• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.11-24
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• 2017

Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.

• Journal of Mechanical Science and Technology
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• v.17 no.8
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• pp.1120-1132
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• 2003

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular. integral equations for edge and temperature dislocation distribution functions are constructed and solved numeric-ally, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1269-1284
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• 2022

This paper is concerned with the following Schrödinger-Poisson system $$\{\begin{array}{lll}-{\Delta}u+V(x)u+K(x){\phi}u=a(x){\mid}u{\mid}^{p-2}u&&\text{ in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=K(x)u^2&&\text{ in }{\mathbb{R}}^3,\end{array}$$ where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].

• Archives of Plastic Surgery
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• v.50 no.4
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• pp.331-334
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• 2023

Historically, the approach to any reconstructive challenge, whether intentionally or intuitively, can be seen to follow distinct guidelines that could aptly be called "reconstructive metaphors." These have been intended to inform us as to the "what, "when" and "where" this attempt can best be achieved. Yet the "how" or means to accomplish this goal, usually also intuitively well understood, in a similar vein can now be expressed to be within our "reconstructive toolbox." The latter will distinctly mirror our individuality and contain not only the various hardware that we deem essential, but also the means to access whatever technology we may be comfortable with. No toolbox, even if overflowing will ever be full, as potential options and the diversity they represent surely approaches infinity. But the truly excellent reconstructive surgeon will know when their toolbox is in any way lacking, and fears not remedying that deficiency even if the talents of another colleague must be sought, so as always to ensure that the patient will obtain the best appropriate treatment!

• Journal of Korean Port Research
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• v.5 no.1
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• pp.71-81
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• 1991

This study deals with the analytical and numerical solution for the combined wave reflection and diffraction near the impermeable rigid upright breakwater, subject to the excitation of a plane simple harmonic wave coming from infinity. Three cases are presented : a) the analytical solution near a thin semi-infinite breakwater, b) the analytical solution near the semi-infinite breakwaters of arbitrary edge angles, $30^{\circ},\;45^{\circ},\;and\;90^{\circ}$, c) the numerical solution near a detached thin breakwater the results are presented in amplification factor and wave height diagrams. Moreover, the amplification factors near the structure(2 wavelength before and behind the structure) are compared for the given cases. A finite difference technique for the numerical solution was applied to the integral equation obtained for the wave potential.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.4
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• pp.257-264
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• 2002

This paper is concerned with the analysis of wave reflection and transmission from multiple floating breakwaters. Linear potential theory was used for modeling wave field, and the behaviors of the floating breakwaters was represented as linearized equation of motions. The boundary value problem for the wave field was discretized by Galerkin technique. The radiation condition at infinity was modeled as infinite elements developed by Park et al.(1991). The validation of the developed model was given through the comparison with hydraulic experimental data conducted by Park et al.(2000). The possibility for the application of multiple floating breakwaters was also discussed based on the numerical experiments.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• Journal of the Korean Institute of Navigation
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• v.17 no.1
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• pp.61-78
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• 1993

Large offshore structure are to be considered for oil storage facilities , marine terminals, power plants, offshore airports, industrial complexes and recreational facilities. Some of them have already been constructed. Some of the envisioned structures will be of the artificial-island type, in which the bulk of structures may act as significant barriers to normal waves and the prediction of the wave intensity will be of importance for design of structure. The present study deals wave scattering problem combining reflection and diffraction of waves due to the shape of the impermeable rigid upright structure, subject to the excitation of a plane simple harmonic wave coming from infinity. In this study, a finite difference technique for the numerical solution is applied to the boundary integral equation obtained for wave potential. The numerical solution is verified with the analytic solution. The model is applied to various structures, such as the detached breakwater (3L${\times}$0.1L), bird-type breakwater(318L${\times}$0.17L), cylinder-type and crescent -type structure (2.89L${\times}$0.6L, 0.8L${\times}$0.26L).The result are presented in wave height amplification factors and wave height diagram. Also, the amplification factors across the structure or 1 or 2 wavelengths away from the structure are compared with each given case. From the numerical simulation for the various boundary types of structure, we could figure out the transformation pattern of waves and predict the waves and predict the wave intensity in the vicinity of large artificial structures.

• The Mathematical Education
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• v.55 no.1
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• pp.21-39
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• 2016

This research examined the Korean and American $6^{th}$ grade students' mathematical problem solving ability and methods via an intuitive thinking. For this, the survey research was used. The researcher developed the questionnaire which consists of problems with intuitive and algorithmic problem solving in number and operation, figure and measurement areas. 57 Korean $6^{th}$ grade students and 60 American $6^{th}$ grade students participated. The result of the analysis showed that Korean students revealed a higher percentage than American students in correct answers. But it was higher in the rate of Korean students attempted to use the algorithm. Two countries' students revealed higher rates in that they tried to solve the problems using intuitive thinking in geometry and measurement areas. Students in both countries showed the lower percentages of correct answer in problem solving to identify the impact of counterintuitive thinking. They were affected by potential infinity concept and the character of intuition in the problem solving process regardless of the educational environments and cultures.

• Korean Institute of Interior Design Journal
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• v.17 no.3
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• pp.148-155
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• 2008

The following research focuses on the formation method of digital space by organistic line extension among various digital formation methods. The paper reflects on the meaning and concept of today's digitalism which enables the application of complex organistic system on space through advanced technology. It also explores the concept of a line in topology which differs in assumptive meaning from traditional Euclidian geometry. The findings of the research are that first, digital space is not optimized, but is a tentative formation in process. A digital space encompasses characteristics such as infinity, possibility, potential, asymmetry, and the force of virtuality such characteristics are expressed through a moving surface constantly changing with direction. Second, a digital space formed by line extension is inseparable and durable since no measurement or dimension is predetermined. Furthermore, its sense of direction and flexibility gives it a feeling of a living organism. Third, a Euclidian methodology called 'NURBS' is being developed to express such a dynamic digital space; this is reflected through three elements, control point, weights, and knots to effectively reflect the characteristics of virtuality. The opportunities of digital space are infinite, and the possibilities of formation methods likewise vast.