Rare-earth orthoferrites with weak ferromagnetism have become one of the most fascinating topics in antiferromagnet research because of their potential application in future information technologies. However, an appro...
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Rare-earth orthoferrites with weak ferromagnetism have become one of the most fascinating topics in antiferromagnet research because of their potential application in future information technologies. However, an appropriate and direct way to reduce the noise in the intrinsic but weak resonances of rare-earth orthoferrites is currently lacking, creating difficulties in analysis. Here, we report a numerical smoothing method to directly denoise the detected terahertz (THz) responses of orthoferrites using a B-spline algorithm. For comparison, the Savitzky-Golay smoothing method, which is a typical and widely used numerical smoothing method, was also used to process the data. The thickness-dependent signals of DyFeO3 were processed by the above methods. LaFeO3, HoFeO3, and DyFeO3 were chosen and prepared, and their thermally tunable signals were processed. The B-spline signal smoothing algorithm was shown to have stability and robustness to noise and was more effective than the Savitzky-Golay smoothing method at reducing noise. This work on smoothing thickness- and temperature-dependent THz signals may help provide a promising approach to reduce noise in the intrinsic but weak resonances of rare-earth orthoferrites.
The equation Au = f with a linear symmetric positive definite operator A : D(A) subset of H -> H having a discrete spectrum and dense image in a complex Hilbert space H is considered. This equation is transferred i...
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The equation Au = f with a linear symmetric positive definite operator A : D(A) subset of H -> H having a discrete spectrum and dense image in a complex Hilbert space H is considered. This equation is transferred into the Hilbert space of finite orbits D(A(n)) as well as into the Frechet space of all orbits D(A(infinity)), that is, the projective limit of the sequence of spaces {D(A(n))}. For an approximate solution of the inverse of A, linear spline central algorithms in these spaces are constructed. The convergence of the sequence of approximate solutions to the exact solution is proved. The obtained results are applied to the quantum harmonic oscillator operator Au (t) = -u ''(t) + t(2)u(t), t is an element of R, in the Hilbert space of finite orbits D(A(n)), and in the Frechet space of all orbits D(A(infinity)) that in this case coincides with the Schwartz space of rapidly decreasing functions. Some quantum mechanical interpretations of obtained results are also given. (C) 2021 Published by Elsevier Inc.
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