• Title, Summary, Keyword: incommensurable

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QUASI-PERIODICITY AND CHAOTIC CONVECTION IN A HORIZONTAL ANNULUS WITH A CONSTANT HEAT FLUX WALL (일정 열 유속 벽을 갖는 수평 환형 공간에서의 준주기성과 혼돈대류)

  • Yoo, Joo-Sik
    • Journal of computational fluids engineering
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    • v.16 no.3
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    • pp.52-58
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    • 2011
  • This study investigates the bifurcation sequence to chaos in a horizontal annulus with a constant heat flux wall. After the first Hopf bifurcation from a steady to a simple time-periodic flow with a fundamental frequency, quasi-periodic flows with two or three incommensurable frequencies appear. A reverse transition from a quasi-periodic flow to a simple periodic flow is observed with increase of Rayleigh number. And finally, chaotic convection is established after appearance of three incommensurable frequencies at a high Rayleigh number. Simple periodic flows exist between quasi periodic flows. The transition route to chaos of the present simulations follows the Ruelle-Takens route.

The Meaning of the Definition of the Real Number by the Decimal Fractions (소수에 의한 실수 정의의 의미)

  • Byun Hee-Hyun
    • Journal for History of Mathematics
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    • v.18 no.3
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    • pp.55-66
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    • 2005
  • In our school mathmatics, the irrational numbers and the real numbers are defined and instructed on the basis of decimal fractions. In relation to this fact, we identified the essences of the real number and the irrational number defined by the decimal fractions through the historical analysis. It is revealed that the formation of real numbers means the numerical measurements of all magnitudes and the formation of irrational numbers means the numerical measurements of incommensurable magnitudes. Finally, we suggest instructional plan for the meaninful understanding of the real number concept.

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Chaotic Thermal Convection of a Intermediate Prandtl-Number Fluid in a Horizontal Annulus: Pr=0.2 (수평 환형 공간에서의 중간 Prandtl 수 유체의 혼돈 열대류: Pr=0.2)

  • Yu, Ju-Sik;Kim, Yong-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.25 no.3
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    • pp.433-441
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    • 2001
  • Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

Inducing Irrational Numbers in Junior High School (중학교에서의 무리수 지도에 관하여)

  • Kim, Boo-Yoon;Chung, Young-Woo
    • Journal for History of Mathematics
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    • v.21 no.1
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    • pp.139-156
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    • 2008
  • We investigate the inducing method of irrational numbers in junior high school, under algebraic as well as geometric point of view. Also we study the treatment of irrational numbers in the 7th national curriculum. In fact, we discover that i) incommensurability as essential factor of concept of irrational numbers is not treated, and ii) the concept of irrational numbers is not smoothly interconnected to that of rational numbers. In order to understand relationally the incommensurability, we suggest the method for inducing irrational numbers using construction in junior high school.

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Constitutive equations for polymer mole and rubbers: Lessons from the $20^{th}$ century

  • Wagner, Manfred H.
    • Korea-Australia Rheology Journal
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    • v.11 no.4
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    • pp.293-304
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    • 1999
  • Refinements of classical theories for entangled or crosslinked polymeric systems have led to incommensurable models for rubber networks and polymer melts, contrary to experimental evidence, which suggests a great deal of similarity. Uniaxial elongation and compression data of linear and branched polymer melts as well as of crosslinked rubbers were analyzed with respect to their nonlinear strain measure. This was found to be the result of two contributions: (1) affine orientation of network strands, and (2) isotropic strand extension. Network strand extension is caused by an increasing restriction of lateral movement of polymer chains due to deformation, and is modelled by a molecular stress function which in the tube concept of Doi and Edwards is the inverse of the relative tube diameter. Up to moderate strains, $f^2$ is found to be linear in the average stretch for melts as well as for rubbers, which corresponds to a constant tube volume. At large strains, rubbers show maximum extensibility, while melts show maximum molecular tension. This maximum value of the molecular stress function governs the ultimate magnitude of the strain-hardening effect of linear and long-chain branched polymer melts in extensional flows.

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The Reconsideration of Comparative Literature through the Untranslatability (번역불가능성을 통한 비교문학의 재사유)

  • Song, EunJu
    • English & American cultural studies
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    • v.14 no.2
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    • pp.159-183
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    • 2014
  • This thesis aims to explore another possibility of comparative literature in the light of translation. Comparative literature has been criticized for its Eurocentrism to attempt to assimilate all differences from other cultures and national literatures into the frame of the Western. On the other hand, it has been haunted by the anxiety of "unhomliness", which means it doesn't have a stable and definable terrain as an independent disciplinary. However, it can offer the possibility to overcome its limitation and thematize in- betweenness of diverse terrains due to its fluid and ambiguous position and identity of discipline. When it deals with the issue of in-betweenness, 'the Untranslatable' can be an helpful apparatus to analyze comparative literature through translation theories. Along with the recent change in the study of comparative literature under the influence of transnationalism and hybridization, the role of translation which has been disregarded for a long time is being reevaluated. Translation functions to transfer literary works beyond boundaries of languages, whereas it visualizes incommensurable differences through the failure of finding ultimate equivalences between languages and arriving at one single meaning. The existence of the untranslatable suggests that the attempt to totalize differences is unfeasible, thereby makes comparison unending. Salman Rushdie's Shalimar the Clown can be an appropriate instance that the untranslatable was used as a literary technique to show unreducible alterity of non-Western language and culture.

Tristram Shandy: A Sentimental Journey Riding a Hobbyhorse

  • Lee, Hye-Soo
    • English & American cultural studies
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    • v.10 no.2
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    • pp.209-230
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    • 2010
  • This paper reads Tristram Shandy around the issue of hobbyhorse, Sterne's main contribution to novelistic techniques as well as his insightful understanding of the modern condition. First, Sterne represents his characters according to the principle of hobbyhorse, declaring "I will draw my uncle Toby's character from his HOBBY-HORSE." Gradually distancing himself from the Juvenalian satiric mode as well as Henry Fielding's grand narrative and Samuel Richardson's psychological realism, as is seen in the early episode of Yorick's death, Sterne suggests that the best way to represent his characters lies in describing their hobbyhorses. Sterne's foregrounding of hobbyhorse is linked with his embrace of madness as part of the modern identity. He accepts that hobbyhorse-riding, a quirky and mad habit of mind or behavior, is indispensable for some people, like Uncle Toby, to survive and get along with their otherwise unbearable lives. Uncle Toby's hobbyhorse of waging mock battles in the bowling green saves him from the perplexing real world of language and sexuality, while the fictionality of his hobbyhorsical world is exposed by Widow Wadman. Since a hobbyhorse is by definition a world of private pleasure and eccentricity, sentimentalism comes along to bridge the two virtually incommensurable hobbyhorsical world in place of linguistic communication. Yet if Tristram Shandy fully stages sentimentalism, a cardinal part of hobbyhorse riding, it also offers an awareness of it, which is a significant development in the cult of sentimentalism in the eighteenth century. Tristram Shandy performs a version of sentimental journey where each character rides his hobbyhorse and the reader is invited to ride his/her own hobbyhorse.

Study on the Promotion Method based on the Scenario of Scientification of Korean Medicine (한의학 과학화의 시나리오에 따른 추진방법 연구)

  • Chi, Gyoo Yong
    • Journal of Physiology & Pathology in Korean Medicine
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    • v.33 no.6
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    • pp.334-340
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    • 2019
  • In order to promote scientification of Korean medicine, two hypothetical scenarios were proposed methodologically. Firstly, the scientification of Korean medicine requires a comprehensive understanding of the process and reality, and new logical procedures and the methods of observation and experiment. Secondly, transformation to revised Korean medicine is to replace traditional Korean medicine with biochemistry-based Western medicine, that is a method of reconstructing the recognition foundation describing symptoms and diseases using anatomical platforms and analytical tools. But there are areas of human training and practice that are not subject to scientification, and there are incommensurable parts as for the methodology between western medicine too. And additionally arbitrary rejection by uniform science with a political reason was done. So these various backgrounds and factors should be considered for the scientification of Korean medicine. And before that, reflection and agreement on the understanding and attitude of the method of scientification within the Korean medical community is necessary.

A review on the change of content and method of geometry in secondary school with a focus on the proportional relations of geometric figures (초.중등 수학 교과서에서 기하 양 사이의 비례관계의 전개 방식에 대한 역사적 분석)

  • Kwon Seok-Il;Hong Jin-Kon
    • Journal for History of Mathematics
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    • v.19 no.2
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    • pp.101-114
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    • 2006
  • The content and method of geometry taught in secondary school is rooted in 'Elements' by Euclid. On the other hand, however, there are differences between the content and structure of the current textbook and the 'Elements'. The gaps are resulted from attempts to develop the geometry education. Specially, the content and method for the proportional relations of geometric figures has been varied. In this study, we reviewed the changes of the proportional relations of geometric figures with pedagogical point of view. The conclusion that we came to is that the proportional relations in incommensurable case Is omitted in secondary school. Teacher's understanding about the proportional relations of geometric figures is needed for meaningful geometry education.

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The Real Nature of "Chomskyan Revolution" ("촘스키혁명"의 실상)

  • Moon, Kyung-Hwan
    • Lingua Humanitatis
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    • v.8
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    • pp.175-198
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    • 2006
  • Quite a few historiographers of language science have measured the applicability of the term 'revolution' toward the line of work initiated by Chomsky, with the conclusion to the positive or negative effect as the case may be. This paper starts out with a brief review of this issue, with an interim conclusion that, while Chomskyan linguistics may be regarded as revolutionary in certain aspects, terms like 'revolution' and 'paradigm' are hardly applicable here in the way they were originally intended by Thomas Kuhn. It can be said, nontechnically, that the model of theory under discussion is at once 'revolutionary' and 'evolutionary' - in the sense that revolutions in linguistics have not resulted in abrupt loss of continuity with past 'paradigms', if there were any such. Chomsky's theory of language plays the same role of consolidation and refinement of structuralism that, say, the neogrmmarians played in their day. It has continued some fundamental traits of its predecessor, recovered others, and unwittingly rediscovered still others. But this is not the main thrust of the present paper. For, even if Chomskyan theory were to be looked upon as straightforwardly 'revolutionary', that revolution has not been a felicitous one. Some critic (Pieter A. M. Seuren, to be specific) goes as far as to say that "largely as a result of Chomsky's actions, linguistics is now sociologically in a very unhealthy state $\cdots$ to the point even of threatening to make that whole school of linguistics intellectually irrelevant." Besides, under the present state of language science that strikes one as typical of what Kuhn has characterized as "pre-paradigmatic" insecurity and disharmony, an unhealthy situation might take place if we were to think of the theoretical disagreements as conflicts between 'incommensurable' viewpoints-between 'rival paradigms' as it were-thereby avoiding or evading rational discussion. Another danger concerns the bandwagon effect, with linguists prematurely boarding each novel theory seemingly destined for popularity, for fear of being left clinging to an outdated 'paradigm.' Here lies another reason why the notion of 'revolution', Kuhnian or not, might as well be put aside, in the historiography of linguistics at the least.

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