The Experts below are selected from a list of 20454 Experts worldwide ranked by ideXlab platform
Michal Ryznar - One of the best experts on this subject based on the ideXlab platform.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains. AMS 2000 subject classifications: Primary 60J35, 60J50; secondary 60J75, 31B25. Keywords and phrases: fractional Laplacian, Dirichlet problem, heat kernel estimate, Lipschitz domain, boundary Harnack principle.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains.
Krzysztof Bogdan - One of the best experts on this subject based on the ideXlab platform.
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principal eigenvalue of the fractional laplacian with a large incompressible drift
Nodea-nonlinear Differential Equations and Applications, 2014Co-Authors: Krzysztof Bogdan, Tomasz KomorowskiAbstract:We study the principal Dirichlet eigenvalue of the operator \({L_A=\Delta^{\alpha/2}+Ab(x)\cdot\nabla}\), on a bounded C1,1 regular domain D. Here \({\alpha\in(1,2)}\), \({\Delta^{\alpha/2}}\) is the fractional Laplacian, \({A\in\mathbb{R}}\), and b is a bounded d-dimensional divergence-free vector field in the Sobolev space W1,2d/(d+α)(D). We prove that the eigenvalue remains bounded, as A→ + ∞, if and only if b has non-trivial first integrals in the domain of the quadratic form of \({\Delta^{\alpha/2}}\) for the Dirichlet Condition.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains. AMS 2000 subject classifications: Primary 60J35, 60J50; secondary 60J75, 31B25. Keywords and phrases: fractional Laplacian, Dirichlet problem, heat kernel estimate, Lipschitz domain, boundary Harnack principle.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains.
Tomasz Grzywny - One of the best experts on this subject based on the ideXlab platform.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains. AMS 2000 subject classifications: Primary 60J35, 60J50; secondary 60J75, 31B25. Keywords and phrases: fractional Laplacian, Dirichlet problem, heat kernel estimate, Lipschitz domain, boundary Harnack principle.
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heat kernel estimates for the fractional laplacian with Dirichlet Conditions
Annals of Probability, 2010Co-Authors: Krzysztof Bogdan, Tomasz Grzywny, Michal RyznarAbstract:We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet Condition for a general class of domains including Lipschitz domains.
Xingfu Zou - One of the best experts on this subject based on the ideXlab platform.
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Dirichlet problem of a delayed reaction diffusion equation on a semi infinite interval
Journal of Dynamics and Differential Equations, 2016Co-Authors: Xingfu ZouAbstract:We consider a nonlocal delayed reaction–diffusion equation in a semi-infinite interval that describes mature population of a single species with two age stages (immature and mature) and a fixed maturation period living in a spatially semi-infinite environment. Homogeneous Dirichlet Condition is imposed at the finite end, accounting for a scenario that boundary is hostile to the species. Due to the lack of compactness and symmetry of the spatial domain, the global dynamics of the equation turns out to be a very challenging problem. We first establish a priori estimate for nontrivial solutions after exploring the delicate asymptotic properties of the nonlocal delayed effect and the diffusion operator. Using the estimate, we are able to show the repellency of the trivial equilibrium and the existence of a positive heterogeneous steady state under the Dirichlet boundary Condition. We then employ the dynamical system arguments to establish the global attractivity of the heterogeneous steady state. As a byproduct, we also obtain the existence and global attractivity of the heterogeneous steady state for the bistable evolution equation in the whole space.
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on Dirichlet problem for a class of delayed reaction diffusion equations with spatial non locality
Journal of Dynamics and Differential Equations, 2013Co-Authors: Xingfu ZouAbstract:We consider a very general class of delayed reaction–diffusion equations in which the reaction term can be non-monotone as well as spatially non-local. By employing comparison technique and a dynamical system approach, we study the global asymptotic behavior of solutions to the equation subject to the homogeneous Dirichlet Condition. Established are threshold results and global attractiveness of the trivial steady state, as well as the existence, uniqueness and global attractiveness of a positive steady state solution to the problem. As illustrations, we apply our main results to the local delayed diffusive Mackey–Glass equation and the nonlocal delayed diffusive Nicholson blowfly equation, leading to some very sharp results for these two particular models.
Masami Ando - One of the best experts on this subject based on the ideXlab platform.
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Differential phase-contrast computed tomography reconstruction based on the projection theorem for Laplacian image
2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), 2016Co-Authors: Naoki Sunaguchi, Tetsuya Yuasa, Rajiv Gupta, Shu Ichihara, Masami AndoAbstract:We propose an efficient reconstruction algorithm from limited-view projections for differential phase-contrast computed tomography, based on the projection theorem for Laplacian image, proved in the research. First, the algorithm first reconstructs the Laplacian image of the target phase-shift-term distribution from the second-derivative projections obtained experimentally with the total variation regularization, which is ensured by the theorem. Then, it obtains the phase-shift-term distribution by solving a Poisson equation with a source being the Laplacian image reconstructed in the previous stage under the Dirichlet Condition. We demonstrate the efficacy of the algorithm using synthetic data generated by computer codes based a differential phase-contrast imaging. The method can efficiently and satisfactorily reconstruct from the limited number of projections.
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an efficient reconstruction algorithm for differential phase contrast tomographic images from a limited number of views
Applied Physics Letters, 2015Co-Authors: Naoki Sunaguchi, Tetsuya Yuasa, Rajiv Gupta, Masami AndoAbstract:The main focus of this paper is reconstruction of tomographic phase-contrast image from a set of projections. We propose an efficient reconstruction algorithm for differential phase-contrast computed tomography that can considerably reduce the number of projections required for reconstruction. The key result underlying this research is a projection theorem that states that the second derivative of the projection set is linearly related to the Laplacian of the tomographic image. The proposed algorithm first reconstructs the Laplacian image of the phase-shift distribution from the second-derivative of the projections using total variation regularization. The second step is to obtain the phase-shift distribution by solving a Poisson equation whose source is the Laplacian image previously reconstructed under the Dirichlet Condition. We demonstrate the efficacy of this algorithm using both synthetically generated simulation data and projection data acquired experimentally at a synchrotron. The experimental phase data were acquired from a human coronary artery specimen using dark-field-imaging optics pioneered by our group. Our results demonstrate that the proposed algorithm can reduce the number of projections to approximately 33% as compared with the conventional filtered backprojection method, without any detrimental effect on the image quality.