• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.177-186
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• 2016

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.29-31
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• 2007

In this paper we propose an directional analytic approach in image data space for X-ray image which is detected from the X-ray projection system. Such a radiographic nondestructive testing has long been used for steel-tube inspection and weld monitoring. The welded area and thickness of steel-tube are detected from gradient radiating mechanism based on the evaluation of biased X-ray source position. The welded area is an ellipse type on low contrast X-ray image including noise. Noise originates from most of elements of the system. such as shielding CCD camera, imaging screen, X-ray source, inspected object, electronic circuits and etc.. Projection incorrectness and noise influence on imaging quality is to be represented by vertical pixels' distribution. Space analysis due to vertical direction also shows the segmental possibility between regions by visual edge evaluation.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1371-1385
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• 2019

Given a topological space X and a non-negative integer k, ${\varepsilon}^{\sharp}_k(X)$ is the set of all self-homotopy equivalences of X that do not change maps from X to an t-sphere $S^t$ homotopically by the composition for all $t{\geq}k$. This set is a subgroup of the self-homotopy equivalence group ${\varepsilon}(X)$. We find certain homotopic tools for computations of ${\varepsilon}^{\sharp}_k(X)$. Using these results, we determine ${\varepsilon}^{\sharp}_k(M(G,n))$ for $k{\geq}n$, where M(G, n) is a Moore space type of (G, n) for a finitely generated abelian group G.

• Journal of Astronomy and Space Sciences
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• v.15 no.1
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• pp.1-26
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• 1998

The structure of the magnetic funnel element in the intermediate polar is con-sidered in terms of an important site for the X-ray absorption and the reemis-sion of the X-ray as the optical light. In this paper the column density and the optiacl depth vary with the filling factor, which is introduced to characterize the structure of matter in the magnetic funnel element. The results of the en-ergy dopendence of the X-ray spectrum and the modulation depth of the X-ray light curve are discussed.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.289-306
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• 2007

We define and study a concept of $H^f-space$ for a map, which is a generalized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration $E_{\kappa}{\rightarrow}X$ induced by ${\kappa}:X{\rightarrow}X'\;from\;{\epsilon}:\;PX'{\rightarrow}X'$, we can obtain a sufficient condition to having an $H^{\bar{f}}-structure\;on\;E_{\kappa}$, which is a generalization of Stasheff's result [17]. Also, we define and study a concept of $co-H^g-space$ for a map, which is a dual concept of $H^f-space$ for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg's result [6].

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.431-441
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• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.317-325
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• 1994

Suppose X is a complex Banach space and write B(X) for the Banach algebra of bounded linear operators on X, X＊ for the dual space of X, and T＊$\in$ B(X＊) for the dual operator of T. For T $\in$ B(X) write a(T) = dim T$^{-1}$ (0) and $\beta$(T) = codim T(X).(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.387-396
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• 2018

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a fixed topology on X and we will regard ${\tau}(X)$ a topological space. Our purpose of this study is to comparison new topologies on the family ${\tau}(X)$ of all topologies induced old one.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.121-126
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• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.