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Showing 1 to 12 of 12 for “"Carleman"”.
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Solving Nonlinear Aeronautical Problems Using the Carleman Linearization Method
… in terms of nonlinear systems of equations. Carleman developed a technique to linearize such equations that could lead to analytical solutions of nonlinear problems. Nonlinear problems are difficult to solve in closed form and therefore the construction of such solutions is usually …
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Qualitative Models of Neural Activity and the Carleman Embedding Technique.
… visualized. In this thesis, it is shown that the Carleman Embedding Technique can be applied to both the Fitzhugh Nagumo model and to Van der Pol's model of nonlinear oscillation, which are both finite nonlinear systems of differential equations. The Carleman technique can thus be used to obtain …
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A Variation of the Carleman Embedding Method for Second Order Systems.
<p>The Carleman Embedding is a method that allows us to embed a finite dimensional system of nonlinear differential equations into a system of infinite dimensional linear differential equations. This technique works well when dealing with first-order nonlinear differential equations. However, for …
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An Extension of the Denjoy-Carleman-Ahlfors Theorem in Subharmonic Form
Made available in DSpace on 2014-12-09T22:17:10Z (GMT). No. of bitstreams: 1 6406154.pdf: 3932803 bytes, checksum: a1b36659f97a6a9630bfc6fe2584ac8f (MD5) Previous issue date: 1963
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Asymptotics of Carleman Polynomials for Level Curves of the Inverse of a Shifted Joukowsky Transformation
Let L be a level curve of the inverse of the shifted Joukowsky transformation w [special characters omitted] w − 1 + (w − 1) –1, that is, [special characters omitted]In this thesis we investigate the asymptotic properties of the sequence of polynomials that are orthonormal over the interior domain …
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Solving the Differential Equation for the Probit Function Using a Variant of the Carleman Embedding Technique.
… of great utility in statistical modelling. The Carleman embedding technique has been shown to be effective in solving first order and, less efficiently, second order nonlinear differential equations. In this thesis, we show that solutions to the second order nonlinear differential equation for …
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Parameter Estimation for a Modified Cable Model Using a Green's Function and Eigenvalue Perturbation.
… We then use the Green's Function to develop a Carleman linear embedding scheme which is used to estimate the effects of a nonlinear ion channel hot-spot on the tapered cylinder solution. Mathematica<sup>©</sup> was used to implement the Carleman embedding scheme.</p>
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The Duffing Oscillator And Linearization Techniques For Its Motion Constants
… A linear representation is found through Carleman Linearization. This is a technique used to linearize a finite dimensional nonlinear system of differential equations to an infinite dimensional, linear, autonomous system of differential equations. Using Carleman Linearization, the Duffing …
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Spectral theory using linear systems and sampling from the spectrum of Hill's equation
… Rc analogous to Rx, such that the roots of their Carleman determinants are elements of the periodic spectrum of Hill’s equation. The latter half concerns sampling from entire functions in Paley–Wiener space. From the periodic spectrum of Hill’s equation we derive a sampling sequence, (tn)n∈Z. …
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The Calderón problem for connections
… exact) can be shown to exist by using suitable Carleman estimates. In the case $m = 1$, we prove the recovery of the connection given the injectivity of the $X$-ray transform on $0$ and $1$-forms on $M_0$. For $m > 1$ and $M_0$ simple we reduce the problem to a certain two dimensional …