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Therefore, the estimated PSD of the signal is related to the modulus of its DFT.
This paper presents a new detector of LFM-signal, which is the integration of the 4th-power modulus of its fractional Fourier transform.
A matrix M is an M-matrix if M = s I − A, where A ≥ O and s ≥ ρ ( A ), where ρ denotes the spectral radius of a matrix, that is, the maximum modulus of its eigenvalues.
The middle plot shows the resonant state corresponding to the resonance closest to the real axis at ( h = 1/16 ) (compare this to the resonances in Fig. 9 generated by the local maxima), and the bottom plot shows the squared modulus of its FBI tranform (which describes a wave function in phase space [281, Chapter 13]).
In order to sketch the general theory in metric spaces, first we need to give (or recall) general definitions for the three main objects that we need in the EDE and EVI properties, characterizing gradient flows: the notion of speed of a curve, that of slope of a function (somehow the modulus of its gradient) and that of (geodesic) convexity.
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Using the Huainan mining area as an example, we calculated the modulus of erosion, its volume and classified the grade of soil erosion for both the original area and the subsidence basin.
Once the real space exit-wave has been computed, the modulus squared of its FFT yields the calculation result at the detector plane.
This combined approach is then implemented in order to obtain optimum designs of an "imperfect" shell structure involving random geometric deviations from its perfect geometry as well as a spatial variability of its modulus of elasticity and thickness.
Compression tests were performed to determine the composites' modulus of elasticity and its ultimate strength.
The elastic modulus of Ti and its alloys can be reduced through the introduction of a porous structure, thereby addressing the stress shielding problem.
Having strong carbon carbon bond in the planar honeycomb structure of graphite [9], the modulus of elasticity at its basal plane is superior than most of the materials known has proved itself trustworthy as per their fabrication is concerned.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com