• Title/Summary/Keyword: Sense of space

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초등수학 기하문제해결에서의 시각화 과정 분석

  • Yun, Yea-Joo;Kim, Sung-Joon
    • East Asian mathematical journal
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    • v.26 no.4
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    • pp.553-579
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    • 2010
  • Geometric education emphasize reasoning ability and spatial sense through development of logical thinking and intuitions in space. Researches about space understanding go along with investigations of space perception ability which is composed of space relationship, space visualization, space direction etc. Especially space visualization is one of the factors which try conclusion with geometric problem solving. But studies about space visualization are limited to middle school geometric education, studies in elementary level haven't been done until now. Namely, discussions about elementary students' space visualization process and ability in plane or space figures is deficient in relation to geometric problem solving. This paper examines these aspects, especially in relation to plane and space problem solving in elementary levels. Firstly we propose the analysis frame to investigate a visualization process for plane problem solving and a visualization ability for space problem solving. Nextly we select 13 elementary students, and observe closely how a visualization process is progress and how a visualization ability is played role in geometric problem solving. Together with these analyses, we propose concrete examples of visualization ability which make a road to geometric problem solving. Through these analysis, this paper aims at deriving various discussions about visualization in geometric problem solving of the elementary mathematics.

The Experience of the Family Whose Child Has Died of Cancer (암으로 자녀를 잃은 가족의 경험에 대한 질적연구)

  • 이정섭;김수지
    • Journal of Korean Academy of Nursing
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    • v.24 no.3
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    • pp.413-431
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    • 1994
  • The purpose of this study was to build a substantive theory about the experience of the family whose child has died of cancer The qualitative re-search method used was grounded theory. The interviewees were 17 mothers who had cared for a child who had died of cancer Traditionally in Korea, mothers are the care givers in the family and are considered sensitive to the family's thoughts, feelings. The data were collected through in-depth interviews by the investigator over a period of nine months. The data were analyzed simultaniously by a constant comparative method in which new data are continuously coded into categories and properties according to Strauss and Corbin's methodology. The 16 concepts which were found as a result of analyzing the grounded data were, -left over time, the empty place, meaninglessness, inner sadness, situational sadness, heartache, physical pain, guilt, resentment, regret, support / stigmatization, finding meaning in the death, changing attitudes about life and living, changing attitudes about health, changing religious practice and changing family relations. Five categories emerged from the analysis. They were emptiness, consisting of left over time, the empty place and meaninglessness ; sadness, consisting of inner sadness and situational sadness ; pain, consisting of heartache and physical pain ; bitterness, consisting of guilt, resentment, regret, sup-port / stigmatization and finding meaning in the death : and transition, consisiting of changing attitudes about life and living, changing attitudes about health, changing religious practice and changing family relations. These categories were synthesized into the core concept, -the process of filling the empty space. The core phenomenon was emptiness. Emptiness varied with the passing of time, was perceived differently according to support / stigmatization and finding meaning in the death, was followed by sad-ness, pain, and bitterness, and finally resulted in changes in attitudes about life and living and about health, and in changes in religious practice and family relations. The process of filling the empty space proceeded by ① accepting realty, ② searching for the reason for the child's death, ③ controlling the bitter feelings, ④ reconstructing the relationships ameng death, illness and health and ⑤ filling the emptiness by resolving causes of child's death, adopting, having another child or with work. Six hypotheses were derived from the analysis. ① The longer the bereavement, the mere the empty space becomes filled. ② The longer the hospitalization, the more sup-port the family needs. ③ The more the sadness, pain and bitterness are expressed, the mere positive changes emerge. ④ Family support faciliates the process of filling the empty space. ⑤ Higher family cohesiveness faciliates the process of filling the empty space. ⑥ The greater the variety of reasons attributed to the child's death, the greater the variety of patterns of change. Four propositions related to emptiness and bitter-ness were developed. ① When the sense of emptiness is great and bitterness is manifested by severe feelings of guilt and resentment, the longer the process of fill-ing the empty space. ② When the sense of emptiness is great and the family is highly motivated to get rid of the bitterness, the shorter the process of filling the empty space. ③ When the sense of emptiness is less and bitter-ness is manifested by severe feelings of guilt and resentment, the process of filling the empty space is delayed. ④ When the sense of emptiness is less and the family is highly motivated to get rid of the bitterness, the process of filling the empty space goes on to completion. Through this substantive theory, nurses under-stand the importance of emptiness and bitterness in helping the family that has lost a child through cancer fill the empty space. Further research to build substantive theories to explain other losses may con-tribute to a formal theory of how family health is restored after human tragedies are experienced.

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TUBES OF FINITE CHEN-TYPE

  • Al-Zoubi, Hassan;Jaber, Khalid M.;Stamatakis, Stylianos
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.581-590
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    • 2018
  • In this paper, we consider surfaces in the 3-dimensional Euclidean space $\mathbb{E}^3$ which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in $\mathbb{E}^3$. We show that tubes are of infinite III-type.

BOUNDEDNESS OF CALDERÓN-ZYGMUND OPERATORS ON INHOMOGENEOUS PRODUCT LIPSCHITZ SPACES

  • He, Shaoyong;Zheng, Taotao
    • Journal of the Korean Mathematical Society
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    • v.59 no.3
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    • pp.469-494
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    • 2022
  • In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES

  • Malkawi, Abed Al-Rahman M.;Talafhah, Abdallah;Shatanawi, Wasfi
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.177-195
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    • 2021
  • In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

FIXED POINTS OF OCCASIONALLY WEAKLY COMPATIBLE MAPPINGS USING IMPLICIT RELATION

  • Pant, Badri Datt;Chauhan, Sunny
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.513-522
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    • 2012
  • In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.

ASSOUAD DIMENSION: ANTIFRACTAL METRIZATION, POROUS SETS, AND HOMOGENEOUS MEASURES

  • Luukkainen, Jouni
    • Journal of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.23-76
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    • 1998
  • We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

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ON THE LARGE DEVIATION PROPERTY OF RANDOM MEASURES ON THE d-DIMENSIONAL EUCLIDEAN SPACE

  • Hwang, Dae-Sik
    • Communications of the Korean Mathematical Society
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    • v.17 no.1
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    • pp.71-80
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    • 2002
  • We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

SOME APPLICATIONS FOR GENERALIZED FRACTIONAL OPERATORS IN ANALYTIC FUNCTIONS SPACES

  • Kilicman, Adem;Abdulnaby, Zainab E.
    • Korean Journal of Mathematics
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    • v.27 no.3
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    • pp.581-594
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    • 2019
  • In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.