The Experts below are selected from a list of 5202 Experts worldwide ranked by ideXlab platform
Jason Levesley - One of the best experts on this subject based on the ideXlab platform.
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an Inhomogeneous Wave Equation and non linear diophantine approximation
Advances in Mathematics, 2008Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:Abstract A non-linear Diophantine condition involving perfect squares and arising from an Inhomogeneous Wave Equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.
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diophantine approximation with perfect squares and the solvability of an Inhomogeneous Wave Equation
arXiv: Analysis of PDEs, 2005Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an Inhomogeneous Wave Equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy to ensure the solvability of the Inhomogeneous Wave Equation by a smooth periodic function. To derive this information, a complete metric theory for a related fully nonlinear Diophantine approximation problem involving perfect squares is established.
K Ziegler - One of the best experts on this subject based on the ideXlab platform.
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rigorous derivation of superposition t matrix approach from solution of Inhomogeneous Wave Equation
Journal of Quantitative Spectroscopy & Radiative Transfer, 2008Co-Authors: Pavel Litvinov, K ZieglerAbstract:The problem of electromagnetic scattering by a system of particles is considered. Starting from the integral solution of the Inhomogeneous Wave Equation, the Equations for Green's and transition operators are derived. By expressing the free space dyadic Green's function in terms of vector spherical Wave functions, the relations between the matrix elements of the dyadic transition operator and T matrix are established. On the basis of these relations the Equations which allow determining the T matrices for a system of particles using T matrices for isolated particles are derived.
Victor Beresnevich - One of the best experts on this subject based on the ideXlab platform.
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an Inhomogeneous Wave Equation and non linear diophantine approximation
Advances in Mathematics, 2008Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:Abstract A non-linear Diophantine condition involving perfect squares and arising from an Inhomogeneous Wave Equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.
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diophantine approximation with perfect squares and the solvability of an Inhomogeneous Wave Equation
arXiv: Analysis of PDEs, 2005Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an Inhomogeneous Wave Equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy to ensure the solvability of the Inhomogeneous Wave Equation by a smooth periodic function. To derive this information, a complete metric theory for a related fully nonlinear Diophantine approximation problem involving perfect squares is established.
Pavel Litvinov - One of the best experts on this subject based on the ideXlab platform.
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rigorous derivation of superposition t matrix approach from solution of Inhomogeneous Wave Equation
Journal of Quantitative Spectroscopy & Radiative Transfer, 2008Co-Authors: Pavel Litvinov, K ZieglerAbstract:The problem of electromagnetic scattering by a system of particles is considered. Starting from the integral solution of the Inhomogeneous Wave Equation, the Equations for Green's and transition operators are derived. By expressing the free space dyadic Green's function in terms of vector spherical Wave functions, the relations between the matrix elements of the dyadic transition operator and T matrix are established. On the basis of these relations the Equations which allow determining the T matrices for a system of particles using T matrices for isolated particles are derived.
Simon Kristensen - One of the best experts on this subject based on the ideXlab platform.
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an Inhomogeneous Wave Equation and non linear diophantine approximation
Advances in Mathematics, 2008Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:Abstract A non-linear Diophantine condition involving perfect squares and arising from an Inhomogeneous Wave Equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.
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diophantine approximation with perfect squares and the solvability of an Inhomogeneous Wave Equation
arXiv: Analysis of PDEs, 2005Co-Authors: Victor Beresnevich, M M Dodson, Simon Kristensen, Jason LevesleyAbstract:The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an Inhomogeneous Wave Equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy to ensure the solvability of the Inhomogeneous Wave Equation by a smooth periodic function. To derive this information, a complete metric theory for a related fully nonlinear Diophantine approximation problem involving perfect squares is established.