The principle of complex frequency scaling—Applicability in inclined continuation of potential fields

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 2019-2023 ◽  
Author(s):  
R. Nagendra ◽  
N. Laxminarayana
Keyword(s):  
Fourier Transforms ◽  
Potential Fields ◽  
Dimensional Structure ◽  
Complex Frequency ◽  
Two Dimensional ◽  
Complex Scaling ◽  
Frequency Scaling ◽  
Space Frequency ◽  
Scaling Principle ◽  
Inclined Planes

A remarkable property of Fourier transforms, especially applicable to inclined continuation of potential geophysical fields, is the principle of “complex frequency scaling.” Briefly stated, let [Formula: see text] be the (gravity/magnetic) field due to a two‐dimensional structure along a principal profile and F(ω) be its Fourier transform. The field along a profile passing through the same reference origin and tilted by an angle ϕ in the counter‐clockwise direction (+X to −Z) is obtained by inverse Fourier transforming F[ωexp(−iϕ)] for positive ω. The complex scaling property and proof of the resulting space‐frequency domain relationship are presented, introducing the total field as the analytic signal of the horizontal component. The applicability of the complex scaling principle is illustrated by considering selected geometric models. This principle can be advantageously applied for continuation of two‐dimensional potential fields onto inclined planes.

DIRECTIONAL AND WIDE‐BAND VELOCITY FILTERING

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 279-280
Author(s):  
Philip L. Jackson
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Wide Band ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Contour Map ◽  
Directional Filtering ◽  
Velocity Filtering ◽  
Monochromatic Illumination

The purpose of this note is to point out that the condition of monochromatic illumination in obtaining a two‐dimensional Fourier transform by optical means may be relaxed for wide‐band velocity filtering, and for the directional filtering of any two‐dimensional structure such as a contour map. Similar considerations hold for two‐dimensional Fourier transforms obtained by any means.

Three-Dimensional Structure of Cloned T3 Connector Protein at 1.6nm Resolution

1990 ◽  
Vol 48 (1) ◽  
pp. 282-283
Author(s):  
José L. Carrascosa ◽  
José M. Valpuesta ◽  
Hisao Fujisawa
Keyword(s):  
Dna Sequences ◽  
Expression Vector ◽  
Three Dimensional ◽  
Deae Cellulose ◽  
Dna Packaging ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Freezing And Thawing ◽  
Three Dimensional Structure ◽  
Dimensional Reconstruction

The head to tail connector of bacteriophages plays a fundamental role in the assembly of viral heads and DNA packaging. In spite of the absence of sequence homology, the structure of connectors from different viruses (T4, Ø29, T3, P22, etc) share common morphological features, that are most clearly revealed in their three-dimensional structure. We have studied the three-dimensional reconstruction of the connector protein from phage T3 (gp 8) from tilted view of two dimensional crystals obtained from this protein after cloning and purification.DNA sequences including gene 8 from phage T3 were cloned, into Bam Hl-Eco Rl sites down stream of lambda promotor PL, in the expression vector pNT45 under the control of cI857. E R204 (pNT89) cells were incubated at 42°C for 2h, harvested and resuspended in 20 mM Tris HC1 (pH 7.4), 7mM 2 mercaptoethanol, ImM EDTA. The cells were lysed by freezing and thawing in the presence of lysozyme (lmg/ml) and ligthly sonicated. The low speed supernatant was precipitated by ammonium sulfate (60% saturated) and dissolved in the original buffer to be subjected to gel nitration through Sepharose 6B, followed by phosphocellulose colum (Pll) and DEAE cellulose colum (DE52). Purified gp8 appeared at 0.3M NaCl and formed crystals when its concentration increased above 1.5 mg/ml.

scholarly journals A First-Principle Study of Monolayer Transition Metal Carbon Trichalcogenides

2021 ◽  
Author(s):  
Muhammad Yar Khan ◽  
Yan Liu ◽  
Tao Wang ◽  
Hu Long ◽  
Miaogen Chen ◽  
...  
Keyword(s):  
Phonon Dispersion ◽  
Magnetic Ordering ◽  
Dimensional Structure ◽  
First Principle ◽  
Two Dimensional ◽  
Biaxial Strain ◽  
Half Metallic ◽  
First Principle Calculations ◽  
Potential Applications ◽  
External Strain

AbstractMonolayer MnCX3 metal–carbon trichalcogenides have been investigated by using the first-principle calculations. The compounds show half-metallic ferromagnetic characters. Our results reveal that their electronic and magnetic properties can be altered by applying uniaxial or biaxial strain. By tuning the strength of the external strain, the electronic bandgap and magnetic ordering of the compounds change and result in a phase transition from the half-metallic to the semiconducting phase. Furthermore, the vibrational and thermodynamic stability of the two-dimensional structure has been verified by calculating the phonon dispersion and molecular dynamics. Our study paves guidance for the potential applications of these two mono-layers in the future for spintronics and straintronics devices.

Generalized signal-tuned Gabor approach for signal representation and analysis

2017 ◽  
Vol 28 (01) ◽  
pp. 1750001 ◽  
Author(s):  
José R. A. Torreão
Keyword(s):  
Fourier Transform ◽  
Visual Cortex ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Receptive Fields ◽  
Gabor Functions ◽  
Plausible Model ◽  
Spectral Signal ◽  
Potential Applications ◽  
Space Frequency

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

STM Study on Quinacridone Derivative Assemblies:  Modulation of the Two-dimensional Structure by Coadsorption with Dicarboxylic Acids

Langmuir ◽  
2005 ◽  
Vol 21 (16) ◽  
pp. 7225-7229 ◽  
Author(s):  
Xunyu Yang ◽  
Zhongcheng Mu ◽  
Zhiqiang Wang ◽  
Xi Zhang ◽  
Jia Wang ◽  
...  
Keyword(s):  
Dicarboxylic Acids ◽  
Dimensional Structure ◽  
Two Dimensional

Synthesis of Inhibitor Nanocontainers with Two-Dimensional Structure and Their Anticorrosion Action in Sol-Gel Coating on AA2024-T3 Aluminum Alloy

2017 ◽  
Vol 164 (12) ◽  
pp. C641-C652 ◽  
Author(s):  
Bing Xue ◽  
Mei Yu ◽  
Jianhua Liu ◽  
Songmei Li ◽  
Liangliang Xiong ◽  
...  
Keyword(s):  
Aluminum Alloy ◽  
Sol Gel ◽  
Dimensional Structure ◽  
Two Dimensional

Data Acquisition and Processing of Weak Low-Frequency Magnetic Signals

2011 ◽  
Vol 65 ◽  
pp. 299-302 ◽  
Author(s):  
Shou Qiang Men ◽  
Christian Resagk
Keyword(s):  
Magnetic Field ◽  
Data Acquisition ◽  
Fourier Transforms ◽  
Low Frequency ◽  
Fast Fourier Transforms ◽  
Two Dimensional ◽  
Calibration System ◽  
Magnetic Field Sensors ◽  
Data Acquisition And Processing

A simple calibration system for magnetic field sensors was designed, and experiments were carried out to calibrate two-dimensional fluxgate sensors and a sensor ring composed of eight fluxgate sensors. Fast Fourier Transforms and trapezoidal numerical integrals were applied to deal with the raw signals. It is found that it is not suitable to apply fast Fourier Transforms only to deal with signals with several peaks close to each other, but trapezoidal numerical integrals should also be used in combination with the FFT method.

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