• 대한수학회보
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• 제58권4호
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• pp.815-828
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• 2021

Under some mild conditions for the weight function K, the boundedness, compactness and essential norm of integral operators T_g and I_g from Morrey type spaces H^p_K to weighted BMOA spaces $BMOAK_{K,{\frac{2}{p}}}$ investigated in this paper.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.31-46
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• 2024

The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators _a⁺𝔍^𝜇_w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

• 대한수학회보
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• 제47권1호
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• pp.113-119
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• 2010

If f is M-harmonic and integrable with respect to a weighted radial measure $\upsilon_{\alpha}$ over the unit ball $B_n$ of $\mathbb{C}^n$, then $\int_{B_n}(f\circ\psi)d\upsilon_{\alpha}=f(\psi(0))$ for every $\psi{\in}Aut(B_n)$. Equivalently f is fixed by the weighted Berezin transform; $T_{\alpha}f = f$. In this paper, we show that if a function f defined on $B_n$ satisfies $R(f\circ\phi){\in}L^{\infty}(B_n)$ for every $\phi{\in}Aut(B_n)$ and Sf = rf for some |r|=1, where S is any convex combination of the iterations of $T_{\alpha}$'s, then f is M-harmonic.

• 대한수학회지
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• 제49권4호
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• pp.795-804
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• 2012

In this paper, we obtain two general laws of precise asymptotics for sums of i.i.d random variables, which contain general weighted functions and boundary functions and also clearly show the relationship between the weighted functions and the boundary functions. As corollaries, we obtain Theorem 2 of Gut and Spataru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883] and Theorem 3 of Gut and Sp$\check{a}$taru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the Baum-Katz and Davids laws of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246].

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1035-1049
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• 2023

Approximation of functions of Lipschitz and Zygmund classes have been considered by various researchers under different summability means. In the proposed study, we investigated an estimation of the order of convergence of a function associated with Hardy-Littlewood series in the weighted Zygmund class W(Z^(𝜔)_r)-class by applying Euler-Hausdorff summability means and subsequently established some (presumably new) results. Moreover, the results obtained here represent the generalization of several known results.

• 한국산학기술학회논문지
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• 제15권7호
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• pp.4475-4481
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• 2014

저화질 이미지의 화질 개선에는 전통적으로 히스토그램균등화 기법이 사용되어 왔다. 히스토그램균등화 기법은 입력 이미지의 누적밀도함수를 변환함수로 사용하는 기법으로 이는 이론상 최대의 엔트로피를 가지지만 주관적 화질 측면에서는 백화현상이 나타나는 문제점이 있다. 본 논문에서는 히스토그램균등화 기법 기반의 가중 히스토그램 균등화 기법을 제안한다. 이는 인간의 시각특성을 반영한 Weber-Fechner 법칙을 사용하며 입력영상에 독립적인 변환함수를 제공하는 여러 이미지 화질 개선 기법들이 가지는 문제점을 해결하기 위해서 동적영역 재조정 과정을 포함한다. 최종적으로 재조정된 동적영역 범위 내에서 Weber-Fechner 법칙을 적용한 변환함수와 히스토그램균등화 기법을 통해 얻어진 변환함수간의 가중 평균을 통하여 변환함수를 생성한다. 실험결과 제안하는 알고리즘은 주관적 화질 측면에서 대비비를 효과적으로 향상시키는 것을 보여주며, 엔트로피 또한 비교에 사용된 여러 이전의 방법들과 비교하여 유사하거나 높은 값을 가지는 것을 볼 수 있었다.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.145-164
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• 2011

In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.653-666
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• 2015

With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author.

• 지식경영연구
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• 제21권1호
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• pp.27-40
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• 2020

Response surface methodology (RSM) empirically studies the relationship between a response variable and input variables in the product or process development phase. The ultimate goal of RSM is to find an optimal condition of the input variables that optimizes (maximizes or minimizes) the response variable. RSM can be seen as a knowledge management tool in terms of creating and utilizing data, information, and knowledge about a product production and service operations. In the field of product or process development, most real-world problems often involve a simultaneous consideration of multiple response variables. This is called a multiple response surface (MRS) problem. Various approaches have been proposed for MRS optimization, which can be classified into loss function approach, priority-based approach, desirability function approach, process capability approach, and probability-based approach. In particular, the loss function approach is divided into univariate and multivariate approaches at large. This paper focuses on the univariate approach. The univariate approach first obtains the mean square error (MSE) for individual response variables. Then, it aggregates the MSE's into a single objective function. It is common to employ the weighted sum or the Tchebycheff metric for aggregation. Finally, it finds an optimal condition of the input variables that minimizes the objective function. When aggregating, the relative weights on the MSE's should be taken into account. However, there are few studies on how to determine the weights systematically. In this study, we propose an interactive procedure to determine the weights through considering a decision maker's preference. The proposed method is illustrated by the 'colloidal gas aphrons' problem, which is a typical MRS problem. We also discuss the extension of the proposed method to the weighted MSE (WMSE).

• Journal of the Korean Data and Information Science Society
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• 제27권4호
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• pp.1059-1066
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• 2016

In this paper we propose a robust version of varying coefficient models, which is based on the regularized regression with L1 regularization. We use the iteratively reweighted least squares procedure to solve L1 regularized objective function of varying coefficient model in locally weighted regression form. It provides the efficient computation of coefficient function estimates and the variable selection for given value of smoothing variable. We present the generalized cross validation function and Akaike information type criterion for the model selection. Applications of the proposed model are illustrated through the artificial examples and the real example of predicting the effect of the input variables and the smoothing variable on the output.