• 한국수학교육학회지시리즈A:수학교육
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• 제21권3호
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• pp.7-11
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• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.

• 제어로봇시스템학회논문지
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• 제8권11호
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• pp.970-975
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• 2002

We suggests an effective method to construct time-varying C-obstacles in the 3-dimensional configuration space (C-space) using free arc. The concept of free arc was defined mathematically and the procedure to find free arc in the case off-dimensional C-space was derived in [1]. We showed that time-varying C-obstacles can be constructed efficiently using this concept, and presented simulation results for two SCARA robot manipulators to verify the efficacy of the proposed approach. In this paper, extensions of this approach to the 3-dimensional C-space is introduced since nearly all industrial manipulators are reasonably treated ill the too or three dimensional C-space f3r collision avoidance problem The free arc concept is summarized briefly and the method to find lice arc in the 3-dimensional f-space is explained. To show that this approach enables us to solve a practical collision avoidance problem simulation results f3r two PUMA robot manipulators are presented.

• 대한수학회보
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• 제47권3호
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• pp.527-540
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• 2010

We characterize the boundedness and compactness of the weighted composition operator on the logarithmic Bloch space $\mathcal{L}\ss=\{f{\in}H(D):sup_D(1-|z|^2)ln(\frac{2}{1-|z|})|f'(z)|$<+$\infty$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$. The results generalize the known corresponding results on the composition operator and the pointwise multiplier on the logarithmic Bloch space ${\mathcal{L}\ss$ and the little logarithmic Bloch space ${\mathcal{L}\ss_0$.

• 한국우주과학회:학술대회논문집(한국우주과학회보)
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• 한국우주과학회 2009년도 한국우주과학회보 제18권1호
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• pp.44.1-44.1
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• 2009

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권1호
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• pp.45-54
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• 1998

We study the space-times that have a unique terminal indecomposable past set or a unique terminal indecomposable future set and examine their causal boundary, and we investigate some conditions for the warped product space-times of the form (a, b) ${\times}_fF$ to have a unique terminal indecomposable past set or a unique terminal indecomposable future set.

• 대한수학회논문집
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• 제18권4호
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• pp.677-685
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• 2003

Let M be the vector space of all real S-measurable functions defined on a measure space (X, S, $\mu$). In this paper, we investigate some topological structure of T on M. Indeed, (M, T) becomes a topological vector space. Moreover, if $\mu$, is ${\sigma}-finite$, we can define a complete invariant metric on M which is compatible with the topology T on M, and hence (M, T) becomes a F-space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• East Asian mathematical journal
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• 제32권3호
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• pp.413-423
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• 2016

In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.

• 건축역사연구
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• 제7권4호
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• pp.29-47
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• 1998

The aim of this study is to understand the original methods of architectural composition in F. L. Wright's works, For this purpose, the principal thoughts based on his organic architecture was examined over all others, and the results of this study are as follows. 1. F. L. Wright knew Taoist Philosophy, especially Lao-tzu's thought about space based on traditional oriental arts included traditional japanese arts by his superior intuition. this is similar to Froebel Thought in the principal theory, that is, his own unique field of abstract architectural education with three-dimensional geometry learned through Froebel Gifts. 2. Space is reality ; such Lao-tzu's thought, reversed the sense of values, influenced F. L. Wright's way to accomplish his own continuous space. that is to say, he attempted taking precedence of spatial organization by the unit of three-dimensional module made the substance, Froebel Blocks (3, 4, 5, 6 Gifts) into non-substance, and trying to do the methods of continuous liberal composition in architecture. which is his original accomplishment, namely his mentioned 'democratic' because of judging the space and the mold of architecture as individualities. 3. F. L. Wright treated the space as a positive entity, so that he created his own architecture organically combined with spaces and forms. : This was the result that he comprehended both formative, physical worth in West and spatial, non-physical worth in East as equivalence. It is understood that F. L. Wright's works combined with East and West are the significance of his architecture and the progress of true internationalities and modernization in modern architecture. 4. From the analyses of his works, we knew the fact that F. L. Wright's architecture, especially in the spatial organization were performed by the reasonable methods with geometric system of Froebel Gifts. In the observation of our fundamental way of thinking on his architecture, this study shows the necessity to let us get out of preconceptions and conclusions that the organic architecture is mysterious and difficult, but to systematize and put his organic methods to practical use.

• Korean Journal of Mathematics
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• 제22권2호
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• pp.339-348
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• 2014

In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.