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Showing 1 to 11 of 11 for “"Laplacian operator"”.
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Generalized integral transforms related to the theory of potential and stokes flow
… The following problems are analyzed: (a) The Laplacian operator in the interior of a Square, (b) the Laplacian operator in the interior and exterior of a Sphere and, (c) the Stokes' operator concerning the irrotational flow of an incompressible, viscous fluid. Moreover, the behaviour of the …
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Variational Methods for p-Laplacian Sturm-Liouville Problems
… we address the problem of eigencurves for the p-Laplacian operator on [0,1]. First we examine the simple case where p=2. Next, we prove the existence and several properties of the first eigencurve and its corresponding eigenfunction. In chapters 4 and 5, the nonhomogeneous case is considered. …
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Completion and validation of the design of a reconfigurable image processing board
… transmit only selected data. It uses the pseudo-laplacian operator, invented by Dr. Nadler, for edge detection. According to a recent survey of various edge detection algorithms by D. E. Pearson, [1], the pseudo-laplacian operator is the most efficient one and it produces the most natural …
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Effects of grid lattice geometry on digital image filtering
… developed that are best approximations to the Laplacian operator applied to continuous two- dimensional mathematical surfaces. Discrepancies between the calculated Laplacian and the digital filtering results are analyzed and a criterion is developed that compares grid lattice effects. The …
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Design of Asymmetric Slope Fractional Band Reject Filters
… 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 filters, …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… theory, including eigenvalues of the Dirichlet Laplacian operator. We discuss the Direct Methods of Calculus of Variations and Critical Point Theory, together with examples of how these techniques are applied to solving PDEs. We show how the existence of solutions to semilinear elliptic …
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Fourth order spectral theory and diffusion-driven instability
… innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second order Laplacian. We find new phenomena when the fourth order and second order terms are competing, meaning one of them stabilizes the system …
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Advanced numerical methods for image denoising and segmentation
… the “block effect”. Second, a weighted sum operator is used to replace the Laplacian operator in the Y-K model. Such replacement can relieve the creation of the speckles which is brought in by the Y-K model and preserve more details. Third, an adaptive relaxation method with a discontinuity …
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Mathematical modelling of complex dynamics
… analysed by making use of different discrete Laplacian operators using well–chosen time steps in CDS. This analysis offers stability conditions for phase–field, based on the Cahn–Hilliard Cook (CHC) equations of which CDS is the finite difference approximation. To overcome grid related …
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Sound and mathematics
Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.
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Sound and mathematics
Laplacian differential operator -- Vibrations of plucked strings and Hollow cylinders.