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MATHEMATICAL ANALYSIS OF AN "SIR" EPIDEMIC MODEL IN A CONTINUOUS REACTOR - DETERMINISTIC AND PROBABILISTIC APPROACHES

  • El Hajji, Miled;Sayari, Sayed;Zaghdani, Abdelhamid
    • Journal of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.45-67
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    • 2021
  • In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

State Feedback Linearization of Discrete-Time Nonlinear Systems via T-S Fuzzy Model (T-S 퍼지모델을 이용한 이산 시간 비선형계통의 상태 궤환 선형화)

  • Kim, Tae-Kue;Wang, Fa-Guang;Park, Seung-Kyu;Yoon, Tae-Sung;Ahn, Ho-Kyun;Kwak, Gun-Pyong
    • Journal of the Korean Institute of Intelligent Systems
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    • v.19 no.6
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    • pp.865-871
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    • 2009
  • In this paper, a novel feedback linearization is proposed for discrete-time nonlinear systems described by discrete-time T-S fuzzy models. The local linear models of a T-S fuzzy model are transformed to a controllable canonical form respectively, and their T-S fuzzy combination results in a feedback linearizable Tagaki-Sugeno fuzzy model. Based on this model, a nonlinear state feedback linearizing input is determined. Nonlinear state transformation is inferred from the linear state transformations for the controllable canonical forms. The proposed method of this paper is more intuitive and easier to understand mathematically compared to the well-known feedback linearization technique which requires a profound mathematical background. The feedback linearizable condition of this paper is also weakened compared to the conventional feedback linearization. This means that larger class of nonlinear systems is linearizable compared to the case of classical linearization.

A Diagnostic Study on High School Students' Health and Quality of Life - Based on the PRECEDE model - (고등학생의 건강 및 삶의 질에 대한 진단적 연구 - PRECEDE 모형을 근간으로 -)

  • Yoo Jae-Soon;Hong Yeo-Shin
    • The Journal of Korean Academic Society of Nursing Education
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    • v.3
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    • pp.78-98
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    • 1997
  • Health education, as the most fundamental concept for national health promotion, alms for developing the self-care ability of the general public. High school days are regarded as the period when most important physical, mental and social developments occur, and most health-related behaviors are formed. School health education is one of the major learning resources influencing health potential in the home and community as well as for the individual student. High school health education in Korea has a fundamental systemic flaw in that health-related subjects are divided and taught under various subjects areas at school. In order to achieve the goal of school health education, it is essential to make a systematic assessment of the learner's concerns connected with his health and life, and the factors affecting them. So far, most of the research projects that had been carried out for improving high school health education were limited in their concerns to a particular aspect of health. Even though some had been done in view of comprehensive school health education, they failed to Include a health assessment of the learner. Therefore, in this study the high school students' concerns related to health and life were investigated in the first place on the basis of the PRECEDE model, developed by Green and others for the purpose of a comprehensive diagnostic research on high school health education. This study was done in two steps : one was the basic study for developing research instrument and the other was the main one. The former was conducted at five high schools in Seoul and Cheongju for 2 months-beginning in March, 1996. The students were asked to respond to questions related to their health and lives in unstructured open-ended question forms. On the basis of analysis of the basic study, the diagnostic instruments for the quality of life, health problems, health behavior and educational factors were constructed to be used for the collection of data for main study. An expert panel and the pilot study were used to improve content validity and reliability of the instruments. The reliability of the instruments was measured at between .7697 and .9611 by the Cronbach $\alpha$. The data for this study were collected from the sample consisted of the junior and senior classes of twenty general and vocational high schools in Seoul and Cheongju for two months period beginning in July, 1996. In analyzing the data, both t-test and $X^2$-test were done by using SAS-$PC^+$ Program to compare data between the sexes of the high school students and the types of high school. A canonical correlation analysis was carried out to determine the relationships among the diagnostic variables, and a multivariate multiple regression analysis was conducted by using LISREL 8.03 to ascertain the influences of variables on the high school students' health and quality of life. The results were as follows : 1) The findings of the hypothesis tests (1) The canonical correlation between the educational diagnosis variables and behavioral, epidemiological, social diagnosis variables was .7221, which was significant at the level of p<.001. (2) The canonical correlation between the educational diagnosis variables and the behavior variables was .6851, which also was significant (p<.001). (3) The canonical correlation between the behavioral diagnosis variables and the epidemiological variables was 4295, which was significant (p<.001). (4) The canonical correlation between the epidemiological diagnosis variables and the social variables was .6005, which was also significant (p<.001). Therefore, the relationship between each diagnosis variable suggested by the PRECEDE model had been experimentally proven to be valid, supporting the conceptual framework of the study as appropriate for assessing the multi-dimensional factors affecting high school students' health and quality of life. Health behavior self-efficacy, the level of parents' interest and knowledge of health, and the level of the perception of school health education, all of which are the educational diagnostic variables, are the most influential variables in students' health and quality of life. In particular, health behavior self-efficacy, a causative factor, was one of the main influential variables in their health and quality of life. Other diagnostic variables suggested in the steps of the PRECEDE model were found to have reciprocal relations rather than a unidirectional causative relationship. The significance of this research is that it has diagnosed the needs of high school health education by the learner-centered assessment of variety of factors related to the health and the life of the students. This research findings suggest an integrated system of school health education to be contrived to enhance the effectiveness of the education by strengthening the influential factors such as self-efficacy to improve the health and quality of the lives of high school students.

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Identication of L328-IRS as a Proto-Brown Dwarf

  • Lee, Chang Won;Kim, Mi-Ryang;Kim, Gwanjeong;Siato, Masao;Myers, Philip C.;Kurono, Yasutaka
    • The Bulletin of The Korean Astronomical Society
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    • v.38 no.2
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    • pp.65.1-65.1
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    • 2013
  • Our understanding of how brown dwarfs form is limited by observational evidence. We report identification of a L328-IRS as a proto-brown dwarf embedded in an isolated dense molecular core. This source exhibits typical properties of a protostar, however, its luminosity (~0.05 $L{\odot}$) is far below than expected from the least massive protostar by the standard star formation theory. The most likely mass accretion rate (~2.4 10-7 $M{\odot}$ yr-1) inferred from its small bipolar outflow is an order of magnitude less than the canonical value for a protostar. The mass available in its envelope is less than 0.1 $M{\odot}$. These points suggest that L328-IRS will accrete the mass of a brown dwarf, but not that of a star. L328 is found to be fairly well isolated from other nearby clouds and seems to be forming three sub-cores simultaneously through a gravitational fragmentation process. Altogether with these, our direct detection of inward motions in L328 which harbors this proto-brown dwarf clearly supports the idea that a brown dwarf forms like a normal star.

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Analysis of Gene Expression in 4,4'-Methylenedianiline-induced Acute Hepatotoxicity

  • Oh, Jung-Hwa;Yoon, Hea-Jin;Lim, Jung-Sun;Park, Han-Jin;Cho, Jae-Woo;Kwon, Myung-Sang;Yoon, Seok-Joo
    • Toxicological Research
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    • v.25 no.2
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    • pp.85-92
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    • 2009
  • 4,4'-Methylenedianiline (MDA) is an aromatic amine that is widely used in the industrial synthetic process. Genotoxic MDA forms DNA adducts in the liver and is known to induce liver damage in human and rats. To elucidate the molecular mechanisms associated with MDA-induced hepatotoxicity, we have identified genes differentially expressed by microarray approach. BALB/c male mice were treated once daily with MDA (20 mg/kg) up to 7 days via intraperitoneal injection (i.p.) and hepatic damages were revealed by histopathological observation and elevation of serum marker enzymes such as AST, ALT, ALP, cholesterol, DBIL, and TBIL. Microarray analysis showed that 952 genes were differentially expressed in the liver of MDA-treated mice and their biological functions and canonical pathways were further analyzed using Ingenuity Pathways Analysis (IPA). Toxicological functional analysis showed that genes related to hepatotoxicity such hyperplasia/hyperproliferation (Timp1), necrosis/cell death (Cd14, Mt1f, Timp1, and Pmaip1), hemorrhaging (Mt1f), cholestasis (Akr1c3, Hpx, and Slc10a2), and inflammation (Cd14 and Hpx) were differentially expressed in MDA-treated group. This gene expression profiling should be useful for elucidating the genetic events associated with aromatic amine-induced hepatotoxicity and for discovering the potential biomarkers for hepatotoxicity.

A Study on the Ontological Meaning of Life in The Canonical Scripture (『전경』에 나타난 생명의 존재론적 위상)

  • Baek Choon-hyoun
    • Journal of the Daesoon Academy of Sciences
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    • v.45
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    • pp.1-35
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    • 2023
  • This study aims at determining the meaning of Life in The Canonical Scripture of the Daesoon Thought upon the ontological bases of occidental philosophies; especially upon those of Plato and Bergson. In western philosophy, the word ontology designates investigating the meanings of being, which is derived from the Greek 'onto (being)' and 'logia (logical discourse).' The various meanings of life have been sought from ancient times all over the world, for these are the critical and vital questions that pertain to the nature of human existence. Plato had asserted that life, in his word, soul, had three different kinds of aspects of meaning. Immortal, reciprocal, and divine. Plato scheme was such that the soul could die, but after death it could became reborn into another various forms of living creatures. The real inner life of humans, the soul, would live eternally. Henri-Louis Bergson, a famous French philosopher from the 20th century, claimed that life had three different kinds of aspects. Self-identity, Élan vital (vital impetus) and liberty. Bergson insisted especially the real meaning of life had been characterized by "unité multiple et multiplicitéune," "unity as something multiple and multiplicity something singular." The meaning of life in Daesoon Thought could be said to have three different characteristics, solidarity, earthly immortality and grievance-resolution. Some similarities can be found between certain western ontological meanings of life and those of Daesoon Thought. Namely, the qualities of eternity, reciprocity, and divinity.

Estimation of smooth monotone frontier function under stochastic frontier model (확률프런티어 모형하에서 단조증가하는 매끄러운 프런티어 함수 추정)

  • Yoon, Danbi;Noh, Hohsuk
    • The Korean Journal of Applied Statistics
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    • v.30 no.5
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    • pp.665-679
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    • 2017
  • When measuring productive efficiency, often it is necessary to have knowledge of the production frontier function that shows the maximum possible output of production units as a function of inputs. Canonical parametric forms of the frontier function were initially considered under the framework of stochastic frontier model; however, several additional nonparametric methods have been developed over the last decade. Efforts have been recently made to impose shape constraints such as monotonicity and concavity on the non-parametric estimation of the frontier function; however, most existing methods along that direction suffer from unnecessary non-smooth points of the frontier function. In this paper, we propose methods to estimate the smooth frontier function with monotonicity for stochastic frontier models and investigate the effect of imposing a monotonicity constraint into the estimation of the frontier function and the finite dimensional parameters of the model. Simulation studies suggest that imposing the constraint provide better performance to estimate the frontier function, especially when the sample size is small or moderate. However, no apparent gain was observed concerning the estimation of the parameters of the error distribution regardless of sample size.

Molecular Mechanism of Runx2-Dependent Bone Development

  • Komori, Toshihisa
    • Molecules and Cells
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    • v.43 no.2
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    • pp.168-175
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    • 2020
  • Runx2 is an essential transcription factor for skeletal development. It is expressed in multipotent mesenchymal cells, osteoblast-lineage cells, and chondrocytes. Runx2 plays a major role in chondrocyte maturation, and Runx3 is partly involved. Runx2 regulates chondrocyte proliferation by directly regulating Ihh expression. It also determines whether chondrocytes become those that form transient cartilage or permanent cartilage, and functions in the pathogenesis of osteoarthritis. Runx2 is essential for osteoblast differentiation and is required for the proliferation of osteoprogenitors. Ihh is required for Runx2 expression in osteoprogenitors, and hedgehog signaling and Runx2 induce the differentiation of osteoprogenitors to preosteoblasts in endochondral bone. Runx2 induces Sp7 expression, and Runx2, Sp7, and canonical Wnt signaling are required for the differentiation of preosteoblasts to immature osteoblasts. It also induces the proliferation of osteoprogenitors by directly regulating the expression of Fgfr2 and Fgfr3. Furthermore, Runx2 induces the proliferation of mesenchymal cells and their commitment into osteoblast-lineage cells through the induction of hedgehog (Gli1, Ptch1, Ihh), Fgf (Fgfr2, Fgfr3), Wnt (Tcf7, Wnt10b), and Pthlh (Pth1r) signaling pathway gene expression in calvaria, and more than a half-dosage of Runx2 is required for their expression. This is a major cause of cleidocranial dysplasia, which is caused by heterozygous mutation of RUNX2. Cbfb, which is a co-transcription factor that forms a heterodimer with Runx2, enhances DNA binding of Runx2 and stabilizes Runx2 protein by inhibiting its ubiquitination. Thus, Runx2/Cbfb regulates the proliferation and differentiation of chondrocytes and osteoblast-lineage cells by activating multiple signaling pathways and via their reciprocal regulation.

Daesoon Thought from the Perspective of Yulgok's Theory of Reason and Energy (栗谷理气论视域观大巡思想)

  • Li, Hongjun
    • Journal of the Daesoon Academy of Sciences
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    • v.34
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    • pp.49-74
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    • 2020
  • Daesoon Thought (大巡思想) emerged from indigenous Korean religion during the Joseon Dynasty. Thinkers within this tradition took Kang Jeungsan (姜甑山 secular name Kang Il-Sun 姜一淳 1871~1909) as their Highest God (上帝) and The Canonical Scripture (典經) as their main scripture. The Tenets, Four Cardinal Mottoes, Three Essential Attitudes, and Aims of Daesoon Thought are related to the concepts, categorical thought, and structure found in Confucianism. In particular, terms such as The Virtuous Concordance of Yin and Yang (陰陽合德), gods and humans* (神人 *also 'divine humans' in some contexts), Dao Governance (道統), Quieting the Mind and Quieting the Body (安心安身), and Sincerity, Respectfulness, and Faithfulness (誠敬信) are all widely used in Confucianism. This paper will examine Daesoon Thought from the perspective of the Confucian Thinker, Yulgok (栗谷), and more specifically, his Theory of Reason and Energy (理氣論) and its key concepts: The Wondrousness of Reason and Energy (理氣之妙), Triggered Energy Transports Reason (氣發理乘), and Reason Pervades and Energy Delimits (理通氣局). It will be shown that Daesoon Thought shares essentially the same thinking and reasoning, and as such, the two systems are organically connected. Furthermore, both schools of thought pursue harmonious adjustment and emphasize practice. Although this study may contain suggestions which seem far-fetched when compared to previous studies, it investigates Daesoon Thought from the perspective of Neo-Confucian discourse on Nature and Principle (性理), which had great value in the mainstream culture of Korea's Joseon Dynasty. Given that Daesoon Thought and Neo-Confucianism both are forms of traditional thought, there is bound to be some connection between them.

A Longitudinal Case Study of Late Babble and Early Speech in Southern Mandarin

  • Chen, Xiaoxiang
    • Cross-Cultural Studies
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    • v.20
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    • pp.5-27
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    • 2010
  • This paper studies the relation between canonical/variegated babble (CB/VB) and early speech in an infant acquiring Mandarin Chinese from 9 to 17 months. The infant was audio-and video-taped in her home almost every week. The data analyzed here come from 1,621 utterances extracted from 23 sessions ranging from 30 minutes to one hour, from age 00:09;07 to 01:05;27. The data was digitized, and segments from 23 sessions were transcribed in narrow IPA and coded for analysis. Babble was coded from age 00:09;07 to 01:00;00, and words were coded from 01:00;00 to 01:05;27, proto-words appeared at 11 months, and some babble was still present after 01:10;00. 3821 segments were counted in CB/VB utterances, plus the segments found in 899 word tokens. The data transcription was completed and checked by the author and was rechecked by two other researchers who majored in Chinese phonetics in order to ensure the reliability, we reached an agreement of 95.65%. Mandarin Chinese is phonetically very rich in consonants, especially affricates: it has aspirated and unaspirated stops in labial, alveolar, and velar places of articulation; affricates and fricatives in alveolar, retroflex, and palatal places; /f/; labial, alveolar, and velar nasals; a lateral;[h]; and labiovelar and palatal glides. In the child's pre-speech phonetic repertoire, 7 different consonants and 10 vowels were transcribed at 00:09;07. By 00:10;16, the number of phones was more than doubled (17 consonants, 25 vowels), but the rate of increase slowed after 11 months of age. The phones from babbling remained active throughout the child's early and subsequent speech. The rank order of the occurrence of the major class types for both CB and early speech was: stops, approximants, nasals, affricates, fricatives and lateral. As expected, unaspirated stops outnumbered aspirated stops, and front stops and nasals were more frequent than back sounds in both types of utterances. The fact that affricates outnumbered fricatives in the child's late babble indicates the pre-speech influence of the ambient language. The analysis of the data also showed that: 1) the phonetic characteristics of CB/VB and early meaningful speech are extremely similar. The similarities of CB/VB and speech prove that the two are deeply related; 2) The infant has demonstrated similar preferences for certain types of sounds in the two stages; 3) The infant's babbling was patterned at segmental level, and this regularity was similarly evident in the early speech of children. The three types being coronal plus front vowel; labial plus central and dorsal plus back vowel exhibited much overlap in the phonetic forms of CB/ VB and early speech. So the child's CB/ VB at this stage already shared the basic architecture, composition and representation of early speech. The evidence of similarity between CB/VB and early speech leaves no doubt that phones present in CB/VB are indeed precursors to early speech.