• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.73-88
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• 2004

A punctured torus $\Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $\cal{C}$ be a matrix presentation of the boundary component of $\Sigma(1,1)$.In the level of the matrix group $\mathbb{SL}$($\mathbb2,R$) we shall show that the trace of $\cal{C}$ is always negative.

• 대한수학회지
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• 제42권3호
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• pp.555-571
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• 2005

A pair of pants $\Sigma(0,3)$ is a building block of oriented surfaces. The purpose of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a pair of pants. In the level of the matrix group $SL(2,\mathbb{R})$, we shall show that an odd number of traces of matrix presentations of the generators of the fundamental group of $\Sigma(0,3)$ should be negative.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.275-288
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• 2010

A one-holed torus ${\Sigma}$(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus ${\Sigma}$(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of ${\Sigma}$(1, 1).

• Structural Engineering and Mechanics
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• 제50권6호
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• pp.797-816
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• 2014

Cooling tower is analyzed as an assembly of layered nonlinear shell elements. Geometric representation of the shell is enabled through layered nonlinear shell elements to define the different layers of reinforcements and concrete by considering the material nonlinearity of each layer for the cooling tower shell. Modal analysis using Ritz vector analysis and nonlinear time history analysis by direct integration method have been carried out to study the effects of the inclination of the supporting columns of the cooling tower shell on its dynamic characteristics. The cooling tower is supported by I-type columns and ${\Lambda}$-type columns supports having the different inclination angles. Relevant comparisons of the dynamic response of the structural system at the base level (at the junction of the column and shell), throat level and at the top of the tower have been made. Dynamic response of the cooling tower is found to be significantly sensitive to the change of the inclination of the supporting columns. It is also found that the stiffness of the structure system increases with increase in inclination angle of the supporting columns, resulting in decrease of the period of the structural system. The participation of the stiffness of the tower in structural response of the cooling tower is fund to be dependent of the change in the inclination angle and even in the types of the supporting columns.

• Structural Engineering and Mechanics
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• 제41권6호
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• pp.711-734
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• 2012

The foundation of a tall building frame resting on settable soil mass undergoes differential settlements which alter the forces in the structural members significantly. For tall buildings it is essential to consider seismic forces in analysis. The building frame, foundation and soil mass are considered to act as single integral compatible structural unit. The stress-strain characteristics of the supporting soil play a vital role in the interaction analysis. The resulting differential settlements of the soil mass are responsible for the redistribution of forces in the superstructure. In the present work, the nonlinear interaction analysis of a two-bay ten-storey plane building frame- layered soil system under seismic loading has been carried out using the coupled finite-infinite elements. The frame has been considered to act in linear elastic manner while the soil mass to act as nonlinear elastic manner. The subsoil in reality exists in layered formation and consists of various soil layers having different properties. Each individual soil layer in reality can be considered to behave in nonlinear manner. The nonlinear layered system as a whole will undergo differential settlements. Thus, it becomes essential to study the structural behaviour of a structure resting on such nonlinear composite layered soil system. The nonlinear constitutive hyperbolic soil model available in the literature is adopted to model the nonlinear behaviour of the soil mass. The structural behaviour of the interaction system is investigated as the shear forces and bending moments in superstructure get significantly altered due to differential settlements of the soil mass.

• 한국지반공학회논문집
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• 제34권12호
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• pp.83-92
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• 2018

사면 구조물은 시간이 경과함에 따라 대상지반에서 각종 열화 현상이 진행되어 내구성의 저하로 인한 붕괴가 발생할 수 있으며, 사용 연한을 감소시키는 결과를 초래하게 된다. 이러한 지반 열화에 따른 사면안정에 대한 접근방안은 지반의 물리적 특성 및 기하학적인 구조에 국한하여 분석하는 기존의 한계 평형 해석과는 또 다른 개념이라 할 수 있다. 본 연구에서는 사면의 열화 특성과 관련하여 각종 문헌 조사를 통하여 비교분석을 수행하고, 전단강도 저감에 대한 최적의 제안식들로서 지수함수, 로그함수 및 역쌍곡선 함수를 제시하고, 열화에 취약한 양산 단층대의 셰일층에서 붕괴가 발생한 경부고속철도 절토사면을 대상으로 사례분석을 실시하였다. 본 연구에서는 사례분석을 통하여 향후 열화로 인한 사면 안전성과 관련하여 정량적인 평가를 위한 최적의 강도 저하 곡선을 도출하고 한계평형해석에 의한 안정해석을 할 수 있는 접근 방법을 제시하였다.

• 한국농공학회논문집
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• 제63권1호
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• pp.103-116
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• 2021

Analysis of runoff is substantial for effective water management in the watershed. Runoff occurs by reaction of a watershed to the rainfall and has non-linearity and uncertainty due to the complex relation of weather and watershed factors. ANN (Artificial Neural Network), which learns from the data, is one of the machine learning technique known as a proper model to interpret non-linear data. The performance of ANN is affected by the ANN's structure, the number of hidden layer nodes, learning rate, and activation function. Especially, the activation function has a role to deliver the information entered and decides the way of making output. Therefore, It is important to apply appropriate activation functions according to the problem to solve. In this paper, ANN models were constructed to estimate runoff with different activation functions and each model was compared and evaluated. Sigmoid, Hyperbolic tangent, ReLU (Rectified Linear Unit), ELU (Exponential Linear Unit) functions were applied to the hidden layer, and Identity, ReLU, Softplus functions applied to the output layer. The statistical parameters including coefficient of determination, NSE (Nash and Sutcliffe Efficiency), NSEln (modified NSE), and PBIAS (Percent BIAS) were utilized to evaluate the ANN models. From the result, applications of Hyperbolic tangent function and ELU function to the hidden layer and Identity function to the output layer show competent performance rather than other functions which demonstrated the function selection in the ANN structure can affect the performance of ANN.

• 한국지반환경공학회 논문집
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• 제2권4호
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• pp.15-27
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• 2001

본 연구에서는 유한요소해석을 통해 파형강판 암거의 단면력(압축력, 휨모멘트) 계산식을 제안하였다. 3단계의 시공과정(정점부까지의 뒷채움, 토피고까지의 뒷채움, 활하중 재하)에 대해 지반-구조물 상호작용을 고려한 거동분석으로부터 최대 압축력 및 최대 휨모멘트 발생조건을 도출하였고, 이러한 거동분석 결과와 반원 아치구조에 대한 Castigliano 제2정리의 적용으로부터 단면력식의 형태를 제안하였다. 또한, 최대 압축력 및 최대 휨모멘트를 유발하는 조건하에서 다양한 기하형태와 지반-구조물의 상대강성을 고려한 유한요소해석 결과로부터 제안된 단면력식을 구성하는 계수를 결정하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제4권1호
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• pp.1-15
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• 1966

In accordance with the tendency of Modern Mathematics laying emphasis on Mathematical structure, that is, on axioms, it is necessary for students to be interested in structure of Geometry on Mathematics Education. In fact, it is of importance not only to obtain new ideas but also to forget old ones in the development of Mathematics. Most students do not understand the Mathematical significance of axioms, and do not know what Mathemetical truth is. Now Non-Euclidean Geometry offers opportunity to understand the essence of Mathematics better, and is no less effective than Euclidean Geometry in training student in logical inference. This thesis is a study with regard to what should be taught and how student should be guided at High school Mathematics. Chiefly Hyperbolic Geometry is discussed in connection with Abosolute Geometry. As Non-Euclidean Geometry has not appeared in our curriculum, some experiments are required before putting it into actual curriculum to find out how much students understand and how much pedagogically useful it can be. This is only a. presentation of a tentative plan, which needs to be criticized by many teachers.

• Earthquakes and Structures
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• 제13권6호
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• pp.589-598
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• 2017

In this paper, dynamic response of the horizontal concrete beam subjected to seismic ground excitation is investigated. The structure is reinforced by $Fe_2O_3$ nanoparticles which have the magnetic properties. The hyperbolic shear deformation beam theory (HSDBT) is used for mathematical modeling of the structure. Based on the Mori-Tanaka model, the effective material properties of concrete beam is calculated considering the agglomeration of $Fe_2O_3$ nanoparticles. Applying energy method and Hamilton's principle, the motion equations are derived. Harmonic differential quadrature method (HDQM) along with Newmark method is utilized for numerical solution of the motion equations. The effects of different parameters such as volume fraction and agglomeration of $Fe_2O_3$ nanoparticles, magnetic field, boundary conditions and geometrical parameters of concrete beam are studied on the dynamic response of the structure. In order to validation of this work, an exact solution is used for comparing the numerical and analytical results. The results indicated that applying magnetic field decreases the of the structure up to 54 percent. In addition, increase too much the magnetic field (Hx>5e8 A/m) does not considerable effect on the reduction of the maximum dynamic displacement.