• Title/Summary/Keyword: geometric problem solving

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Evaluating the Effectiveness of Unconventional Intersections on Operation and Environment (회전교통량 분산식 임계 교차로의 운영 및 환경 효과 분석)

  • Moon, Jae-Pil;Kim, Hoe-Ryong;Lee, Suk-Ki;Jeong, Jun-Hwa
    • International Journal of Highway Engineering
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    • v.16 no.3
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    • pp.75-84
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    • 2014
  • PURPOSES : Traffic congestions which occur in the intersections of arterials lead to mobility and environment problem, and then traffic agencies and engineers have been struggling for mitigating congestions with greenhouse gas emissions. As an alternative of solving theses problems, this study is to introduce a low-cost and high-effectiveness countermeasure as unconventional intersections which are successfully in operation in U.S.. The main feature of unconventional intersections is to reroute turning movement on an approach to other approach, which consequently more green time is available for the progression of through traffic. Due to improved progression, this unique geometric design contributes to reduce delays with greenhouse gas emission and provides a viable alternative to interchanges. This study is to evaluate the potential operation and environment benefits of unconventional intersections. METHODS : This study used the VISSIM model with Synchro and EnViVer. Synchro is to optimize signal phases and EnViVer model to estimate the amount of greenhouse gas emissions by each condition. RESULTS : The result shows that unconventional intersections lead to increase the capacity and to reduce greenhouse gas emissions, compared to existing intersections. CONCLUSIONS : Unconventional intersections have the ability to positively impact operations and environments as a low-cost and high-effectiveness countermeasure.

How Do Elementary School Students Understand Tables? : From Functional Thinking Perspective (초등학생들은 표를 어떻게 이해할까? : 함수적 사고의 관점에서)

  • Kim, JeongWon
    • Education of Primary School Mathematics
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    • v.20 no.1
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    • pp.53-68
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    • 2017
  • Although the table, as one of the representations for helping mathematics understanding, steadily has been shown in the mathematics textbooks, there have been little studies that focus on the table and analyze how the table may be used in understanding students' functional thinking. This study investigated the elementary school 5th graders' abilities to design function tables. The results showed that about 75% of the students were able to create tables for themselves, which shaped horizontal and included information only from the problem contexts. And the students had more difficulties in solving geometric growing pattern problems than story problems. Building on these results, this paper is expected to provide implications of instructional directions of how to use the table as 'function table'.

Free vibration analysis of angle-ply laminated composite and soft core sandwich plates

  • Sahla, Meriem;Saidi, Hayat;Draiche, Kada;Bousahla, Abdelmoumen Anis;Bourada, Fouad;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • v.33 no.5
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    • pp.663-679
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    • 2019
  • In this work, a simple four-variable trigonometric shear deformation model with undetermined integral terms to consider the influences of transverse shear deformation is applied for the dynamic analysis of anti-symmetric laminated composite and soft core sandwich plates. Unlike the existing higher order theories, the current one contains only four unknowns. The equations of motion are obtained using the principle of virtual work. The analytical solution is determined by solving the eigenvalue problem. The influences of geometric ratio, modular ratio and fibre angle are critically evaluated for different problems of laminated composite and sandwich plates. The eigenfrequencies obtained using the current theory are verified by comparing the results with those of other theories and with the exact elasticity solution, if any.

Analysis by reduction in the development of algebra (분석의 환원적 기능이 대수 발달에 미친 영향)

  • Kim, Jae-Hong;Kwon, Seok-Il;Hong, Jin-Kon
    • Journal for History of Mathematics
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    • v.20 no.3
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    • pp.167-180
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    • 2007
  • In this study, we explored the role of analysis in the algebra development. For this, we classified ancient geometric analysis into an analysis by reduction and a Pappusian problematic analysis. this shows that both analyses have the function of reduction. Pappus' analysis consists of four steps; transformation, resolution, construction, demonstration. The transformation, by which conditions of given problem is transformed into other conditions which suggest a problem-solving, seems to be a kind of reduction. Mathematicians created new problems as a result of the reductional function of analysis, and became to see mathematics in the different view. An analytical thinking was a background at the birth of symbolic algebra, the reductional function of analysis played an important role in the development of symbolic algebra.

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A Study on Shape Optimization of Plane Truss Structures (평면(平面) 트러스 구조물(構造物)의 형상최적화(形狀最適化)에 관한 구연(究研))

  • Lee, Gyu won;Byun, Keun Joo;Hwang, Hak Joo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.3
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    • pp.49-59
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    • 1985
  • Formulation of the geometric optimization for truss structures based on the elasticity theory turn out to be the nonlinear programming problem which has to deal with the Cross sectional area of the member and the coordinates of its nodes simultaneously. A few techniques have been proposed and adopted for the analysis of this nonlinear programming problem for the time being. These techniques, however, bear some limitations on truss shapes loading conditions and design criteria for the practical application to real structures. A generalized algorithm for the geometric optimization of the truss structures which can eliminate the above mentioned limitations, is developed in this study. The algorithm developed utilizes the two-phases technique. In the first phase, the cross sectional area of the truss member is optimized by transforming the nonlinear problem into SUMT, and solving SUMT utilizing the modified Newton-Raphson method. In the second phase, the geometric shape is optimized utilizing the unidirctional search technique of the Rosenbrock method which make it possible to minimize only the objective function. The algorithm developed in this study is numerically tested for several truss structures with various shapes, loading conditions and design criteria, and compared with the results of the other algorithms to examme its applicability and stability. The numerical comparisons show that the two-phases algorithm developed in this study is safely applicable to any design criteria, and the convergency rate is very fast and stable compared with other iteration methods for the geometric optimization of truss structures.

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Ensemble Learning with Support Vector Machines for Bond Rating (회사채 신용등급 예측을 위한 SVM 앙상블학습)

  • Kim, Myoung-Jong
    • Journal of Intelligence and Information Systems
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    • v.18 no.2
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    • pp.29-45
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    • 2012
  • Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.

Computer Graphic Animation based on Forward Dynamic Simulation (Forward Dynamic 시뮬래이션을 이용한 컴퓨터 그래픽 애니매이션)

  • Park, Jihun
    • Journal of the Korea Computer Graphics Society
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    • v.2 no.1
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    • pp.48-60
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    • 1996
  • This paper present a new technique for doing realistic computer animation. The method is based on forward dynamic simulation and nonlinear problem solving (parameter optimization) technique. Objects are modelled physically and simulated faithfully while satisfying kinematic and geometric constraints. This forward dynamic simulation gives us very realistic motions especially for non-voluntary motions. Then we extend simulation technique to do animation using parameter optimization. The basic idea is to add motion control over the entire animation. The motion control is finding optimal solutions while satisfying user's animation goals. We provide two different animation technique; one is for rigid body without joint actuators and the other is for rigid body with linear joint actuators. To achieve motion control, we convert single simulation to single nonliner function evaluation while either setting initial conditions as variables for the function or allocating control variables in terms of time. This method is presented with two animation examples: dice-magic and human stand-up.

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Simplified Analytical Model for Investigating the Output Power of Solar Array on Stratospheric Airship

  • Zhang, Yuanyuan;Li, Jun;Lv, Mingyun;Tan, Dongjie;Zhu, Weiyu;Sun, Kangwen
    • International Journal of Aeronautical and Space Sciences
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    • v.17 no.3
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    • pp.432-441
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    • 2016
  • Solar energy is the ideal power choice for long-endurance stratospheric airships. The output performance of solar array on stratospheric airship is affected by several major factors: flying latitude, flight date, airship's attitude and the temperature of solar cell, but the research on the effect of these factors on output performance is rare. This paper establishes a new simplified analytical model with thermal effects to analyze the output performance of the solar array. This model consisting of the geometric model of stratospheric airship, solar radiation model and incident solar radiation model is developed using MATLAB computer program. Based on this model, the effects of the major factors on the output performance of the solar array are investigated expediently and easily. In the course of the research, the output power of solar array is calculated for five airship's latitudes of $0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$, four special dates and different attitudes of five pitch angles and four yaw angles. The effect of these factors on output performance is discussed in detail. The results are helpful for solving the energy problem of the long endurance airship and planning the airline.

Finite Element Analysis of Unbalance Response of a High Speed Flexible Polygon Mirror Scanner Motor Considering the Flexibility of Supporting Structure (지지구조의 유연성을 고려한 고속 유연 폴리곤 미러 스캐너 모터의 유한 요소 불평형 응답 해석)

  • Jung, Kyung-Moon;Seo, Chan-Hee;Kim, Myung-Gyu;Jang, Gun-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.859-865
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    • 2007
  • This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

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Analysis of cable structures through energy minimization

  • Toklu, Yusuf Cengiz;Bekdas, Gebrail;Temur, Rasim
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.749-758
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    • 2017
  • In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.