• 대한수학회논문집
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• 제33권3호
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• pp.889-899
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• 2018

In this paper, we present some upper bounds for unitarily invariant norms inequalities. Among other inequalities, we show some upper bounds for the Hilbert-Schmidt norm. In particular, we prove $${\parallel}f(A)Xg(B){\pm}g(B)Xf(A){\parallel}_2{\leq}{\Large{\parallel}}{\frac{(I+{\mid}A{\mid})X(I+{\mid}B{\mid})+(I+{\mid}B{\mid})X(I+{\mid}A{\mid})}{^dA^dB}}{\Large{\parallel}}_2$$, where A, B, $X{\in}{\mathbb{M}}_n$ such that A, B are Hermitian with ${\sigma}(A){\cup}{\sigma}(B){\subset}{\mathbb{D}}$ and f, g are analytic on the complex unit disk ${\mathbb{D}}$, g(0) = f(0) = 1, Re(f) > 0 and Re(g) > 0.

• 대한수학회보
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• 제50권5호
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• pp.1451-1469
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• 2013

We present various new sharp assertions on multipliers in mixed norm, weighted Hardy and new Lizorkin-Triebel spaces of harmonic functions in higher dimension. Some results are new even in onedimensional case.

• 한국정보통신학회논문지
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• 제11권10호
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• pp.1828-1834
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• 2007

본 논문에서는 웨이블릿 변환을 기반으로 한 새로운 컬러영상 워터마킹 기법을 제안한다. 먼저 RGB컬러영역을 YCbCr 좌표계로 변환한다. 그리고 워터마크에 대해 Arnold 변환을 하여 워터마크의 상관성을 적게 만든다. 그 후, 선형비트확장 기법을 적용하여 확대된 워터마크를 웨이블릿 변환된 컬러 영상의 Y 영역-저주파대에 일정한 강도로 삽입한다. 워터마크를 추출할 때는 F-노름(norm) 함수를 이용한다. 다양한 칼라영상에 대해 실험을 한 결과 제안한 방법은 충실도와 강인성 측면에서 우수한 특성을 가짐을 확인하였다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2002년도 추계학술대회 및 정기총회
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• pp.29-32
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• 2002

We consider the question whether, for given fuzzy numbers, there are different Pairs of f-norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.

• 대한수학회논문집
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• 제32권4호
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

• 대한수학회지
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• 제45권6호
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2006년도 춘계종합학술대회
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• pp.167-170
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• 2006

본 논문에서는 선형계수확장 기반의 웨이블릿 워터마킹 기법을 제안하였다. 워터마크의 안정성을 위하여 먼저 워터마크에 대하여 Amold 변환을 진행한다. 다음 워터마크와 원 영상에 웨이블릿 변환을 진행한다. 워터마크의 크기를 원 영상의 1/4 정도로 선택하였기 때문에 선형계수확장을 적용하여 워터마크를 원 영상 크기만큼 확대한다. 마지막으로 본 논문에서 제안한 웨이블릿 변환된 영상의 저주파대에 일정한 강도로 워터마크를 삽입한다. 워터마크의 추출 시에 기존 방법과 달리 F 노름(norm) 함수를 적용하여 추출된 워터마크와 원 워터마크의 유사도를 비교한다.

• 대한수학회보
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• 제37권4호
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• pp.743-753
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• 2000

In the space $C_1(X)$ of real-valued continuous functions with $L_1-norm$, every bounded set has a relative Chebyshev center in a finite-dimensional subspace S. Moreover, the set function $F\rightarrowZ_S(F)$ corresponding to F the set of its relative Chebyshev centers, in continuous on the space B[$C_1(X)$(X)] of nonempty bounded subsets of $C_1(X)$ (X) with the Hausdorff metric. In particular, every bounded set has a relative Chebyshev center in the closed convex set S(F) of S and the set function $F\rightarrowZ_S(F)$(F) is continuous on B[$C_1(X)$ (X)] with a condition that the sets S(.) are equal.

• 대한수학회보
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• 제50권2호
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• pp.589-599
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• 2013

In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GVI(K, F, $g$)). The condition is also necessary when F is a $g-P^M_*$ function. We also investigate the boundedness of the solution set of (GVI(K, F, $g$)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP(K, F, $g$)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, $g$)).

• 충청수학회지
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• 제19권4호
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• pp.325-334
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• 2006

For $f{\in}L^2(B,d{\nu})$, ${\parallel}f{\parallel}_{BMO}=\widetilde{{\mid}f{\mid}^2}(z)-{\mid}{\tilde{f}}(z){\mid}^2$. For f continuous on B, ${\parallel}f{\parallel}_{BO}=sup\{w(f)(z):z{\in}B\}$ where $w(f)(z)=sup\{{\mid}f(z)-f(w){\mid}:{\beta}(z,w){\leq}1\}$. In this paper, we will show that if $f{\in}BMO$, then ${\parallel}f{\parallel}_{BO}{\leq}M{\parallel}f{\parallel}_{BMO}$. We will also show that if $f{\in}BO$, then ${\parallel}f{\parallel}_{BMO}{\leq}M{\parallel}f{\parallel}_{BO}^2$. A homomorphic function $f:B{\rightarrow}{\mathbb{C}}$ is called a Bloch function ($f{\in}{\mathcal{B}}$) if ${\parallel}f{\parallel}_{\mathcal{B}}=sup_{z{\in}B}\;Qf(z)$<${\infty}$. In this paper, we will show that if $f{\in}{\mathcal{B}}$, then ${\parallel}f{\parallel}_{BO}{\leq}{\parallel}f{\parallel}_{\mathcal{B}}$. We will also show that if $f{\in}BMO$ and f is holomorphic, then ${\parallel}f{\parallel}_{\mathcal{B}}^2{\leq}M{\parallel}f{\parallel}_{BMO}$.