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Relevant bibliographies by topics / LAURENT TRANSFORM

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Journal articles

Academic literature on the topic 'LAURENT TRANSFORM'

Author: Grafiati

Published: 11 September 2023

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Journal articles on the topic "LAURENT TRANSFORM"

1

SUN, YAN-KUI. "SYMMETRIC LIFTING FACTORIZATION AND MATRIX REPRESENTATION OF BIORTHOGONAL WAVELET TRANSFORMS." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 04 (2003): 465–79. http://dx.doi.org/10.1142/s0219691303000244.

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This paper introduces some properties of symmetric Laurent polynomials, and then extends Euclidean algorithm to symmetric Laurent polynomials. The new results are used to investigate factorization of polyphase matrix for biorthogonal finite filters. It is shown that there exists one and only one symmetric factorization of the polyphase matrix, and the symmetric factorization can be determined directly and efficiently by Euclidean algorithm for symmetric Laurent polynomials. Finally, symmetric implementation and matrix representation of biorthogonal wavelet transforms are introduced, and the st

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2

Fischer, Jens. "Four Particular Cases of the Fourier Transform." Mathematics 6, no. 12 (2018): 335. http://dx.doi.org/10.3390/math6120335.

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In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under

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3

Sinclair, Christopher D. "The distribution of Mahler's measures of reciprocal polynomials." International Journal of Mathematics and Mathematical Sciences 2004, no. 52 (2004): 2773–86. http://dx.doi.org/10.1155/s0161171204312469.

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We study the distribution of Mahler's measures of reciprocal polynomials with complex coefficients and bounded even degree. We discover that the distribution function associated to Mahler's measure restricted to monic reciprocal polynomials is a reciprocal (or antireciprocal) Laurent polynomial on[1,∞)and identically zero on[0,1). Moreover, the coefficients of this Laurent polynomial are rational numbers times a power ofπ. We are led to this discovery by the computation of the Mellin transform of the distribution function. This Mellin transform is an even (or odd) rational function with poles

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4

Settu, S. A. "SP Transform and Uniform Convergence of Laurent and Power Series." Canadian Mathematical Bulletin 30, no. 1 (1987): 114–23. http://dx.doi.org/10.4153/cmb-1987-017-1.

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AbstractIf the Laurent seriesis transformed toit is shown that convergence of the former at z = 1 implies the uniform convergence of the latter on a symmetric arc of |z - 1/P| = 1/P - 1 not containing z = 1 and that the uniform convergence of the former over a symmetric arc of |z| = 1 containing z = 1 implies uniform convergence of the latter on the entire circle |z — 1/P| = 1/P — 1.

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5

Berriochoa, Elías, Alicia Cachafeiro, and Jaime Díaz. "Hermite Interpolation on the Unit Circle Considering up to the Second Derivative." ISRN Mathematical Analysis 2014 (March 10, 2014): 1–10. http://dx.doi.org/10.1155/2014/808519.

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The paper is devoted to study the Hermite interpolation problem on the unit circle. The interpolation conditions prefix the values of the polynomial and its first two derivatives at the nodal points and the nodal system is constituted by complex numbers equally spaced on the unit circle. We solve the problem in the space of Laurent polynomials by giving two different expressions for the interpolation polynomial. The first one is given in terms of the natural basis of Laurent polynomials and the remarkable fact is that the coefficients can be computed in an easy and efficient way by means of th

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6

Watts, Benjamin. "Calculation of the Kramers-Kronig transform of X-ray spectra by a piecewise Laurent polynomial method." Optics Express 22, no. 19 (2014): 23628. http://dx.doi.org/10.1364/oe.22.023628.

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7

Coussement, J., A. B. J. Kuijlaars, and W. Van Assche. "Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials." Inverse Problems 18, no. 3 (2002): 923–42. http://dx.doi.org/10.1088/0266-5611/18/3/325.

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8

Alam, Parvez, Santimoy Kundu, and Shishir Gupta. "Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source." Journal of Intelligent Material Systems and Structures 29, no. 11 (2018): 2508–21. http://dx.doi.org/10.1177/1045389x18770877.

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Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool

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9

Zemanian, A. H., and B. Anderson. "Modeling of borehole resistivity measurements using infinite electrical grids." GEOPHYSICS 52, no. 11 (1987): 1525–34. http://dx.doi.org/10.1190/1.1442269.

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An infinite electrical resistive grid generated by a finite‐difference approximation to Poisson’s equation in cylindrical coordinates with no azimuthal variation has been used to model borehole resistivity measurements. The medium surrounding the borehole is infinite in extent and its resistivity varies only in the radial direction. As a result, the branch resistance values of the infinite grid also vary only in the radial direction. A continued fraction of Laurent operators determines the node voltages along the borehole’s surface. Use of an operational calculus based upon the finite Fourier

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10

Muro, Masakazu. "Singular invariant hyperfunctions on the square matrix space and the alternating matrix space." Nagoya Mathematical Journal 169 (2003): 19–75. http://dx.doi.org/10.1017/s0027763000008448.

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AbstractFundamental calculations on singular invariant hyperfunctions on the n ×n square matrix space and on the 2n × 2n alternating matrix space are considered in this paper. By expanding the complex powers of the determinant function or the Pfaffian function into the Laurent series with respect to the complex parameter, we can construct singular invariant hyperfunctions as their Laurent expansion coefficients. The author presents here the exact orders of the poles of the complex powers and determines the exact supports of the Laurent expansion coefficients. By applying these results, we prov

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