• 한국수학사학회지
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• 제18권3호
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• pp.1-24
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• 2005

중국의 부정방정식은 구장산술에서 시작되어 손자산경과 장구건산경에서 취급되었다. 진구소가 수서구장에서 대연총수술을 도입하여 일반적인 연립합동식의 해법을 얻어낼 때까지 부정방정식은 아무런 발전이 없었다. 먼저 진구소의 대연술을 소개하고, 조선에서 부정방정식의 발전 과정을 조사한다. 남병길의 산학정의와 진구소 수서구장의 대연술을 비교한다.

• 한국농공학회논문집
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• 제57권6호
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• pp.59-68
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• 2015

Traditional structure analysis method is based on numerical matrix analysis to use the geometries consisting of the structure. The characteristics require a lot of computer memories and computational time. To avoid these weaknesses, new approach to analyze truss structure was suggested by adopting topological load redistribution method. The axial forces to be not structurely analyzed yet against outside loads were redistributed by using nodal equation of equilibrium randomly at each node without constructing global matrix. However, this method could not calculate the axial forces if structure is statically indeterminate due to degree of many indeterminacies. Therefore, to apply the method suggested in this research, all redundancies of truss structure were replaced by unit loads. Each unit load could make the deformation of a whole structure, and a superposition method was finally adopted to solve the simultaneous equations. The axial forces and deflections agreed with the result of commercial software within the relative error of 1 %, whereas in the case that the axial forces are relatively very smaller than others, the relative errors were increased to 2 %. However, as the values were small enough not to be considered, it was practically useful as a structural analysis model. This model will be used for structural analysis of truss type of large structure such as agricultural farming facility.

• 대한토목학회논문집
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• 제28권2A호
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• pp.269-279
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• 2008

본 논문에서는 전편논문에서 제안한 부정정 스트럿-타이 모델 및 하중분배율 결정식을 ACI 318-05 스트럿-타이 모델 설계기준에 적용하여 파괴실험이 수행된 229개 단순지지 철근콘크리트 깊은 보의 극한강도를 평가하였다. 또한 229개 깊은 보의 극한강도를 실험식, 실험 전단강도모델에 기초한 설계기준, 이론 전단강도모델에 기초한 설계기준, 그리고 현 스트럿-타이 모델 설계기준 등으로 평가하고, 그 결과를 본 연구의 방법에 의한 결과와 비교분석하여 본 연구에서 제안한 방법의 적합성을 검증하였다.

• 대한수학회보
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• 제44권1호
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• Computers and Concrete
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• 제16권3호
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• pp.357-380
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• 2015

In this study, a simple indeterminate strut-tie model which reflects complicated characteristics of the ultimate structural behavior of continuous reinforced concrete deep beams was proposed. In addition, the load distribution ratio, defined as the fraction of applied load transferred by a vertical tie of truss load transfer mechanism, was proposed to help structural designers perform the analysis and design of continuous reinforced concrete deep beams by using the strut-tie model approaches of current design codes. In the determination of the load distribution ratio, a concept of balanced shear reinforcement ratio requiring a simultaneous failure of inclined concrete strut and vertical steel tie was introduced to ensure the ductile shear failure of reinforced concrete deep beams, and the primary design variables including the shear span-to-effective depth ratio, flexural reinforcement ratio, and compressive strength of concrete were reflected upon. To verify the appropriateness of the present study, the ultimate strength of 58 continuous reinforced concrete deep beams tested to shear failure was evaluated by the ACI 318M-11's strut-tie model approach associated with the presented indeterminate strut-tie model and load distribution ratio. The ultimate strength of the continuous deep beams was also estimated by the experimental shear equations, conventional design codes that were based on experimental and theoretical shear strength models, and current strut-tie model design codes. The validity of the proposed strut-tie model and load distribution ratio was examined through the comparison of the strength analysis results classified according to the primary design variables. The present study associated with the indeterminate strut-tie model and load distribution ratio evaluated the ultimate strength of the continuous deep beams fairly well compared with those by other approaches. In addition, the present approach reflected the effects of the primary design variables on the ultimate strength of the continuous deep beams consistently and reasonably. The present study may provide an opportunity to help structural designers conduct the rational and practical strut-tie model design of continuous deep beams.

• Steel and Composite Structures
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• 제3권3호
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• pp.169-184
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• 2003

This paper presents a generic modelling of composite steel-concrete beams with elastic shear connection. It builds on the well-known seminal technique of Newmark, Siess and Viest, in order to formulate the partial interaction formulation for solution under a variety of end conditions, and lends itself well for modification to enable direct quantification of effects such as shrinkage, creep, and limited shear connection slip capacity. This application is possible because the governing differential equations are set up and solved in a fashion whereby inclusion of the kinematic and static end conditions merely requires a statement of the appropriate constants of integration that are generated in the solution of the linear differential equations. The method is applied in the paper for the solution of the well-studied behaviour of simply supported beams with partial interaction, as well as to provide solutions for a beam encastr$\acute{e}$ at its ends, and for a propped cantilever.

• 대한인간공학회:학술대회논문집
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• 대한인간공학회 1992년도 추계학술대회논문집
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• pp.46-53
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• 1992

Finger movements in the sagittal plane mainly consist of flexion and extension about the metacarpophalangeal(MCP) and proximal interphalangeal(PIP) joints. A kinematic finger model was developed with the assumption of constant tendon moment arms. Equations of static equilibrium were derived for the finger model using the principle of virtual work. Equations of static equilibrium for the finger model were indeterminate since only three equations were available for five unknown variables(forces). The number of variables was reduced based on information on muscular activities in finger movements. Then the amounts of forces which muscles exerted to maintain static equilibrium against external loads were computed from the equilibrium equations. The muscular forces were expressed mathematically as functions of finger positions, tendon moment arms, lengths of phalanges, and the magnitude and direction of external load. The external finger strength were computed using the equations of muscular forces and anatomical data. Experiments were performed to measure finger strengths. Measurements were taken in combinations of four finger positions and four directions of force exertions. Validation of the finger models and of procedure to estimate finger strengths was done by comparing the results of computations and experiments. Significang differences were found between the predicted and measured finger strengths. However, the trends of finger strengths with respect to finger positions were similar inboth the predicted and measured. These findings indicate that the finger model and the procedure to predict finger strengths were correctly developed.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제37권3호
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• pp.419-442
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• 2023

본 연구는 초기 대수의 일반화된 산술 관점과 함수적 관점에서 초등학교 5학년 학생들의 변수에 대한 이해 실태를 조사하였다. 구체적으로 전자에서는 1의 성질, 덧셈의 교환법칙, 곱셈의 결합법칙, 산술 맥락에서의 문제 상황을 포함하였고, 후자에서는 덧셈 관계, 곱셈 관계, 제곱 관계, 선형 관계를 다루었다. 11개 학교에서 246명의 학생들을 대상으로 조사한 결과, 학생들은 공통적으로 변수에 해당하는 특정한 값을 구할 수 있었고, 변수를 활용한 식에서 다른 기호를 사용하여 식을 바꿔 쓸 수도 있다는 점을 이해하는 것으로 드러났다. 그러나 정해지지 않은 양을 포함한 산술 맥락에서의 문제 상황을 변수를 활용하여 일반화된 식으로 나타내는 데 많은 어려움을 겪었다. 또한 1의 성질과 덧셈의 교환법칙을 나타낸 식에서 변수는 자연수만 된다고 생각하는 경향이 있었으며, 약 25%의 학생들은 변수가 한 가지 수로 정해져 있다고 생각하였다. 이와 같은 연구 결과를 바탕으로 본 논문은 초등학생들의 변수 이해 및 지도에 대한 시사점을 제시하였다.

• 한국수학사학회지
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• 제19권4호
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• pp.13-30
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• 2006

중국, 한국, 인도, 아라비아 등 동양 수학에서는 수학 내용을 구결, 즉 내용을 입으로 전하기 위해 싯구의 형식을 빌려 표현한 경우가 종종 있다. 본 연구에서는 우선 동양 수학책에서 발견되는 구체적인 구결 및 그것이 담고 있는 수학적 지식에 대해 고찰한다. 그리고 구결의 형식을 빌려 수학 지식을 제시한 이유에 대해 추론함으로써 수학 활동에서 구결의 역할에 대해 생각해보고, 나아가 수학교육적 관점에서 절차나 알고리즘 지도와 관련하여 구결을 활용하는 방법에 대해 제안한다.

• 콘크리트학회논문집
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• 제23권1호
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• pp.13-22
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• 2011

이 논문에서는 전편 논문에서 제안한 부정정 스트럿-타이 모델 및 하중분배율 결정식을 ACI 318M-08 스트럿-타이 모델 설계기준에 적용하여 파괴실험이 수행된 51개 연속지지 철근콘크리트 깊은 보의 극한강도를 평가하였다. 또한 연속 깊은 보의 극한강도를 실험식, 실험 및 이론 전단강도모델에 기초한 설계기준, 그리고 현 스트럿-타이 모델설계기준 등으로 평가하고, 그 결과를 이 연구의 방법에 의한 결과와 비교분석하여 이 연구에서 제안한 방법의 적합성을 검증하였다. 이 연구의 방법은 기존의 여러 방법에 비해 극한강도를 비교적 양호하게 평가하였으며, 또한 극한강도평가 시 연속 깊은 보의 강도 및 거동에 영향을 미치는 전단경간비, 콘크리트의 압축강도, 그리고 휨철근비 등 주요설계변수들의 영향을 기존 방법들에 비해 정확하고 일관성 있게 반영하였다. 따라서 이 연구의 방법은 부정정 스트럿-타이 모델 방법을 이용한 연속 깊은 보의 합리적이고 실용적인 설계를 가능하게 할 것으로 판단된다.