• Journal of the Chungcheong Mathematical Society
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• v.32 no.3
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• pp.319-326
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• 2019

The concept of the stability is very important in dynamical systems. This paper is devoted to the study some properties of stability on a TVS-cone metric space.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.439-449
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• 2021

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for group actions on metric spaces and give a version of Walters's stability theorem for group actions on locally compact metric spaces. Moreover, we show that if G is a finitely generated virtually nilpotent group and there exists g ∈ G such that if Tg is expansive and has the shadowing property, then T is topologically stable.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.407-416
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• 2023

In this paper, we introduce the concept of C^*-algebra-valued quasi b-metric space and prove some existence and uniqueness theorems. Furthermore, we prove the Hyers-Ulam stability results for fixed point problems via C^*-algebra-valued extended quasi b-metric space.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.29 no.3
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• pp.283-291
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• 2011

In case of metric cameras, not only fiducial marks but also various parameters related to camera lens are provided to users for the interior orientation process. The parameters have been acquired through precise camera calibration in laboratory by camera maker. But, in case of non-metric cameras, the interior orientation parameters should be determined in person by users through camera calibration with great number of control points. The interior orientation parameters of metric cameras are practically used for long time. But in case of non-metric cameras, the long-term stability of the interior orientation parameters have not been established. Generally, the interior orientation parameters of non-metric cameras are determined in every photogrammetric work. It's been an obstacle to use the non-metric camera in photogrammetric project because so many control points are required to get the interior orientation parameters. In this study, camera calibrations and photogrammetric observations using a non-metric camera have been implemented 25 times periodically for 6 months and the results have been analyzed. As a result, long-them stability of the interior orientation parameters of a non-metric camera is analyzed.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.93-104
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• 2024

In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.767-779
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• 2020

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.5
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• pp.2245-2266
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• 2016

The hop count routing metric is widely used in routing protocols of Wireless Sensor Networks (WSNs) due to its simplicity and effectiveness. With a lower hop count route, fewer transmissions are required to send a packet from the source to the destination. This can improve the throughput of a network because fewer transmissions results in less channel contention and interference. Despite this, the hop count routing metric may not be ideal for mobile scenarios where the topology of a network changes constantly and rapidly. In this paper, we propose to increase route stability in mobile WSNs by discovering paths that are more stable during route discoveries using routing metrics. Two routing metrics were proposed, the true beauty of these routing metrics lies in the fact that they can even be used even without specialized hardware such as GPS and other sensors. We implemented the proposed routing metrics in the AODV routing protocol and found that they are highly effective and outperform other stability-based routing metrics and the hop count routing metric.

• Journal of rehabilitation welfare engineering & assistive technology
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• v.10 no.2
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• pp.133-139
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• 2016

An electric wheelchair is a assistive device to maneuver on the ground. Tip-over of an electric wheelchair is increasing every year. Dynamic stability metric test item in KS P 7176 has not ensured safety of electric wheelchair on the slope. This study presents design the foldable electric wheelchair that can load in the car and analysis of tip-over measurement which is easily computed for electric wheelchair. Wheelchair frame is designed with a four-bar link mechanism for a foldable structure, and seat module, battery and power driving module can be separated. This analysis is performed during a maneuver on the ground by force-moment stability metric. Several elements, center of gravity position, rotational radius and acceleration, were evaluated how to affect stability metric. This stability metric can reduce tip-over of wheelchair and provide a clue to make of dynamic stability test item.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.1
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• pp.63-73
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• 2014

For robust stability analysis of parameters uncertainty missiles, the traditional frequency domain method can only analyze each respective channel at several interval points within uncertain parameter space. Discontinuous calculation and couplings between channels will lead to inaccurate analysis results. A method based on the ${\nu}$-gap metric is proposed, which is able to comprehensively evaluate the robust stability of missiles with uncertain parameters; and then a genetic-simulated annealing hybrid optimization algorithm, which has global and local searching ability, is used to search for a parameters combination that leads to the worst stability within the space of uncertain parameters. Finally, the proposed method is used to analyze the robust stability of a re-entry missile with uncertain parameters; the results verify the feasibility and accuracy of the method.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.287-300
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• 2020

We introduce and study notions of expansivity, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that on Mandelkern locally compact metric spaces expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.