• 호남수학학술지
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• 제44권3호
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• pp.384-390
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• 2022

In this paper, we study the obstruction on the jets of an almost complex structure J to the existence of a symplectic form ω such that J is compatible with ω. We describe some almost complex structures on ℝ⁴ and on ℝ⁶, respectively, that cannot be calibrated by any symplectic forms. In particular, these examples pertain to the model almost complex structure on ℝ⁴ in [3], and the simple model structure on ℝ⁶ in [7].

• 한국구조물진단유지관리공학회 논문집
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• 제4권1호
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• pp.121-129
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• 2000

In general. service life of the sea-shore concrete structures is largely influenced by the corrosion of reinforcing steel due to the chloride contamination, and the penetration of chloride ions into concrete is governed by concrete condition state as a micro-structure. In this study, characteristics of chloride diffusion in concrete are analyzed in accordance with the mixing properties and durability of concrete, by considering the facts that micro-structure of concrete varies with the mixing properties and can indirectly be analyzed by using the durability test. In order to predict the service life of existing concrete structures, chloride diffusion equation for the concrete structures under various service conditions and the major parameters used in that equation are formulated as the mathematical models. Based on the results of chloride diffusion analysis in accordance with the mixing properties and durability of concrete and mathematical models formulated in this study, a prediction system is developed to predict the corrosion initiation of reinforcing steel in the sea-shore concrete structures.

• Structural Engineering and Mechanics
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• 제76권6호
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• pp.799-821
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• 2020

The optimum design of truss structures is one of the significant categories in structural optimization that has widely been applied by researchers. In the present study, new mathematical programming called Consistent Approximation (CONAP) method is utilized for the simultaneous optimization of the size and shape of truss structures. The CONAP algorithm has already been introduced to optimize some structures and functions. In the CONAP algorithm, some important parameters are designed by employing design sensitivities to enhance the capability of the method and its consistency in various optimum design problems, especially structural optimization. The cross-sectional area of the bar elements and the nodal coordinates of the truss are assumed to be the size and shape design variables, respectively. The displacement, allowable stress and the Euler buckling stress are taken as the design constraints for the problem. In the proposed method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the sequential quadratic programming (SQP) algorithm. Several truss structures are designed by employing the CONAP method to illustrate the efficiency of the algorithm for simultaneous shape and size optimization. The optimal solutions are compared with some of the mathematical programming algorithms, the approximation methods and metaheuristic algorithms those reported in the literature. Results demonstrate that the accuracy of the optimization is improved and the convergence rate speeds up.

• Coupled systems mechanics
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• 제10권1호
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• pp.1-19
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• 2021

Composite nature of the masonry structures in general causes complex and non-linear behaviour, especially in intense vibration conditions. The presence of different types and forms of structural elements and different materials is a major problem for the analysis of these type of structures. For this reason, the analysis of the behaviour of masonry structures requires a combination of experimental tests and non-linear mathematical modelling. The famous UNESCO Heritage Old Bridge in Mostar was selected as an example for the analysis of the global behaviour of reinforced stone arch masonry bridges. As part of the experimental research, a model of the Old Bridge was constructed in a scale of 1:9 and tested on a shaking table platform for different levels of seismic excitation. Non-linear mathematical modelling was performed using a combined finite-discrete element method (FDEM), including the effect of connection elements. The paper presents the horizontal displacement of the top of the arch and the failure mechanism of the Old Bridge model for the experimental and the numerical phase, as well as the comparison of the results. This research provided a clearer insight into the global behaviour of stone arch masonry structures reinforced with steel clamps and steel dowels, which is significant for the structures classified as world cultural heritage.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권2호
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• pp.101-112
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• 2020

본 연구의 목적은 문장제 이해 과정에서 교사와 학생 간의 상호 작용 양상에 따른 교사의 담론 구조를 분석하는 것이다. 이를 위해 학생들의 참여를 촉진하는 교수법을 다년간 실행해 온 경력교사의 한 학기 수업 중에서 문제 해결 과정을 대표할 수 있는 수업 4차시를 추출하였다. 4차시 수업에서 교사와 학생 간에 중요하게 생각하는 부분에 대한 일치 여부에 따라 교사 담론의 구조는 어떠한 특징이 있는지를 분석하였다. 분석 결과, 교사와 학생 간의 상호 작용 양상에 따라 문장제에서 중요하게 생각하는 부분을 협의하고 수학적인 의미를 만들어 가는 교사 담론의 구조는 학생들의 수업 참여를 촉진함으로써 문장제 이해에 도움을 주는 것으로 볼 수 있었다. 교사와 학생 간의 상호 작용 양상에 따라 학생들의 문제 이해를 위한 교사 담론의 구조를 바탕으로 향후 교사들이 문제 이해를 위해 학생들과 어떻게 소통해야 하는지에 대한 구체적인 방법론을 제공하였다고 볼 수 있다.

• Kyungpook Mathematical Journal
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• 제30권2호
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• pp.171-179
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• 1990

• Kyungpook Mathematical Journal
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• 제23권1호
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• pp.49-61
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• 1983

• Architectural research
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• 제15권4호
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• pp.207-214
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• 2013

A form-finding technique is proposed for three-dimensional spatial structures. Two-step discrete finite element (FE) mesh generator based on computer aided geometric design (CAGD) is introduced and used to control the shape of three-dimensional spatial structures. Mathematical programming technique is adopted to search new forms (or shapes) of spatial structures. For this purpose, the strain energy is introduced as the objective function to be minimized and the initial volume (or the initial weight) is considered as constraint function. Numerical examples are carried out to test the capability of the proposed form-finding techniques and provided as benchmark tests.

• 대한수학회논문집
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• 제38권2호
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• pp.629-641
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• 2023

The aim of this paper is two-fold. First, we study the Chinea-Gonzalez class C₁₂ of almost contact metric manifolds and we discuss some fundamental properties. We show there is a one-to-one correspondence between C₁₂ and Kählerian structures. Secondly, we give some basic results for Riemannian curvature tensor of C₁₂-manifolds and then establish equivalent relations among 𝜑-sectional curvature. Concrete examples are given.

• 대한수학회논문집
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• 제39권1호
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• pp.247-257
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• 2024

We use the structure of skew braces to enhance the biquandle counting invariant for virtual knots and links for finite biquandles defined from skew braces. We introduce two new invariants: a single-variable polynomial using skew brace ideals and a two-variable polynomial using the skew brace group structures. We provide examples to show that the new invariants are not determined by the counting invariant and hence are proper enhancements.