• 대한수학회보
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• 제22권1호
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• pp.11-15
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• 1985

Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.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 non-degenerate (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)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) 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 U9R). 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 $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

• 대한수학회논문집
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• 제12권2호
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• Kyungpook Mathematical Journal
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• 제52권1호
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• pp.33-38
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• 2012

The purpose of the present paper is to investigate mapping properties of an integral operator in which we show that the function g defined by $$g(z)=\{\frac{c+{\alpha}}{z^c}{\int}_{o}^{z}t^{c-1}(D^nf)^{\alpha}(t)dt\}^{1/{\alpha}}$$. belongs to the class $S(A,B)$ if $f{\in}S(n,A,B)$.

• Asian-Australasian Journal of Animal Sciences
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• 제19권8호
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• pp.1085-1089
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• 2006

The objectives of this study were to confirm a location of the calpastatin (CAST) gene in chromosome 2 and to detect associations of genetic variations with economic traits in the porcine CAST gene as a candidate gene for growth and meat quality traits in pigs. Calpastatin is a specific endogenous inhibitor of calpains. The calpain protease system is ubiquitous, and is involved in numerous growth and metabolic processes. Three single nucleotide variations were identified within a 1.6 kb fragment of the porcine CAST gene and these polymorphisms were used for genetic linkage mapping. Linkage and QTL mapping were performed with the National Livestock Research Institute (NLRI) reference families using eight microsatellites and SNP makers in the CAST gene. The porcine CAST gene was mapped adjacent to the markers, SW395 and SW1695 on SSC2 with LOD scores of 15.32 and 8.50, respectively. According to the QTL mapping, a significant association was detected at 82 cM between SW395 and CAST-Hinf I for weight at the age of 30 weeks. In addition, an association study was performed with the $F_2$ animals of NLRI reference families for Hinf I, Msp I and Rsa I polymorphisms in the CAST gene. Two polymorphisms, CAST-Rsa I and CAST-Hinf I, showed significant correlation for growth traits at p<0.01 and p<0.05, respectively.

• East Asian mathematical journal
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• 제1권
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• pp.89-100
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• 1985

A mapping f: X$\rightarrow$Y is introduced to be weakly irresolute if, for each x $\varepsilon$ X and each semi-neighborhood V of f(x), there exists a semi-neighborhood U of x in X such that $f(U){\subset}scl(V)$. It will be shown that a mapping f: X$\rightarrow$Y is weakly irresolute iff(if and only if) $f^{-1}(V){\subset}sint(f^{_1}(scl(V)))$ for each semiopen subset V of Y. The relationship between mappings described in [3,5, 6,8] and a weakly irresolute mapping. will be investigated and it will be shown that every irresolute retract of a $T_2$-space is semiclosed.

• 한국멀티미디어학회논문지
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• 제6권1호
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• pp.15-27
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• 2003

Recently, the volume of data is increasing rapidly in server for multimedia service, according to development of multimedia application environment. In recent research for storage technology the technology like of the SAN(Storage Area Network) advantages in scalibility of storage devices, and can read data from multiple disk arrays through RAID 0, 5. The RAID 0 and 5 translate to logical address to physical address using equation, but in case of adding disks at the system with equation -based mapping, the problem that we must rearrange the whole data in the previous disks happens. We use the mapping table to solve this problem in recent, but we can not load the whole mapping table in main memory because it occupies too large space. Therefore the extra I/Os are demanded to evaluate real physical address of data, so total performance of the system is degraded. In this paper, we propose the mapping method that supports the scalibility in RAID 0 or 5 system. The proposing method applies small metadata, so- called SZIT and simple equation, so it is possible that we make translate logical address to physical address rapidly and it is scalable in disk extending simultaneously Our suggesting method, if we add disks to the striping system for expanding of storage capacity, has an advantage of never stop service. So, SZlT-based mapping method can do online-disk-expanding in real-time service.

• 한국의학물리학회지:의학물리
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• 제6권2호
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• pp.83-92
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• 1995

인체내 구조물의 T$_1$ 영상화 (T$_1$ mapping)는 각각 다른 조직들사이 또는 정상/병변 조직들사이에 독특한 음영대조를 준다. 이 논문에서는 각각다른 TR의 몇 영상들로부터 비선형 curve-fitting을 이용하여 T$_1$을 만드는 방법을 기술하겠다. 일반적인 curve-fitting 알고리즘은 주어진 자료로부터 찾아내고자하는 변수들에 대한 초기시행치 (T$_{1}$$^{t}$ 와 M$_{0}$ $^{t}$ )를 요구한다. 본 연구에서는 이들 초기시행치를 입력하는 방법으로서 세 가지를 다른 방법들을 제시하고 각각의 정확도와 계산 속도를 비교하였다. Curve-fitting을 위하여 SUN 윅스테이션에서 ANSI C를 이용하여 프로그램하고 실행하였다. Curve-fitting의 정확성을 검증하기 위하여 몇가지 다른 농도의 Gd-DTPA/증류수는 혼합물 모형들을 만들었다. 이들 모형들을 이용한 MR 영상 하나를 이론적인 양성자 밀도영상으로 가정하고 T$_1$이 각각 250, 500, 1000msec인 영상들을 만들고, 각각의 군들에 대하여 1, 5, 10%의 임의잡음(random noise)을 첨가하였다. 이들 영상들을 이용하여 T$_1$ map을 계산하여 만들고, 계산되는 T$_1$ map에 자기공명영상 화시에 발생하는 잠음의 크기가 어떻게 영향을 미치는지 분석하였다.

• Investigative Magnetic Resonance Imaging
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• 제22권1호
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• pp.37-49
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• 2018

Purpose: The effect of global inhomogeneity on quantitative susceptibility mapping (QSM) was investigated. A technique referred to as Simultaneous Unwrapping Phase with Error Recovery from inhomogeneity (SUPER) is suggested as a preprocessing to QSM to remove global field inhomogeneity-induced phase by polynomial fitting. Materials and Methods: The effect of global inhomogeneity on QSM was investigated by numerical simulations. Three types of global inhomogeneity were added to the tissue susceptibility phase, and the root mean square error (RMSE) in the susceptibility map was evaluated. In-vivo QSM imaging with volunteers was carried out for 3.0T and 7.0T MRI systems to demonstrate the efficacy of the proposed method. Results: The SUPER technique removed harmonic and non-harmonic global phases. Previously only the harmonic phase was removed by the background phase removal method. The global phase contained a non-harmonic phase due to various experimental and physiological causes, which degraded a susceptibility map. The RMSE in the susceptibility map increased under the influence of global inhomogeneity; while the error was consistent, irrespective of the global inhomogeneity, if the inhomogeneity was corrected by the SUPER technique. In-vivo QSM imaging with volunteers at 3.0T and 7.0T MRI systems showed better definition in small vascular structures and reduced fluctuation and non-uniformity in the frontal lobes, where field inhomogeneity was more severe. Conclusion: Correcting global inhomogeneity using the SUPER technique is an effective way to obtain an accurate susceptibility map on QSM method. Since the susceptibility variations are small quantities in the brain tissue, correction of the inhomogeneity is an essential element for obtaining an accurate QSM.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.103-111
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• 2014

Let X be a uniformly convex Banach space, and S, T be pair of mean nonexpansive mappings. Some necessary and sufficient conditions are given for Ishikawa iterative sequence converge to common fixed points, and we prove that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. This generalizes former results proved by Z. Gu and Y. Li [4].

• East Asian mathematical journal
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• 제15권2호
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• pp.325-336
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• 1999

In this paper, we prove that any $\lambda$-firmly nonexpansive mapping ($0<\lambda<1)T:C{\rightarrow}C$ has a fixed point in C whenever C is a finite union of nonempty, bounded, closed and convex subsets of a metric space of hyperbolic type.