Global ETD Search
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Showing 1 to 9 of 9 for “"Fractional Laplacian"”.
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A tensor product approach to non-local differential complexes
… non-local operators, such as operators of fractional Laplacian type. We show that these complexes can be used to approximate complexes of differential forms in a non-local-to-local convergence on the level of cores. Under an absolute continuity condition, we construct Hilbert complexes, …
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Design of Asymmetric Slope Fractional Band Reject Filters
… functions are presented based on the concept of fractional Laplacian operator, s^(α) where 0 < α < 1. It is possible to achieve asymmetric slopes, large values of notch magnitude up to 90 dB and high Q values for appropriate values of α using these filters. In addition, unlike integer order …
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Qualitative Properties Of Solutions Of Fully Nonlinear Equations And Overdetermined Problems
… of balls in terms of the Riesz potential and fractional Laplacian. These results answer two open questions W. Reichel to some extent.</p>
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Stability of Periodic Waves in Nonlocal Dispersive Equations
… class of periodic bound state solutions of the Fractional Nonlinear Schrodinger Equation, where the nonlocality of the fractional Laplacian presents formidable analytical challenges and elicits the development of functional-analytic tools to complement the absence of more-understood techniques …
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On intrinsic ultracontractivity of perturbed Levy processes and applications of Levy processes in actuarial mathematics
… the intrinsic ultracontractivity of the Laplacian (corresponding to Brownian motions) and the fractional Laplacian (corresponding to symmetric $\alpha$-stable processes) perturbed by a class of nonlocal operators. Conditions on the nonlocal perturbations are given in order to guarantee …
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Heat trace and heat content asymptotics for Schrodinger Operators of stable processes/fractional Laplacians
… <em>V</em>. The former operator is known as the fractional Laplacian whereas the latter one is known as the fractional Schrödinger Operator. ^ The study of the small time behaviour of the above quantities is motivated by the asymptotic expansion as <em>t</em> ↓ 0 of the following spectral …
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Nonuniqueness of Laws on State and Path Space: Flow Selections and Superposition for Fokker-Planck-Kolmogorov Equations and Convex Integration for Stochastic Hypodissipative Navier-Stokes Equations
… integration} to the incompressible fractional Navier--Stokes equations on the $3$D torus, with the exponent $\alpha$ of the fractional Laplacian in the range $0<\alpha < 1/2$, perturbed by an additive Brownian noise. Similar to comparable existing results for other stochastic …
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On the derivation of non-local diffusion equations in confined spaces
The subject of the thesis is the derivation of non-local diffusion equations from kinetic models with heavy-tailed equilibrium in velocity. We are particularly interested in confining the kinetic equations and developing methods that allow us, from the confined kinetic models, to derive confined …