• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.321-334
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• 2022

We introduce a special class of structured frames having single generators in finite dimensional Hilbert spaces. We call them as pseudo B-Gabor like frames and present a characterisation of the frame operators associated with these frames. The concept of Gabor semi-frames is also introduced and some significant properties of the associated semi-frame operators are discussed.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.315-328
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• 2021

A characterization of frame operators of finite Gabor frames is presented here. Regularity aspects of Gabor frames in 𝑙²(ℤ_N) are discussed by introducing associated semi-frame operators. Gabor type frames in finite dimensional Hilbert spaces are also introduced and discussed.

• Journal of Biosystems Engineering
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• v.40 no.1
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• pp.19-27
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• 2015

Purpose: A system to measure the visibility of agricultural tractor operators was designed and evaluated according to ISO standards, and a blind area diagram around the tested tractor was created based on the manual method recommended by the National Institute for Occupational Safety and Health (NIOSH). Methods: A visibility measurement system was designed and evaluated based on the ISO 5006 and ISO 5721-1 standards. Two bulbs used to simulate the operator's eyes were mounted on a bar with a supporting frame. A wooden frame was used to determine the seat index point position. The 12-m visibility test circle was divided into six sectors of vision, and the test tractor was placed at the center of the circle. Artificial light was supplied in the darkened environment, and shadow or masking effects were measured manually around the 12-m circle. Results: When the bulbs were placed at the operator's eye level, front visibility was good; no masking was found in the "A" vision sector, but larger masking widths were found in the "B" and "C" vision sectors. Since the masking width exceeded 700 mm, additional tests, such as movement of the light sources to both sides of the operator's eye level, were performed. Less than six masking effects were found in the semi-circle of vision to the front, and more than one masking was found in the "B" and "C" visual fields. The minimum distance between the centers of two masking effects exceeded 2500 mm when measured as a chord on the semi-circle of vision. A blind area diagram was created to define the exact nature of the blind spots and mirror visibility. Conclusions: Visibility evaluation is an effective way to enable proper and safe operation for agricultural tractor operators. Inclusion of this visibility evaluation test in the general testing process might aid tractor manufacturers.