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컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료 개발 및 활용 방안

  • Im, Hae-Gyeong;Park, Eun-Yeong
    • Communications of Mathematical Education
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    • v.13 no.2
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    • pp.563-589
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    • 2002
  • 고학년으로 갈수록 지필 환경에만 머무르는 현실 속에서 생활 및 예술 작품 등에서 수학적 원리와 개념을 발견하도록 하는 테셀레이션 수업은 학생들의 흥미와 호기심을 유발하고 수학의 아름다움을 느끼게 하는 것 이상으로 기하학적 사고의 기초를 학습하는데 도움을 줄 수 있다. 이에 본 연구는 4학년까지 적용되고 있는 7차 교육과정을 중심으로 새롭게 등장하고 있는 테셀레이션에 대한 이해 및 교수 학습 자료가 체계적으로 정비되어 있지 못한 현실적인 문제의 해결 방안으로서 테셀레이션을 활용한 수학 학습의 내용을 분석하여 교사들에게는 테셀레이션의 이해 및 교수 학습 자료로서 , 학생들에게는 수학의 기하적 개념들을 쉽고 재미있게 학습할 수 있는 학습도구로서 활용할 수 있도록 하는 것을 목적으로 테셀레이션을 구현할 수 있는 컴퓨터 소프트웨어를 활용하여 테셀레이션 교수 학습 자료를 개발하였고 이를 위해 다음과 같은 연구 내용을 설정하였다. 가. 테셀레이션의 정의와 예 그리고 종류를 알아보고 테셀레이션 속의 수학적 개념을 활용방법과 함께 제시한다. 나. 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 테셀레이션을 적용할 수 있는 내용영역을 분석하고 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한다. 다. 제작된 테셀레이션 교수 학습 자료의 효과적 활용을 위한 활용 방안을 탐색한다. 라. 제작된 테셀레이션 교수 학습 자료의 활용 효과를 알아보기 위해 적용 실험을 하고 이에 대한 학생들의 반응을 분석하여 학습의 효과를 밝힌다. 제작된 테셀레이션 교수 학습 자료의 적용 실험을 위하여 광주대성초등학교 6학년 한 반을 선정하였고 약 4주에 걸쳐 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료를 투입하여 4번의 활동수업을 실시하였다. 수업 후 작성된 학습지와 소감문 및 연구자에 의해 관찰된 수업내용을 바탕으로 다음과 같은 연구 결과를 얻을 수 있었다. 첫째, 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한 결과 지필적 환경에서 제한적이었던 탐구하고 조작해보는 활동을 할 수 있는 역동적인 수학 실험실 환경이 제공됨으로써 도구적 이해가 아닌 관계적 이해를 하는 것을 확인할 수 있었다. 수학적 개념을 암기하는 것에서 벗어나 자연스런 조작을 통해 학생들이 개념을 이해하고 탐구하는 과정 속에서 학생들은 수학을 공부한다기 보다는 수학 속에서 재미있게 놀이한다는 생각을 가지고 수업에 참여하였고 배우는 즐거움을 알고 자신감을 가지며 더 나아가 창의적인 생각을 하도록 하는 기회를 줄 수 있었다. 둘째, 테셀레이션은 우리 생활 속에서 쉽게 발견할 수 있는 것으로 수학이 단순히 책에서만 한정되지 않고 다양한 분야 즉 디자인, 생활 속에서의 벽지문양과 포장지, 예술작품 등에 활용되고 있음을 체험함으로써 수학이 실생활에 광범위하게 활용되고 있음을 알게 하였다. 역으로 생활 속에서의 테셀레이션을 통해 수학적 개념을 찾는 과정을 통해 수학이 아름다우면서도 실용적이라는 생각을 심어줄 수 있었다. 셋째, 테셀매니아, GSP, 캐브리, 거북기하 등 평소 수업에서는 활용도가 적은 컴퓨터 소프트웨어를 활용함으로써 컴퓨터 소프트웨어 자체에서 오는 호기심뿐만이 아니라 직접 조작하여 테셀레이션 작품과 개념을 익히고 새로운 작품과 학습을 해 내는 과정을 통해 자신감과 성취감 등에 있어 큰 변화가 있음을 발견할 수 있었다. 컴퓨터 기능이 미숙한 학생의 경우 처음에는 당황해 하고 어려워하는 부분도 있었으나 조작할 시간적 여유를 주고 교사와 우수한 학생들이 도우미로서 역할을 잘해내어 나중에는 큰 어려움 없이 마칠 수 있었다. 테셀레이션이라는 용어가 아직은 생소한 현장에서 교수 학습 자료가 부족하고 그에 따른 이해도 부족한 현실 속에서 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료가 교수 학습 현장에 투입되어 유용하게 사용될 수 있는지 그 가능성을 조사한 것을 목적으로 한 본 연구의 결과로서 테셀레이션이라는 주제는 도형 영역과 규칙성과 함수 영역에서 평면 도형의 각과 모양 등의 성질을 탐구하게 하고, 대칭변환의 개념을 효율적으로 학습하게 할 수 있고, 반복되는 모양에서 규칙성을 발견하고 부분과 전체를 파악하여 패턴을 인지할 수 있게 하며 제작하고 분석하는 과정을 통해 여러 가지 수학적 개념과 수학적 창의성, 수학적인 아름다움을 느끼게 할 수 있음을 발견할 수 있었다. 또한 테셀레이션은 수학적 개념은 물론 수학과 미술, 수학과 일상 생활과의 연결성을 논의하고 확인하는 데 흥미로운 주제가 될 수 있다. 초등학교 교육과정에서 새롭게 도입되고 있는 테셀레이션을 활용하여 지도하기 위한 교수 학습 자료로 유용하게 사용될 수 있고 앞으로는 테셀레이션과 관련된 내용이 직접적으로 교육과정 내에서 다루어지고, 또한 테셀레이션을 적용한 수업이 학생들의 기하학적 사고 및 수학적 태도에 미치는 영향과 관련한 연구가 뒤따라야 할 것으로 본다.

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A Case Study on Students' Mathematical Concepts of Algebra, Connections and Attitudes toward Mathematics in a CAS Environment (CAS 그래핑 계산기를 활용한 수학 수업에 관한 사례 연구)

  • Park, Hui-Jeong;Kim, Kyung-Mi;Whang, Woo-Hyung
    • Communications of Mathematical Education
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    • v.25 no.2
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    • pp.403-430
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    • 2011
  • The purpose of the study was to investigate how the use of graphing calculators influence on forming students' mathematical concept of algebra, students' mathematical connection, and attitude toward mathematics. First, graphing calculators give instant feedback to students as they make students compare their written answers with the results, which helps students learn equations and linear inequalities for themselves. In respect of quadratic inequalities they help students to correct wrong concepts and understand fundamental concepts, and with regard to functions students can draw graphs more easily using graphing calculators, which means that the difficulty of drawing graphs can not be hindrance to student's learning functions. Moreover students could understand functions intuitively by using graphing calculators and explored math problems volunteerly. As a result, students were able to perceive faster the concepts of functions that they considered difficult and remain the concepts in their mind for a long time. Second, most of students could not think of connection among equations, equalities and functions. However, they could understand the connection among equations, equalities and functions more easily. Additionally students could focus on changing the real life into the algebraic expression by modeling without the fear of calculating, which made students relieve the burden of calculating and realize the usefulness of mathematics through the experience of solving the real-life problems. Third, we identified the change of six students' attitude through preliminary and an ex post facto attitude test. Five of six students came to have positive attitude toward mathematics, but only one student came to have negative attitude. However, all of the students showed positive attitude toward using graphing calculators in math class. That's because they could have more interest in mathematics by the strengthened and visualization of graphing calculators which helped them understand difficult algebraic concepts, which gave them a sense of achievement. Also, students could relieve the burden of calculating and have confidence. In a conclusion, using graphing calculators in algebra and function class has many advantages : formulating mathematics concepts, mathematical connection, and enhancing positive attitude toward mathematics. Therefore we need more research of the effect of using calculators, practical classroom materials, instruction models and assessment tools for graphing calculators. Lastly We need to make the classroom environment more adequate for using graphing calculators in math classes.

The Relationships among Mathematics Achievement, Spatial Ability, and Verbal Achievement for Engineering Freshmen and Gender Differences (공과대학 신입생들의 공간 시각화 능력, 수학 성취도와 언어 성취도 사이의 관계 및 성별 차이에 관한 연구)

  • Kim, Yon Mi
    • Communications of Mathematical Education
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    • v.29 no.3
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    • pp.553-571
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    • 2015
  • Mathematical, verbal, and spatial abilities are known as three important indicators for the success in the STEM disciplines. In this study, Purdue Spatial Visualization Test-Rotation, College Entrance Scholastic Aptitude Test- Math and Verbal score of engineering freshmen students have been used to find the relationships among these areas. In addition, gender differences in spatial visualization, verbal achievement and mathematical achievement have been investigated, too. In this research, I found that gender difference was highest in spatial visualization ability, followed by verbal achievement and smallest in mathematical achievement. Substantial number of male students possess high level of spatial abilities, but only half of female students were at the same level where their male colleagues were. The correlation between spatial ability and mathematical ability was negligible, contrary to former researches on elementary and middle school students. But the correlation was stronger for female students than male students. The correlation between mathematical achievement and verbal achievement was negative. It reflects the fact that when one section of SAT score is low, score of other sections should be higher to get admitted to college. Gender difference in mathematics was smallest for high achieving spatial ability group. For low spatial ability group gender difference in mathematics achievement has been observed, too. To find the combined contribution of spatial and verbal abilities to mathematics achievement, students were divided into 4 ability groups. Mathematics achievement decreased in the order of (1) high spatial -low verbal group, (2) low spatial - low verbal group, (3) high spatial - high verbal group, (4) low spatial - high verbal group.

Current Status and Improvements of Transfered PET/CT Data from Other Hospitals (외부 반출 PET/CT 영상 현황 및 개선점)

  • Kim, Gye-Hwan;Choi, Hyeon-Joon;Lee, Hong-Jae;Kim, Jin-Eui;Kim, Hyun-Joo
    • The Korean Journal of Nuclear Medicine Technology
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    • v.14 no.2
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    • pp.38-40
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    • 2010
  • Purpose: This study was performed to find the current problems of PET/CT data from other hospitals. Materials and Methods: The subjects were acquired from 64 hospitals referred to our department for image interpretation. The formats and contents of PET/CT data were reviewed and the phone questionnaire survey about these were performed. Results: PET/CT data from 39 of 64 hospitals (61%) included all transaxial CT and PET images with DICOM (Digital Imaging Communications in Medicine) standard format which were required for authentic interpretation. PET/CT data from the others included only secondary capture images or fusion PET/CT images. Conclusion: The majority of hospitals provided limited PET/CT data which could be inadequate for accurate interpretation and clinical decision making. It is necessary to standardize the format of PET/CT data to transfer including all transaxial CT and PET images with DICOM standard format.

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Usefulness of "Volumetrix Suite" with SPECT/CT (SPECT/CT 영상에서 Volumetrix Suite의 유용성)

  • Cho, Seung-Wook;Shin, Byeong-Ho;Kim, Jong-Pil;Yoon, Seok-Hwan;Kim, Tae-Yeub;Seung, Yong-Joon;Moon, Il-Sang;Woo, Jae-Ryong;Lee, Ho-Young
    • The Korean Journal of Nuclear Medicine Technology
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    • v.14 no.2
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    • pp.166-171
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    • 2010
  • Purpose: The SPECT/CT is able to acquire diagnostic information resolved the difficult problems that discriminate regions of focals by intergrating functional images and anatomical images. We introduce the usefulness of "Volumetrix Suite" which can describe 3D images by the convergence of the SPECT/CT images and reference CT images. Materials and Methods: We applied Volumetrix Suite program (Volumetrix IR, Volumetrix 3D) to patients, Bone, Venography, Parathyroid, WBC, taken diagnostic CT examination which have same regions of focal in Seoul Metropolitan Government Seoul National University Boramae Medical Center. After acquiring SPECT/CT images and reference CT images, we fused a couple of scans applying for this programs. The CT scan of Infinia Hawkeye 4 shows limitation of anatomical information. For this reason, we tried to transfer CT images that have lots of diagnostic informations as the form of Dicom file in PACS, and changed from 2D images to 3D images after image registering in Xeleris Workstaion of Hawkeye 4. Results & Conclusion: By using Volumetrix Suite program, we're able to acquire more accurate anatomical informations with 3D rendering which can distinguish both location and range of focals in Infinia Hawkeye 4. Thus, the result of utilizing this program indicate that nuclear medicine anatomical images can be improved by providing more diagnostic imformations produced by its program.

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A Study on Mobile Antenna System Design with Tri-band Operation for Broadband Satellite Communications and DBS Reception (광대역 위성 통신/방송용 삼중 대역 이동형 안테나 시스템 설계에 관한 연구)

  • Eom Soon-Young;Jung Young-Bae;Son Seong-Ho;Yun Jae-Seung;Jeon Soon-Ick
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.17 no.5 s.108
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    • pp.461-475
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    • 2006
  • In this paper, it is described about the tri-band mobile antenna system design to provide broadband multimedia and direct broadcasting services using goo-stationary Koreasat 3, simultaneously operated in Ka/K/Ku band. The radiating part of the antenna system with a fan beam characteristic in the elevation plane is composed of the quasi-offset dual shaped reflector and the tri-band feeder. The tri-band feeder is also composed of the Ka/K dual band feeder with the protruding dielectric rod, the circular polarizer, the ortho-mode transducer and the circular-polarized Ku band feed array. Especially, the Ka/K dual band circular polarizer was realized firstly using the comb-type structure. For fast satellite-tracking on the movement, the Ku band feed array has the structure of the $2{\times}2$ active phased array which can make electrical beams. And, the circular-polarized characteristic in the feed array was improved by $90^{\circ}$ rotating arrangement of four radiating elements polarized circularly by a $90^{\circ}$ hybrid coupler, respectively. Four beam forming channels to make electrical beams at Ku band are divided into the main beam channel and the tracking beam channel in the output, and noise temperature characteristics of each channel were analyzed on the basis of the contributions of internal sub_units. From the fabricated antenna system, the output power at $P_{1dBc}$ of Ka_Tx channel was measured more than 34.1 dBm and the measured noise figures of K/Ku_Rx channels were less than 2.4 dB and 1.5 dB, respectively, over the operating band. The radiation patterns with co- and cross-polarization in the tri-band were measured using a near-field measurement in the anechoic chamber. Especially, Ku radiation patterns were measured after correcting each initial phase of active channels with partial radiation patterns obtained from the independent excitation of each channel. The antenna gains measured in Ka/K/Ku band of the antenna system were more than 39.6 dBi, 37.5 dBi, 29.6 dBi, respectively. And, the antenna system showed good system performances such as Ka_Tx EIRP more than 43.7 dBW and K/Ku_Rx G/T more than 13.2 dB/K and 7.12 dB/K, respectively.

Development and application of a Teaching and Learning Plan and Practical Performance Assessment Tools to Promote Communication Between Teenagers Children and Their Parents: focusing on conversation analysis of real conversation in UCC video projects (청소년 자녀와 부모간 의사소통 개선을 위한 교수학습 과정안과 실제 상황적 수행평가 개발 및 적용 - 부모자녀의 실제대화 UCC동영상을 활용한 대화분석을 토대로 -)

  • You, Hye-Jung;Cho, Byung-Eun
    • Journal of Korean Home Economics Education Association
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    • v.23 no.3
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    • pp.139-160
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    • 2011
  • The purpose of this study is twofold: (i) to develop a teaching and learning plan and practical performance assessment tools for the improvement of teenager-parent communication and relationships as well as explore their effects on the communication in the everyday family life; and (ii) to find the underlying problems of teenager- parent communication through conversation analysis and to provide a improved dialogue model. We provided the experimental group with a performance task of communication training between teenagers and their parents in the real family situation while the control group practiced communication skills in a learning situation. However for both classes, before and after performance tasks were equally provided. The experimental group exhibited a longer conversation time with their parents, better communication skills, and higher degrees of relational satisfaction than the control group. Conversation analysis revealed that the experimental group reduced the use of blocking techniques in the teenager-parent conversations more than the control group, and all so raised the frequency of functional communications more than the control group. In both areas of communication in the experimental group was significantly improved, Most notably, a problem-solving case through no-lose conflict resolution methods was effective, succeeding by 70% in the e experimental group and 43.3% in the control group. Parents use blocking techniques like admonition, lecturing, blaming. sarcastic remarking, ordering and so forth, while teenagers use dispute, avoidance, blaming, and teasing in this order. The communication problems during the conversation process, teenagers' evasive and rebellious way of speaking instigates adverse communication responses from parents, so their conversation tends to unfold as ambiguous evasion opposed to: inquiring or evasion by short answers vs. ordering-preaching, or disputing vs. criticizing-making sarcastic, disputing vs. disputing-teaching, and criticizing vs. criticizing.

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A Case Study on the classroom life and the identity of the Elementary Mathematics Gifted Education (초등수학 영재교육원의 교실 생활과 정체성에 대한 사례연구)

  • Lee, Hak-Ro;Ryu, Sung-Rim
    • Communications of Mathematical Education
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    • v.25 no.1
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    • pp.99-118
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    • 2011
  • For this case study of gifted education, two classrooms in two locations, show life in general of the gifted educational system. And for this case study the identity of teachers and the gifted, help to activate the mathematically gifted education for these research questions, which are as followed: Firstly, how is the gifted education classroom life? Secondly, what kind of identity do the teachers and gifted students bring to mathematics, mathematics teaching and mathematics learning? Being selected in the gifted children's education center solves the research problem of characteristic and approach. Backed by the condition and the permission possibility, 2 selected classes and 2 people, which are coming and going. Gifted education classroom life, the identity of teachers and gifted students in mathematics and mathematics teaching and mathematic learning. It will be for 3 months, with various recordings and vocal instruction between teacher and students. Collected observations and interviews will be analyzed over the course of instruction. The results analyzed include, social participation, structure, and the formation of the gifted education classroom life. The organization of classes were analyzed by the classes conscious levels to collect and retain data. The classes verification levels depended on the program's first class incentive, teaching and learning levels and understanding of gifted math. A performance assessment will be applied after the final lesson and a consultation with parents and students after the final class. The six kinds of social participation structure come out of the type of the most important roles in gifted education accounts, for these types of group discussions and interactions, students must have an interaction or individual activity that students can use, such as a work product through the real materials, which release teachers and other students for that type of questions to evaluate. In order for the development of meaningful mathematical concepts to formulate, mathematical principles require problem solving among all students, which will appear in the resolution or it will be impossible to map the meaning of the instruction from which it was formed. These results show the analysis of the mathematics, mathematics teaching, mathematics learning and about the identity of the teachers and gifted. Gifted education teachers are defined by gifted math, which is more difficult and requires more differentiated learning, suitable for gifted students. Gifted was defined when higher level math was created and challenged students to deeper thinking. Gifted students think that gifted math is creative learning and they are forward or passive to one-way according to the education atmosphere.

A development of DS/CDMA MODEM architecture and its implementation (DS/CDMA 모뎀 구조와 ASIC Chip Set 개발)

  • 김제우;박종현;김석중;심복태;이홍직
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.22 no.6
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    • pp.1210-1230
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    • 1997
  • In this paper, we suggest an architecture of DS/CDMA tranceiver composed of one pilot channel used as reference and multiple traffic channels. The pilot channel-an unmodulated PN code-is used as the reference signal for synchronization of PN code and data demondulation. The coherent demodulation architecture is also exploited for the reverse link as well as for the forward link. Here are the characteristics of the suggested DS/CDMA system. First, we suggest an interlaced quadrature spreading(IQS) method. In this method, the PN coe for I-phase 1st channel is used for Q-phase 2nd channels and the PN code for Q-phase 1st channel is used for I-phase 2nd channel, and so on-which is quite different from the eisting spreading schemes of DS/CDMA systems, such as IS-95 digital CDMA cellular or W-CDMA for PCS. By doing IQS spreading, we can drastically reduce the zero crossing rate of the RF signals. Second, we introduce an adaptive threshold setting for the synchronization of PN code, an initial acquistion method that uses a single PN code generator and reduces the acquistion time by a half compared the existing ones, and exploit the state machines to reduce the reacquistion time Third, various kinds of functions, such as automatic frequency control(AFC), automatic level control(ALC), bit-error-rate(BER) estimator, and spectral shaping for reducing the adjacent channel interference, are introduced to improve the system performance. Fourth, we designed and implemented the DS/CDMA MODEM to be used for variable transmission rate applications-from 16Kbps to 1.024Mbps. We developed and confirmed the DS/CDMA MODEM architecture through mathematical analysis and various kind of simulations. The ASIC design was done using VHDL coding and synthesis. To cope with several different kinds of applications, we developed transmitter and receiver ASICs separately. While a single transmitter or receiver ASC contains three channels (one for the pilot and the others for the traffic channels), by combining several transmitter ASICs, we can expand the number of channels up to 64. The ASICs are now under use for implementing a line-of-sight (LOS) radio equipment.

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Energy-Efficient Division Protocol for Mobile Sink Groups in Wireless Sensor Network (무선 센서 네트워크에서 이동 싱크 그룹의 분리를 지원하기 위한 라우팅 프로토콜)

  • Jang, Jaeyoung;Lee, Euisin
    • KIPS Transactions on Computer and Communication Systems
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    • v.6 no.1
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    • pp.1-8
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    • 2017
  • Communications for mobile sink groups such as rescue teams or platoons bring about a new challenging issue for handling mobility in wireless sensor networks. To do this, many studies have been proposed to support mobile sink groups. When closely looking at mobile sink groups, they can be divided into (multiple) small groups according to the property of applications. For example, a platoon can be divided into multiple squads to carry out its mission in the battle field. However, the previous studies cannot efficiently support the division of mobile sink groups because they do not address three challenging issues engendered by the mobile sink group division. The first issue is to select a leader sink for a new small mobile sink group. The efficient data delivery from a source to small mobile sink groups is the second issue. Last, the third issue is to share data between leader sinks of small mobile sink groups. Thus, this paper proposes a routing protocol to efficiently support the division of mobile sink groups by solving the three challenging issues. For the first issue, the proposed protocol selects a leader sink of a new small mobile sink group which provide a minimum summation of the distance between the new leader sink and the previous leader sink and the distance from the new leader sink to all of its member sinks. For the efficient data delivery from a source to small mobile sink groups in the second issue, the proposed protocol determines the path to minimize the data dissemination distance from source to small mobile sink group by calculating with the location information of both the source and the leader sinks. With regard to the third issue, the proposed protocol exploits member sinks located among leader sinks to provide efficient data sharing among leaders sinks by considering the location information of member sinks. Simulation results verified that the proposed protocol is superior to the previous protocol in terms of the energy consumption.