• Korean Journal of Mathematics
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• v.29 no.4
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.206-214
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• 2003

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos robot meets an obstacle in an Arnold equation or Chua's equation trajectory, the obstacle reflects the robot. We also show computer simulation results of Arnold equation and Chua's equation and random walk chaos trajectories with one or more Van der Pol obstacles and compare the coverage rates of each trajectory. We show that the Chua's equation is slightly more efficient in coverage rates when two robots are used, and the optimal number of robots in either the Arnold equation or the Chua's equation is also examined.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.883-888
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• 2004

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos UAVs meet an obstacle in an Arnold equation, Chua's equation and hyper-chaos equation trajectory the obstacle reflects the UAV( Unmanned Aerial Vehicle).

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5B
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• pp.493-496
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• 2009

In this study, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. First, we follow Kim and Bai (2004) who derive the complementary mild-slope equation in terms of the stream function using the Euler-Lagrange equation and we compare their equation to the existing extended mild-slope equations of the velocity potential. Second, we derive the extended mild-slope equation in terms of the velocity potential using the Euler-Lagrange equation. In the developed equation, the higher-order bottom variation terms are newly developed and found to be the same as those of Massel (1993) and Chamberlain and Porter (1995). The present study makes wide the area of coastal engineering by developing the extended mild-slope equation with a way which has never been used before.

• Computers and Concrete
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• v.24 no.5
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• pp.423-436
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• 2019

Design equations to evaluate the bursting force in a post-tensioned anchorage zone have been introduced in many design codes, and one equation in AASHTO LRFD is widely used. However, this equation may not determine the bursting force exactly because it was designed on the basis of two-dimensional numerical analyses without considering various design parameters such as the duct hole and shape of the bearing plate. To improve the design equation, modification of the AASHTO LRFD design equation was considered. The behavior of the anchorage zone was investigated using three-dimensional linear elastic finite element analysis with design parameters such as bearing plate size and diameter of sheath hole. Upon the suggestion of a modified design equation for evaluating the bursting force in an anchorage block with a rectangular anchorage plate (Kim and Kwak 2018), additional influences of design parameters that could affect the evaluation of bursting force were investigated. An improved equation was introduced for determining the bursting force in an anchorage block with a circular anchorage plate, using the same procedure introduced in the design equation for an anchorage block with a rectangular anchorage plate. The validity of the introduced design equation was confirmed by comparison with AASHTO LRFD.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.7-10
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• 2004

In this paper, we propose a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface. We assume all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos UAVs meet an obstacle in an Arnold equation or Chua's equation trajectory, the obstacle reflects the UAV

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.10a
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• pp.11-14
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• 2004

In this paper, we propose a method to target searching method that have unstable limit cycles in a chaos trajectory surface. We assume all targets in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle When a chaos UAV meet the target in the Arnold equation, Chua's equation trajectory, the target absorptive the UAV

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.1-18
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• 2012

The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

• Journal of Korean Association for Spatial Structures
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• v.17 no.3
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• pp.75-82
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• 2017

The Kingery-Bulmash equation is the most common equation to calculate blast load. However, the Kingery-Bulmash equation is complicated. In this paper, a modified equation for surface blast load is proposed. The equation is based on Kingery-Bulmash equation. The proposed equation requires a brief calculation process, and the number of coefficients is reduced under 5. As a result, each parameter obtained by using the modified equation has less than 1% of error range comparing with the result by using Kingery-Bulmash equation. The modified equation may replace the original equation with brief process to calculate.