• Journal of Intelligence and Information Systems
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• v.24 no.2
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• pp.21-35
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• 2018

Since the introduction of MP3 players, CD recordings have gradually been vanishing, and the music consuming environment of music users is shifting to mobile devices. The introduction of smart devices has increased the utilization of music through music playback, mass storage, and search functions that are integrated into smartphones and tablets. At the time of initial MP3 player supply, the bitrate of the compressed music contents generally was 128 Kbps. However, as increasing of the demand for high quality music, sound quality of 384 Kbps appeared. Recently, music content of FLAC (Free License Audio Codec) format using lossless compression method is becoming popular. The download service of many music sites in Korea has classified by unlimited download with technical protection and limited download without technical protection. Digital Rights Management (DRM) technology is used as a technical protection measure for unlimited download, but it can only be used with authenticated devices that have DRM installed. Even if music purchased by the user, it cannot be used by other devices. On the contrary, in the case of music that is limited in quantity but not technically protected, there is no way to enforce anyone who distributes it, and in the case of high quality music such as FLAC, the loss is greater. In this paper, the author proposes an audio watermarking technology for copyright protection of high quality stereo music. Two kinds of information, "Copyright" and "Copy_free", are generated by using the turbo code. The two watermarks are composed of 9 bytes (72 bits). If turbo code is applied for error correction, the amount of information to be inserted as 222 bits increases. The 222-bit watermark was expanded to 1024 bits to be robust against additional errors and finally used as a watermark to insert into stereo music. Turbo code is a way to recover raw data if the damaged amount is less than 15% even if part of the code is damaged due to attack of watermarked content. It can be extended to 1024 bits or it can find 222 bits from some damaged contents by increasing the probability, the watermark itself has made it more resistant to attack. The proposed algorithm uses quantization in DCT so that watermark can be detected efficiently and SNR can be improved when stereo music is converted into mono. As a result, on average SNR exceeded 40dB, resulting in sound quality improvements of over 10dB over traditional quantization methods. This is a very significant result because it means relatively 10 times improvement in sound quality. In addition, the sample length required for extracting the watermark can be extracted sufficiently if the length is shorter than 1 second, and the watermark can be completely extracted from music samples of less than one second in all of the MP3 compression having a bit rate of 128 Kbps. The conventional quantization method can extract the watermark with a length of only 1/10 compared to the case where the sampling of the 10-second length largely fails to extract the watermark. In this study, since the length of the watermark embedded into music is 72 bits, it provides sufficient capacity to embed necessary information for music. It is enough bits to identify the music distributed all over the world. 272 can identify $4*10^{21}$, so it can be used as an identifier and it can be used for copyright protection of high quality music service. The proposed algorithm can be used not only for high quality audio but also for development of watermarking algorithm in multimedia such as UHD (Ultra High Definition) TV and high-resolution image. In addition, with the development of digital devices, users are demanding high quality music in the music industry, and artificial intelligence assistant is coming along with high quality music and streaming service. The results of this study can be used to protect the rights of copyright holders in these industries.

• Journal of agricultural medicine and community health
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• v.24 no.2
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• pp.315-329
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• 1999

Recently, dissatisfaction with aspects of health care has been complemented by directly at complaints such as informal, formal and litigation. But some people take action and other not in spite of feeling of dissatisfaction. This study was to investigate an accounts of patient's disagreement with doctor's care from a community sample, and make a distinction between felt disagreement and disagreement actions. This study was done in six hundred forty residents in Sungjoo County of Kyungbuk Province and Nonman city of Chungnam Province. The questionnaires of interview included sociodemographic data, health status data, a nature of patient's disagreement with doctor and actions taken following or during the disagreement episode. Approximately sixteen percent of sample reported a disagreement, and nine percent reported action taken following or during the disagreement episode. Age, educational attainment, income and area were significantly related with experience of disagreement episode in univariate analysis. In people who experienced the disagreement episode, nearly forty-one percent reported on disagreement about the diagnosis related, twenty-eight percent reported doctor-patients relationship related, twenty percent reported treatment related, and eleven percent reported prescription drug related. In people who experienced actions taken following or during the disagreement episode, nearly fifty-four percent acted as 'sought a second opinion or visit other doctor', thirty-six percent acted as 'verbally challenged the doctor', thirty-two percent acted as 'stopped prescribed treatment or medication', twenty-nine percent acted as 'made repeat visits to the same doctor', twenty-five percent acted as 'eventually left and changed doctor'. Results of multivariate analysis, age, marital status, have or haven't chronic disease, and general satisfaction with health service were significantly related with experience of disagreement episode and marital status was significantly related with experience of actions taken following or during the disagreement episode. This study is experimental and exploratory trial about a relationship between patient's disagreement with doctor and actions taken following or during the disagreement episode in some community of Korea. We find that patient's disagreement with doctor and actions taken following or during the disagreement episode is latent in our community. We suggest that the relationship between felt disagreement and disagreement action is more complicated and worthy of further study.

• KDI Journal of Economic Policy
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• v.32 no.1
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• pp.131-169
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• 2010

I develop a matching model in which risk-averse workers face borrowing constraints and make a labor force participation decision as well as a job search decision. A sharp distinction between unemployment and out of the labor force is made: those who look for work for a certain period but find no job are classified as the unemployed and those who do not look for work are classified as those out of the labor force. In the model, the job search decision consists of two steps. First, each individual who is not working obtains information about employment opportunities. Second, each individual who decides to search has to take costly actions to find a job. Since individuals differ with respect to asset holdings, they have different reservation job-finding probabilities at which an individual is indifferent between searching and not searching. Individuals, who have large asset holdings and thereby are less likely to participate in the labor market, have high reservation job-finding probability, and they are less likely to search if they have less quality of information. In other words, if individuals with large asset holdings search for job, they must have very high quality of information and face very high actual job-finding probability. On the other hand, individuals with small asset holdings have low reservation job-finding probability and they are likely to search for less quality of information. They face very low actual job-finding probability and seem to remain unemployed for a long time. Therefore, differences in the quality of information explain heterogeneous job search decisions among individuals as well as higher job finding probability for those who reenter the labor market than for those who remain in the labor force. The effect of the extended maximum duration of unemployment insurance benefits on the aggregate labor market and the labor market flows is investigated. The benchmark benefit duration is set to three months. As maximum benefit duration is extended up to six months, the employment-population ratio decreases while the unemployment rate increases because individuals who are eligible for benefits have strong incentives to remain unemployed and decide to search even if they obtain less quality of information, which leads to low job-finding probability and then high unemployment rate. Then, the vacancy-unemployment ratio decreases and, in turn, the job-finding probability for both the unemployed and those out of the labor force decrease. Finally, the outflow from nonparticipation decreases with benefit duration because the equilibrium job-finding probability decreases. As the job-finding probability decreases, those who are out of the labor force are less likely to search for the same quality of information. I also consider the matching model with two states of employment and unemployment. Compared to the results of the two-state model, the simulated effects of changes in benefit duration on the aggregate labor market and the labor market flows are quite large and significant.

• Journal of Korean Medical Ki-Gong Academy
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• v.1 no.1
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• pp.13-59
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• 1996

Dep. of Classics &Medical History, College of Oriental Medicint, Kyung Hee University Today, many people are more interested Today, many people are more interested in preventing the disease than curing it. Chi-Kung(氣功) is the way of Life-Cultivation(養生法) peculiar to the orient, it is reported in china that Chi-Kung has an excellent curative value not only in curing the disease but also in preventing it. But the full-scale study of Chi-Kung is not be made up to now in Korea, so I studied the developmental history of chinese Chi-Kung through the oriental medical books. From this study, I reached the following conclusions; 1. Chi-Kung is naturally derived from the self-preservation instinct to adapt oneself to circumstances of the nature, but in the investigation from the documentational records, it is originated in the treatment method of the Sam-Huang-O-Jae(三皇五帝) period to cure the abnormal circulation of the vital force and blood caused by damp(濕). 2. As the principle and the method of the Life-Cultivation of the Chun-Chu-Jeon-Kook(春秋戰國) period were recorded in Huang-Jae-Nai-Gyung(黃帝內經) detailly and the remedy examples by ancient Chi-Kung such as Tao-Yin(導引), Haeng-Chi(行氣) were presented, we considered that theoretical basis of the development of Life-cultivation and Chi-Kung study was furnished in that period. 3. A famous doctor, Hwa-Ta(華引) lived in Han dynasty, researched the theory and practice of Tao-Yin transmitted from the former generations, as that result, he formed a kind of medical, gymnastics what is called O-Keum-Hi(五禽?). It is considered that 'O-Keum-Hi' is a Tao-Yin method developed more practically and systemetically than the Tao-Yin appeared in the 'Jang-Ja'(莊子) or 'Hoy-Nam-Ja'(淮南子). 4. In Wui-Jin-Nambook-Jo(魏曺南北朝) periods, the contents of Chi-Kung were more abundant under the influence of Buddhism(佛敎) and Taoism(道敎). Galhong(葛洪), the author of 'Po-Bak-Ja'(抱朴子) arranged the ancient Chi-Kung method systematically first of all, Tao-Goeng-Gyung, the author of 'Yang-Seong-Yeun-Myung-Rok'(養性延命錄) recorded the 'Yook-Ja-Geul'(六字訣) first time. 5. There is a new development of Chi-Kung therapy in Soo-Tang-Odae(隋唐五代) periods, especially So-Won-Bang(巢元方), the author of 'Jey-Bang-Won-Hwu-Ron' collected almost all of the Chi-Kung method, for curing the disease formed before Soo(隋) period. From that fact, we supposed that Chi-Kung was utilized more widely in curing the disease. 6. 'So-Ju-Cheon-Hwa-Hu-Peob'(小周天火候法) was adopted as the best orthodox approach under the influence of Nae-Tan-Taoist(道敎內丹學波) in Song-Keum-Won(宋金元) periods, especially in the song dynasty, 'Pal-Dan-Geum'(八段錦) was appearde and assignment of six-Chi(六氣) for bowel and viscera in the 'Yook-Ja-Geul'(六字訣) was decided firmly, that is to say Lung-Si(肺-?), Heart-Kha(心-呵), Spleen-Hoa(脾-呼), liver-Hoe(肝-噓), Kidney-chui(賢-吹), Three-Burner-shi(三焦-?). 7. In Myung-Cheong(明淸) periods, The general practitioner applied the principle of 'Byun-Jeng-Ron-Chi(辨證論治) to the Chi-Kung field, and after Myung dynasty the style of doing 'Yook-Ja-Gyel'(六字訣) was developed to the moving style. 8. Today, in china, the study on the Chi-Kyung is being progressed constantly under the positive assistance of government, Chi-Kung-Hak(氣功學) has taking its place as a branch of study step by step. It is considered that the establishment of Chi-Kung-Hak Classroom(氣功學敎室) and Medical Chi-Kung Center(氣功療法室) for special and systematic research are needed, at the same time the settlement of institutional system for training the Chi-Kung technician(氣功師) is also needed.

• Journal of Korean Public Health Nursing
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• v.6 no.1
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• pp.32-45
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• 1992

An important role of community health nurses in health centers is to solve community health problems found through data collection methodology which has been used to identify the health needs of the community, diagnose the health problems and to plan health programs suitable for the health problems. Also community health nurses must be prepared to know the community health needs and to participate in the planning process. Since 1956 when the health center law was established, community health nurses have really implemented only the services which the government has asked them to do. This has kept them busy enough. But these days as society is in rapid change, community health nurses should have the flexibility to deal with the social change and demands that are unique to their community each which has different health needs and demands. So community health nurses need to identify what community health problems exist in their particular communities. The purposes of this study were as follows. 1) To explore the suitability of the health programs which the government has asked the community health nurses to do for their own communities and if these programs are not suitable, to explore the reasons why. 2) To explore the degree to which the community health nurses have the ability to identify health problems in their own communities and activate the community diagnostic process. 3) To identify the degree that the community health nurses have the ability to implement plans related to community diagnosis. 4) To find out how much data related to community health problems, the community health nurses have and how they are utilizing it. 5) To measure the community health nurses self-confidence concerning diagnostic activities for community health. The study subjects were 454 Community Health Nurses working in Health Centers in Seoul, Korea. The period of data collection was 6 days(Nov. 9th 1991-Nov. 15th 1991). A questionnaire used for data collection was composed of three different items; general characteristics, community health diagnostic activities and self-confidence in performing diagnostic activities. The results of the study are as follows. First, over one third of the respondents replied that the government required activities for their communities are not appropriate. Of these activities the most frequent reply $(51.2\%)$ indicated that many of the activities in the community were inappropriate to the actual situation. Further, $25\%$ of the replies indicated that many activities were only administratively oriented and as such not appropriate. Second, $49.8\%$ of the respondents replied that they had done general assessments and had a general idea of the health problems of their community. Effective solutions to health problems could be found with an increase in health personnel and management ability according to $41.5\%$ of the respondents. Third, to the question as to whether they had ever independently implemented a plan towards solving community diagnosed problems, $52\%$ of nurses replied 'never', $40\%$ 'occasionally' but only $7.5\%$ replied that they did it frequently. Actually there was very little done even in the basic work of collecting the necessary data. Fourth, when asked how much of basic information they had collected that might be used in community diagnosis activity, of 26 items in 5 areas, there was hardly one for which complete data had been collected. Fifteen percent did have data on the geographical aspects of their area, housing distribution and types of housing, while $17.8\%$ knew the frequency with which the health center was used. Concerning community resources, even with a list of community resources, only $12.3\%$ had data on any of these resources, and this data was incomplete. Further, information about social work institutions, and facilities was also incomplete, only $14.2\%$ of the respondents had any data and even it was incomplete; that is, in general, the nurses did not have this information. Fifth, concerning the confidence of the community health nurse in their ability to carry out community diagnoses activities, $60\%$ replied that they were very or at least nominally confident, indicating that although they were not doing community diagnostic activities they felt they could do so, as they were carrying out home visits and program planning as part of their official duties. The following recommendations are made based on the results of this study. First; since the community health nurses have a high perception of the need for community diagnostic activities and. high confidence in their ability to carry out this activity and high percentage of respondents replied that with a little training they could do this even better it is recommended that community diagnostic activity training be included in the continuing education program for community health nurses. Second, in order for the Community Health Nurses to successfully solve the health problems of their respective community they reported to a need to increase the number of health personnel, improve the facilities and the system of managing their work. Considering this, it is recommended that ways be sought to remedy these deficits.

• Journal of the Korean earth science society
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• v.18 no.6
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• pp.453-463
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• 1997

The contents of high school 'Common science' textbooks was analyzed qualitatively and quantitatively. Seven common science textbooks were selected and its contents, structure, inquiry, activities, appendix and its characteristics were investigated, and analyzed using the Goal Clusters of Project Synthesis and Romey's indices of text evaluation were calculated. The contents of each unit are not much different among textbooks because they are written according to the curriculum ordinance and textbook guidelines of the Ministry of Education. The textbooks was consist of $471{\sim}519$ pages. It was distribute similarly among the chapter of 'materials', 'forces', lives' and 'earth'. The chapter of 'energy' and 'environment' was treat significantly. The contents and structure of common science is a mere physical consolidation. I make an alternative plan that a topic form. Inquiry activities used in the textbooks are 11 type, however most of that is interpretation of data, experiment, survey and discussion. Ninety six percents of the experiment, belong to the 1st level, four percents of that belong to the 2nd level of the Schwab's inquiry level and there are no activities of the 3rd level. Little attention is given to Goal Cluster I, II, IV in the common science textbooks currently employed. Its content should be broadened to include all Goal Clusters of Project Synthesis. Homey's indices representing the degrees of student involvement. are $0.57{\sim}1.14$ for sentence analysis, $0.60{\sim}1.67$ for figure and diagram analysis, $0.67{\sim}1.50$ for analysis of questions at chapter ends, respectively, student activity per page investigated being $0.6{\sim}0.9$. But chapter summaries cease to repeats the conclusions of the chapter also it be rather formally and inattentively written.

• Journal of The Korean Association For Science Education
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• v.20 no.2
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• pp.221-233
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• 2000

Many investigators have reported difficulties in changing the high school students' misconceptions on mechanics. By one possible solution to this problem, some researchers suggested that the students should be taught mechanics at a younger age to make conceptual changes possible. because as they get older they become less willing to change their ideas. The purpose of this study was to compare the patterns of students' conceptual changes on force by age, to find out whether older students were less ready to change their conceptions than younger students. Individual interviews were carried out with 35 students (average ages 13) in middle school class and 50 students (average ages 17) in high school class near by the middle school. Those students who held the misconcetpion that "motion-implies-force (Impetus conception)" were asked to read a student-centered refutational text (anomalous data). In the immediate and delayed posttest, the types of responses of the students were analyzed to find out the patterns of student's conceptual changes on force by age. In result, first, most of students had impetus conception. Some of the students aged 13 understood the force as terminologies related with everyday experiences, while the students aged 17 understood the force as scientific terminologies. Second, there was no evidence to suggest that conceptual change is more difficult for the students aged 17 than aged 13. Third, the students aged 13 showed diverse responses (plain acceptance, critical acceptance, plain rejection, critical rejection) to the refutational text, while the students aged 17 showed restricted responses (critical acceptance, critical rejection). A month later those students who showed the plain acceptance retrogressed unscientific conceptions, while those students who showed critical acceptance maintained scientific conceptions. We did not find out any evidence to suggest that conceptual change is more difficult for older students. These results need deeper investigation on the nature of the loss of plasticity in comparison with other important variables.

• Journal of Aquaculture
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• v.21 no.2
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• pp.82-88
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• 2008

A 12-week feeding trial was conducted to investigate the effects of dietary supplementation of probiotics as a feed additive for juvenile Korean rockfish Sebastes schlegeli. Four experimental diets supplemented with no probiotic(Control), Bacillus polyfermenticus(BP), Bacillus licheniformis(BL) or Bacillus polyfermenticus plus Saccharomyces cerevisiae(BP+SC) at $1.0{\times}10^7$ CFU/kg diet as a dry-mater(DM) basis were prepared by mixing with a basal diet. After 12 weeks of the feeding trial, fish fed BP+SC diet showed significantly higher weight gain(WG), feed efficiency(FE), specific growth rate(SGR) and protein efficiency ratio(PER) than those of fish fed control diet(P<0.05), however there were no significant differences in WG, FE, SGR and PER among fish fed the BP, BL and BP+SC diets. Fish fed BP and BP+SC diets showed significantly higher condition factor(CF) than that of fish fed control and BL diets. Fish fed BP, BL, BP+SC diets showed significantly higher hepatosomatic index(HSI) than that of fish fed control diet, however there was no significant difference in HSI among fish fed BP, BL and BP+SC diets. Fish fed BP+SC diet showed significantly lower serum glucose than that of fish fed control diet, however there was no significant difference in serum glucose among fish fed BP, BL and BP+SC diets. Fish fed BP+SC diet showed significantly higher respiratory burst activity(NBT assay) than that of the fish fed control and BL diets, however there was no significant difference in NBT assay between fish fed BP and BP+SC diets. Fish fed BP and BL diets showed significantly higher lysozyme activity than that of the fish fed control diet, however there was no significant difference in lysozyme activity among fish fed BP, BL and BP+SC diets. Fish fed BP and BP+SC diets showed significantly lower cumulative mortality than that of the fish fed control diet, however there was no significant difference in cumulative mortality among fish fed BP, BL and BP+SC diets after the challenge test. From these results, dietary B. polyfermenticus, B. licheniformis and B. polyfermenticus plus S. cerevisiae supplementation in juvenile Korean rockfish diet could enhance growth performances, non-speicific immunities and a higher resistance against the specific pathogen.

• Sleep Medicine and Psychophysiology
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• v.10 no.1
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• pp.39-51
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• 2003

Objectives: The Profile of Mood States (POMS) has been used broadly and frequently in various medical studies with various subjects. For the development and application of the Korean edition of POMS, called K-POMS, we translated POMS into Korean and then evaluated the reliability and validity of K-POMS. Methods: The subjects were 161 male students with a mean age of 18.1 years (15-30) and 244 female students with a mean age of 16.6 years (14-23). They were requested to perform K-POMS and SCL-90-R (Korean version) at the same time. Means, reliability coefficients, and test-retest correlations of K-POMS were calculated. Content validities, correlations with SCL-90-R, and discrimination validities in comparison with 76 depressive patients were obtained, and factor analyses were carried out. Results: Mean scores of Total Mood Disturbance (TMD) and some subscales (T, F, C, V factor) showed a significant difference between male and female students. The internal consistency coefficient ($\alpha$) of the total 65 items was 0.93, and ranged from 0.67 to 0.90 for subscales. Test-retest correlations of 43 subjects ranged from 0.27 to 0.63. Seven psychiatrists rated the properness of the content of each item as more than moderate degree (mean scale points=2.66, in the range of 0 to 4). Every subscale of KPOMS exhibited significant correlation with the matching subscale of SCL-90-R. Mean scores of K-POMS of the total 405 subjects were significantly different from those of the 76 depressive subjects after age correction. Six factors were extracted, accounting for 51.2% of total variance. Factor 6 consisted of 6 items which came from various subscales of POMS and represented "uncertainty and helplessness," which may be somewhat different to depression or sadness proper. Conclusion: The validity and reliability of K-POMS could be confirmed. The significant difference in K-POMS scores between depressive subjects and normal subjects suggests that K-POMS can be used clinically for the evaluation and screening of depression. The main structure of K-POMS is very similar to that of POMS, except the Confusion-Bewilderment factor which shows weak factor consistency in K-POMS. This may reflect some emotional characteristic of Koreans such as an undifferentiated aspect of cognitive efficiency. The sixth factor newly extracted from K-POMS also may be indicative of an unique emotional aspect of young Koreans.

• The Journal of Korean Academy of Prosthodontics
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• v.39 no.6
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• pp.709-734
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• 2001

The aims of this experiment were to investigate the strain and temperature changes simultaneously within autopolymerzing acrylic resin specimens. A computerized data acquisition system with an electrical resistance strain gauge and a thermocouple was used over time periods up to 180 minutes. The overall strain kinetics, the effects of stress relaxation and additional heat supply during the polymerization were evaluated. Stone mold replicas with an inner butt-joint rectangular cavity ($40.0{\times}25.0mm$, 5.0mm in depth) were duplicated from a brass master mold. A strain gauge (AE-11-S50N-120-EC, CAS Inc., Korea) and a thermocouple were installed within the cavity, which had been connected to a personal computer and a precision signal conditioning amplifier (DA1600 Dynamic Strain Amplifier, CAS Inc., Korea) so that real-time recordings of both polymerization-induced strain and temperature changes were performed. After each of fresh resin mixture was poured into the mold replica, data recording was done up to 180 minutes with three-second interval. Each of two poly(methyl methacrylate) products (Duralay, Vertex) and a vinyl ethyl methacrylate product (Snap) was examined repeatedly ten times. Additionally, removal procedures were done after 15, 30 and 60 minutes from the start of mixing to evaluate the effect of stress relaxation after deflasking. Six specimens for each of nine conditions were examined. After removal from the mold, the specimen continued bench-curing up to 180 minutes. Using a waterbath (Hanau Junior Curing Unit, Model No.76-0, Teledyne Hanau, New York, U.S.A.) with its temperature control maintained at $50^{\circ}C$, heat-soaking procedures with two different durations (15 and 45 minutes) were done to evaluate the effect of additional heat supply on the strain and temperature changes within the specimen during the polymerization. Five specimens for each of six conditions were examined. Within the parameters of this study the following results were drawn: 1. The mean shrinkage strains reached $-3095{\mu}{\epsilon},\;-1796{\mu}{\epsilon}$ and $-2959{\mu}{\epsilon}$ for Duralay, Snap and Vertex, respectively. The mean maximum temperature rise reached $56.7^{\circ}C,\;41.3^{\circ}C$ and $56.1^{\circ}C$ for Duralay, Snap, and Vertex, respectively. A vinyl ethyl methacrylate product (Snap) showed significantly less polymerization shrinkage strain (p<0.01) and significantly lower maximum temperature rise (p<0.01) than the other two poly(methyl methacrylate) products (Duralay, Vertex). 2. Mean maximum shrinkage rate for each resin was calculated to $-31.8{\mu}{\epsilon}/sec,\;-15.9{\mu}{\epsilon}/sec$ and $-31.8{\mu}{\epsilon}/sec$ for Duralay, Snap and Vertex, respectively. Snap showed significantly lower maximum shrinkage rate than Duralay and Vertex (p<0.01). 3. From the second experiment, some expansion was observed immediately after removal of specimen from the mold, and the amount of expansion increased as the removal time was delayed. For each removal time, Snap showed significantly less strain changes than the other two poly(methyl methacrylate) products (p<0.05). 4. During the external heat supply for the resins, higher maximum temperature rises were found. Meanwhile, the maximum shrinkage rates were not different from those of room temperature polymerizations. 5. From the third experiment, the external heat supply for the resins during polymerization could temporarily decrease or even reverse shrinkage strains of each material. But, shrinkage re-occurred in the linear nature after completion of heat supply. 6. Linear thermal expansion coefficients obtained from the end of heat supply continuing for an additional 5 minutes, showed that Snap exhibited significantly lower values than the other two poly(methyl methacrylate) products (p<0.01). Moreover, little difference was found between the mean linear thermal expansion coefficients obtained from two different heating durations (p>0.05).