A. F. Quesada’s research while affiliated with United States Air Force and other places

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Publications (4)


The power spectrum of the Mellin transformation with applications to scaling of physical quantities
  • Article

June 1974

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8 Reads

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17 Citations

H. E. Moses

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A. F. Quesada

The Mellin transform is used to diagonalize the dilation operator in a manner analogous to the use of the Fourier transform to diagonalize the translation operator. A power spectrum is also introduced for the Mellin transform which is analogous to that used for the Fourier transform. Unlike the case for the power spectrum of the Fourier transform where sharp peaks correspond to periodicities in translation, the peaks in the power spectrum of the Mellin transform correspond to periodicities in magnification. A theorem of Wiener‐Khinchine type is introduced for the Mellin transform power spectrum. It is expected that the new power spectrum will play an important role extracting meaningful information from noisy data and will thus be a useful complement to the use of the ordinary Fourier power spectrum.


A Meteorological and a Geophysical Example of the Use of the Scale Autocorrelation Coefficient to Determine Ratios of Frequencies Present in Periodic Phenomena

September 1973

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3 Reads

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2 Citations

Journal of Geophysical Research Atmospheres

In a previous work it was shown that the scale autocorrelation coefficient, which compares a function of time with itself when the scale of time is stretched, could be used to determine ratios of frequencies that occur in phenomena with periodicities. We review the properties of the scale autocorrelation coefficient and apply it to the finding of some of the ratios of the frequencies in atmospheric pressures measured daily for 8766 days. We also apply it to measurements of the international magnetic character figure Ci, which was measured daily for 27,258 days. We regard these applications as the first test of the utility of the scale autocorrelation coefficient. The results indicate that the scale autocorrelation coefficient may indeed prove to be a valuable supplement to the use of the usual autocorrelation coefficient and the Fourier transformation of time-dependent functions.


The expansion of physical quantities in terms of the irreducible representations of the scale-Euclidean group and applications to the construction of scale-invariant correlation functions. II: Three- dimensional problems; generalizations of the Helmholtz vector decomposition theorem

January 1973

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7 Reads

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12 Citations

Archive for Rational Mechanics and Analysis

The irreducible representations of the scale-Euclidean group in three dimensions are introduced, and the general tensor is expanded in terms of these representations. The cases of zero-rank tensor (scalar), rank-1 tensor (vector), and rank-2 tensor are studied in detail. The expansion is shown to be a generalization of the Helmholtz expansion of a vector into rotational and irrotational parts. As in Part I of this work (Concepts: One-Dimensional Problems), the correlations that are introduced are invariant under changes of frames of reference. Correlations are set up between tensors of different ranks and dimensions. A correlation that measures a degree of isotropy is defined.


The expansion of physical quantities in terms of the irreducible representations of the scale-Euclidean group and applications to the construction of scale-invariant correlation functions

August 1972

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10 Reads

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15 Citations

Archive for Rational Mechanics and Analysis

The group of transformations is introduced which consists of translation, rotation, and dilation of a Euclidean coordinate system. It is shown how physical quantities can be expanded in the irreducible representations of the group. It is then possible to introduce correlations which are invariant under the transformations of the group. The most novel feature is the introduction of a scale autocorrelation which compares a quantity with itself when “stretched”. This autocorrelation is expected to find use in problems involving noise and turbulence. It is shown in the present paper how this new autocorrelation enables one to find relationships between periodicities. This paper is concerned with concepts and the one-dimensional problem. Part II will deal with three-dimensional problems.

Citations (3)


... When written in the equivalent form in Equation (28), Equation (13) coincides with the invariant scalar product for the relevant representations of the scale-Euclidean group in [40,Equation (29)]. The extra 1/|k| 2 in Equation (29) of [40] with respect to Equation (28) in this paper is compensated by the extra 1/|k| factor in the plane wave decomposition in [40,Equation (57)] as compared to Equation (10). ...

Reference:

A Scalar Product for Computing Fundamental Quantities in Matter
The expansion of physical quantities in terms of the irreducible representations of the scale-Euclidean group and applications to the construction of scale-invariant correlation functions. II: Three- dimensional problems; generalizations of the Helmholtz vector decomposition theorem
  • Citing Article
  • January 1973

Archive for Rational Mechanics and Analysis

... The expressions are obtained as a scalar product Φ|Γ|Φ , where |Φ represents {ρ(r), M(r)}, and Γ is the Hermitian operator * ivan.fernandez-corbaton@kit.edu representing the particular quantity of interest. The expression of the scalar product for static matter is derived for the static fields that are bijectively connected to ρ(r) and M(r) by first considering the largest group of transformations that leave the Maxwell equations invariant, the conformal group, then excluding the transformations that would not preserve the ω = 0 condition of static fields, and finally obtaining a scalar product invariant under the remaining group of transformations, which is the scale-Euclidean group composed by translations, rotations and spatial scalings [10,11]. The form of the scalar product that we obtain for static fields with ω = 0 is very similar to the form of the scalar product for dynamic fields with ω > 0. Such similarity allows one to reuse for the static case expressions that are known for dynamic fields. ...

The expansion of physical quantities in terms of the irreducible representations of the scale-Euclidean group and applications to the construction of scale-invariant correlation functions
  • Citing Article
  • August 1972

Archive for Rational Mechanics and Analysis