• Title/Summary/Keyword: Differentiation problem solving

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Design and Development of White-box e-Learning Contents for Science-Engineering Majors using Mathematica (이공계 대학생을 위한 Mathematica 기반의 화이트박스 이러닝 콘텐츠 설계 및 개발)

  • Jun, Youngcook
    • Journal of the Korean School Mathematics Society
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    • v.18 no.2
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    • pp.223-240
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    • 2015
  • This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.

Stress Constraint Topology Optimization using Backpropagation Method in Design Sensitivity Analysis (설계민감도 해석에서 역전파 방법을 사용한 응력제한조건 위상최적설계)

  • Min-Geun, Kim;Seok-Chan, Kim;Jaeseung, Kim;Jai-Kyung, Lee;Geun-Ho, Lee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.6
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    • pp.367-374
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    • 2022
  • This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

Species Adaptation Evolutionary Algorithm for Solving the Optimization Problems

  • Lee, Dong-Wook;Sim, Kwee-Bo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.2
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    • pp.233-238
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    • 2003
  • Living creatures maintain their variety through speciation, which helps them to have more fitness for an environment. So evolutionary algorithm based on biological evolution must maintain variety in order to adapt to its environment. In this paper, we utilize the concept of speciation. Each individual of population creates their offsprings using mutation, and next generation consists of them. Each individual explores search space determined by mutation. Useful search space is extended by differentiation, then population explorers whole search space very effectively. If evolvable hardware evolves through mutation, it is useful way to explorer search space because of less varying inner structure. We verify the effectiveness of the proposed method by applying it to two optimization problems.

3D stress-fractional plasticity model for granular soil

  • Song, Shunxiang;Gao, Yufeng;Sun, Yifei
    • Geomechanics and Engineering
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    • v.17 no.4
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    • pp.385-392
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    • 2019
  • The present fractional-order plasticity models for granular soil are mainly established under the triaxial compression condition, due to its difficult in analytically solving the fractional differentiation of the third stress invariant, e.g., Lode's angle. To solve this problem, a three dimensional fractional-order elastoplastic model based on the transformed stress method, which does not rely on the analytical solution of the Lode's angle, is proposed. A nonassociated plastic flow rule is derived by conducting the fractional derivative of the yielding function with respect to the stress tensor in the transformed stress space. All the model parameters can be easily determined by using laboratory test. The performance of this 3D model is then verified by simulating multi series of true triaxial test results of rockfill.

Improvement of Search Efficiency in Optimization Algorithm using Self-adaptive Harmony Search Algorithms (매개변수 자가적응 화음탐색 알고리즘의 성능 비교를 통한 최적해 탐색 효율 향상)

  • Choi, Young Hwan;Lee, Ho Min;Yoo, Do Guen;Kim, Joong Hoo
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.1
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    • pp.1-11
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    • 2018
  • In various engineering fields, determining the appropriate parameter set is a cumbersome and difficult task when solving optimization problems. Despite the appropriate parameter setting through parameter sensitivity analysis, there are limits to evaluating whether the parameters are appropriate for all optimization problems. For this reason, kinds of a Self-adaptive Harmony searches have been developed to solve various engineering problems by the appropriate setting of algorithm's own parameters according to the problem. In this study, various types of Self-adaptive Harmony searches were investigated and the characteristics of optimization were categorized. Six algorithms with a differentiation of optimization process were applied and compared with not only the mathematical optimization problem, but also the engineering problem, which has been applied widely in the algorithm performance comparisons. The performance of each algorithm was compared, and the statistical performance indicators were used to evaluate the application results quantitatively.

Analysis of Start-up Success Factors by AER Case (AER(Asan Entrepreneur Review)사례를 통한 스타트업 기업의 성공요인 분석)

  • Lee, Sangjo;Nam, Jungmin
    • Asia-Pacific Journal of Business Venturing and Entrepreneurship
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    • v.13 no.2
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    • pp.39-50
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    • 2018
  • A main purpose of this research is to identify success factors of start-up based on the AER case study. As a result of case analysis, In the early stage, the success factors of start-up are the entrepreneur's history, experience, expertise, prompt judgment, problem-solving ability, the capacity and teamwork of its members, business networks and supporting government start-ups. In the commercialization stage, securing commercialization and investment funds, timing, differentiation strategy, overseas advancement, and acceptance of customer feedback are important. In the growth stage (maturity stage), new product launches and diversification, and establishment of organizational culture are important. Based on the results of this analysis, this study sought success factors and implications for each stage and sought research directions in the future.

Magnetic Resonance Imaging in Thoracic Disease (흉부질환의 자기공명영상)

  • Song, Koun-Sik
    • Tuberculosis and Respiratory Diseases
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    • v.40 no.4
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    • pp.345-352
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    • 1993
  • The role of magnetic resonance(MR) imaging in the evaluation of thoracic disease has been limited Nontheless, MR has inherent properties of better contrast resolution than CT allowing tissue-specific diagnosis. MR has capability of direct imaging in sagittal, coronal, and oblique planes which provide better anatomic information than axial images of CT such as lesions in the pulmonary apex, aorticopulmonary window, peridiaphragmatic region, and subcarinal region. MR is sensitive to blood flow making it an ideal imaging modality for the evaluation of cardiovascular system of the thorax without the need for intravenous contrast media. Technical developments and better control of motion artifacts have resulted in improved image quality, and clinical applications of MR imaging in thoracic diseases have been expanded. Although MR imaging is considered as a problem-solving tool in patients with equivocal CT findings, MR should be used as the primary imaging modality in the following situations: 1) Evaluation of the cardiovascular abnormalities of the thorax 2) Evaluation of the superior sulcus tumors 3) Evaluation of the chest wall invasion or mediastinal invasion by tumor 4) Evaluation of the posterior mediastinal mass, especially neurogenic tumor 5) Differentiation of fibrosis and residual or recurrent tumor, especially in lymphoma 6) Evaluation of brachial plexopathy With technical developments and fast scan capabilities, clinical indications for MR imaging in thorax will increase in the area of pulmonary parenchymal and pulmonary vascular imaging.

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Solutions for Design Creativity Barriers (디자인 창의성 저해요소의 해결방안)

  • Kim, Dong-Ha
    • The Journal of the Korea Contents Association
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    • v.20 no.11
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    • pp.15-27
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    • 2020
  • In the design process that focuses on problem solving, in general, two or three barriers to design creativity appear at the same time and are linked to increase difficulty. Because the design problem always arises in unusual, unique, weird, and difficult to define, it is not possible to extract the correct answer through the formula and the answer is always plural. This study aims to present solutions and prove their effectiveness as a follow-up study that seeks to overcome the representative obstacles to design creativity discussed in the previous study. To this end, a qualitative study was conducted to find solutions to the obstacles suggested in the previous study and to devise key solutions(creativity development cards). At the same time, a quantitative research methodology using experiments and statistical analysis was adopted. After grasping the core characteristics of an object using the creativity development card, it was able to approach the creative solution by utilizing the reductive analysis of the original such as transformation of the core characteristics, reconsideration of essential problems and intentional differentiation. As a result, it was confirmed that the proposed solutions were effective not only as a method of overcoming the barriers to design creativity, but also in improving creativity.

The Network Analysis for Community Voluntary Organizations and Its Implication for Community Capacity Building Toward Health Promotion (지역사회 자발적 결사체의 연결망과 지역사회 역량)

  • Jung, Min-Soo;Cho, Byong-Hee;Lee, Sung-Cheon
    • Health Policy and Management
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    • v.17 no.4
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    • pp.54-81
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    • 2007
  • The paradigm of health promotion requests community participation and its active problem-solving. Community is conceptualized as a resource pool to be organized. Such resource is called community capacity. Community participation is a process of capacity building. Community voluntary associations are considered as valuable resource to be used for health promotion. This paper tried to identify the network structure among community voluntary associations and to infer the possibility to make such network of organizations participate in health promotion programs. Two survey data were used for this research: 1) Measurements and Evaluations of Community Capacity on Dobong-gu (N=94) 2) A development plan of health medicine service to be Healthy Gangdong-gu (N=69). The questionnaire included such variables measuring community capacity as leadership, membership, organizational resources, and inter-organizational network, etc. Both regions had the following common characteristics: 1) There were positive correlations between the organization's budget and membership. 2) Organizational types were associated with their founded years. Two regions showed the following differences: Dobong displayed the high density of community organizations, but Gangdong showed the low density. Dobong community organizations were able to be classified into three network clusters such as women & environments, youth & adolescent, and sports organizations. Each cluster of organizations favored the different type of health promotion programs. Gangdong community organizations were less developed, and not possible to be clustered. Depending upon the level of community capacity or community organizations' differentiation, the strategy of community participation could be settle down in different ways. Particularly the health agency had to pay more attention to support the growth of civil organizations.

Structural Damage Assessment Using Transient Dynamic Response (동적과도응답을 사용한 구조물의 손상진단)

  • 신수봉;오성호;곽임종;고현무
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.13 no.4
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    • pp.395-404
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    • 2000
  • A damage detection and assessment algorithm is developed by measuring accelerations at limited locations of a structure under forced vibrations. The developed algorithm applies a time-domain system identification (SI) method that identifies a structure by solving a linearly constrained nonlinear optimization problem for optimal structural parameters. An equation error of the dynamic equilibrium of motion is minimized to estimate optimal parameters. An adaptive parameter grouping scheme is applied to localize damaged members with sparse measured accelerations. Damage is assessed in a statistical manner by applying a time-windowing technique to the measured time history of acceleration. Displacements and velocities at the measured degrees of freedom (DOF) are computed by integrating the measured accelerations. The displacements at the unmeasured DOF are estimated as additional unknowns to the unknown structural parameters, and the corresponding velocities and accelerations we computed by a numerical differentiation. A numerical simulation study with a truss structure is carried out to examine the efficiency of the algorithm. A data perturbation scheme is applied to determine the thresholds lot damage indices and to compute the damage possibility of each member.

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