• 대한수학회지
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• 제31권4호
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• pp.679-689
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• 1994

Let ${X_\underline{j} : \underline{j} \in Z^d}$ be a random field on some probability space $(\Omega, F, P)$ with $EX_\underline{j} = 0, EX_\underline{j}^2 < \infty$.

• 호남수학학술지
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• 제21권1호
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• pp.139-147
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• 1999

In this paper we generalize the definition of strongly close-to-convex functions by using the functions g(z) of bounded boundary rotation and investigate the distortion and rotation theorem, coefficient inequalities, invariance property and inclusion relation for the new class $G_{k}[A,\;B]$.

• 대한수학회논문집
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• 제28권3호
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• pp.511-516
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• 2013

We establish an easy proof of an integral identity using the unitary invariance, which is applied to compare harmonicity and M-harmonicity.

• 충청수학회지
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• 제1권1호
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• pp.55-64
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• 1988

We introduce the concept of a w-Lindel$\ddot{o}$f space which is a more general concept than that of a Lindel$\ddot{o}$f spaces. We obtain some characterization about H-closed sapces and w-Lindel$\ddot{o}$f spaces. Also, we investigate their invariance properties.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.213-228
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• 2010

A weighted version of the geometric mean of k ($\geq\;3$) positive invertible operators is given. For operators $A_1,{\ldots},A_k$ and for nonnegative numbers ${\alpha}_1,\ldots,{\alpha}_k$ such that $\sum_\limits_{i=1}^k\;\alpha_i=1$, we define weighted geometric means of two types, the first type by a direct construction through symmetrization procedure, and the second type by an indirect construction through the non-weighted (or uniformly weighted) geometric mean. Both of them reduce to $A_1^{\alpha_1}{\cdots}A_k^{{\alpha}_k}$ if $A_1,{\ldots},A_k$ commute with each other. The first type does not have the property of permutation invariance, but satisfies a weaker one with respect to permutation invariance. The second type has the property of permutation invariance. We also show a reverse inequality for the arithmetic-geometric mean inequality of the weighted version.

• 호남수학학술지
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• 제13권1호
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• pp.53-63
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• 1991

In this paper we first present the elements of the theory of families of distributions and corresponding estimators having structual properties which are preserved under certain groups of transformations, called "Invariance Principle". The invariance principle is an intuitively appealing decision principle which is frequently used, even in classical statistics. It is interesting not only in its own right, but also because of its strong relationship with several other proposal approaches to statistics, including the fiducial inference of Fisher [3, 4], the structural inference of Fraser [5], and the use of noninformative priors of Jeffreys [6]. Unfortunately, a space precludes the discussion of fiducial inference and structural inference. Many of the key ideas in these approaches will, however, be brought out in the discussion of invarience and its relationship to the use of noninformatives priors. This principle is also applied to the problem of finding the best scale invariant estimator in the scale parameter problem. Finally, several examples are subsequently given.

• 대한수학회보
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• 제47권6호
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• pp.1139-1153
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• 2010

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

• 대한수학회지
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• 제58권2호
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• pp.265-281
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• 2021

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

• Journal of applied mathematics & informatics
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• 제2권1호
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• pp.11-16
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• 1995

Scale Invariant Transforms are defined for both one- and two- dimensioned input functions. These have the desirable properties of linearity and invariance to scale change of the input.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.61-69
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• 2001

The purpose of this paper is to introduce the Nielsen root number for the complement N(f:X-A,c) which shares such properties with the Nielsen root number N(f;c) as lower bound and homotopy invariance.