MLA Handbook (7^th Edition):

Mouysset, Sandrine. “Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications.” 2010. Web. 17 Jan 2020.

Vancouver:

Mouysset S. Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications. [Internet] [Doctoral dissertation]. INP Toulouse; 2010. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2010INPT0088.

Council of Science Editors:

Mouysset S. Contributions à l'étude de la classification spectrale et applications : Contributions to the study of spectral clustering and applications. [Doctoral Dissertation]. INP Toulouse; 2010. Available from: http://www.theses.fr/2010INPT0088

Kyoto University

18. Nakamura, Chikara. Asymptotic behaviors of random walks; application of heat kernel estimates .

Degree: 2018, Kyoto University

URL: http://hdl.handle.net/2433/232222

Subjects/Keywords: random walk; heat kernel estimate; random environment; mixing time and cutoff; fractal

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

APA (6^th Edition):

Nakamura, C. (2018). Asymptotic behaviors of random walks; application of heat kernel estimates . (Thesis). Kyoto University. Retrieved from http://hdl.handle.net/2433/232222

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):

Nakamura, Chikara. “Asymptotic behaviors of random walks; application of heat kernel estimates .” 2018. Thesis, Kyoto University. Accessed January 17, 2020. http://hdl.handle.net/2433/232222.

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

MLA Handbook (7^th Edition):

Nakamura, Chikara. “Asymptotic behaviors of random walks; application of heat kernel estimates .” 2018. Web. 17 Jan 2020.

Vancouver:

Nakamura C. Asymptotic behaviors of random walks; application of heat kernel estimates . [Internet] [Thesis]. Kyoto University; 2018. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/2433/232222.

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

Council of Science Editors:

Nakamura C. Asymptotic behaviors of random walks; application of heat kernel estimates . [Thesis]. Kyoto University; 2018. Available from: http://hdl.handle.net/2433/232222

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

Université de Lorraine

19. Kayser, Laurent. Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels.

Degree: Docteur es, Mathématiques, 2015, Université de Lorraine

URL: http://www.theses.fr/2015LORR0259

►

Nous revisitons la méthode classique des paramétrices pour en déduire une minoration et une majoration gaussiennes, pour la solution fondamentale d'un opérateur parabolique général sous… (more)

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Nous revisitons la méthode classique des paramétrices pour en déduire une minoration et une majoration gaussiennes, pour la solution fondamentale d'un opérateur parabolique général sous forme non divergentielle. Nous utilisons ensuite le fait que la fonction de Neumann Green, d'un opérateur parabolique général sur un ouvert borné régulier, peut être construite comme somme de la solution fondamentale et d'une intégrale de type simple couche parabolique pour établir une minoration gaussienne pour cette fonction de Neumann Green. Le point clef de la preuve réside dans l'effet régularisant, en temps, de l'intégrale de type simple couche. Nous démontrons aussi que cette approche peut être adaptée pour démontrer une minoration gaussienne pour la fonction de Green-Neumann correspondante à l'opérateur de Laplace-Beltrami sur un ouvert régulier d'une variété riemannienne compacte sans bord. Nous démontrons ensuite une nouvelle majoration gaussienne pour la fonction de Neumann Green correspondante à l'opérateur de Laplace-Beltrami sur un ouvert Lipschitz d'une variété riemannienne complète. L'intérêt de cette nouvelle majoration est qu'elle ne contient pas le terme habituel d'une exponentielle en temps. Finalement, comme application des estimations gaussiennes, nous donnons un résultat de compacité des potentiels isospectraux en relation avec une formule asymptotique pour les noyaux de la chaleur

We revisit the parametrix method in order to obtain a gaussian two-sided bound for the fundamental solution of a general parabolic operator which is not in a divergence form. Then we use the fact that the Neumann Green function of a general parabolic operator on a regular bounded domain can be constructed as a perturbation of the fundamental solution by a simple-layer potential in order to establish a Gaussian lower bound for this Neumann Green function. The key point of the proof lies in the time-regularising effect of the single-layer potential. We also prove that this method can be adapted to get a lower Gaussian bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold. In a second part, we prove a new Gaussian upper bound for the Neumann heat kernel of the Laplace-Beltrami operator on a Lipschitz domain of a complete Riemannian manifold. The principal interest of this new upper bound is that we do not have the usual exponentiel terme in time in this upper bound. In a last part, as an application of the Gaussian estimates, we give a compactness result of isospectral potentials which is in relation to an asymptotic formule for the heat kernels

Advisors/Committee Members: Choulli, Mourad (thesis director).

Subjects/Keywords: Opérateur parabolique; Solution fondamentale; Fonction de Neumann Green; Noyau de la chaleur; Parabolic operator; Fundamental solution; Neumann Green function; Heat kernel; 512.556

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

APA (6^th Edition):

Kayser, L. (2015). Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2015LORR0259

Chicago Manual of Style (16^th Edition):

Kayser, Laurent. “Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels.” 2015. Doctoral Dissertation, Université de Lorraine. Accessed January 17, 2020. http://www.theses.fr/2015LORR0259.

MLA Handbook (7^th Edition):

Kayser, Laurent. “Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels.” 2015. Web. 17 Jan 2020.

Vancouver:

Kayser L. Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels. [Internet] [Doctoral dissertation]. Université de Lorraine; 2015. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2015LORR0259.

Council of Science Editors:

Kayser L. Estimations gaussiennes des noyaux de la chaleur : Gaussian estimates for heat kernels. [Doctoral Dissertation]. Université de Lorraine; 2015. Available from: http://www.theses.fr/2015LORR0259

Université Paris-Sud – Paris XI

20. Chen, Li. Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates.

Degree: Docteur es, Mathématiques, 2014, Université Paris-Sud – Paris XI

URL: http://www.theses.fr/2014PA112068

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Dans cette thèse nous étudions les transformées de Riesz et les espaces de Hardy associés à un opérateur sur un espace métrique mesuré. Ces deux… (more)

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Dans cette thèse nous étudions les transformées de Riesz et les espaces de Hardy associés à un opérateur sur un espace métrique mesuré. Ces deux sujets sont en lien avec des estimations du noyau de la chaleur associé à cet opérateur. Dans les Chapitres 1, 2 et 4, on étudie les transformées quasi de Riesz sur les variétés riemannienne et sur les graphes. Dans le Chapitre 1, on prouve que les quasi transformées de Riesz sont bornées dans Lp pour 1<p<2. Dans le Chapitre 2, on montre que les quasi transformées de Riesz est aussi de type faible (1,1) si la variété satisfait la propriété de doublement du volume et l'estimation sous-gaussienne du noyau de la chaleur. On obtient des résultats analogues sur les graphes dans le Chapitre 4. Dans le Chapitre 3, on développe la théorie des espaces de Hardy sur les espaces métriques mesurés avec des estimations différentes localement et globalement du noyau de la chaleur. On définit les espaces de Hardy par les molécules et par les fonctions quadratiques. On montre tout d'abord que ces deux espaces H1 sont les mêmes. Puis, on compare l'espace Hp défini par par les fonctions quadratiques et Lp. On montre qu'ils sont équivalents. Mais on trouve des exemples tels que l'équivalence entre Lp et Hp défini par les fonctions quadratiques avec l'homogénéité t2 n'est pas vraie. Finalement, comme application, on montre que les quasi transformées de Riesz sont bornées de H1 dans L1 sur les variétés fractales. Dans le Chapitre 5, on prouve des inégalités généralisées de Poincaré et de Sobolev sur les graphes de Vicsek. On montre aussi qu'elles sont optimales.

In this thesis, we mainly study Riesz transforms and Hardy spaces associated to operators. The two subjects are closely related to volume growth and heat kernel estimates. In Chapter 1, 2 and 4, we study Riesz transforms on Riemannian manifold and on graphs. In Chapter 1, we prove that on a complete Riemannian manifold, the quasi Riesz transform is always Lp bounded on for p strictly large than 1 and no less than 2. In Chapter 2, we prove that the quasi Riesz transform is also weak L1 bounded if the manifold satisfies the doubling volume property and the sub-Gaussian heat kernel estimate. Similarly, we show in Chapter 4 the same results on graphs. In Chapter 3, we develop a Hardy space theory on metric measure spaces satisfying the doubling volume property and different local and global heat kernel estimates. Firstly we define Hardy spaces via molecules and via square functions which are adapted to the heat kernel estimates. Then we show that the two H1 spaces via molecules and via square functions are the same. Also, we compare the Hp space defined via square functions with Lp. The corresponding Hp space for p large than 1 defined via square functions is equivalent to the Lebesgue space Lp. However, it is shown that in this situation, the Hp space corresponding to Gaussian estimates does not coincide with Lp any more. Finally, as an application of this Hardy space theory, we proved that quasi Riesz transforms are bounded from H1 to L1…

Advisors/Committee Members: Auscher, Pascal (thesis director), Coulhon, Thierry (thesis director).

Subjects/Keywords: Transformées de Riesz; Espaces de Hardy; Espaces métriques mesurés; Graphes; Estimations du noyau de la chaleur; Riesz transforms; Hardy spaces; Metric measure spaces; Graphs; Heat kernel estimates

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

APA (6^th Edition):

Chen, L. (2014). Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates. (Doctoral Dissertation). Université Paris-Sud – Paris XI. Retrieved from http://www.theses.fr/2014PA112068

Chicago Manual of Style (16^th Edition):

Chen, Li. “Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates.” 2014. Doctoral Dissertation, Université Paris-Sud – Paris XI. Accessed January 17, 2020. http://www.theses.fr/2014PA112068.

MLA Handbook (7^th Edition):

Chen, Li. “Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates.” 2014. Web. 17 Jan 2020.

Vancouver:

Chen L. Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates. [Internet] [Doctoral dissertation]. Université Paris-Sud – Paris XI; 2014. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2014PA112068.

Council of Science Editors:

Chen L. Quasi transformées de Riesz, espaces de Hardy et estimations sous-gaussiennes du noyau de la chaleur : Quasi Riesz transforms, Hardy spaces and generalized sub-Gaussian heat kernel estimates. [Doctoral Dissertation]. Université Paris-Sud – Paris XI; 2014. Available from: http://www.theses.fr/2014PA112068

21. Danelakis, Antonios. Facial expression retrieval using 3-dimensional mesh sequences.

Degree: 2016, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/38226

► In recent years, the increased availability of inexpensive 3D object acquisition hardware and simplified 3D modeling software has resulted in the creation of massive 3D… (more)

▼ In recent years, the increased availability of inexpensive 3D object acquisition hardware and simplified 3D modeling software has resulted in the creation of massive 3D facial expression mesh sequences datasets that are either publicly available or for proprietary use. Consiquently, two new problems for the research community arose: Facial Expression Recognition from 3D mesh sequences and Facial Expression Retrieval from 3D mesh sequences. The first problem has gained a lot of interest among the research community. On the contrary, no sufficient research has been conducted on the second problem that deals with Retrieval.This dissertation focuses on the problem of facial expression retrieval from large datasets of 3D facial expressions mesh sequences. In order to address this problem we develop a 3-step retrieval scheme: (i) initially, eight 3D facial landmarks are automatically detected on each 3D face mesh of the sequence. (ii) Next, the landmarks extracted in the previous step, are used in order for the descriptors of the 3D facial expression mesh sequence to be created. (iii) Finally, appropriate distance functions are used in order for different descriptors (i.e. query descriptor vs dataset descriptor) to be compared and the retrieval list is produced. The core of the problem is the creation of appropriate descriptors. Six pioneer descriptors were created during this dissertation for 3D mesh sequence facial expression retrieval purposes (GeoTopo, GeoTopo+, DCT-GeoTopo, WT-GeoTopo+, CVD, WT-CVD). The aforementioned descriptors steadily increased the retrieval evaluation metrics. Two of them are spatial, which means that they are based only on spatial modifications of the facial expressions across time, and the remaining four are spatio-temporal, which means that they are based on both time and space modifications of the facial expressions.GeoTopo is a hybrid spatial descriptor which captures the topological as well as the geometric information of the 3D face meshes along time. This is achieved by concatenating two different sub-descriptors, one for the topology and one for the geometry of the 3D face mesh. GeoTopo+ is a hybrid spatial descriptor and is an improved version of GeoTopo. GeoTopo+ used two sub-descriptors for capturing the facial geometry and one for capturing facial topology.The motivation behind the proposed spatial, hybrid facial expression descriptors is the fact that some facial expressions, like happiness and surprise, are characterized by obvious changes in the mouth topology while others, like anger, fear and sadness, produce geometric but no significant topological changes.DCT-GeoTopo is the first attempt of constructing a spatio-temporal descriptor for 3D mesh sequence facial expression retrieval purposes. Initially, DCT-GeoTopo descriptor captures topological information of the 3D facial expression sequence. In the sequel, Discrete Cosine Transformation is applied on the aforementioned information consulting to the final spatio-temporal descriptor. WT-GeoTopo+ is a hybrid spatio-temporal…

Subjects/Keywords: Δυναμική τριδιάστατη πλεγματοσειρά; Aνάκτηση αντικειμένου; Κυρτότητα; Υπογραφή θερμότητας κελύφους; Κανονικά διανύσματα; Μετασχηματισμός συνημίτονου/κυματιδίων; Dynamic 3D mesh sequence; Object retrieval; Curvature; Heat kernel signature; Normal vectors; Cosine/Wavelet transformation

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

APA (6^th Edition):

Danelakis, A. (2016). Facial expression retrieval using 3-dimensional mesh sequences. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/38226

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):

Danelakis, Antonios. “Facial expression retrieval using 3-dimensional mesh sequences.” 2016. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed January 17, 2020. http://hdl.handle.net/10442/hedi/38226.

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

MLA Handbook (7^th Edition):

Danelakis, Antonios. “Facial expression retrieval using 3-dimensional mesh sequences.” 2016. Web. 17 Jan 2020.

Vancouver:

Danelakis A. Facial expression retrieval using 3-dimensional mesh sequences. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2016. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/10442/hedi/38226.

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

Council of Science Editors:

Danelakis A. Facial expression retrieval using 3-dimensional mesh sequences. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2016. Available from: http://hdl.handle.net/10442/hedi/38226

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

Loughborough University

22. Li, Liangpan. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.

Degree: PhD, 2016, Loughborough University

URL: http://hdl.handle.net/2134/23004

► In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact,… (more)

▼ In this dissertation we study non-negative self-adjoint Laplace type operators acting on smooth sections of a vector bundle. First, we assume base manifolds are compact, boundaryless, and Riemannian. We start from the Fourier integral operator representation of half-wave operators, continue with spectral zeta functions, heat and resolvent trace asymptotic expansions, and end with the quantitative Wodzicki residue method. In particular, all of the asymptotic coefficients of the microlocalized spectral counting function can be explicitly given and clearly interpreted. With the auxiliary pseudo-differential operators ranging all smooth endomorphisms of the given bundle, we obtain certain asymptotic estimates about the integral kernel of heat operators. As applications, we study spectral asymptotics of Dirac type operators such as characterizing those for which the second coefficient vanishes. Next, we assume vector bundles are trivial and base manifolds are Euclidean domains, and study non-negative self-adjoint extensions of the Laplace operator which acts component-wise on compactly supported smooth functions. Using finite propagation speed estimates for wave equations and explicit Fourier Tauberian theorems obtained by Yuri Safarov, we establish the principle of not feeling the boundary estimates for the heat kernel of these operators. In particular, the implied constants are independent of self-adjoint extensions. As a by-product, we affirmatively answer a question about upper estimate for the Neumann heat kernel. Finally, we study some specific values of the spectral zeta function of two-dimensional Dirichlet Laplacians such as spectral determinant and Casimir energy. For numerical purposes we substantially improve the short-time Dirichlet heat trace asymptotics for polygons. This could be used to measure the spectral determinant and Casimir energy of polygons whenever the first several hundred or one thousand Dirichlet eigenvalues are known with high precision by other means.

Subjects/Keywords: 515; Local spectral asymptotics; Heat kernel; Dirac operators; Laplace operators; Pseudo-differential operators; Fourier integral operators; Wodzicki residue; Finite propagation speed; Spectral determinant

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

APA (6^th Edition):

Li, L. (2016). Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/23004

Chicago Manual of Style (16^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Doctoral Dissertation, Loughborough University. Accessed January 17, 2020. http://hdl.handle.net/2134/23004.

MLA Handbook (7^th Edition):

Li, Liangpan. “Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators.” 2016. Web. 17 Jan 2020.

Vancouver:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Internet] [Doctoral dissertation]. Loughborough University; 2016. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/2134/23004.

Council of Science Editors:

Li L. Local spectral asymptotics and heat kernel bounds for Dirac and Laplace operators. [Doctoral Dissertation]. Loughborough University; 2016. Available from: http://hdl.handle.net/2134/23004

23. Duan, Xiaoxi. Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates.

Degree: PhD, Mathematics & Statistics, 2016, York University

URL: http://hdl.handle.net/10315/32286

► We first construct the minimal and maximal operators of the Hermite operator.Then we apply a classical reslult by Askey and Wainger, to prove that for… (more)

Subjects/Keywords: Mathematics; Heat kernel; Green function; Fourth-order operator; L^p-estimates; Minimal and maximal operators; Hermite operator; Twisted Laplacian; Twisted bi-Laplacian; Trace; Zeta function regularization; Spectral theory.

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

APA (6^th Edition):

Duan, X. (2016). Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates. (Doctoral Dissertation). York University. Retrieved from http://hdl.handle.net/10315/32286

Chicago Manual of Style (16^th Edition):

Duan, Xiaoxi. “Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates.” 2016. Doctoral Dissertation, York University. Accessed January 17, 2020. http://hdl.handle.net/10315/32286.

MLA Handbook (7^th Edition):

Duan, Xiaoxi. “Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates.” 2016. Web. 17 Jan 2020.

Vancouver:

Duan X. Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates. [Internet] [Doctoral dissertation]. York University; 2016. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/10315/32286.

Council of Science Editors:

Duan X. Complex Powers of a Fourth-Order Operator: Heat Kernels, Green Functions and Lp - Lp1 Estimates. [Doctoral Dissertation]. York University; 2016. Available from: http://hdl.handle.net/10315/32286

Université de Grenoble

24. Sharma, Avinash. Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel.

Degree: Docteur es, Mathématiques, 2012, Université de Grenoble

URL: http://www.theses.fr/2012GRENM053

►

Analyse de la forme 3D est un sujet de recherche extrêmement actif dans les deux l'infographie et vision par ordinateur. Dans la vision par ordinateur,… (more)

▼

Analyse de la forme 3D est un sujet de recherche extrêmement actif dans les deux l'infographie et vision par ordinateur. Dans la vision par ordinateur, l'acquisition de formes et de modélisation 3D sont généralement le résultat du traitement des données complexes et des méthodes d'analyse de données. Il existe de nombreuses situations concrètes où une forme visuelle est modélisé par un nuage de points observés avec une variété de capteurs 2D et 3D. Contrairement aux données graphiques, les données sensorielles ne sont pas, dans le cas général, uniformément répartie sur toute la surface des objets observés et ils sont souvent corrompus par le bruit du capteur, les valeurs aberrantes, les propriétés de surface (diffusion, spécularités, couleur, etc), l'auto occlusions, les conditions d'éclairage variables. Par ailleurs, le même objet que l'on observe par différents capteurs, à partir de points de vue légèrement différents, ou à des moments différents cas peuvent donner la répartition des points tout à fait différentes, des niveaux de bruit et, plus particulièrement, les différences topologiques, par exemple, la fusion des mains. Dans cette thèse, nous présentons une représentation de multi-échelle des formes articulés et concevoir de nouvelles méthodes d'analyse de forme, en gardant à l'esprit les défis posés par les données de forme visuelle. En particulier, nous analysons en détail le cadre de diffusion de chaleur pour représentation multi-échelle de formes 3D et proposer des solutions pour la segmentation et d'enregistrement en utilisant les méthodes spectrales graphique et divers algorithmes d'apprentissage automatique, à savoir, le modèle de mélange gaussien (GMM) et le Espérance-Maximisation (EM). Nous présentons d'abord l'arrière-plan mathématique sur la géométrie différentielle et l'isomorphisme graphique suivie par l'introduction de la représentation spectrale de formes 3D articulés. Ensuite, nous présentons une nouvelle méthode non supervisée pour la segmentation de la forme 3D par l'analyse des vecteurs propres Laplacien de graphe. Nous décrivons ensuite une solution semi-supervisé pour la segmentation de forme basée sur un nouveau paradigme d'apprendre, d'aligner et de transférer. Ensuite, nous étendre la représentation de forme 3D à une configuration multi-échelle en décrivant le noyau de la chaleur cadre. Enfin, nous présentons une méthode d'appariement dense grâce à la représentation multi-échelle de la chaleur du noyau qui peut gérer les changements topologiques dans des formes visuelles et de conclure par une discussion détaillée et l'orientation future des travaux.

3D shape analysis is an extremely active research topic in both computer graphics and computer vision. In computer vision, 3D shape acquisition and modeling are generally the result of complex data processing and data analysis methods. There are many practical situations where a visual shape is modeled by a point cloud observed with a variety of 2D and 3D sensors. Unlike the graphical data, the sensory data are not, in the general case,…

Advisors/Committee Members: Horaud, Radu (thesis director).

Subjects/Keywords: Vision par ordinateur; Analyse de forme 3D articulée; Formes visuelles; Noyau de la chaleur; Appariement dense; Segmentation non supervisée; Computer Vision; Articulated 3D Shape Analysis; Visual Shapes; Heat Kernel; Dense Matching; Unsupervised Segmentation

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

APA (6^th Edition):

Sharma, A. (2012). Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel. (Doctoral Dissertation). Université de Grenoble. Retrieved from http://www.theses.fr/2012GRENM053

Chicago Manual of Style (16^th Edition):

Sharma, Avinash. “Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel.” 2012. Doctoral Dissertation, Université de Grenoble. Accessed January 17, 2020. http://www.theses.fr/2012GRENM053.

MLA Handbook (7^th Edition):

Sharma, Avinash. “Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel.” 2012. Web. 17 Jan 2020.

Vancouver:

Sharma A. Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel. [Internet] [Doctoral dissertation]. Université de Grenoble; 2012. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2012GRENM053.

Council of Science Editors:

Sharma A. Représentation et enregistrement de formes visuelles 3D à l'aide de Laplacien graphe et noyau de la chaleur : Representation & Registration of 3D Visual Shapes using Graph Laplacian and Heat Kernel. [Doctoral Dissertation]. Université de Grenoble; 2012. Available from: http://www.theses.fr/2012GRENM053

25. El Khoury, Rachid. Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D.

Degree: Docteur es, Informatique, 2013, Evry, Institut national des télécommunications

URL: http://www.theses.fr/2013TELE0009

►

Un nombre croissant d’applications graphiques 3D ont un impact sur notre société. Ces applications sont utilisées dans plusieurs domaines allant des produits de divertissement numérique,… (more)

▼

Un nombre croissant d’applications graphiques 3D ont un impact sur notre société. Ces applications sont utilisées dans plusieurs domaines allant des produits de divertissement numérique, la conception assistée par ordinateur, aux applications médicales. Dans ce contexte, un moteur de recherche d’objets 3D avec de bonnes performances en résultats et en temps d’exécution devient indispensable. Nous proposons une nouvelle méthode pour l’indexation de modèles 3D basée sur des courbes fermées. Nous proposons ensuite une amélioration de notre méthode pour l’indexation partielle de modèles 3D. Notre approche commence par la définition d’une nouvelle fonction d’application invariante. Notre fonction d’application possède des propriétés importantes : elle est invariante aux transformations rigides et non rigides, elle est insensible au bruit, elle est robuste à de petits changements topologiques et elle ne dépend pas de paramètres. Cependant, dans la littérature, une telle fonction qui respecte toutes ces propriétés n’existe pas. Pour respecter ces propriétés, nous définissons notre fonction basée sur la distance de diffusion et la distance de migration pendulaire. Pour prouver les propriétés de notre fonction, nous calculons le graphe de Reeb de modèles 3D. Pour décrire un modèle 3D complet, en utilisant notre fonction d’application, nous définissons des courbes de niveaux fermées à partir d’un point source détecté automatiquement au centre du modèle 3D. Chaque courbe décrit alors une région du modèle 3D. Ces courbes créent un descripteur invariant à différentes transformations. Pour montrer la robustesse de notre méthode sur différentes classes de modèles 3D dans différentes poses, nous utilisons des objets provenant de SHREC 2012. Nous comparons également notre approche aux méthodes de l’état de l’art à l’aide de la base SHREC 2010. Pour l’indexation partielle de modèles 3D, nous améliorons notre approche en utilisant la technique sacs de mots, construits à partir des courbes fermées extraites, et montrons leurs bonnes performances à l’aide de la base précédente

A growing number of 3D graphic applications have an impact on today’s society. These applications are being used in several domains ranging from digital entertainment, computer aided design, to medical applications. In this context, a 3D object search engine with a good performance in time consuming and results becomes mandatory. We propose a novel approach for 3D-model retrieval based on closed curves. Then we enhance our method to handle partial 3D-model retrieval. Our method starts by the definition of an invariant mapping function. The important properties of a mapping function are its invariance to rigid and non rigid transformations, the correct description of the 3D-model, its insensitivity to noise, its robustness to topology changes, and its independance on parameters. However, current state-of-the-art methods do not respect all these properties. To respect these properties, we define our mapping function based on the diffusion and the commute-time…

Advisors/Committee Members: Vandeborre, Jean-Philippe (thesis director), Daoudi, Mohamed (thesis director).

Subjects/Keywords: Modèles 3D; Noyau de la chaleur; Distance de diffusion; Distance de migration pendulaire; Graphes de Reeb; Indexation; Indexation partielle; Sacs de mots; 3D-models; Heat kernel; Diffusion distance; Commute time distance; Reeb graphs; Retrieval; Partial retrieval; Bag-of-features

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

APA (6^th Edition):

El Khoury, R. (2013). Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D. (Doctoral Dissertation). Evry, Institut national des télécommunications. Retrieved from http://www.theses.fr/2013TELE0009

Chicago Manual of Style (16^th Edition):

El Khoury, Rachid. “Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D.” 2013. Doctoral Dissertation, Evry, Institut national des télécommunications. Accessed January 17, 2020. http://www.theses.fr/2013TELE0009.

MLA Handbook (7^th Edition):

El Khoury, Rachid. “Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D.” 2013. Web. 17 Jan 2020.

Vancouver:

El Khoury R. Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D. [Internet] [Doctoral dissertation]. Evry, Institut national des télécommunications; 2013. [cited 2020 Jan 17]. Available from: http://www.theses.fr/2013TELE0009.

Council of Science Editors:

El Khoury R. Partial 3D-shape indexing and retrieval : Indexation partielle de modèles 3D. [Doctoral Dissertation]. Evry, Institut national des télécommunications; 2013. Available from: http://www.theses.fr/2013TELE0009

26. 福田, 真; フクダ, マコト. 高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　.

Degree: Kumamoto University / 熊本大学

URL: http://hdl.handle.net/2298/14291

本論文では高次元におけるfermionのheat kernel（ヒートカーネル）に現れる諸量及びそれらの積や導関数をγ行列の完全反対称積で与えられる行列について既約分解する公式を求めた。また量子効果の計算に対してhear kernelを用いる手法が有効であることから、6次元においてこの漸近展開係数を求めるために必要な諸量も既約な行列について分解された形で求めた。任意の次元でfermionが全ての種類の背景場と相互作用する場合を仮定したため、非常に一般的な結果が得られた。

Subjects/Keywords: Heat kernel; 量子効果; 2階微分演算子; HMDS係数; γ

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

APA (6^th Edition):

福田, 真; フクダ, �. (n.d.). 高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　. (Thesis). Kumamoto University / 熊本大学. Retrieved from http://hdl.handle.net/2298/14291

Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

福田, 真; フクダ, マコト. “高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　.” Thesis, Kumamoto University / 熊本大学. Accessed January 17, 2020. http://hdl.handle.net/2298/14291.

Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

福田, 真; フクダ, マコト. “高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　.” Web. 17 Jan 2020.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

福田, 真; フクダ �. 高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　. [Internet] [Thesis]. Kumamoto University / 熊本大学; [cited 2020 Jan 17]. Available from: http://hdl.handle.net/2298/14291.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.

Council of Science Editors:

福田, 真; フクダ �. 高次元におけるヒートカーネルの漸近展開係数に対するガンマ行列の既約分解について : コウジゲンニオケルヒートカーネルノゼンキンテンカイケイスウニタイスルガンマギョウレツノキヤクブンカイニツイテ　. [Thesis]. Kumamoto University / 熊本大学; Available from: http://hdl.handle.net/2298/14291

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.

27. Yang, Xue. Neumann Problems for Second Order Elliptic Operators with Singular Coefficients.

Degree: 2012, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:161090

► In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients,… (more)

Subjects/Keywords: Dirichlet form; Neumann boundary problem; Heat kernel; Fukushima's decomposition; Mixed boundary condition; Reflecting diffusion

…conditions. Here we mention three papers. Two-sided estimates of the heat kernel of reflecting ˆ… …are not established for the heat kernel there. Using the estimates on heat kernels… …lower bound estimates on the heat kernel of Gaussian type associated with operator L equipped… …t, x, y) which is the heat kernel associated with the semigroup Tt in the sense: Tt g… …estimates for the heat kernel l(t, x, y) associated with operator L equipped with the…

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

APA (6^th Edition):

Yang, X. (2012). Neumann Problems for Second Order Elliptic Operators with Singular Coefficients. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:161090

Chicago Manual of Style (16^th Edition):

Yang, Xue. “Neumann Problems for Second Order Elliptic Operators with Singular Coefficients.” 2012. Doctoral Dissertation, University of Manchester. Accessed January 17, 2020. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:161090.

MLA Handbook (7^th Edition):

Yang, Xue. “Neumann Problems for Second Order Elliptic Operators with Singular Coefficients.” 2012. Web. 17 Jan 2020.

Vancouver:

Yang X. Neumann Problems for Second Order Elliptic Operators with Singular Coefficients. [Internet] [Doctoral dissertation]. University of Manchester; 2012. [cited 2020 Jan 17]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:161090.

Council of Science Editors:

Yang X. Neumann Problems for Second Order Elliptic Operators with Singular Coefficients. [Doctoral Dissertation]. University of Manchester; 2012. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:161090

28. Hong, Seunghun. A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces.

Degree: PhD, Mathematics, 2012, Penn State University

URL: https://etda.libraries.psu.edu/catalog/15454

► Using a K-theory point of view, R. Bott related the Atiyah-Singer index theorem for elliptic operators on compact homogeneous spaces to the Weyl character formula.… (more)

Subjects/Keywords: local index theory; cubic Dirac operator; heat kernel asymptotics; compact homogeneous spaces; quantum Weil algebra

…called heat kernel proof of the index theorem. This is not the original approach took by M… …Atiyah and I. M. Singer. But the heat kernel proof is stronger in that we have a local index… …local index theorem. Our strategy is to deduce /2 / the heat kernel of D k)2 . To that g… …k via the heat kernel of D(g, / end, we consider the preimage L of D(g, k)2… …that the asymptotic / expansion of the heat kernel of D(g, k)2 follows immediately…

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

APA (6^th Edition):

Hong, S. (2012). A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/15454

Chicago Manual of Style (16^th Edition):

Hong, Seunghun. “A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces.” 2012. Doctoral Dissertation, Penn State University. Accessed January 17, 2020. https://etda.libraries.psu.edu/catalog/15454.

MLA Handbook (7^th Edition):

Hong, Seunghun. “A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces.” 2012. Web. 17 Jan 2020.

Vancouver:

Hong S. A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces. [Internet] [Doctoral dissertation]. Penn State University; 2012. [cited 2020 Jan 17]. Available from: https://etda.libraries.psu.edu/catalog/15454.

Council of Science Editors:

Hong S. A Lie-algebraic Approach to the Local Index Theorem on Compact Homogeneous Spaces. [Doctoral Dissertation]. Penn State University; 2012. Available from: https://etda.libraries.psu.edu/catalog/15454

29. ZHANG XI. Handwritten Document Image Retrieval.

Degree: 2014, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/118200

Subjects/Keywords: Text line segmentation; handwritten word recognition; heat kernel signature; keyword spotting; handwritten document image retrieval

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

APA (6^th Edition):

XI, Z. (2014). Handwritten Document Image Retrieval. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/118200

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):

XI, ZHANG. “Handwritten Document Image Retrieval.” 2014. Thesis, National University of Singapore. Accessed January 17, 2020. http://scholarbank.nus.edu.sg/handle/10635/118200.

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

MLA Handbook (7^th Edition):

XI, ZHANG. “Handwritten Document Image Retrieval.” 2014. Web. 17 Jan 2020.

Vancouver:

XI Z. Handwritten Document Image Retrieval. [Internet] [Thesis]. National University of Singapore; 2014. [cited 2020 Jan 17]. Available from: http://scholarbank.nus.edu.sg/handle/10635/118200.

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

Council of Science Editors:

XI Z. Handwritten Document Image Retrieval. [Thesis]. National University of Singapore; 2014. Available from: http://scholarbank.nus.edu.sg/handle/10635/118200

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

Université de Neuchâtel

30. Reviron, Guillemette. Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur.

Degree: 2005, Université de Neuchâtel

URL: http://doc.rero.ch/record/5123

► Les théorèmes de (pré)compacité ou de " bornitude " s'établissent généralement sur l'ensemble des variétés de dimension, diamètre et courbure bornés, qui n'est pas complet… (more)

Subjects/Keywords: Metric spaces; volume entropy; topoligical rigidity; Gromov-Hausdorff distance; spectral distance; precompactness; convergence; heat kernel; length spectrum; volume of balls; covers

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

APA (6^th Edition):

Reviron, G. (2005). Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur. (Thesis). Université de Neuchâtel. Retrieved from http://doc.rero.ch/record/5123

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):

Reviron, Guillemette. “Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur.” 2005. Thesis, Université de Neuchâtel. Accessed January 17, 2020. http://doc.rero.ch/record/5123.

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

MLA Handbook (7^th Edition):

Reviron, Guillemette. “Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur.” 2005. Web. 17 Jan 2020.

Vancouver:

Reviron G. Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur. [Internet] [Thesis]. Université de Neuchâtel; 2005. [cited 2020 Jan 17]. Available from: http://doc.rero.ch/record/5123.

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

Council of Science Editors:

Reviron G. Espaces de longueur d’entropie majorée: Rigidité topologique, adhérence des variétés, noyau de la chaleur. [Thesis]. Université de Neuchâtel; 2005. Available from: http://doc.rero.ch/record/5123

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

Open Access Theses and Dissertations