• Title/Summary/Keyword: second fundamental form

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A Study on Family Ethic of Buddhism (종교의 가정윤리에 관한연구)

  • 서병숙
    • Journal of Families and Better Life
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    • v.11 no.2
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    • pp.111-120
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    • 1993
  • The purpose of the study is to find how the family moral principles are placed in the Buddhist Sutra how they come up to the surface through certain course. We set up the following five kinds of question for aim of this study First in which form are the family moral principles placed in the Buddhist Sutra ? That is are they shown devided into two between the fundamental though of Buddhism and the concrete description? Second how are the family moral principles melted into the fundamental though of Bud-dhism ? Buddhism takes a cognitive method of pursuiting one from divesification,. If that is so the family moral principles will establish the fundamental thought of Buddhism melted along with other phenomena. When the fundamental thought of Buddhism is restored to the family moral principles which image are they presented with us? Third if the family moral princprinciples melted into the fundamental thought of Buddhism in itself came up to the surface ? Buddhism has a and is mixed together. The family moral principles of Buddhism are named from the fundamental thoughts to the family moral principles and do not come up to the surface but are melted into the important concepts of Buddism that is charity kama nirvara emptiness the principle of middle way. The aspects of the family moral principles which are melted into theses thoughts: 1) The concept of loving-kindness including equality non-self practice is shown in the family moral principles. 2) The thought of karma includes the moral principles for interdependence between the building up of home and family members. 3) Home should be a place of self-realization from the suffering realization This kind of home salvation should be set up by family members themselves and the consciousness of the master that such salvation is neither to be made by others not to be given by god is presented one should be the master of one's life 4) The thought of emptiness includes the social extension of home and those of the moral principles of collective body of family. 5) The Buddnist family is morality is based on the principle of the middle way shich means neither too extrim nor lacking.

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A Study on Epistemological Critique between Philosophy and Architecture (건축과 철학의 인식론적 논의에 관한 연구)

  • Lee, Yong-Jae
    • Korean Institute of Interior Design Journal
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    • v.21 no.1
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    • pp.111-118
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    • 2012
  • The purpose of this study is to classify the epistemological critique between philosophy and architecture. Although there are various interpretations and criticism about the architecture, the fundamental critique of architecture is difficult. It is necessary to approach by the philosophic paradigm rather than architectural one. Therefore the procedure and method of study is to define the epistemology within philosophy and architecture, and present the classification viewpoint and the architecture case. The conclusions of this study based on purpose and process are as follows : The First, the philosophic epistemology is to mean the unity of subjective and objective. And the epistemological viewpoint of architectural philosophy is to define the construction's universality. The second, the architectural philosophy is a kind of the philosophy of art, and It is associated with the basis of aesthetics. Thus, the category of architectural philosophy like the aesthetics is classified with function directivity and form directivity, content directivity. The Last, epistemological critiques between philosophy and architecture are as follows ; 1) subject-object-integrated recognition critique (function directivity), 2) object-oriented recognition critique (form directivity), 3) subject-oriented recognition critique (content directivity).

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CONTACT CR-WARPED PRODUCT SUBMANIFOLDS IN KENMOTSU SPACE FORMS

  • ARSLAN, KADRI;EZENTAS, RIDVAN;MIHAl, ION;MURATHAN, CENGIZHAN
    • Journal of the Korean Mathematical Society
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    • v.42 no.5
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    • pp.1101-1110
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    • 2005
  • Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

STRUCTURE OF STABLE MINIMAL HYPERSURFACES IN A RIEMANNIAN MANIFOLD OF NONNEGATIVE RICCI CURVATURE

  • Kim, Jeong-Jin;Yun, Gabjin
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1201-1207
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    • 2013
  • Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a complete noncompact oriented stable minimal hypersurface in N. We prove that if M has at least two ends and ${\int}_M{\mid}A{\mid}^2\;dv={\infty}$, then M admits a nonconstant harmonic function with finite Dirichlet integral, where A is the second fundamental form of M. We also show that the space of $L^2$ harmonic 1-forms on such a stable minimal hypersurface is not trivial. Our result is a generalization of one of main results in [12] because if N has nonnegative sectional curvature, then M admits no nonconstant harmonic functions with finite Dirichlet integral. And our result recovers a main theorem in [3] as a corollary.

ON GENERALIZED SPHERICAL SURFACES IN EUCLIDEAN SPACES

  • Bayram, Bengu;Arslan, Kadri;Bulca, Betul
    • Honam Mathematical Journal
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    • v.39 no.3
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    • pp.363-377
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    • 2017
  • In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

An efficient seismic analysis of regular skeletal structures via graph product rules and canonical forms

  • Kaveh, A.;Zakian, P.
    • Earthquakes and Structures
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    • v.10 no.1
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    • pp.25-51
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    • 2016
  • In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.

A study on vocabularies related to four fundamental rules of arithmetic used in elementary school mathematics (초등학교 수학에서 사용하는 사칙계산 관련 어휘에 관한 연구)

  • Park, Kyo Sik
    • Journal of Elementary Mathematics Education in Korea
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    • v.17 no.2
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    • pp.185-205
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    • 2013
  • In this study, to begin with, it was discussed to gather vocabularies which are expected to be vocabularies related to four fundamental rules of arithmetic and classify them according to kinds and groups, to demarcate vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics which are associated with addition, subtraction, multiplication, and division directly. Next, the basic vocabularies related to four fundamental rules of arithmetic were discussed. At this time, regarding vocabularies related addition, subtraction, multiplication, and division as coming from the verb add, subtract, multiply, divide respectively, vocabularies that contains the stem of each verb were considered as the basic vocabularies related to four fundamental rules of arithmetics. Following it, vocabularies which assist the operation and indicate the result of the operation were included, then, vocabularies related to four fundamental rules of arithmetic for using in elementary school mathematics were demarcated and presented according to the following criteria. First, a newly coined verb or derivative using the noun form of a certain verb as a root should not be used. Second, such vocabularies of which examples do not exist or rarely exist in textbooks/workbooks should not be used, even though they are registered in mathematics glossary book published by ministry of education or Korean dictionary published by the national institute of Korean language. Third, vocabularies which are not replaceable and vocabularies which have some didactical reasons for using them should be used.

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An Analysis of Character for Community Vitality in Urban Public Space - Focus on the Urban Squares - (커뮤니티 활성화를 위한 도시공공공간 특성 분석 - 도시광장 사례를 중심으로 -)

  • Kim, Mi-Young;Moon, Jeong-Min
    • Korean Institute of Interior Design Journal
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    • v.20 no.6
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    • pp.291-299
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    • 2011
  • As our lifestyles have changed due to rapid industrialization and urbanization, new social and communication problems have been caused and there have been lots of discussion on regional communication. For communities to become alternatives with realistic meanings in this changed society, considerations on social and spatial conditions are needed. Therefore, public space which works as a device of physical environment for activation of communities needs more active changes which encourages social communication. In respect to the activation of communities, the following suggestions are given: First, physical devices of a urban plaza should be arranged to support various programs presented along with consideration of human behaviors as users. Second, fundamental facilities of the plaza should accommodate various activities through connections with programs and commercial space. Third, when cultural and historical characteristics of the community are understood, the plaza can form regionality and symbolism through artistic representation. And users can form the identity of community. Fourth, transportation facilities should be separated from or coexist with areas of passengers and the plaza should have its own identity through symbolic sculptures.

RIGIDITY OF PROPER HOLOMORPHIC MAPS FROM Bn+1 TO B3n-1

  • Wang, Sung-Ho
    • Journal of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.895-905
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    • 2009
  • Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.

EUCLIDEAN SUBMANIFOLDS WITH CONFORMAL CANONICAL VECTOR FIELD

  • Chen, Bang-Yen;Deshmukh, Sharief
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1823-1834
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    • 2018
  • The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component $x^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field $x^T$ the canonical vector field of the Euclidean submanifold M. In earlier articles [4,5,9,11,12], we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.