Thus far, we have seen a number of different approaches to extracting information from data. This week, we will discuss the Fourier transform, and other related transformations that map data into a rather different space, while preserving the information. The Fourier transformation is usually presented as an operation that transforms data from the “time” or “space” domain, into “frequency” doma...

I apply Fourier and Chebyshev spectral methods to derive accurate and efficient algorithms for velocity continuation. As expected, the accuracy of the spectral methods is noticeably superior to that of the finite-difference approach. Both methods apply a transformation of the time axis to squared time. The Chebyshev method is slightly less efficient than the Fourier method, but has less problem...

Thus far, we have seen a number of different approaches to extracting information from data. This week, we will discuss the Fourier transform, and other related transformations that map data into a rather different space, while preserving the information. The Fourier transformation is usually presented as an operation that transforms data from the “time” or “space” domain, into “frequency” doma...

Thus far, we have seen a number of different approaches to extracting information from data. This week, we will discuss the Fourier transform, and other related transformations that map data into a rather different space, while preserving the information. The Fourier transformation is usually presented as an operation that transforms data from the “time” or “space” domain, into “frequency” doma...

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

By using a spectral approach, we derive a Gaussian-like quadrature of the continuous fractional Fourier transform. The quadrature is obtained from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials. These eigenvectors are discrete approximations of the Hermite functions, which are eigenfunctions of the fractional Fourier transform oper...

: In this study we fabricated Zinc Oxide thin film by sol-gel dip coating method on glass substrate. X-ray reflectivity (XRR) and its optimization have been used for characterization and extracting physical parameters of the film. Genetic Algorithm (GA) has been applied for this optimization process. Independent information was exploited from Fourier transform of Fresnel reflectivity normalized...

We calculate the local Fourier transformations for a class of Q l -sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([L] 2.6.3).

We calculate the local Fourier transformations for a class of Q l -sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([L] 2.6.3).

We calculate the local Fourier transformations for a class of Q l -sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([L] 2.6.3).