• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.513-519
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• 1996

The stability problem of functional equations has been originally raised by S. M. Ulam. In 1940, he posed the following problem: Give conditions in order for a linear mapping near an approximately additive mapping to exist (see [9]).

• Journal of Electrical Engineering and Technology
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• v.1 no.1
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• pp.8-15
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• 2006

Since the power swing depends on the operating time of the relay, the swing's magnitude can be reduced by an autoreclosure relaying system with an optimal reclosing algorithm. This paper proposes a method for stability improvement using optimal reclosure relaying. An optimal reclosure algorithm is applied to identify both temporary and permanent faults, and to predict system stability by applying WAM and high speed communication technology. It provides optimal control by predicting and determining the degree of stability, considering the real time transient stability using EEEAC. For temporary faults, the algorithm determines the system's stability and either recloses optimally for stable systems, or inserts series capacitance before optimal reclosure for unstable systems. It also applies an optimal reclosure algorithm to minimize shock and damage to the power system when reclosure fails due to permanent faults.

• Ocean Systems Engineering
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• v.9 no.2
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• pp.157-177
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• 2019

Studies on motion response of a vessel is of great interest to researchers, since a long time. But intensive researches on stability of vessel during motion under dynamic conditions are few. A numerical model of vessel is developed and responses are analyzed in head, beam and quartering sea conditions. Variation of response amplitude operator (RAO) of vessel based on Strip Theory for different wave heights is plotted. Validation of results was done experimentally and numerical results was considered to obtain effect of damping on vessel stability. A scale model ratio of 1:125 was used which is suitable for dimensions of wave flume at National Institute of Technology Calicut. Stability chart are developed based on Mathieu's equation of stability. Ince-Strutt chart developed can help to capture variations of stability with damping.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.401-410
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• 2002

We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.297-305
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• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.73-81
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• 2015

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• The Journal of Korean Academy of Orthopedic Manual Physical Therapy
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• v.24 no.2
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• pp.59-67
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• 2018

Background: The purpose of this study was to investigate the effects of gluteus medius strength exercise on the ankle stability of high school student with chronic ankle sprains. Methods: A total of 30 participants were divided two groups. Experimental group was 15 participants applied gluteus medius strength exercise. Control group was 15 participants performing ankle strength exercise. This study was performed for 50 minutes per day, three a week for 6 weeks. All measurements were taken to a pre and post test. Strength was measured using Power Track ll. Balance was measured using Biodex balance system for Limits of Stability and Postural Stability. Ankle Stability was measured using Cumberland Ankle Instability Tool (CAIT). Results: In the case of gluteus medius strength, there were statistically significant differences between the experimental group and the control group. For ankle stability were statistically significant differences within the experimental group according to measurements taken by Limits of Stability, Postural Stability, and CAIT. A between group comparison showed a statistically significant difference for CAIT only. Conclusion: According to our measurements it appears that gluteus medius strength training was effective in benefiting muscular strength, balance and ankle stability among the physical education.

• Advances in concrete construction
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• v.7 no.2
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• pp.97-105
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• 2019

In this paper, the workability and static stability were evaluated using a proposed test method. Workability and static stability represent a key property of self-compacting concrete (SCC) in fresh state. A number of standardized test methods were developed to assess these properties. However, no accelerated test method reliably predicts both workability and static stability of SCC. In the present work, a modified K-slump test method was developed to evaluate workability and static stability of SCC. In order to take implicit mixture variations of SCC constituents that can affect fresh SCC properties, a central composite design was adopted to highlight the effect of gravel to sand ratio (G/S), gravel 3/8 to gravel 8/15 ratio (G1/G2), water to cement ratio (W/C), marble powder to cement ratio (MP/C) and superplasticizer content (SP) on workability measured with slump and flow time (T50) tests and static stability measured with sieve stability test (Pi), segregation test index (SSI), Penetration test (Pd) and the proposed K-slump test (Km). The obtained results show that G/S ratio close to 1 and G1/G2 ratio close to 60% can be considered as optimal values to achieve a good workability while ensuring a sufficient static stability of SCC. Acceptable relationships were obtained between Slump flow, Pi, Pd and Km. Results show that the proposed K-slump test allow to assess both workability and static stability of fresh SCC mixtures.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.03a
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• pp.494-504
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• 2008

Successful design, construction and maintenance of NATM tunnel demands prediction, control, stability estimation and monitoring of surface settlement, gradient and ground displacement with high accuracy. Back analysis using measured data and forward analysis have been and are indispensable tools to achieve this goal. Sakurai provided the hazard warning levels for assessing the stability of tunnels using the relation of critical strain and apparent Young's modulus. This paper performed the estimation of tunnel stability on construction. Firstly, the apparent Young's modulus concept and back analysis method is introduced for the assessment of tunnel safety during excavation a brief framework. Secondly, this paper deals with case study using "Apparent Young's modulus" and "Back analysis" for the purpose of estimating the stability of NATM tunnel in Korea. Finally, a general method that can be estimated the tunnel stability discussed by a flow chart.