• 대한수학회지
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• 제54권3호
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• pp.1031-1047
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• 2017

In this paper, we introduce two general iterative algorithms (one implicit algorithm and other explicit algorithm) for nonexpansive mappings in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Strong convergence theorems for the sequences generated by the proposed algorithms are established.

• 대한수학회논문집
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• 제12권3호
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• pp.619-629
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• 1997

In this paper, we give some properties of the sets $D_z(x_o, G)P_{G, z}(x)$. We also provide the relation between $P_{G, z}(x)$ and G$\hat{a}$teaux derivatives.

• 호남수학학술지
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• 제32권2호
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• pp.227-237
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• 2010

For a discrete group G, the kernel of a homomorphism from bounded cohomology $\hat{H}^*(G)$ of G to the ordinary cohomology $H^*(G)$ of G is called the singular part of $\hat{H}^*(G)$. We give some results on the space of the singular part of the second bounded cohomology of G. Also some results on the second bounded cohomology of a uniformly perfect group are given.

• 대한수학회보
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• 제51권4호
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• pp.1205-1210
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• 2014

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that $$E/S{\sim_=}G$$ is finite. For a prime p, $\hat{S}=S/S^{\prime}S^p$ may be regarded as an $F_pG$-module via conjugation in E. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

• 대한수학회보
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• 제39권4호
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.495-511
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• 2012

In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.993-1003
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• 2012

The family of graphs $\hat{W}_{4n}$ is defined by taking the simple whee graph $W_{n+1}$ with $n$ rim vertices and then adding three extra vertices on every rim edge of the wheel. In this paper, the critical group of this whole family of graphs is investigated.

• 한국CDE학회논문집
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• 제14권2호
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• pp.122-128
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• 2009

The failure responses of adhesively bonded, hat stiffened structures are studied through numerical analysis using the finite element method. The responses are evaluated numerically for the bonded hat section/substrate structures containing different combinations of materials. It is studied what kind of material combinations causes the easier crack initiation in the structure. This study is conducted under plane strain conditions and J-integral via a commercial code ABAQUS as a total critical energy release criterion was used for observation on crack initiation. Also, the influence of adhesive on the structure is studied.

• 품질경영학회지
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• 제17권1호
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• pp.107-115
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• 1989

This study is suggested tn find a methodology of influential subset detecting by using diagonal elements of the hat matrix, $h_{ij}$, and off-diagonal elements of the modified hat matrix, $h_{ij^*}$. And this study shows that elements of two matrix is very useful to detect a masking subset in various situations by analytic and emperical explanations. Also a desirable procedure to detect the significant subset and the calibration points for $h_{ij}$ and $h_{ij^*}$ are recommended.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.471-477
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• 2007

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.