• Economic and Environmental Geology
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• v.20 no.2
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• pp.119-123
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• 1987

Hankel transform of order 0 can be represented by a combination of Abel transform and Fourier transform. This Abel-Fourier method can offer computational advantages over a conventional digital linear filter method through the uses of a rapid Abel transform with shift variant recursive filter and of a fast Fourier transform. The Abel-Fourier method, however, is generally less accurate than a well-designed digital linear filter method. In geoelectrical applications, the digital linear filter method seems to be more flexible than the Abel-Fourier method.

• Korean Journal of Optics and Photonics
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• v.23 no.4
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• pp.135-142
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• 2012

We have developed a measurement method of the refractive index profile of an optical fiber by using diffraction phase microscopy. In the microscope system, the reference light was extracted directly from the probe light that passed through the sample by means of pinhole filtering with a diffraction grating. The spatial interference pattern produced by the probe light and the reference light was processed to generate the phase image of the sample fiber. The index profile was obtained by the inverse Abel transform of the phase profile. In order to remove the background phase that originated from the index difference between the cladding and the surrounding medium, the background phase was calculated from the phase data of the cladding to make a core phase profile that can be directly transformed to the index profile of the core without the full phase image that includes the entire cladding part.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Environmental Engineering Research
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• v.24 no.3
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• pp.463-473
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• 2019

Nanoscale zero-valent iron (nZVI) has proved to be an effective tool in applied environmental nanotechnology, where the decreased particle diameter provides a drastic change in the properties and efficiency of nanomaterials used in water purification. However, the agglomeration and colloidal instability represent a problematic and a remarkable reduction in nZVI reactivity. In view of that, this study reports a simple and cost-effective new strategy for ultra-small (< 7.5%) distributed functionalized nZVI-EG (1-9 nm), with high colloidal stability and reduction capacity. These were obtained without inert conditions, using a simple, economical synthesis methodology employing two stabilization mechanisms based on the use of non-aqueous solvent (methanol) and ethylene glycol (EG) as a stabilizer. The information from UV-Vis absorption spectroscopy and Fourier transform infrared spectroscopy suggests iron ion coordination by interaction with methanol molecules. Subsequently, after nZVI formation, particle-surface modification occurs by the addition of the EG. Size distribution analysis shows an average diameter of 4.23 nm and the predominance (> 90%) of particles with sizes < 6.10 nm. Evaluation of the stability of functionalized nZVI by sedimentation test and a dynamic light-scattering technique, demonstrated very high colloidal stability. The ultra-small particles displayed a rapid and high nitrate removal capacity from water.