• Title/Summary/Keyword: mathematical structures

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Using an appropriate rotation-based criterion to account for torsional irregularity in reinforced concrete buildings

  • Akshara S P;M Abdul Akbar;T M Madhavan Pillai;Rakesh Pasunuti;Renil Sabhadiya
    • Earthquakes and Structures
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    • v.26 no.5
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    • pp.349-361
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    • 2024
  • Excessive torsional behaviour is one of the major reasons for failure of buildings, as inferred from past earthquakes. Numerous seismic codes across the world specify a displacement-based or drift-based criterion for classifying buildings as torsionally irregular. In recent years, quite a few researchers have pointed out some of the inherent deficiencies associated with the current codal guidelines on torsional irregularity. This short communication paper aims to envisage the need for a revision of the displacement-based guidelines on torsional irregularity, and further highlight the appropriateness of a rotation-based criterion. A set of 6 reinforced concrete building models with asymmetric shear walls are analysed using ETABS v18.0.2, by varying the number of stories from 1 to 9, and the torsional irregularity coefficient of various stories is calculated using the displacement-based formula. Since rotation about the vertical axis is a direct indication of the twist experienced by a building, the calculated torsional irregularity coefficients of all stories are compared with the corresponding floor rotations. The conflicting results obtained for the torsional irregularity coefficients are projected through five categories, namely mismatch with floor rotations, inconsistency in trend, lack of clarity in incorporation of negative values, sensitivity to low values of displacement and error conceived in the mathematical formulation. The findings indicate that the irregularity coefficient does not accurately represent the torsional behaviour of buildings in a realistic sense. The Indian seismic code-based values of 1.2 and 1.4, which are used to characterize buildings as torsionally irregular are observed to be highly sensitive to the numerical values of displacements, rather than the actual degree of rotation. The study thus emphasizes the revision of current guidelines based on a more relevant rotation-based or eccentricity-based approach.

A Mathematics Teacher's Reflective Practice as a Process of Professional Development (전문성 신장 과정으로서의 한 수학교사의 성찰적 실천)

  • Kim, Dong-Won
    • Communications of Mathematical Education
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    • v.23 no.3
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    • pp.735-760
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    • 2009
  • Most of every teachers' life is occupied with his or her instruction, and a classroom is a laboratory for mutual development between teacher and students also. Namely, a teacher's professionalism can be enhanced by circulations of continual reflection, experiment, verification in the laboratory. Professional development is pursued primarily through teachers' reflective practices, especially instruction practices which is grounded on $Sch\ddot{o}n's$ epistemology of practices. And a thorough penetration about situations or realities and an exact understanding about students that are now being faced are foundations of reflective practices. In this study, at first, we explored the implications of earlier studies for discussing a teacher's practice. We could found two essential consequences through reviewing existing studies about classroom and instructions. One is a calling upon transition of perspectives about instruction, and the other is a suggestion of necessity of a teachers' reflective practices. Subsequently, we will talking about an instance of a middle school mathematics teacher's practices. We observed her instructions for a year. She has created her own practical knowledges through circulation of reflection and practices over the years. In her classroom, there were three mutual interaction structures included in a rich expressive environments. The first one is students' thinking and justifying in their seats. The second is a student's explaining at his or her feet. The last is a student's coming out to solve and explain problem. The main substances of her practical know ledges are creating of interaction structures and facilitating students' spontaneous changes. And the endeavor and experiment for diagnosing trouble and finding alternative when she came across an obstacles are also main elements of her practical knowledges Now, we can interpret her process of creating practical knowledge as a process of self-directed professional development when the fact that reflection and practices are the kernel of a teacher's professional development is taken into account.

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The Development and Application of Girih tiling Program for the Math-Gifted Student in Elementary School (Girih 타일링을 이용한 초등수학영재 프로그램 개발 및 적용 연구)

  • Park, Hye-Jeong;Cho, Young-Mi
    • Journal of Gifted/Talented Education
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    • v.22 no.3
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    • pp.619-637
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    • 2012
  • The purpose of this study is to develop a new program for elementary math-gifted students by using 'Girih Tililng' and apply it to the elementary students to improve their math-ability. Girih Tililng is well known for 'the secrets of mathematics hidden in Mosque decoration' with lots of recent attention from the world. The process of this study is as follows; (1) Reference research has been done for various tiling theories and the theories have been utilized for making this study applicable. (2) The characteristic features of Mosque tiles and their basic structures have been analyzed. After logical examination of the patterns, their mathematic attributes have been found out. (3) After development of Girih tiling program, the program has been applied to math-gifted students and the program has been modified and complemented. This program which has been developed for math-gifted students is called 'Exploring the Secrets of Girih Hidden in Mosque Patterns'. The program was based on the Renzulli's three-part in-depth learning. The first part of the in-depth learning activity, as a research stage, is designed to examine Islamic patterns in various ways and get the gifted students to understand and have them motivated to learn the concept of the tiling, understanding the characteristics of Islamic patterns, investigating Islamic design, and experiencing the Girih tiles. The second part of the in-depth learning activity, as a discovery stage, is focused on investigating the mathematical features of the Girih tile, comparing Girih tiled patterns with non-Girih tiled ones, investigating the mathematical characteristics of the five Girih tiles, and filling out the blank of Islamic patterns. The third part of the in-depth learning activity, as an inquiry or a creative stage, is planned to show the students' mathematical creativity by thinking over different types of Girih tiling, making the students' own tile patterns, presenting artifacts and reflecting over production process. This program was applied to 6 students who were enrolled in an unified(math and science) gifted class of D elementary school in Daejeon. After analyzing the results produced by its application, the program was modified and complemented repeatedly. It is expected that this program and its materials used in this study will guide a direction of how to develop methodical materials for math-gifted education in elementary schools. This program is originally developed for gifted education in elementary schools, but for further study, it is hoped that this study and the program will be also utilized in the field of math-gifted or unified gifted education in secondary schools in connection with 'Penrose Tiling' or material of 'quasi-crystal'.

The Impact of the Internet Channel Introduction Depending on the Ownership of the Internet Channel (도입주체에 따른 인터넷경로의 도입효과)

  • Yoo, Weon-Sang
    • Journal of Global Scholars of Marketing Science
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    • v.19 no.1
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    • pp.37-46
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    • 2009
  • The Census Bureau of the Department of Commerce announced in May 2008 that U.S. retail e-commerce sales for 2006 reached $ 107 billion, up from $ 87 billion in 2005 - an increase of 22 percent. From 2001 to 2006, retail e-sales increased at an average annual growth rate of 25.4 percent. The explosive growth of E-Commerce has caused profound changes in marketing channel relationships and structures in many industries. Despite the great potential implications for both academicians and practitioners, there still exists a great deal of uncertainty about the impact of the Internet channel introduction on distribution channel management. The purpose of this study is to investigate how the ownership of the new Internet channel affects the existing channel members and consumers. To explore the above research questions, this study conducts well-controlled mathematical experiments to isolate the impact of the Internet channel by comparing before and after the Internet channel entry. The model consists of a monopolist manufacturer selling its product through a channel system including one independent physical store before the entry of an Internet store. The addition of the Internet store to this channel system results in a mixed channel comprised of two different types of channels. The new Internet store can be launched by the independent physical store such as Bestbuy. In this case, the physical retailer coordinates the two types of stores to maximize the joint profits from the two stores. The Internet store also can be introduced by an independent Internet retailer such as Amazon. In this case, a retail level competition occurs between the two types of stores. Although the manufacturer sells only one product, consumers view each product-outlet pair as a unique offering. Thus, the introduction of the Internet channel provides two product offerings for consumers. The channel structures analyzed in this study are illustrated in Fig.1. It is assumed that the manufacturer plays as a Stackelberg leader maximizing its own profits with the foresight of the independent retailer's optimal responses as typically assumed in previous analytical channel studies. As a Stackelberg follower, the independent physical retailer or independent Internet retailer maximizes its own profits, conditional on the manufacturer's wholesale price. The price competition between two the independent retailers is assumed to be a Bertrand Nash game. For simplicity, the marginal cost is set at zero, as typically assumed in this type of study. In order to explore the research questions above, this study develops a game theoretic model that possesses the following three key characteristics. First, the model explicitly captures the fact that an Internet channel and a physical store exist in two independent dimensions (one in physical space and the other in cyber space). This enables this model to demonstrate that the effect of adding an Internet store is different from that of adding another physical store. Second, the model reflects the fact that consumers are heterogeneous in their preferences for using a physical store and for using an Internet channel. Third, the model captures the vertical strategic interactions between an upstream manufacturer and a downstream retailer, making it possible to analyze the channel structure issues discussed in this paper. Although numerous previous models capture this vertical dimension of marketing channels, none simultaneously incorporates the three characteristics reflected in this model. The analysis results are summarized in Table 1. When the new Internet channel is introduced by the existing physical retailer and the retailer coordinates both types of stores to maximize the joint profits from the both stores, retail prices increase due to a combination of the coordination of the retail prices and the wider market coverage. The quantity sold does not significantly increase despite the wider market coverage, because the excessively high retail prices alleviate the market coverage effect to a degree. Interestingly, the coordinated total retail profits are lower than the combined retail profits of two competing independent retailers. This implies that when a physical retailer opens an Internet channel, the retailers could be better off managing the two channels separately rather than coordinating them, unless they have the foresight of the manufacturer's pricing behavior. It is also found that the introduction of an Internet channel affects the power balance of the channel. The retail competition is strong when an independent Internet store joins a channel with an independent physical retailer. This implies that each retailer in this structure has weak channel power. Due to intense retail competition, the manufacturer uses its channel power to increase its wholesale price to extract more profits from the total channel profit. However, the retailers cannot increase retail prices accordingly because of the intense retail level competition, leading to lower channel power. In this case, consumer welfare increases due to the wider market coverage and lower retail prices caused by the retail competition. The model employed for this study is not designed to capture all the characteristics of the Internet channel. The theoretical model in this study can also be applied for any stores that are not geographically constrained such as TV home shopping or catalog sales via mail. The reasons the model in this study is names as "Internet" are as follows: first, the most representative example of the stores that are not geographically constrained is the Internet. Second, catalog sales usually determine the target markets using the pre-specified mailing lists. In this aspect, the model used in this study is closer to the Internet than catalog sales. However, it would be a desirable future research direction to mathematically and theoretically distinguish the core differences among the stores that are not geographically constrained. The model is simplified by a set of assumptions to obtain mathematical traceability. First, this study assumes the price is the only strategic tool for competition. In the real world, however, various marketing variables can be used for competition. Therefore, a more realistic model can be designed if a model incorporates other various marketing variables such as service levels or operation costs. Second, this study assumes the market with one monopoly manufacturer. Therefore, the results from this study should be carefully interpreted considering this limitation. Future research could extend this limitation by introducing manufacturer level competition. Finally, some of the results are drawn from the assumption that the monopoly manufacturer is the Stackelberg leader. Although this is a standard assumption among game theoretic studies of this kind, we could gain deeper understanding and generalize our findings beyond this assumption if the model is analyzed by different game rules.

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A Study on Shape Optimum Design for Stability of Elastic Structures (탄성 구조물의 안정성을 고려한 형상최적설계)

  • Yang, Wook-Jin;Choi, Joo-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.1
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    • pp.75-82
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    • 2007
  • This paper addresses a method for shape optimization of a continuous elastic body considering stability, i.e., buckling behavior. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Unlike the conventional finite difference method (FDM), this method is efficient in that only a couple of analyses are required regardless of the number of design parameters. Commercial software such as ANSYS can be employed since the method requires only the result of the analysis in computation of the sensitivity. Though the buckling problem is more efficiently solved by structural elements such as a beam and shell, elastic solids have been chosen for the buckling analysis because solid elements can generally be used for any kind of structure whether it is thick or thin. Sensitivity is then computed by using the mathematical package MATLAB with the initial stress and buckling analysis of ANSYS. Several problems we chosen in order to illustrate the efficiency of the presented method. They are applied to the shape optimization problems to minimize weight under allowed critical loads and to maximize critical loads under same volume.

Analysis of the Sixth Graders' Strategies and Errors of Division-With-Remainder Problems (나머지가 있는 나눗셈 문장제에 대한 초등학교 6학년 학생들의 해결 전략 및 오류 분석)

  • Ha, Mihyun;Chang, Hyewon
    • Journal of Elementary Mathematics Education in Korea
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    • v.20 no.4
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    • pp.717-735
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    • 2016
  • For teaching division-with-remainder(DWR) problems, it is necessary to know students' strategies and errors about DWR problems. The purpose of this study is to investigate and analyze students' strategies and errors of DWR problems and to make some meaningful suggestions for teaching various methods of solving DWR problems. We constructed a test which consists of fifteen DWR problems to investigate students' solving strategies and errors. These problems include mathematical as well as syntactic structures. To apply this test, we selected 177 students from eight elementary schools in various districts of Seoul. The results were analyzed both qualitatively and quantitatively. The sixth graders' strategies can be classified as follows : Single strategies, Multi strategies and Assistant strategies. They used Division(D) strategy, Multiplication(M) strategy, and Additive Approach(A) strategy as sub-strategies. We noticed that frequently used strategies do not coincide with strategies for their success. While students in middle group used Assistant strategies frequently, students in higher group used Single strategies frequently. The sixth graders' errors can be classified as follows : Formula error(F error), Calculation error(C error), Calculation Product error(P error) and Interpretation error(I error). In this study, there were 4 elements for syntaxes in problems : large number, location of divisor and dividend, divisor size, vocabularies. When students in lower group were solving the problems, F errors appeared most frequently. However, in case of higher group, I errors appeared most frequently. Based on these results, we made some didactical suggestions.

Probable Volcanic Flood of the Cheonji Caldera Lake Triggered by Volcanic Eruption of Mt. Baekdusan (백두산 화산분화로 인해 천지에서 발생 가능한 화산홍수)

  • Lee, Khil-Ha;Kim, Sung-Wook;Yoo, Soon-Young;Kim, Sang-Hyun
    • Journal of the Korean earth science society
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    • v.34 no.6
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    • pp.492-506
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    • 2013
  • The historical accounts and materials about the eruption of Mt. Baekdusan as observed by the geological survey is now showing some signs of waking from a long slumber. As a response of the volcanic eruption of Mt. Baekdusan, water release may occur from the stored water in Lake Cheonjii caldera. The volcanic flood is crucial in that it has huge potential energy that can destruct all kinds of man-made structures and that its velocity can reach up to 100 km $hr^{-1}$ to cover hundreds of kilometers of downstream of Lake Cheonji. The ultimate goal of the study is to estimate the level of damage caused by the volcanic flood of Lake Cheon-Ji caldera. As a preliminary study a scenario-based numerical analysis is performed to build hydrographs as a function of time. The analysis is performed for each scenario (breach, magma uplift, combination of uplift and breach, formation of precipitation etc.) and the parameters to require a model structure is chosen on the basis of the historic records of other volcanos. This study only considers the amount of water at the rim site as a function of time for the estimation whereas the downstream routing process is not considered in this study.

A Model for Radiological Dose Assessment in an Urban Environment (도시환경에서 방사성물질 오염에 따른 선량평가모델)

  • Hwang, Won-Tae;Kim, Eun-Han;Jeong, Hyo-Joon;Suh, Kyung-Suk;Han, Moon-Hee
    • Journal of Radiation Protection and Research
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    • v.32 no.1
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    • pp.1-8
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    • 2007
  • A model for radiological dose assessment in an urban environment, METRO-K has been developed. Characteristics of the model are as follows ; 1) mathematical structures are simple (i.e. simplified input parameters) and easy to understand due to get the results by analytical methods using experimental and empirical data, 2) complex urban environment can easily be made up using only 5 types of basic surfaces, 3) various remediation measures can be applied to different surfaces by evaluating the exposure doses contributing from each contamination surface. Exposure doses contributing from each contamination surface at a particular location of a receptor were evaluated using the data library of kerma values as a function of gamma energy and contamination surface. A kerma data library was prepared fur 7 representative types of Korean urban buildings by extending those data given for 4 representative types of European urban buildings. Initial input data are daily radionuclide concentration in air and precipitation, and fraction of chemical type. Final outputs are absorbed dose rate in air contributing from the basic surfaces as a function of time following a radionuclide deposition, and exposure dose rate contributing from various surfaces constituting the urban environment at a particular location of a receptor. As the result of a contaminative scenario for an apartment built-up area, exposure dose rates show a distinct difference for surrounding environment as well as locations of a receptor.

A Study on the Feedforward Control Algorithm for Dynamic Positioning System Using Ship Motion Prediction (선체운동 예측을 이용한 Dynamic Positioning System의 피드포워드 제어 알고리즘에 관한 연구)

  • Song, Soon-Seok;Kim, Sang-Hyun;Kim, Hee-Su;Jeon, Ma-Ro
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.22 no.1
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    • pp.129-137
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    • 2016
  • In the present study we verified performance of feed-forward control algorithm using short term prediction of ship motion information by taking advantage of developed numerical simulation model of FPSO motion. Up until now, various studies have been conducted about thrust control and allocation for dynamic positioning systems maintaining positions of ships or marine structures in diverse sea environmental conditions. In the existing studies, however, the dynamic positioning systems consist of only feedback control gains using a motion of vessel derived from environmental loads such as current, wind and wave. This study addresses dynamic positioning systems which have feedforward control gain derived from forecasted value of a motion of vessel occurred by current, wind and wave force. In this study, the future motion of vessel is forecasted via Brown's Exponential Smoothing after calculating the vessel motion via a selected mathematical model, and the control force for maintaining the position and heading angle of a vessel is decided by the feedback controller and the feedforward controller using PID theory and forecasted vessel motion respectively. For the allocation of thrusts, the Lagrange Multiplier Method is exploited. By constructing a simulation code for a dynamic positioning system of FPSO, the performance of feedforward control system which has feedback controller and feedforward controller was assessed. According to the result of this study, in case of using feedforward control system, it shows smaller maximum thrust power than using conventional feedback control system.

An Evaluation Method of X-ray Imaging System Resolution for Non-Engineers (비공학도를 위한 X-ray 영상촬영 시스템 해상력 평가 방법)

  • Woo, Jung-Eun;Lee, Yong-Geum;Bae, Seok-Hwan;Kim, Yong-Gwon
    • Journal of radiological science and technology
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    • v.35 no.4
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    • pp.309-314
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    • 2012
  • Nowadays, digital Radiography (DR) systems are widely used in clinical sites and substitute the analog-film x-ray imaging systems. The resolution of DR images depends on several factors such as characteristic contrast and motion of the object, the focal spot size and the quality of x-ray beam, x-ray scattering, the performance of the DR detector (x-ray conversion efficiency, the intrinsic resolution). The DR detector is composed of an x-ray capturing element, a coupling element and a collecting element, which systematically affect the system resolution. Generally speaking, the resolution of a medical imaging system is the discrimination ability of anatomical structures. Modulation transfer function (MTF) is widely used for the quantification of the resolution performance for an imaging system. MTF is defined as the frequency response of the imaging system to the input of a point spread function and can be obtained by doing Fourier transform of a line spread function, which is extracted from a test image. In clinic, radiologic technologists, who are in charge of system maintenance and quality control, have to evaluate or make routine check on their imaging system. However, it is not an easy task for the radiologic technologists to measure MTF accurately due to lack of their engineering and mathematical backgrounds. The objective of this study is to develop and provide for radiologic technologists a medical system imaging evaluation tool, so that they can measure and quantify system performance easily.