Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 8 of 8 for “"Hermite polynomials"”.
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A New Asymptotic Expansion for Sums of Random Variables
… involves the cumulants of X, as well as Hermite polynomials. The expansion defined in this thesis uses a rival sequence of coefficients dependent on the probability function p, which does not require the calculation of cumulants, or the use of Hermite polynomials. The advantages of this …
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Digital Transmission by Hermite N-Dimensional Antipodal Scheme
… signs baseband orthogonal waveforms derived from Hermite polynomials. Orthogonality guarantees recoverability of the data from N simultaneously transmitted Hermite waveforms. The signed Hermite waveform is transmitted over a radio link using either amplitude or frequency modulation. The bandwidth …
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Discrete Sparse Fourier Hermite Approximations in High Dimensions
… this dissertation, the discrete sparse Fourier Hermite approximation of a function in a specified Hilbert space of arbitrary dimension is defined, and theoretical error bounds of the numerically computed approximation are proven. Computing the Fourier Hermite approximation in high dimensions …
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The stochastic modelling of the neuronal membrane potential in response to synaptic input
… Through the use of a spectral procedure based on Hermite Polynomials it is shown that the marginal probability density function of the membrane potential can be estimated to arbitrarily accuracy. The procedure is illustrated for one level of approximation.
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A study of local approximations in information theory
… of additive white Gaussian noise channels are Hermite polynomials, and the singular vectors of Poisson channels are Laguerre polynomials. We characterize the set of infinite alphabet channels whose singular value decompositions produce singular vectors that are orthogonal polynomials by …
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Approximation of wave packets on the whole real line
… for a wave packet in stretched Fourier, Hermite and Malmquist--Takenaka bases respectively. These estimates are extremely accurate in the high frequency regime. The results within these chapters allow us to compare the speed of convergence of the expansion coefficients to determine which …
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Numerical and Analytical Studies of Electromagnetic Waves: Hermite Methods, Supercontinuum Generation, and Multiple Poles in the SEM
The dissertation consists of three parts: Hermite methods, scattering from a lossless sphere, and analysis of supercontinuum generation. Hermite methods are a new class of arbitrary order algorithms to solve partial differential equations (PDE). In the first chapter, we discuss the fundamentals of …
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A Meshless Method for Magnetohydrodynamics and Applications to Protoplanetary Disks
This thesis presents an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares …