• Title/Summary/Keyword: Solvable

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Bending of steel fibers on partly supported elastic foundation

  • Hu, Xiao Dong;Day, Robert;Dux, Peter
    • Structural Engineering and Mechanics
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    • v.12 no.6
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    • pp.657-668
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    • 2001
  • Fiber reinforced cementitious composites are nowadays widely applied in civil engineering. The postcracking performance of this material depends on the interaction between a steel fiber, which is obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the corresponding differential equation. At the first glance, it is a classical beam on foundation problem. However, the differential equation is not analytically solvable due to the non-linear distribution of the foundation stiffness. Moreover, since the second order deformation effect is included, the boundary conditions become complex and hence conventional numerical tools such as the spline or difference methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam, direct integration is performed. For the non-linearly supported part, a transformation is carried out to reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta technique is employed for the solution within the boundary domain. Finally, multi-dimensional optimization approaches are carefully tested and applied to find the boundary values that are of interest. The numerical solution procedure is demonstrated to be stable and convergent.

An Analysis of Using TI-73 Calculator for the 5th Grade Students in an Elementary Math Gifted Class (TI-73 계산기를 활용한 초등 5학년 수학 영재 학급의 수업 분석)

  • Kang, Young Ran
    • Education of Primary School Mathematics
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    • v.16 no.3
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    • pp.315-331
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    • 2013
  • In this study, lessons on coordinate, percentage, and factorization in prime factors were taken with TI-73 calculator for 20 elementary school students in the 5th grade math gifted class in Pohang city. Through these lessons, the researcher examined with cases how using the calculator would influenced the lessons for the gifted students, and attempted to obtain implications on using calculators as learning tools in class. Activity sheets were made for this study and a 80-minute lesson was held three times for three weeks. In order to collect data, the class was recorded on videotape, the students were interviewed, and documents used in the class were collected. Then all the data were transcribed. Data analysis was completed through several readings of transcripts and main themes were derived by classifying, comparing, and contrasting coding. As a result of the study, the calculator played a role the tool as the mediation to communicate and the challenge their solvable tasks beyond the limitation of paper and pencil environments. But, in using the calculator, there was differences in gender between boys and girls. Above all, to enter commands into the calculator resulted in obstacles for learning process.

The Investigation and Analysis of Field Condition on the Electrical Shock Hazard of Electrical Facilities Used for Temporary Power Supply at Construction Site (임시전력 건설현장에 사용되는 전기설비의 감전위험에 관한 현장실태 조사 및 분석)

  • Gil, Hyoung-Jun;Lee, Bok-Hee
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.18 no.6
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    • pp.197-204
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    • 2004
  • The temporary power installations are to be used for temporarily supplying power during work at construction sites and have a minimum of protective devices to differ from permanent installations. There are many risk factors caused by loose working environments, deterioration of installations at construction sites. To analyze risk factors of temporary power installations, the investigation and the questionnaire were carried out side by side for power receiving system patch and panel boards, and were performed by researcher, the related expert, engineer of Korea Electrical Safety Corporation all over the country. The objects were variable such as an airport, an apartment, a municipal playground As a result, there are many problems such as a bad lock, poor protection of charging department. Solvable methods are improvement of the related regulation safety education, safety check and so on. In the future, the analytical data can be applied to prevent the electrical shock at construction site, and can be used to stabilize electrical installations.

Notes On Inverse Interval Graph Coloring Problems

  • Chung, Yerim;Kim, Hak-Jin
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.10
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    • pp.57-64
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    • 2019
  • In this paper, we study a polynomially solvable case of the inverse interval graph coloring problem. Given an interval graph associated with a specific interval system, the inverse interval graph coloring problem is defined with the assumption that there is no proper K-coloring for the given interval graph, where K is a fixed integer. The problem is to modify the system of intervals associated with the given interval graph by shifting some of the intervals in such a way that the resulting interval graph becomes K-colorable and the total modification is minimum with respect to a certain norm. In this paper, we focus on the case K = 1 where all intervals associated with the interval graph have length 1 or 2, and interval displacement is only allowed to the righthand side with respect to its original position. To solve this problem in polynomial time, we propose a two-phase algorithm which consists of the sorting and First Fit procedure.

Efficient Non-Cryptographic Protocols for Public key Authentication in Wireless Sensor Network (WSN에서의 협력적인 공개키 인증 프로토콜)

  • Mohaisen, Abedelaziz;Maeng, Young-Jae;Nyang, Dae-Hun
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.17 no.3
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    • pp.101-108
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    • 2007
  • We follow the promising recent results of deploying the public key cryptography in sensor networks. Recent results have shown that the public key algorithms are computationally feasible on the typical sensor nodes. However, once the public key cryptography is brought to the sensor network, security services such like key authentication will be critically required. In this paper we investigate the public key authentication problem in the sensor network and provide several authentication protocols. Our protocols are mainly based on the non-solvable overhearing in the wireless environment and a distributed voting mechanism. To show the value of our protocols, we provide an extensive analysis of the used resources and the resulting security level. As well, we compare our work with other existing works. For further benefit of our protocols, we list several additional applications in the sensor network where our protocols provide a sufficient authentication under the constrained resources.

Verification of educational goal of reading area in Korean SAT through natural language processing techniques (대학수학능력시험 독서 영역의 교육 목표를 위한 자연어처리 기법을 통한 검증)

  • Lee, Soomin;Kim, Gyeongmin;Lim, Heuiseok
    • Journal of the Korea Convergence Society
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    • v.13 no.1
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    • pp.81-88
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    • 2022
  • The major educational goal of reading part, which occupies important portion in Korean language in Korean SAT, is to evaluated whether a given text can be fully understood. Therefore given questions in the exam must be able to solely solvable by given text. In this paper we developed a datatset based on Korean SAT's reading part in order to evaluate whether a deep learning language model can classify if the given question is true or false, which is a binary classification task in NLP. In result, by applying language model solely according to the passages in the dataset, we were able to acquire better performance than 59.2% in F1 score for human performance in most of language models, that KoELECTRA scored 62.49% in our experiment. Also we proved that structural limit of language models can be eased by adjusting data preprocess.

A Stress-Based Gradient Elasticity in the Smoothed Finite Element Framework (평활화 유한요소법을 도입한 응력기반 구배 탄성론)

  • Changkye Lee;Sundararajan Natarajan
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.37 no.3
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    • pp.187-195
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    • 2024
  • This paper presents two-dimensional boundary value problems of the stress-based gradient elasticity within the smoothed finite element method (S-FEM) framework. Gradient elasticity is introduced to address the limitations of classical elasticity, particularly its struggle to capture size-dependent mechanical behavior at the micro/nano scale. The Ru-Aifantis theorem is employed to overcome the challenges of high-order differential equations in gradient elasticity. This theorem effectively splits the original equation into two solvable second-order differential equations, enabling its incorporation into the S-FEM framework. The present method utilizes a staggered scheme to solve the boundary value problems. This approach efficiently separates the calculation of the local displacement field (obtained over each smoothing domain) from the non-local stress field (computed element-wise). A series of numerical tests are conducted to investigate the influence of the internal length scale, a key parameter in gradient elasticity. The results demonstrate the effectiveness of the proposed approach in smoothing stress concentrations typically observed at crack tips and dislocation lines.

Optimal Sequence Alignment Algorithm Using Space Division Technique (공간 분할 방법을 이용한 최적 서열정렬 알고리즘)

  • Ahn, Heui-Kook;Roh, Hi-Young
    • Journal of KIISE:Software and Applications
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    • v.34 no.5
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    • pp.397-406
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    • 2007
  • The problem of finding an optimal alignment between sequence A and B can be solved by dynamic programming algorithm(DPA) efficiently. But, if the length of string was longer, the problem might not be solvable because it requires O(m*n) time and space complexity.(where, $m={\mid}A{\mid},\;n={\mid}B{\mid}$) For space, Hirschberg developed a linear space and quadratic time algorithm, so computer memory was no longer a limiting factor for long sequences. As computers's processor and memory become faster and larger, a method is needed to speed processing up, although which uses more space. For this purpose, we present an algorithm which will solve the problem in quadratic time and linear space. By using division method, It computes optimal alignment faster than LSA, although requires more memory. We generalized the algorithm about division problem for not being divided into integer and pruned additional space by entry/exit node concept. Through the proofness and experiment, we identified that our algorithm uses d*(m+n) space and a little more (m*n) time faster than LSA.

Problem Solving Ability and Mental Capacity of High School Students under Complex Concept Situations (복합개념상황에서 고등학생들의 문제해결력과 정신용량)

  • Choi, Hyuk-Joon;Park, Ho-Jeen;Kwon, Jae-Sool
    • Journal of The Korean Association For Science Education
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    • v.24 no.5
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    • pp.937-945
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    • 2004
  • In this study, we examined high school students' abilities for solving problems under single concept situations and complex concept situations and their mental capacities. Single concept situations are defined as the problems which can be solved with a scientific concept or principle and complex concept situations are the problems combined with more than 2 single concept situations. 152 11th-graders were participated in this study, who had taken natural science track. FIT 752 was used to measure their mental capacities. And an instrument, made up of six questions under three single concept situations and three complex concept situations, was used to assess students' problem solving abilities. As results, students' problem solving abilities were lower in complex concept situations than in single concept situations. There wasn't significant difference in mental capacities between of students who succeeded in solving problems and ones who did not under both single and complex concept situations. Although students solved the problems of single concept situations, some of them failed in solving the problems of complex concept situations composed of single concept situations which they succeeded in solving. They belonged to relatively low mental capacity group, of which students who failed in solving problems of complex situations had lower metal capacities than ones who succeeded in solving them. According to these results, it could be concluded that mental capacity is one of main variables which have influence on problem solving of complex concept situations composed of solvable single concept situations.

The Prototype Study of Resistivity and Porosity Measurement for the Samples Collected Near Marine Hydrothermal Deposit (해저열수광상 주변 암석 시료의 공극률과 전기비저항 측정 기초실험)

  • Lee, Sang-Kyu;Lee, Seong-Kon
    • Geophysics and Geophysical Exploration
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    • v.13 no.4
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    • pp.378-387
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    • 2010
  • We present the results of laboratory measurement of porosity and electrical resistivity for the samples collected near marine hydrothermal deposit to provide fundamental perspective of physical properties for future electromagnetic survey. The rock cores are sampled from the host rock, pumice, hydrothermal altered zone, and chimney. These samples are featured as easily brittle, rough surface with large pores, having components easily solvable in the water. We suggest systematic approach for measuring weights, volumes of core samples to calculate density and porosity. Measurements reveal that the resistivities of black host rock, gray host rock, pumice and chimney are 102, 39, 11, 0.1 ohm-m, respectively, when the core samples are saturated with saline water of $32,000\;{\mu}S$/cm (0.5 ohm-m) at temperature of $2.5^{\circ}C$ and these correspond to the factors of 5 for sea water, 110 for pumice and 390~1020 for host rocks with respect to the resistivity of chimney. We also confirm that resistivity of rock samples saturated with water decrease with temperature linearly over the temperature range of $20{\sim}80^{\circ}C$.